diff --git a/Changelog b/Changelog index 0e538069..7cfc2997 100644 --- a/Changelog +++ b/Changelog @@ -1,5 +1,21 @@ Changelog. A lot less detailed than usual, at least for past history. +2019/12/18: New internals and algorithms for FND_OWNER, faster and less + memory hungry. +2019/07/20: New SCAN collective; improve handling of SYMmetric +2019/07/08: Fix memory usage in conversions to/from coo +2019/07/01: Timer facility +2019/06/25: Fix memory footprint in spspmm and other borderline cases +2019/06/17: Make ADD default assembly action. +2019/05/30: new insertion routines in CSR mode +2019/05/27: Fix matrix generation. +2019/05/26: New timer facility (undocumented). +2019/05/20: Change checks on vectors +2019/05/05: Reworked linmap internals +2019/04/15: Improved sphalo and test programs printout +2019/04/09: bump version to 3.6.1 +2019/04/09: new fnd_owner_halo method +2019/03/31: New RENUM_BLK descriptor method 2019/01/16: In bldext, implement ALL_TO_ALLV by hand for certain compilers. 2018/10/10: New ICTXT argument in prec%init diff --git a/README.md b/README.md index cc1a77e6..07eb378e 100644 --- a/README.md +++ b/README.md @@ -1,4 +1,4 @@ -PSBLAS library, version 3.6 +PSBLAS library, version 3.7 =========================== The architecture of the Fortran 2003 sparse BLAS is described in: @@ -110,6 +110,25 @@ Fix all reamining bugs. Bugs? We dont' have any ! ;-) The PSBLAS team. +--------------- +Project lead: +Salvatore Filippone + +Contributors (roughly reverse cronological order): + +Soren Rasmussen +Zaak Beekman +Ambra Abdullahi Hassan +Pasqua D'Ambra +Alfredo Buttari +Daniela di Serafino +Michele Martone +Michele Colajanni +Fabio Cerioni +Stefano Maiolatesi +Dario Pascucci + + RELATED SOFTWARE ---------------- diff --git a/ReleaseNews b/ReleaseNews index 7b1829da..0b1937e3 100644 --- a/ReleaseNews +++ b/ReleaseNews @@ -1,5 +1,21 @@ WHAT'S NEW +Version 3.7.0 + 1. Major change at API level: integer kinds reorganization. + Local indices are now of kind PSB_IPK_, whereas global indices + are of kind PSB_LPK_; at configure time it is possible to + choose them independently to be PSB_MPK_ (4 bytes) or PSB_EPK_ + (8 bytes), with the constraint that LPK is always at least as + large as IPK. + 2. The internals have also been reorganized heavily, with a much + more coherent design and split of functionalities into source + files. + + +Version 3.6.1 + 1. Multiple improvements to CDASB. + 2. Some additional methods required by the latest versions of MLD + Version 3.5. 1. New Krylov methods methods FCG and GCR are now available. @@ -86,29 +102,9 @@ The solution: either take out the -g option, or, if you really need to debug, edit Make.inc to force -DMPI_H in place of -DMPI_MOD. - -The PSBLAS team. - RELATED SOFTWARE If you are looking for more sophisticated preconditioners, you may be interested in the package MLD2P4 from http://github.com/sfilippone/mld2p4-2 -Contact: https://github.com/sfilippone/psblas3 - -Contributors -Salvatore Filippone -Alfredo Buttari -Soren Rasmussen -Ambra Abdullahi Hassan -Pasqua D'Ambra -Daniela di Serafino -Michele Martone -Michele Colajanni -Fabio Cerioni -Stefano Maiolatesi -Dario Pascucci - - - diff --git a/base/comm/internals/psi_covrl_restr.f90 b/base/comm/internals/psi_covrl_restr.f90 index 98ecdd8b..996e85ad 100644 --- a/base/comm/internals/psi_covrl_restr.f90 +++ b/base/comm/internals/psi_covrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_covrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_covrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_covrl_restr_vect use psb_c_base_vect_mod diff --git a/base/comm/internals/psi_covrl_restr_a.f90 b/base/comm/internals/psi_covrl_restr_a.f90 index 46eb0563..3c814a81 100644 --- a/base/comm/internals/psi_covrl_restr_a.f90 +++ b/base/comm/internals/psi_covrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_covrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_covrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_covrl_restrr1 diff --git a/base/comm/internals/psi_covrl_save.f90 b/base/comm/internals/psi_covrl_save.f90 index 41e65943..c48d2ade 100644 --- a/base/comm/internals/psi_covrl_save.f90 +++ b/base/comm/internals/psi_covrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_covrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_covrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_covrl_save_vect diff --git a/base/comm/internals/psi_covrl_save_a.f90 b/base/comm/internals/psi_covrl_save_a.f90 index d853db8d..d017d921 100644 --- a/base/comm/internals/psi_covrl_save_a.f90 +++ b/base/comm/internals/psi_covrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_covrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_covrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_covrl_saver1 diff --git a/base/comm/internals/psi_covrl_upd.f90 b/base/comm/internals/psi_covrl_upd.f90 index f99cbb66..ce33845e 100644 --- a/base/comm/internals/psi_covrl_upd.f90 +++ b/base/comm/internals/psi_covrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_covrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_covrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_covrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_covrl_upd_a.f90 b/base/comm/internals/psi_covrl_upd_a.f90 index 633747e5..33297731 100644 --- a/base/comm/internals/psi_covrl_upd_a.f90 +++ b/base/comm/internals/psi_covrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_covrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_covrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_covrl_updr1 diff --git a/base/comm/internals/psi_cswapdata.F90 b/base/comm/internals/psi_cswapdata.F90 index 9d350044..fed8afbf 100644 --- a/base/comm/internals/psi_cswapdata.F90 +++ b/base/comm/internals/psi_cswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_cswapdata.F90 ! -! Subroutine: psi_cswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_cswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_cswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_cswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_cswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_complex_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_cswap_vidx_vect ! Subroutine: psi_cswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_cswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_cswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_complex_swap_tag diff --git a/base/comm/internals/psi_cswapdata_a.F90 b/base/comm/internals/psi_cswapdata_a.F90 index ebf5b2f2..2a113b17 100644 --- a/base/comm/internals/psi_cswapdata_a.F90 +++ b/base/comm/internals/psi_cswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_cswapdata.F90 ! ! Subroutine: psi_cswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:,:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_cswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_cswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_complex_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_cswapidxm ! ! ! Subroutine: psi_cswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_cswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_cswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_cswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_cswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_complex_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_cswaptran.F90 b/base/comm/internals/psi_cswaptran.F90 index 93910dd8..152cb045 100644 --- a/base/comm/internals/psi_cswaptran.F90 +++ b/base/comm/internals/psi_cswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_cswaptran.F90 ! -! Subroutine: psi_cswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_cswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - complex Choose overwrite or sum. +! y - type(psb_c_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_cswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_cswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_cswaptran_vect ! Subroutine: psi_ctran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_ctran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_ctran_vidx_vect ! ! ! -! Subroutine: psi_cswaptran_vect +! Subroutine: psi_cswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_cswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_ctran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_cswaptran_a.F90 b/base/comm/internals/psi_cswaptran_a.F90 index 63f98df4..ed061be6 100644 --- a/base/comm/internals/psi_cswaptran_a.F90 +++ b/base/comm/internals/psi_cswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_cswaptran.F90 ! ! Subroutine: psi_cswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:,:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_ctranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_ctranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_complex_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_ctranidxm ! ! ! Subroutine: psi_cswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_ctranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_ctranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_ctranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_ctranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_complex_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/internals/psi_dovrl_restr.f90 b/base/comm/internals/psi_dovrl_restr.f90 index 326f32df..1d6695cc 100644 --- a/base/comm/internals/psi_dovrl_restr.f90 +++ b/base/comm/internals/psi_dovrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_dovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_dovrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_dovrl_restr_vect use psb_d_base_vect_mod diff --git a/base/comm/internals/psi_dovrl_restr_a.f90 b/base/comm/internals/psi_dovrl_restr_a.f90 index 2d83c416..df47403b 100644 --- a/base/comm/internals/psi_dovrl_restr_a.f90 +++ b/base/comm/internals/psi_dovrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_dovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_dovrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_dovrl_restrr1 diff --git a/base/comm/internals/psi_dovrl_save.f90 b/base/comm/internals/psi_dovrl_save.f90 index 3f8a923b..0689ee1b 100644 --- a/base/comm/internals/psi_dovrl_save.f90 +++ b/base/comm/internals/psi_dovrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_dovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_dovrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_dovrl_save_vect diff --git a/base/comm/internals/psi_dovrl_save_a.f90 b/base/comm/internals/psi_dovrl_save_a.f90 index 6bf57d87..fcc19e08 100644 --- a/base/comm/internals/psi_dovrl_save_a.f90 +++ b/base/comm/internals/psi_dovrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_dovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_dovrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_dovrl_saver1 diff --git a/base/comm/internals/psi_dovrl_upd.f90 b/base/comm/internals/psi_dovrl_upd.f90 index 867281ff..efbb2495 100644 --- a/base/comm/internals/psi_dovrl_upd.f90 +++ b/base/comm/internals/psi_dovrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_dovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_dovrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_dovrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_dovrl_upd_a.f90 b/base/comm/internals/psi_dovrl_upd_a.f90 index ccdfba89..8ad3db6b 100644 --- a/base/comm/internals/psi_dovrl_upd_a.f90 +++ b/base/comm/internals/psi_dovrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_dovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_dovrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_dovrl_updr1 diff --git a/base/comm/internals/psi_dswapdata.F90 b/base/comm/internals/psi_dswapdata.F90 index 929db361..a59b9b79 100644 --- a/base/comm/internals/psi_dswapdata.F90 +++ b/base/comm/internals/psi_dswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_dswapdata.F90 ! -! Subroutine: psi_dswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_dswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_dswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_dswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_dswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_double_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_dswap_vidx_vect ! Subroutine: psi_dswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_dswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_dswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_double_swap_tag diff --git a/base/comm/internals/psi_dswapdata_a.F90 b/base/comm/internals/psi_dswapdata_a.F90 index c6c52fbc..b9d0aaae 100644 --- a/base/comm/internals/psi_dswapdata_a.F90 +++ b/base/comm/internals/psi_dswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_dswapdata.F90 ! ! Subroutine: psi_dswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y(:,:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_dswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_dswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_double_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_dswapidxm ! ! ! Subroutine: psi_dswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_dswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_dswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - real Choose overwrite or sum. +! y(:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_dswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_dswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_double_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_dswaptran.F90 b/base/comm/internals/psi_dswaptran.F90 index 1ac09bfb..1feee33c 100644 --- a/base/comm/internals/psi_dswaptran.F90 +++ b/base/comm/internals/psi_dswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_dswaptran.F90 ! -! Subroutine: psi_dswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_dswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - real Choose overwrite or sum. +! y - type(psb_d_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_dswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_dswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_dswaptran_vect ! Subroutine: psi_dtran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_dtran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_dtran_vidx_vect ! ! ! -! Subroutine: psi_dswaptran_vect +! Subroutine: psi_dswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_dswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_dtran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_dswaptran_a.F90 b/base/comm/internals/psi_dswaptran_a.F90 index ffc4be1b..aad6348e 100644 --- a/base/comm/internals/psi_dswaptran_a.F90 +++ b/base/comm/internals/psi_dswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_dswaptran.F90 ! ! Subroutine: psi_dswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y(:,:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_dtranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_dtranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_double_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_dtranidxm ! ! ! Subroutine: psi_dswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_dtranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_dtranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - real Choose overwrite or sum. +! y(:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_dtranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_dtranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_double_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/internals/psi_eovrl_restr_a.f90 b/base/comm/internals/psi_eovrl_restr_a.f90 index fe981855..3dbb2ac4 100644 --- a/base/comm/internals/psi_eovrl_restr_a.f90 +++ b/base/comm/internals/psi_eovrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_eovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_eovrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_eovrl_restrr1 diff --git a/base/comm/internals/psi_eovrl_save_a.f90 b/base/comm/internals/psi_eovrl_save_a.f90 index de6878f0..4f0b7d30 100644 --- a/base/comm/internals/psi_eovrl_save_a.f90 +++ b/base/comm/internals/psi_eovrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_eovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_eovrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_eovrl_saver1 diff --git a/base/comm/internals/psi_eovrl_upd_a.f90 b/base/comm/internals/psi_eovrl_upd_a.f90 index f8589e41..e8e40738 100644 --- a/base/comm/internals/psi_eovrl_upd_a.f90 +++ b/base/comm/internals/psi_eovrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_eovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_eovrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_eovrl_updr1 diff --git a/base/comm/internals/psi_eswapdata_a.F90 b/base/comm/internals/psi_eswapdata_a.F90 index 0c0f7220..f7c67ac3 100644 --- a/base/comm/internals/psi_eswapdata_a.F90 +++ b/base/comm/internals/psi_eswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_eswapdata.F90 ! ! Subroutine: psi_eswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:,:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_eswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_eswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_int8_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_eswapidxm ! ! ! Subroutine: psi_eswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_eswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_eswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_eswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_eswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_int8_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_eswaptran_a.F90 b/base/comm/internals/psi_eswaptran_a.F90 index 2a78e47d..42954369 100644 --- a/base/comm/internals/psi_eswaptran_a.F90 +++ b/base/comm/internals/psi_eswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_eswaptran.F90 ! ! Subroutine: psi_eswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:,:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_etranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_etranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_int8_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_etranidxm ! ! ! Subroutine: psi_eswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_etranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_etranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_etranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_etranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_int8_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/internals/psi_iovrl_restr.f90 b/base/comm/internals/psi_iovrl_restr.f90 index 89ff5ee0..b0efa2ee 100644 --- a/base/comm/internals/psi_iovrl_restr.f90 +++ b/base/comm/internals/psi_iovrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_iovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_iovrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_iovrl_restr_vect use psb_i_base_vect_mod diff --git a/base/comm/internals/psi_iovrl_save.f90 b/base/comm/internals/psi_iovrl_save.f90 index b48a7dbc..cc7619f9 100644 --- a/base/comm/internals/psi_iovrl_save.f90 +++ b/base/comm/internals/psi_iovrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_iovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_iovrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_iovrl_save_vect diff --git a/base/comm/internals/psi_iovrl_upd.f90 b/base/comm/internals/psi_iovrl_upd.f90 index a84a1cc0..988bf006 100644 --- a/base/comm/internals/psi_iovrl_upd.f90 +++ b/base/comm/internals/psi_iovrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_iovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_iovrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_iovrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_iswapdata.F90 b/base/comm/internals/psi_iswapdata.F90 index 4774da99..d05ab8ac 100644 --- a/base/comm/internals/psi_iswapdata.F90 +++ b/base/comm/internals/psi_iswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_iswapdata.F90 ! -! Subroutine: psi_iswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_iswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_iswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_iswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_iswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_int_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_iswap_vidx_vect ! Subroutine: psi_iswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_iswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_iswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_int_swap_tag diff --git a/base/comm/internals/psi_iswaptran.F90 b/base/comm/internals/psi_iswaptran.F90 index 2fb590e5..e5719735 100644 --- a/base/comm/internals/psi_iswaptran.F90 +++ b/base/comm/internals/psi_iswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_iswaptran.F90 ! -! Subroutine: psi_iswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_iswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - integer Choose overwrite or sum. +! y - type(psb_i_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_iswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_iswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_iswaptran_vect ! Subroutine: psi_itran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_itran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_itran_vidx_vect ! ! ! -! Subroutine: psi_iswaptran_vect +! Subroutine: psi_iswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_iswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_itran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_lovrl_restr.f90 b/base/comm/internals/psi_lovrl_restr.f90 index ba96e9c0..dc33bbb1 100644 --- a/base/comm/internals/psi_lovrl_restr.f90 +++ b/base/comm/internals/psi_lovrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_lovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_lovrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_lovrl_restr_vect use psb_l_base_vect_mod diff --git a/base/comm/internals/psi_lovrl_save.f90 b/base/comm/internals/psi_lovrl_save.f90 index 5a06c697..496eec90 100644 --- a/base/comm/internals/psi_lovrl_save.f90 +++ b/base/comm/internals/psi_lovrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_lovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_lovrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_lovrl_save_vect diff --git a/base/comm/internals/psi_lovrl_upd.f90 b/base/comm/internals/psi_lovrl_upd.f90 index 4364ac6f..d20d80cc 100644 --- a/base/comm/internals/psi_lovrl_upd.f90 +++ b/base/comm/internals/psi_lovrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_lovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_lovrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_lovrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_lswapdata.F90 b/base/comm/internals/psi_lswapdata.F90 index f1f8de5c..939f9596 100644 --- a/base/comm/internals/psi_lswapdata.F90 +++ b/base/comm/internals/psi_lswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_lswapdata.F90 ! -! Subroutine: psi_lswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_lswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_lswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_lswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_lswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_long_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_lswap_vidx_vect ! Subroutine: psi_lswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_lswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_lswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_long_swap_tag diff --git a/base/comm/internals/psi_lswaptran.F90 b/base/comm/internals/psi_lswaptran.F90 index d960e0f9..ccc1b6e3 100644 --- a/base/comm/internals/psi_lswaptran.F90 +++ b/base/comm/internals/psi_lswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_lswaptran.F90 ! -! Subroutine: psi_lswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_lswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - integer Choose overwrite or sum. +! y - type(psb_l_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_lswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_lswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_lswaptran_vect ! Subroutine: psi_ltran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_ltran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_ltran_vidx_vect ! ! ! -! Subroutine: psi_lswaptran_vect +! Subroutine: psi_lswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_lswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_ltran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_movrl_restr_a.f90 b/base/comm/internals/psi_movrl_restr_a.f90 index a5759f98..92e06793 100644 --- a/base/comm/internals/psi_movrl_restr_a.f90 +++ b/base/comm/internals/psi_movrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_movrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_movrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_movrl_restrr1 diff --git a/base/comm/internals/psi_movrl_save_a.f90 b/base/comm/internals/psi_movrl_save_a.f90 index 7935333f..fbc021cf 100644 --- a/base/comm/internals/psi_movrl_save_a.f90 +++ b/base/comm/internals/psi_movrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_movrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_movrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_movrl_saver1 diff --git a/base/comm/internals/psi_movrl_upd_a.f90 b/base/comm/internals/psi_movrl_upd_a.f90 index 92bfccce..03670659 100644 --- a/base/comm/internals/psi_movrl_upd_a.f90 +++ b/base/comm/internals/psi_movrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_movrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_movrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_movrl_updr1 diff --git a/base/comm/internals/psi_mswapdata_a.F90 b/base/comm/internals/psi_mswapdata_a.F90 index bdeb28e2..b71e61ef 100644 --- a/base/comm/internals/psi_mswapdata_a.F90 +++ b/base/comm/internals/psi_mswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_mswapdata.F90 ! ! Subroutine: psi_mswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:,:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_mswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_mswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_int4_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_mswapidxm ! ! ! Subroutine: psi_mswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_mswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_mswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_mswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_mswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_int4_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_mswaptran_a.F90 b/base/comm/internals/psi_mswaptran_a.F90 index 013e21b6..add5a608 100644 --- a/base/comm/internals/psi_mswaptran_a.F90 +++ b/base/comm/internals/psi_mswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_mswaptran.F90 ! ! Subroutine: psi_mswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:,:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_mtranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_mtranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_int4_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_mtranidxm ! ! ! Subroutine: psi_mswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_mtranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_mtranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - integer Choose overwrite or sum. +! y(:) - integer The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - integer Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_mtranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_mtranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_int4_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/internals/psi_sovrl_restr.f90 b/base/comm/internals/psi_sovrl_restr.f90 index b74c4335..3854040c 100644 --- a/base/comm/internals/psi_sovrl_restr.f90 +++ b/base/comm/internals/psi_sovrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_sovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_sovrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_sovrl_restr_vect use psb_s_base_vect_mod diff --git a/base/comm/internals/psi_sovrl_restr_a.f90 b/base/comm/internals/psi_sovrl_restr_a.f90 index 5ff1a9f7..e66297d5 100644 --- a/base/comm/internals/psi_sovrl_restr_a.f90 +++ b/base/comm/internals/psi_sovrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_sovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_sovrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_sovrl_restrr1 diff --git a/base/comm/internals/psi_sovrl_save.f90 b/base/comm/internals/psi_sovrl_save.f90 index a10ae218..9b06fef7 100644 --- a/base/comm/internals/psi_sovrl_save.f90 +++ b/base/comm/internals/psi_sovrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_sovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_sovrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_sovrl_save_vect diff --git a/base/comm/internals/psi_sovrl_save_a.f90 b/base/comm/internals/psi_sovrl_save_a.f90 index 5766dede..cf400127 100644 --- a/base/comm/internals/psi_sovrl_save_a.f90 +++ b/base/comm/internals/psi_sovrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_sovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_sovrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_sovrl_saver1 diff --git a/base/comm/internals/psi_sovrl_upd.f90 b/base/comm/internals/psi_sovrl_upd.f90 index b95a49ba..636261b1 100644 --- a/base/comm/internals/psi_sovrl_upd.f90 +++ b/base/comm/internals/psi_sovrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_sovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_sovrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_sovrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_sovrl_upd_a.f90 b/base/comm/internals/psi_sovrl_upd_a.f90 index d553b5f7..82211657 100644 --- a/base/comm/internals/psi_sovrl_upd_a.f90 +++ b/base/comm/internals/psi_sovrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_sovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_sovrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_sovrl_updr1 diff --git a/base/comm/internals/psi_sswapdata.F90 b/base/comm/internals/psi_sswapdata.F90 index e05ff5e9..b5185198 100644 --- a/base/comm/internals/psi_sswapdata.F90 +++ b/base/comm/internals/psi_sswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_sswapdata.F90 ! -! Subroutine: psi_sswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_sswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_sswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_sswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_sswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_real_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_sswap_vidx_vect ! Subroutine: psi_sswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_sswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_sswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_real_swap_tag diff --git a/base/comm/internals/psi_sswapdata_a.F90 b/base/comm/internals/psi_sswapdata_a.F90 index 81d11859..de8587c1 100644 --- a/base/comm/internals/psi_sswapdata_a.F90 +++ b/base/comm/internals/psi_sswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_sswapdata.F90 ! ! Subroutine: psi_sswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y(:,:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_sswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_sswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_real_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_sswapidxm ! ! ! Subroutine: psi_sswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_sswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_sswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - real Choose overwrite or sum. +! y(:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_sswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_sswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_real_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_sswaptran.F90 b/base/comm/internals/psi_sswaptran.F90 index 0616ee6c..cb3ccc75 100644 --- a/base/comm/internals/psi_sswaptran.F90 +++ b/base/comm/internals/psi_sswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_sswaptran.F90 ! -! Subroutine: psi_sswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_sswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - real Choose overwrite or sum. +! y - type(psb_s_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_sswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_sswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_sswaptran_vect ! Subroutine: psi_stran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_stran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_stran_vidx_vect ! ! ! -! Subroutine: psi_sswaptran_vect +! Subroutine: psi_sswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_sswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_stran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_sswaptran_a.F90 b/base/comm/internals/psi_sswaptran_a.F90 index 983a8457..f0f82965 100644 --- a/base/comm/internals/psi_sswaptran_a.F90 +++ b/base/comm/internals/psi_sswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_sswaptran.F90 ! ! Subroutine: psi_sswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - real Choose overwrite or sum. +! y(:,:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_stranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_stranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_real_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_stranidxm ! ! ! Subroutine: psi_sswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_stranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_stranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - real Choose overwrite or sum. +! y(:) - real The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - real Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_stranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_stranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_real_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/internals/psi_zovrl_restr.f90 b/base/comm/internals/psi_zovrl_restr.f90 index bd83e618..e52232e7 100644 --- a/base/comm/internals/psi_zovrl_restr.f90 +++ b/base/comm/internals/psi_zovrl_restr.f90 @@ -28,8 +28,13 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_zovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! +! ! - subroutine psi_zovrl_restr_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_zovrl_restr_vect use psb_z_base_vect_mod diff --git a/base/comm/internals/psi_zovrl_restr_a.f90 b/base/comm/internals/psi_zovrl_restr_a.f90 index a0a22a31..379efdcb 100644 --- a/base/comm/internals/psi_zovrl_restr_a.f90 +++ b/base/comm/internals/psi_zovrl_restr_a.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_zovrl_restr +! These subroutines restore the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_zovrl_restrr1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_zovrl_restrr1 diff --git a/base/comm/internals/psi_zovrl_save.f90 b/base/comm/internals/psi_zovrl_save.f90 index 16238573..acf65181 100644 --- a/base/comm/internals/psi_zovrl_save.f90 +++ b/base/comm/internals/psi_zovrl_save.f90 @@ -28,6 +28,11 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_zovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! ! subroutine psi_zovrl_save_vect(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_zovrl_save_vect diff --git a/base/comm/internals/psi_zovrl_save_a.f90 b/base/comm/internals/psi_zovrl_save_a.f90 index 32d5d212..1e8fdb89 100644 --- a/base/comm/internals/psi_zovrl_save_a.f90 +++ b/base/comm/internals/psi_zovrl_save_a.f90 @@ -28,8 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! -! - +! +! +! Subroutine: psi_zovrl_save +! These subroutines save the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap. +! subroutine psi_zovrl_saver1(x,xs,desc_a,info) use psi_mod, psi_protect_name => psi_zovrl_saver1 diff --git a/base/comm/internals/psi_zovrl_upd.f90 b/base/comm/internals/psi_zovrl_upd.f90 index 83fcf702..cd7ea0de 100644 --- a/base/comm/internals/psi_zovrl_upd.f90 +++ b/base/comm/internals/psi_zovrl_upd.f90 @@ -28,8 +28,14 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_zovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! +! ! - subroutine psi_zovrl_upd_vect(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_zovrl_upd_vect use psb_realloc_mod diff --git a/base/comm/internals/psi_zovrl_upd_a.f90 b/base/comm/internals/psi_zovrl_upd_a.f90 index b149addb..9ea2fbae 100644 --- a/base/comm/internals/psi_zovrl_upd_a.f90 +++ b/base/comm/internals/psi_zovrl_upd_a.f90 @@ -28,6 +28,12 @@ ! ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE ! POSSIBILITY OF SUCH DAMAGE. ! +! +! Subroutine: psi_zovrl_update +! These subroutines update the overlap region of a vector; they are used +! for the transpose matrix-vector product when there is a nonempty overlap, +! or for the application of Additive Schwarz preconditioners. +! ! subroutine psi_zovrl_updr1(x,desc_a,update,info) use psi_mod, psi_protect_name => psi_zovrl_updr1 diff --git a/base/comm/internals/psi_zswapdata.F90 b/base/comm/internals/psi_zswapdata.F90 index 7f8c3357..7d34012e 100644 --- a/base/comm/internals/psi_zswapdata.F90 +++ b/base/comm/internals/psi_zswapdata.F90 @@ -32,8 +32,10 @@ ! ! File: psi_zswapdata.F90 ! -! Subroutine: psi_zswapdatam -! Does the data exchange among processes. Essentially this is doing +! +! +! Subroutine: psi_zswapdata_vect +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -43,12 +45,15 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a send on (PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y - type(psb_@x@_vect_type) The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -83,14 +88,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! -! -! -! Subroutine: psi_zswapdata_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! -! ! subroutine psi_zswapdata_vect(flag,beta,y,desc_a,work,info,data) @@ -263,7 +260,7 @@ subroutine psi_zswap_vidx_vect(iictxt,iicomm,flag,beta,y,idx, & nesd = idx%v(pnti+nerv+psb_n_elem_send_) rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_dcomplex_swap_tag @@ -426,7 +423,7 @@ end subroutine psi_zswap_vidx_vect ! Subroutine: psi_zswapdata_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_zswapdata_multivect(flag,beta,y,desc_a,work,info,data) @@ -602,7 +599,7 @@ subroutine psi_zswap_vidx_multivect(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt p2ptag = psb_dcomplex_swap_tag diff --git a/base/comm/internals/psi_zswapdata_a.F90 b/base/comm/internals/psi_zswapdata_a.F90 index 3a1ab111..6e821f4f 100644 --- a/base/comm/internals/psi_zswapdata_a.F90 +++ b/base/comm/internals/psi_zswapdata_a.F90 @@ -33,9 +33,9 @@ ! File: psi_zswapdata.F90 ! ! Subroutine: psi_zswapdatam -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but -! it is capable of pruning empty exchanges, which are very likely in out +! it is capable of pruning empty exchanges, which are very likely in our ! application environment. All the variants have the same structure ! In all these subroutines X may be: I Integer ! S real(psb_spk_) @@ -49,6 +49,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -69,10 +70,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:,:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -236,7 +237,7 @@ subroutine psi_zswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -349,7 +350,7 @@ subroutine psi_zswapidxm(iictxt,iicomm,flag,n,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_dcomplex_swap_tag call mpi_irecv(rcvbuf(rcv_pt),n*nerv,& @@ -507,7 +508,7 @@ end subroutine psi_zswapidxm ! ! ! Subroutine: psi_zswapdatav -! Does the data exchange among processes. Essentially this is doing +! Implements the data exchange among processes. Essentially this is doing ! a variable all-to-all data exchange (ALLTOALLV in MPI parlance), but ! it is capable of pruning empty exchanges, which are very likely in out ! application environment. All the variants have the same structure @@ -523,6 +524,7 @@ end subroutine psi_zswapidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -543,10 +545,10 @@ end subroutine psi_zswapidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -721,7 +723,7 @@ subroutine psi_zswapidxv(iictxt,iicomm,flag,beta,y,idx, & proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -835,7 +837,7 @@ subroutine psi_zswapidxv(iictxt,iicomm,flag,beta,y,idx, & nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nerv>0).and.(proc_to_comm /= me)) then p2ptag = psb_dcomplex_swap_tag call mpi_irecv(rcvbuf(rcv_pt),nerv,& diff --git a/base/comm/internals/psi_zswaptran.F90 b/base/comm/internals/psi_zswaptran.F90 index 2f7b93e4..c78a5e1a 100644 --- a/base/comm/internals/psi_zswaptran.F90 +++ b/base/comm/internals/psi_zswaptran.F90 @@ -32,8 +32,8 @@ ! ! File: psi_zswaptran.F90 ! -! Subroutine: psi_zswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Subroutine: psi_zswaptran_vect +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -47,12 +47,16 @@ ! C complex(psb_spk_) ! Z complex(psb_dpk_) ! Basically the operation is as follows: on each process, we identify -! sections SND(Y) and RCV(Y); then we do a SEND(PACK(SND(Y))); -! then we receive, and we do an update with Y = UNPACK(RCV(Y)) + BETA * Y -! but only on the elements involved in the UNPACK operation. +! sections SND(Y) and RCV(Y); then we do a SEND(PACK(GTH(SND(Y)))); +! then we receive, and we do an update with Y = SCT(RCV(Y)) + BETA * Y +! but only on the elements involved in the SCT operation. ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. +! This version works on encapsulated vectors, and uses their methods to do GTH and SCT, +! so that special versions (i.e. GPU vectors can override them +! ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +77,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area -! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! beta - complex Choose overwrite or sum. +! y - type(psb_z_vect_type) The data area +! desc_a - type(psb_desc_type). The communication descriptor. +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -86,13 +90,6 @@ ! psb_comm_ovrl_ use ovrl_index ! psb_comm_mov_ use ovr_mst_idx ! -! -! -! Subroutine: psi_zswaptran_vect -! Data exchange among processes. -! -! Takes care of Y an exanspulated vector. -! ! subroutine psi_zswaptran_vect(flag,beta,y,desc_a,work,info,data) @@ -171,7 +168,7 @@ end subroutine psi_zswaptran_vect ! Subroutine: psi_ztran_vidx_vect ! Data exchange among processes. ! -! Takes care of Y an exanspulated vector. Relies on the gather/scatter methods +! Takes care of Y an encapsulated vector. Relies on the gather/scatter methods ! of vectors. ! ! The real workhorse: the outer routine will only choose the index list @@ -269,7 +266,7 @@ subroutine psi_ztran_vidx_vect(iictxt,iicomm,flag,beta,y,idx,& snd_pt = 1+pnti+nerv+psb_n_elem_send_ rcv_pt = 1+pnti+psb_n_elem_recv_ - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),rcv_pt call mpi_irecv(y%combuf(snd_pt),nesd,& @@ -436,10 +433,10 @@ end subroutine psi_ztran_vidx_vect ! ! ! -! Subroutine: psi_zswaptran_vect +! Subroutine: psi_zswaptran_multivect ! Data exchange among processes. ! -! Takes care of Y an encaspulated vector. +! Takes care of Y an encaspulated multivector. ! ! subroutine psi_zswaptran_multivect(flag,beta,y,desc_a,work,info,data) @@ -616,7 +613,7 @@ subroutine psi_ztran_vidx_multivect(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx%v(pnti+psb_proc_id_) nerv = idx%v(pnti+psb_n_elem_recv_) nesd = idx%v(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then if (debug) write(*,*) me,'Posting receive from',prcid(i),snd_pt call mpi_irecv(y%combuf(snd_pt),n*nesd,& diff --git a/base/comm/internals/psi_zswaptran_a.F90 b/base/comm/internals/psi_zswaptran_a.F90 index fa694378..aaf305ac 100644 --- a/base/comm/internals/psi_zswaptran_a.F90 +++ b/base/comm/internals/psi_zswaptran_a.F90 @@ -33,7 +33,7 @@ ! File: psi_zswaptran.F90 ! ! Subroutine: psi_zswaptranm -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -53,6 +53,7 @@ ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -73,10 +74,10 @@ ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:,:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:,:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -241,7 +242,7 @@ subroutine psi_ztranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = n*nerv @@ -359,7 +360,7 @@ subroutine psi_ztranidxm(iictxt,iicomm,flag,n,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_dcomplex_swap_tag call mpi_irecv(sndbuf(snd_pt),n*nesd,& @@ -516,7 +517,7 @@ end subroutine psi_ztranidxm ! ! ! Subroutine: psi_zswaptranv -! Does the data exchange among processes. This is similar to Xswapdata, but +! Implements the data exchange among processes. This is similar to Xswapdata, but ! the list is read "in reverse", i.e. indices that are normally SENT are used ! for the RECEIVE part and vice-versa. This is the basic data exchange operation ! for doing the product of a sparse matrix by a vector. @@ -536,6 +537,7 @@ end subroutine psi_ztranidxm ! Thus: for halo data exchange, the receive section is confined in the ! halo indices, and BETA=0, whereas for overlap exchange the receive section ! is scattered in the owned indices, and BETA=1. +! The first routine picks the desired exchange index list and passes it to the second. ! ! Arguments: ! flag - integer Choose the algorithm for data exchange: @@ -556,10 +558,10 @@ end subroutine psi_ztranidxm ! ! ! n - integer Number of columns in Y -! beta - X Choose overwrite or sum. -! y(:) - X The data area +! beta - complex Choose overwrite or sum. +! y(:) - complex The data area ! desc_a - type(psb_desc_type). The communication descriptor. -! work(:) - X Buffer space. If not sufficient, will do +! work(:) - complex Buffer space. If not sufficient, will do ! our own internal allocation. ! info - integer. return code. ! data - integer which list is to be used to exchange data @@ -734,7 +736,7 @@ subroutine psi_ztranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(proc_to_comm) = psb_get_rank(ictxt,proc_to_comm) + prcid(proc_to_comm) = psb_get_mpi_rank(ictxt,proc_to_comm) brvidx(proc_to_comm) = rcv_pt rvsz(proc_to_comm) = nerv @@ -852,7 +854,7 @@ subroutine psi_ztranidxv(iictxt,iicomm,flag,beta,y,idx,& proc_to_comm = idx(pnti+psb_proc_id_) nerv = idx(pnti+psb_n_elem_recv_) nesd = idx(pnti+nerv+psb_n_elem_send_) - prcid(i) = psb_get_rank(ictxt,proc_to_comm) + prcid(i) = psb_get_mpi_rank(ictxt,proc_to_comm) if ((nesd>0).and.(proc_to_comm /= me)) then p2ptag = psb_dcomplex_swap_tag call mpi_irecv(sndbuf(snd_pt),nesd,& diff --git a/base/comm/psb_cgather.f90 b/base/comm/psb_cgather.f90 index d4e675c2..f4ed3f4a 100644 --- a/base/comm/psb_cgather.f90 +++ b/base/comm/psb_cgather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_cgather.f90 ! -! Subroutine: psb_cgatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_cgather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - complex,dimension(:,:). The local matrix into which gather +! globx - complex,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - complex,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_c_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_cgather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_cgather_vect +! Subroutine: psb_cgather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_cgather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_cgather_multivect diff --git a/base/comm/psb_cgather_a.f90 b/base/comm/psb_cgather_a.f90 index 09e35678..5f75abd6 100644 --- a/base/comm/psb_cgather_a.f90 +++ b/base/comm/psb_cgather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_cgather.f90 ! -! Subroutine: psb_cgatherm +! Subroutine: psb_cgather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_chalo.f90 b/base/comm/psb_chalo.f90 index e34168c6..ad483a51 100644 --- a/base/comm/psb_chalo.f90 +++ b/base/comm/psb_chalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_chalo.f90 ! -! Subroutine: psb_chalom +! Subroutine: psb_chalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - complex,dimension(:,:). The local part of the dense matrix. +! x - type(psb_c_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - complex(optional). Work area. +! work - complex(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_chalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_chalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_chalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_chalo_vect - +! +! Subroutine: psb_chalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_c_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - complex(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_chalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_chalo_multivect use psi_mod diff --git a/base/comm/psb_covrl.f90 b/base/comm/psb_covrl.f90 index f6155ffe..7ac851b6 100644 --- a/base/comm/psb_covrl.f90 +++ b/base/comm/psb_covrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_covrl.f90 ! -! Subroutine: psb_covrlm +! Subroutine: psb_covrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - complex The local part of the dense matrix. +! x - type(psb_c_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_covrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_covrl_vect - +! +! Subroutine: psb_covrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_c_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - complex(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_covrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_covrl_multivect use psi_mod diff --git a/base/comm/psb_cscatter.F90 b/base/comm/psb_cscatter.F90 index 77036d04..7ac22a68 100644 --- a/base/comm/psb_cscatter.F90 +++ b/base/comm/psb_cscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_cscatter.f90 ! -! Subroutine: psb_cscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_cscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - complex,dimension(:,:). The global matrix to scatter. -! locx - complex,dimension(:,:). The local piece of the distributed matrix. +! globx - complex,dimension(:) The global matrix to scatter. +! locx - type(psb_c_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_cscatter_a.F90 b/base/comm/psb_cscatter_a.F90 index 81e69be4..d16ae980 100644 --- a/base/comm/psb_cscatter_a.F90 +++ b/base/comm/psb_cscatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_cscatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - complex,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_cscatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_cscatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_cscatterm ! Subroutine: psb_cscatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - complex,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_cscatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_cscatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_cspgather.F90 b/base/comm/psb_cspgather.F90 index b9401061..45dcc667 100644 --- a/base/comm/psb_cspgather.F90 +++ b/base/comm/psb_cspgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_cspgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_c_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_lc_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_csp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/comm/psb_dgather.f90 b/base/comm/psb_dgather.f90 index 3659b487..c767c8ec 100644 --- a/base/comm/psb_dgather.f90 +++ b/base/comm/psb_dgather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_dgather.f90 ! -! Subroutine: psb_dgatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_dgather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - real,dimension(:,:). The local matrix into which gather +! globx - real,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - real,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_d_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_dgather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_dgather_vect +! Subroutine: psb_dgather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_dgather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_dgather_multivect diff --git a/base/comm/psb_dgather_a.f90 b/base/comm/psb_dgather_a.f90 index 277eb3d0..5ae9ed50 100644 --- a/base/comm/psb_dgather_a.f90 +++ b/base/comm/psb_dgather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_dgather.f90 ! -! Subroutine: psb_dgatherm +! Subroutine: psb_dgather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_dhalo.f90 b/base/comm/psb_dhalo.f90 index 85caa81f..b5f584dc 100644 --- a/base/comm/psb_dhalo.f90 +++ b/base/comm/psb_dhalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_dhalo.f90 ! -! Subroutine: psb_dhalom +! Subroutine: psb_dhalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - real,dimension(:,:). The local part of the dense matrix. +! x - type(psb_d_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - real(optional). Work area. +! work - real(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_dhalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_dhalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_dhalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_dhalo_vect - +! +! Subroutine: psb_dhalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_d_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - real(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_dhalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_dhalo_multivect use psi_mod diff --git a/base/comm/psb_dovrl.f90 b/base/comm/psb_dovrl.f90 index 28b2cd24..1177be29 100644 --- a/base/comm/psb_dovrl.f90 +++ b/base/comm/psb_dovrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_dovrl.f90 ! -! Subroutine: psb_dovrlm +! Subroutine: psb_dovrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - real The local part of the dense matrix. +! x - type(psb_d_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_dovrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_dovrl_vect - +! +! Subroutine: psb_dovrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_d_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - real(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_dovrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_dovrl_multivect use psi_mod diff --git a/base/comm/psb_dscatter.F90 b/base/comm/psb_dscatter.F90 index d559fa12..157af3c6 100644 --- a/base/comm/psb_dscatter.F90 +++ b/base/comm/psb_dscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_dscatter.f90 ! -! Subroutine: psb_dscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_dscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - real,dimension(:,:). The global matrix to scatter. -! locx - real,dimension(:,:). The local piece of the distributed matrix. +! globx - real,dimension(:) The global matrix to scatter. +! locx - type(psb_d_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_dscatter_a.F90 b/base/comm/psb_dscatter_a.F90 index 998028b3..e0b39f57 100644 --- a/base/comm/psb_dscatter_a.F90 +++ b/base/comm/psb_dscatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_dscatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - real,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_dscatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_dscatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_dscatterm ! Subroutine: psb_dscatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - real,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_dscatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_dscatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_dspgather.F90 b/base/comm/psb_dspgather.F90 index d5593504..62084d48 100644 --- a/base/comm/psb_dspgather.F90 +++ b/base/comm/psb_dspgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_dspgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_d_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_ld_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_dsp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/comm/psb_egather_a.f90 b/base/comm/psb_egather_a.f90 index 54b77bc9..b910a4f7 100644 --- a/base/comm/psb_egather_a.f90 +++ b/base/comm/psb_egather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_egather.f90 ! -! Subroutine: psb_egatherm +! Subroutine: psb_egather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_escatter_a.F90 b/base/comm/psb_escatter_a.F90 index 0095636d..dbb2026f 100644 --- a/base/comm/psb_escatter_a.F90 +++ b/base/comm/psb_escatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_escatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - integer,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_escatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_escatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_escatterm ! Subroutine: psb_escatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - integer,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_escatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_escatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_igather.f90 b/base/comm/psb_igather.f90 index a6e59497..48a4f2fe 100644 --- a/base/comm/psb_igather.f90 +++ b/base/comm/psb_igather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_igather.f90 ! -! Subroutine: psb_igatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_igather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - integer,dimension(:,:). The local matrix into which gather +! globx - integer,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - integer,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_i_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_igather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_igather_vect +! Subroutine: psb_igather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_igather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_igather_multivect diff --git a/base/comm/psb_ihalo.f90 b/base/comm/psb_ihalo.f90 index ed4d2c10..4bccfc10 100644 --- a/base/comm/psb_ihalo.f90 +++ b/base/comm/psb_ihalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_ihalo.f90 ! -! Subroutine: psb_ihalom +! Subroutine: psb_ihalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - integer,dimension(:,:). The local part of the dense matrix. +! x - type(psb_i_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - integer(optional). Work area. +! work - integer(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_ihalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_ihalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_ihalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_ihalo_vect - +! +! Subroutine: psb_ihalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_i_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - integer(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_ihalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_ihalo_multivect use psi_mod diff --git a/base/comm/psb_iovrl.f90 b/base/comm/psb_iovrl.f90 index 1e3ca4f3..06f720b0 100644 --- a/base/comm/psb_iovrl.f90 +++ b/base/comm/psb_iovrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_iovrl.f90 ! -! Subroutine: psb_iovrlm +! Subroutine: psb_iovrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - integer The local part of the dense matrix. +! x - type(psb_i_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_iovrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_iovrl_vect - +! +! Subroutine: psb_iovrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_i_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - integer(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_iovrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_iovrl_multivect use psi_mod diff --git a/base/comm/psb_iscatter.F90 b/base/comm/psb_iscatter.F90 index 1a545e9b..f159d5b4 100644 --- a/base/comm/psb_iscatter.F90 +++ b/base/comm/psb_iscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_iscatter.f90 ! -! Subroutine: psb_iscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_iscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - integer,dimension(:,:). The global matrix to scatter. -! locx - integer,dimension(:,:). The local piece of the distributed matrix. +! globx - integer,dimension(:) The global matrix to scatter. +! locx - type(psb_i_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_ispgather.F90 b/base/comm/psb_ispgather.F90 index a19d24d9..d13c2e7c 100644 --- a/base/comm/psb_ispgather.F90 +++ b/base/comm/psb_ispgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_ispgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_i_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_@LX@_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_isp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/comm/psb_lgather.f90 b/base/comm/psb_lgather.f90 index 45ea0d94..1f6f448f 100644 --- a/base/comm/psb_lgather.f90 +++ b/base/comm/psb_lgather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_lgather.f90 ! -! Subroutine: psb_lgatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_lgather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - integer,dimension(:,:). The local matrix into which gather +! globx - integer,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - integer,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_l_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_lgather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_lgather_vect +! Subroutine: psb_lgather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_lgather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_lgather_multivect diff --git a/base/comm/psb_lhalo.f90 b/base/comm/psb_lhalo.f90 index 49b4d13d..b35613a1 100644 --- a/base/comm/psb_lhalo.f90 +++ b/base/comm/psb_lhalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_lhalo.f90 ! -! Subroutine: psb_lhalom +! Subroutine: psb_lhalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - integer,dimension(:,:). The local part of the dense matrix. +! x - type(psb_l_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - integer(optional). Work area. +! work - integer(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_lhalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_lhalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_lhalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_lhalo_vect - +! +! Subroutine: psb_lhalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_l_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - integer(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_lhalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_lhalo_multivect use psi_mod diff --git a/base/comm/psb_lovrl.f90 b/base/comm/psb_lovrl.f90 index 75b816b8..bb3ece65 100644 --- a/base/comm/psb_lovrl.f90 +++ b/base/comm/psb_lovrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_lovrl.f90 ! -! Subroutine: psb_lovrlm +! Subroutine: psb_lovrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - integer The local part of the dense matrix. +! x - type(psb_l_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_lovrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_lovrl_vect - +! +! Subroutine: psb_lovrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_l_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - integer(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_lovrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_lovrl_multivect use psi_mod diff --git a/base/comm/psb_lscatter.F90 b/base/comm/psb_lscatter.F90 index ed4051fa..ceb60e4f 100644 --- a/base/comm/psb_lscatter.F90 +++ b/base/comm/psb_lscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_lscatter.f90 ! -! Subroutine: psb_lscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_lscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - integer,dimension(:,:). The global matrix to scatter. -! locx - integer,dimension(:,:). The local piece of the distributed matrix. +! globx - integer,dimension(:) The global matrix to scatter. +! locx - type(psb_l_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_lspgather.F90 b/base/comm/psb_lspgather.F90 index 81c9c67c..2f588116 100644 --- a/base/comm/psb_lspgather.F90 +++ b/base/comm/psb_lspgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_lspgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_l_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_@LX@_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_lsp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/comm/psb_mgather_a.f90 b/base/comm/psb_mgather_a.f90 index 1ee8e7f4..251e06c9 100644 --- a/base/comm/psb_mgather_a.f90 +++ b/base/comm/psb_mgather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_mgather.f90 ! -! Subroutine: psb_mgatherm +! Subroutine: psb_mgather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_mscatter_a.F90 b/base/comm/psb_mscatter_a.F90 index 6a5a2552..f85a3849 100644 --- a/base/comm/psb_mscatter_a.F90 +++ b/base/comm/psb_mscatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_mscatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - integer,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_mscatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_mscatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_mscatterm ! Subroutine: psb_mscatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - integer,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_mscatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_mscatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_sgather.f90 b/base/comm/psb_sgather.f90 index 10c6b7c2..538d1c43 100644 --- a/base/comm/psb_sgather.f90 +++ b/base/comm/psb_sgather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_sgather.f90 ! -! Subroutine: psb_sgatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_sgather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - real,dimension(:,:). The local matrix into which gather +! globx - real,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - real,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_s_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_sgather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_sgather_vect +! Subroutine: psb_sgather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_sgather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_sgather_multivect diff --git a/base/comm/psb_sgather_a.f90 b/base/comm/psb_sgather_a.f90 index 68076959..47a8c79a 100644 --- a/base/comm/psb_sgather_a.f90 +++ b/base/comm/psb_sgather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_sgather.f90 ! -! Subroutine: psb_sgatherm +! Subroutine: psb_sgather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_shalo.f90 b/base/comm/psb_shalo.f90 index 2948624c..78ab39e3 100644 --- a/base/comm/psb_shalo.f90 +++ b/base/comm/psb_shalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_shalo.f90 ! -! Subroutine: psb_shalom +! Subroutine: psb_shalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - real,dimension(:,:). The local part of the dense matrix. +! x - type(psb_s_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - real(optional). Work area. +! work - real(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_shalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_shalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_shalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_shalo_vect - +! +! Subroutine: psb_shalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_s_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - real(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_shalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_shalo_multivect use psi_mod diff --git a/base/comm/psb_sovrl.f90 b/base/comm/psb_sovrl.f90 index 25af2d48..3930645a 100644 --- a/base/comm/psb_sovrl.f90 +++ b/base/comm/psb_sovrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_sovrl.f90 ! -! Subroutine: psb_sovrlm +! Subroutine: psb_sovrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - real The local part of the dense matrix. +! x - type(psb_s_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_sovrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_sovrl_vect - +! +! Subroutine: psb_sovrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_s_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - real(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_sovrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_sovrl_multivect use psi_mod diff --git a/base/comm/psb_sscatter.F90 b/base/comm/psb_sscatter.F90 index 60bdd342..960c5bac 100644 --- a/base/comm/psb_sscatter.F90 +++ b/base/comm/psb_sscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_sscatter.f90 ! -! Subroutine: psb_sscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_sscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - real,dimension(:,:). The global matrix to scatter. -! locx - real,dimension(:,:). The local piece of the distributed matrix. +! globx - real,dimension(:) The global matrix to scatter. +! locx - type(psb_s_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_sscatter_a.F90 b/base/comm/psb_sscatter_a.F90 index 51627072..d756b712 100644 --- a/base/comm/psb_sscatter_a.F90 +++ b/base/comm/psb_sscatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_sscatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - real,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_sscatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_sscatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_sscatterm ! Subroutine: psb_sscatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - real,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_sscatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_sscatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_sspgather.F90 b/base/comm/psb_sspgather.F90 index 27444ecd..7123a988 100644 --- a/base/comm/psb_sspgather.F90 +++ b/base/comm/psb_sspgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_sspgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_s_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_ls_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_ssp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/comm/psb_zgather.f90 b/base/comm/psb_zgather.f90 index d22e6644..b8b9a6c8 100644 --- a/base/comm/psb_zgather.f90 +++ b/base/comm/psb_zgather.f90 @@ -31,14 +31,14 @@ ! ! File: psb_zgather.f90 ! -! Subroutine: psb_zgatherm -! This subroutine gathers pieces of a distributed dense matrix into a local one. +! Subroutine: psb_zgather_vect +! This subroutine gathers pieces of a distributed vector into a local one. ! ! Arguments: -! globx - complex,dimension(:,:). The local matrix into which gather +! globx - complex,dimension(:). The local matrix into which gather ! the distributed pieces. -! locx - complex,dimension(:,:). The local piece of the distributed -! matrix to be gathered. +! locx - type(psb_z_vect_type@ The local piece of the distributed +! vector to be gathered. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer. The process that has to own the @@ -159,6 +159,8 @@ subroutine psb_zgather_vect(globx, locx, desc_a, info, iroot) end subroutine psb_zgather_vect +! Subroutine: psb_zgather_multivect +! This subroutine gathers pieces of a distributed multivector into a local one. subroutine psb_zgather_multivect(globx, locx, desc_a, info, iroot) use psb_base_mod, psb_protect_name => psb_zgather_multivect diff --git a/base/comm/psb_zgather_a.f90 b/base/comm/psb_zgather_a.f90 index d2c9bd91..1c3838cb 100644 --- a/base/comm/psb_zgather_a.f90 +++ b/base/comm/psb_zgather_a.f90 @@ -31,7 +31,7 @@ ! ! File: psb_zgather.f90 ! -! Subroutine: psb_zgatherm +! Subroutine: psb_zgather ! This subroutine gathers pieces of a distributed dense matrix into a local one. ! ! Arguments: diff --git a/base/comm/psb_zhalo.f90 b/base/comm/psb_zhalo.f90 index 57fe43ee..595cbc03 100644 --- a/base/comm/psb_zhalo.f90 +++ b/base/comm/psb_zhalo.f90 @@ -31,17 +31,17 @@ ! ! File: psb_zhalo.f90 ! -! Subroutine: psb_zhalom +! Subroutine: psb_zhalo_vect ! This subroutine performs the exchange of the halo elements in a -! distributed dense matrix between all the processes. +! distributed vector between all the processes. ! ! Arguments: -! x - complex,dimension(:,:). The local part of the dense matrix. +! x - type(psb_z_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The starting column of the global matrix. ! ik - integer(optional). The number of columns to gather. -! work - complex(optional). Work area. +! work - complex(optional). Work area. ! tran - character(optional). Transpose exchange. ! mode - integer(optional). Communication mode (see Swapdata) ! data - integer Which index list in desc_a should be used @@ -52,7 +52,6 @@ ! psb_comm_mov_ use ovr_mst_idx ! ! - subroutine psb_zhalo_vect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_zhalo_vect use psi_mod @@ -185,7 +184,28 @@ subroutine psb_zhalo_vect(x,desc_a,info,work,tran,mode,data) return end subroutine psb_zhalo_vect - +! +! Subroutine: psb_zhalo_multivect +! This subroutine performs the exchange of the halo elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_z_multivect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The starting column of the global matrix. +! ik - integer(optional). The number of columns to gather. +! work - complex(optional). Work area. +! tran - character(optional). Transpose exchange. +! mode - integer(optional). Communication mode (see Swapdata) +! data - integer Which index list in desc_a should be used +! to retrieve rows, default psb_comm_halo_ +! psb_comm_halo_ use halo_index +! psb_comm_ext_ use ext_index +! psb_comm_ovrl_ use ovrl_index +! psb_comm_mov_ use ovr_mst_idx +! +! subroutine psb_zhalo_multivect(x,desc_a,info,work,tran,mode,data) use psb_base_mod, psb_protect_name => psb_zhalo_multivect use psi_mod diff --git a/base/comm/psb_zovrl.f90 b/base/comm/psb_zovrl.f90 index 66b42303..c7463e19 100644 --- a/base/comm/psb_zovrl.f90 +++ b/base/comm/psb_zovrl.f90 @@ -32,12 +32,12 @@ ! ! File: psb_zovrl.f90 ! -! Subroutine: psb_zovrlm +! Subroutine: psb_zovrl_vect ! This subroutine performs the exchange of the overlap elements in a -! distributed dense matrix between all the processes. +! distributed dense vector between all the processes. ! ! Arguments: -! x(:,:) - complex The local part of the dense matrix. +! x - type(psb_z_vect_type) The local part of the vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code. ! jx - integer(optional). The starting column of the global matrix @@ -180,7 +180,38 @@ subroutine psb_zovrl_vect(x,desc_a,info,work,update,mode) return end subroutine psb_zovrl_vect - +! +! Subroutine: psb_zovrl_multivect +! This subroutine performs the exchange of the overlap elements in a +! distributed multivector between all the processes. +! +! Arguments: +! x - type(psb_z_vect_type) The local part of the multivector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code. +! jx - integer(optional). The starting column of the global matrix +! ik - integer(optional). The number of columns to gather. +! work - complex(optional). A work area. +! update - integer(optional). Type of update: +! psb_none_ do nothing +! psb_sum_ sum of overlaps +! psb_avg_ average of overlaps +! mode - integer(optional). Choose the algorithm for data exchange: +! this is chosen through bit fields. +! - swap_mpi = iand(flag,psb_swap_mpi_) /= 0 +! - swap_sync = iand(flag,psb_swap_sync_) /= 0 +! - swap_send = iand(flag,psb_swap_send_) /= 0 +! - swap_recv = iand(flag,psb_swap_recv_) /= 0 +! - if (swap_mpi): use underlying MPI_ALLTOALLV. +! - if (swap_sync): use PSB_SND and PSB_RCV in +! synchronized pairs +! - if (swap_send .and. swap_recv): use mpi_irecv +! and mpi_send +! - if (swap_send): use psb_snd (but need another +! call with swap_recv to complete) +! - if (swap_recv): use psb_rcv (completing a +! previous call with swap_send) +! subroutine psb_zovrl_multivect(x,desc_a,info,work,update,mode) use psb_base_mod, psb_protect_name => psb_zovrl_multivect use psi_mod diff --git a/base/comm/psb_zscatter.F90 b/base/comm/psb_zscatter.F90 index 008f8084..10c2c78d 100644 --- a/base/comm/psb_zscatter.F90 +++ b/base/comm/psb_zscatter.F90 @@ -31,13 +31,13 @@ ! ! File: psb_zscatter.f90 ! -! Subroutine: psb_zscatterm -! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! Subroutine: psb_zscatter_vect +! This subroutine scatters a global vector locally owned by one process +! into pieces that are local to all the processes. ! ! Arguments: -! globx - complex,dimension(:,:). The global matrix to scatter. -! locx - complex,dimension(:,:). The local piece of the distributed matrix. +! globx - complex,dimension(:) The global matrix to scatter. +! locx - type(psb_z_vect_type) The local piece of the distributed matrix. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Error code. ! iroot - integer(optional). The process that owns the global matrix. diff --git a/base/comm/psb_zscatter_a.F90 b/base/comm/psb_zscatter_a.F90 index 6b7f7d7d..b206d8d3 100644 --- a/base/comm/psb_zscatter_a.F90 +++ b/base/comm/psb_zscatter_a.F90 @@ -33,7 +33,7 @@ ! ! Subroutine: psb_zscatterm ! This subroutine scatters a global matrix locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - complex,dimension(:,:). The global matrix to scatter. @@ -107,8 +107,8 @@ subroutine psb_zscatterm(globx, locx, desc_a, info, root) m = desc_a%get_global_rows() n = desc_a%get_global_cols() - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,me) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,me) if (iroot==-1) then lda_globx = size(globx, 1) @@ -159,7 +159,7 @@ subroutine psb_zscatterm(globx, locx, desc_a, info, root) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. @@ -278,7 +278,7 @@ end subroutine psb_zscatterm ! Subroutine: psb_zscatterv ! This subroutine scatters a global vector locally owned by one process -! into pieces that are local to alle the processes. +! into pieces that are local to all the processes. ! ! Arguments: ! globx - complex,dimension(:). The global vector to scatter. @@ -347,8 +347,8 @@ subroutine psb_zscatterv(globx, locx, desc_a, info, root) iroot = psb_root_ end if - icomm = psb_get_mpicomm(ictxt) - myrank = psb_get_rank(ictxt,iam) + icomm = psb_get_mpi_comm(ictxt) + myrank = psb_get_mpi_rank(ictxt,iam) iglobx = 1 jglobx = 1 @@ -394,7 +394,7 @@ subroutine psb_zscatterv(globx, locx, desc_a, info, root) locx(i)=globx(ltg(i)) end do else - rootrank = psb_get_rank(ictxt,iroot) + rootrank = psb_get_mpi_rank(ictxt,iroot) ! ! This is potentially unsafe when IPK=8 ! But then, IPK=8 is highly experimental anyway. diff --git a/base/comm/psb_zspgather.F90 b/base/comm/psb_zspgather.F90 index fbcae1f3..f4a27681 100644 --- a/base/comm/psb_zspgather.F90 +++ b/base/comm/psb_zspgather.F90 @@ -30,6 +30,17 @@ ! ! ! File: psb_zspgather.f90 +! +! Gathers a sparse matrix onto a single process. +! Two variants: +! 1. Gathers to PSB_z_SPARSE_MAT (i.e. to matrix with IPK_ indices) +! 2. Gathers to PSB_lz_SPARSE_MAT (i.e. to matrix with LPK_ indices) +! +! Note: this function uses MPI_ALLGATHERV. At this time, the size of the +! resulting matrix must be within the range of 4 bytes because of the +! restriction on MPI displacements to be 4 bytes. +! +! subroutine psb_zsp_allgather(globa, loca, desc_a, info, root, dupl,keepnum,keeploc) #if defined(HAVE_ISO_FORTRAN_ENV) use iso_fortran_env diff --git a/base/internals/psi_a2a_fnd_owner.F90 b/base/internals/psi_a2a_fnd_owner.F90 index 3ee6ef9a..52e8b0ae 100644 --- a/base/internals/psi_a2a_fnd_owner.F90 +++ b/base/internals/psi_a2a_fnd_owner.F90 @@ -30,20 +30,22 @@ ! ! ! -! File: psi_fnd_owner.f90 +! File: psi_a2a_fnd_owner.f90 ! -! Subroutine: psi_fnd_owner +! Subroutine: psi_a2a_fnd_owner ! Figure out who owns global indices. ! ! Arguments: -! nv - integer Number of indices required on the calling -! process ! idx(:) - integer Required indices on the calling process. ! Note: the indices should be unique! ! iprc(:) - integer(psb_ipk_), allocatable Output: process identifiers for the corresponding ! indices -! desc_a - type(psb_desc_type). The communication descriptor. +! idxmap - class(psb_indx_map). The index map ! info - integer. return code. +! +! This version does not assume any prior knowledge about the process topology, +! so it goes for an all-to-all by building an auxiliary neighbours list and +! reusing the neighbour version. ! subroutine psi_a2a_fnd_owner(idx,iprc,idxmap,info) use psb_serial_mod @@ -99,7 +101,7 @@ subroutine psi_a2a_fnd_owner(idx,iprc,idxmap,info) end if ! - ! Reuse the other version by tricking it with an adjcncy list + ! Reuse the adjcncy version by tricking it with an adjcncy list ! that contains everybody but ME. ! nv = size(idx) diff --git a/base/internals/psi_adjcncy_fnd_owner.F90 b/base/internals/psi_adjcncy_fnd_owner.F90 index fd1422f1..f26bb38f 100644 --- a/base/internals/psi_adjcncy_fnd_owner.F90 +++ b/base/internals/psi_adjcncy_fnd_owner.F90 @@ -29,13 +29,29 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! +! ! -! File: psi_fnd_owner.f90 +! File: psi_adjcncy_fnd_owner.f90 ! -! Subroutine: psi_fnd_owner +! Subroutine: psi_adjcncy_fnd_owner ! Figure out who owns global indices. ! ! Arguments: +! idx(:) - integer Required indices on the calling process. +! Note: the indices should be unique! +! iprc(:) - integer(psb_ipk_), allocatable Output: process identifiers for the corresponding +! indices +! adj(:) - integer(psb_ipk_) Input: list of topological neighbours for current process. +! +! idxmap - class(psb_indx_map). The index map +! info - integer. return code. +! +! This version takes on input a list of processes that are assumed to +! be topological neighbours of the current one. Each process will send to all +! of its neighbours the list of indices for which it is trying to find the +! owner, prepare its own answers, and collect answers from others. +! There are three possibile implementations: using mpi_alltoallv, using mpi_isend/irecv, +! using psb_snd/psb_rcv. The default is mpi_alltoallv. ! subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) use psb_serial_mod @@ -43,6 +59,7 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) use psb_error_mod use psb_penv_mod use psb_realloc_mod + use psb_timers_mod use psb_indx_map_mod, psb_protect_name => psi_adjcncy_fnd_owner #ifdef MPI_MOD use mpi @@ -69,8 +86,11 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) & last_ih, last_j, nidx, nrecv, nadj integer(psb_lpk_) :: mglob, ih integer(psb_ipk_) :: ictxt,np,me - logical, parameter :: gettime=.false., new_impl=.true. - logical, parameter :: a2av_impl=.true., debug=.false. + logical, parameter :: gettime=.true., debug=.false. + integer(psb_mpk_) :: xchg_alg + logical, parameter :: do_timings=.false. + integer(psb_ipk_), save :: idx_phase1=-1, idx_phase2=-1, idx_phase3=-1 + integer(psb_ipk_), save :: idx_phase11=-1, idx_phase12=-1, idx_phase13=-1 real(psb_dpk_) :: t0, t1, t2, t3, t4, tamx, tidx character(len=20) :: name @@ -84,6 +104,19 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) n_row = idxmap%get_lr() n_col = idxmap%get_lc() iictxt = ictxt + if ((do_timings).and.(idx_phase1==-1)) & + & idx_phase1 = psb_get_timer_idx("ADJ_FND_OWN: phase1 ") + if ((do_timings).and.(idx_phase2==-1)) & + & idx_phase2 = psb_get_timer_idx("ADJ_FND_OWN: phase2") + if ((do_timings).and.(idx_phase3==-1)) & + & idx_phase3 = psb_get_timer_idx("ADJ_FND_OWN: phase3") + if ((do_timings).and.(idx_phase11==-1)) & + & idx_phase11 = psb_get_timer_idx("ADJ_FND_OWN: phase11 ") + if ((do_timings).and.(idx_phase12==-1)) & + & idx_phase12 = psb_get_timer_idx("ADJ_FND_OWN: phase12") + if ((do_timings).and.(idx_phase13==-1)) & + & idx_phase13 = psb_get_timer_idx("ADJ_FND_OWN: phase13") + call psb_info(ictxt, me, np) @@ -111,8 +144,11 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) end if iprc = -1 ! write(0,*) me,name,' Going through ',nidx,nadj + xchg_alg = psi_get_adj_alg() + select case(xchg_alg) + case(psi_adj_fnd_a2av_) + if (do_timings) call psb_tic(idx_phase1) - if (a2av_impl) then ! ! First simple minded version with auxiliary arrays ! dimensioned on NP. @@ -128,6 +164,7 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) ! ! First, send sizes according to adjcncy list ! + if (do_timings) call psb_tic(idx_phase11) sdsz = 0 do j=1, nadj sdsz(adj(j)) = nidx @@ -136,15 +173,20 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) call mpi_alltoall(sdsz,1,psb_mpi_mpk_,& & rvsz,1,psb_mpi_mpk_,icomm,minfo) + if (do_timings) call psb_toc(idx_phase11) + if (do_timings) call psb_tic(idx_phase12) rvidx(0) = 0 do i=0, np-1 rvidx(i+1) = rvidx(i) + rvsz(i) end do hsize = rvidx(np) + ! write(0,*)me,' Check on sizes from a2a:',hsize,rvsz(:) ! ! Second, allocate buffers and exchange data ! + if (do_timings) call psb_toc(idx_phase12) + if (do_timings) call psb_tic(idx_phase13) Allocate(rmtidx(hsize),lclidx(max(hsize,nidx*nadj)),& & tproc(max(hsize,nidx)),stat=info) @@ -155,7 +197,9 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) call mpi_alltoallv(idx,sdsz,sdidx,psb_mpi_lpk_,& & rmtidx,rvsz,rvidx,psb_mpi_lpk_,icomm,iret) - + if (do_timings) call psb_toc(idx_phase13) + if (do_timings) call psb_toc(idx_phase1) + if (do_timings) call psb_tic(idx_phase2) ! ! Third, compute local answers ! @@ -164,6 +208,8 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) tproc(i) = -1 if ((0 < lclidx(i)).and. (lclidx(i) <= n_row)) tproc(i) = me end do + if (do_timings) call psb_toc(idx_phase2) + if (do_timings) call psb_tic(idx_phase3) ! ! Fourth, exchange the answers @@ -175,194 +221,215 @@ subroutine psi_adjcncy_fnd_owner(idx,iprc,adj,idxmap,info) call mpi_alltoallv(tproc,rvsz,rvidx,psb_mpi_ipk_,& & lclidx,sdsz,sdidx,psb_mpi_ipk_,icomm,iret) + ! + ! Because IPRC has been initialized to -1, the MAX operation selects + ! the answers. + ! do i=0, np-1 if (sdsz(i)>0) then ! Must be nidx == sdsz(i) iprc(1:nidx) = max(iprc(1:nidx), lclidx(sdidx(i)+1:sdidx(i)+sdsz(i))) end if end do + if (do_timings) call psb_toc(idx_phase3) if (debug) write(0,*) me,' End of adjcncy_fnd ',iprc(1:nidx) - else - if (new_impl) then - ! - ! First simple minded version with auxiliary arrays - ! dimensioned on NP. - ! Could it be improved with a loop based on the maximum length - ! of adj(:) ??? - ! - Allocate(hidx(0:np),hsz(np),sdsz(0:np-1),rvsz(0:np-1),& - & sdhd(0:np-1), rvhd(0:np-1), p2pstat(mpi_status_size,0:np-1),& - & stat=info) - sdhd(:) = mpi_request_null - rvhd(:) = mpi_request_null - ! - ! First, send sizes according to adjcncy list - ! - sdsz = 0 - do j=1, nadj - sdsz(adj(j)) = nidx - end do - !write(0,*)me,' Check on sizes into a2a:',adj(:),nadj,':',sdsz(:) - - call mpi_alltoall(sdsz,1,psb_mpi_mpk_,& - & rvsz,1,psb_mpi_mpk_,icomm,minfo) - hidx(0) = 0 - do i=0, np-1 - hidx(i+1) = hidx(i) + rvsz(i) - end do - hsize = hidx(np) - ! write(0,*)me,' Check on sizes from a2a:',hsize,rvsz(:) - ! - ! Second, allocate buffers and exchange data - ! - Allocate(rmtidx(hsize),lclidx(max(hsize,nidx*nadj)),tproc(max(hsize,nidx)),stat=info) - - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') - goto 9999 + + case(psi_adj_fnd_irecv_) + + if (do_timings) call psb_tic(idx_phase1) + ! + ! First simple minded version with auxiliary arrays + ! dimensioned on NP. + ! Could it be improved with a loop based on the maximum length + ! of adj(:) ??? + ! + Allocate(hidx(0:np),hsz(np),sdsz(0:np-1),rvsz(0:np-1),& + & sdhd(0:np-1), rvhd(0:np-1), p2pstat(mpi_status_size,0:np-1),& + & stat=info) + if (do_timings) call psb_tic(idx_phase11) + sdhd(:) = mpi_request_null + rvhd(:) = mpi_request_null + ! + ! First, send sizes according to adjcncy list + ! + sdsz = 0 + do j=1, nadj + sdsz(adj(j)) = nidx + end do + !write(0,*)me,' Check on sizes into a2a:',adj(:),nadj,':',sdsz(:) + + call mpi_alltoall(sdsz,1,psb_mpi_mpk_,& + & rvsz,1,psb_mpi_mpk_,icomm,minfo) + hidx(0) = 0 + do i=0, np-1 + hidx(i+1) = hidx(i) + rvsz(i) + end do + hsize = hidx(np) + ! write(0,*)me,' Check on sizes from a2a:',hsize,rvsz(:) + ! + ! Second, allocate buffers and exchange data + ! + Allocate(rmtidx(hsize),lclidx(max(hsize,nidx*nadj)),tproc(max(hsize,nidx)),stat=info) + + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') + goto 9999 + end if + do i = 0, np-1 + if (rvsz(i)>0) then + ! write(0,*) me, ' First receive from ',i,rvsz(i) + prc = psb_get_mpi_rank(ictxt,i) + p2ptag = psb_long_swap_tag + !write(0,*) me, ' Posting first receive from ',i,rvsz(i),prc + call mpi_irecv(rmtidx(hidx(i)+1),rvsz(i),& + & psb_mpi_lpk_,prc,& + & p2ptag, icomm,rvhd(i),iret) + end if + end do + if (do_timings) call psb_toc(idx_phase11) + if (do_timings) call psb_tic(idx_phase12) + do j=1, nadj + if (nidx > 0) then + prc = psb_get_mpi_rank(ictxt,adj(j)) + p2ptag = psb_long_swap_tag + !write(0,*) me, ' First send to ',adj(j),nidx, prc + call mpi_send(idx,nidx,& + & psb_mpi_lpk_,prc,& + & p2ptag, icomm,iret) + end if + end do + if (do_timings) call psb_toc(idx_phase12) + if (do_timings) call psb_tic(idx_phase13) + call mpi_waitall(np,rvhd,p2pstat,iret) + if (do_timings) call psb_toc(idx_phase13) + if (do_timings) call psb_toc(idx_phase1) + if (do_timings) call psb_tic(idx_phase2) + + ! + ! Third, compute local answers + ! + call idxmap%g2l(rmtidx(1:hsize),lclidx(1:hsize),info,owned=.true.) + do i=1, hsize + tproc(i) = -1 + if ((0 < lclidx(i)).and. (lclidx(i) <= n_row)) tproc(i) = me + end do + if (do_timings) call psb_toc(idx_phase2) + if (do_timings) call psb_tic(idx_phase3) + ! + ! At this point we can reuse lclidx to receive messages + ! + rvhd(:) = mpi_request_null + do j=1, nadj + !write(0,*) me, ' First send to ',adj(j),nidx + if (nidx > 0) then + prc = psb_get_mpi_rank(ictxt,adj(j)) + p2ptag = psb_int_swap_tag + !write(0,*) me, ' Posting second receive from ',adj(j),nidx, prc + call mpi_irecv(lclidx((j-1)*nidx+1),nidx, & + & psb_mpi_ipk_,prc,& + & p2ptag, icomm,rvhd(j),iret) end if - do i = 0, np-1 - if (rvsz(i)>0) then - ! write(0,*) me, ' First receive from ',i,rvsz(i) - prc = psb_get_rank(ictxt,i) - p2ptag = psb_long_swap_tag - !write(0,*) me, ' Posting first receive from ',i,rvsz(i),prc - call mpi_irecv(rmtidx(hidx(i)+1),rvsz(i),& - & psb_mpi_lpk_,prc,& - & p2ptag, icomm,rvhd(i),iret) - end if - end do - do j=1, nadj - if (nidx > 0) then - prc = psb_get_rank(ictxt,adj(j)) - p2ptag = psb_long_swap_tag - !write(0,*) me, ' First send to ',adj(j),nidx, prc - call mpi_send(idx,nidx,& - & psb_mpi_lpk_,prc,& - & p2ptag, icomm,iret) - end if - end do - call mpi_waitall(np,rvhd,p2pstat,iret) - - ! - ! Third, compute local answers - ! - call idxmap%g2l(rmtidx(1:hsize),lclidx(1:hsize),info,owned=.true.) - do i=1, hsize - tproc(i) = -1 - if ((0 < lclidx(i)).and. (lclidx(i) <= n_row)) tproc(i) = me - end do - ! - ! At this point we can reuse lclidx to receive messages - ! - rvhd(:) = mpi_request_null - do j=1, nadj - !write(0,*) me, ' First send to ',adj(j),nidx - if (nidx > 0) then - prc = psb_get_rank(ictxt,adj(j)) - p2ptag = psb_int_swap_tag - !write(0,*) me, ' Posting second receive from ',adj(j),nidx, prc - call mpi_irecv(lclidx((j-1)*nidx+1),nidx, & - & psb_mpi_ipk_,prc,& - & p2ptag, icomm,rvhd(j),iret) - end if - end do - - ! - ! Fourth, send data back; - ! - do i = 0, np-1 - if (rvsz(i)>0) then - prc = psb_get_rank(ictxt,i) - p2ptag = psb_int_swap_tag - !write(0,*) me, ' Second send to ',i,rvsz(i), prc - call mpi_send(tproc(hidx(i)+1),rvsz(i),& - & psb_mpi_ipk_,prc,& - & p2ptag, icomm,iret) - end if - end do - ! - ! Fifth: receive and combine. MAX works because default - ! answer is -1. - ! - call mpi_waitall(np,rvhd,p2pstat,iret) - do j = 1, nadj - iprc(1:nidx) = max(iprc(1:nidx), lclidx((j-1)*nidx+1:(j-1)*nidx+nidx)) - end do - if (debug) write(0,*) me,' End of adjcncy_fnd ',iprc(1:nidx) - - else - - Allocate(hidx(0:np),hsz(np),& - & sdsz(0:np-1),rvsz(0:np-1),stat=info) - ! - ! First, send sizes according to adjcncy list - ! - sdsz = 0 - do j=1, nadj - sdsz(adj(j)) = nidx - end do - !write(0,*)me,' Check on sizes into a2a:',adj(:),nadj,':',sdsz(:) - - call mpi_alltoall(sdsz,1,psb_mpi_mpk_,& - & rvsz,1,psb_mpi_mpk_,icomm,minfo) - hidx(0) = 0 - do i=0, np-1 - hidx(i+1) = hidx(i) + rvsz(i) - end do - hsize = hidx(np) - ! write(0,*)me,' Check on sizes from a2a:',hsize,rvsz(:) - ! - ! Second, allocate buffers and exchange data - ! - Allocate(rmtidx(hsize),lclidx(hsize),tproc(max(hsize,nidx)),stat=info) - - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') - goto 9999 + end do + + ! + ! Fourth, send data back; + ! + do i = 0, np-1 + if (rvsz(i)>0) then + prc = psb_get_mpi_rank(ictxt,i) + p2ptag = psb_int_swap_tag + !write(0,*) me, ' Second send to ',i,rvsz(i), prc + call mpi_send(tproc(hidx(i)+1),rvsz(i),& + & psb_mpi_ipk_,prc,& + & p2ptag, icomm,iret) end if - do j=1, nadj - !write(0,*) me, ' First send to ',adj(j),nidx - if (nidx > 0) call psb_snd(ictxt,idx(1:nidx),adj(j)) - end do - do i = 0, np-1 - if (rvsz(i)>0) then - ! write(0,*) me, ' First receive from ',i,rvsz(i) - call psb_rcv(ictxt,rmtidx(hidx(i)+1:hidx(i)+rvsz(i)),i) - end if - end do - - ! - ! Third, compute local answers - ! - call idxmap%g2l(rmtidx(1:hsize),lclidx(1:hsize),info,owned=.true.) - do i=1, hsize - tproc(i) = -1 - if ((0 < lclidx(i)).and. (lclidx(i) <= n_row)) tproc(i) = me - end do - - ! - ! Fourth, send data back; - ! - do i = 0, np-1 - if (rvsz(i)>0) then - !write(0,*) me, ' Second send to ',i,rvsz(i) - call psb_snd(ictxt,tproc(hidx(i)+1:hidx(i)+rvsz(i)),i) - end if - end do - ! - ! Fifth: receive and combine. MAX works because default - ! answer is -1. Reuse tproc - ! - do j = 1, nadj - !write(0,*) me, ' Second receive from ',adj(j), nidx - if (nidx > 0) call psb_rcv(ictxt,tproc(1:nidx),adj(j)) - iprc(1:nidx) = max(iprc(1:nidx), tproc(1:nidx)) - end do + end do + ! + ! Fifth: receive and combine. MAX works because default + ! answer is -1. + ! + call mpi_waitall(np,rvhd,p2pstat,iret) + do j = 1, nadj + iprc(1:nidx) = max(iprc(1:nidx), lclidx((j-1)*nidx+1:(j-1)*nidx+nidx)) + end do + if (do_timings) call psb_toc(idx_phase3) + if (debug) write(0,*) me,' End of adjcncy_fnd ',iprc(1:nidx) + + case(psi_adj_fnd_pbrcv_) + + Allocate(hidx(0:np),hsz(np),& + & sdsz(0:np-1),rvsz(0:np-1),stat=info) + ! + ! First, send sizes according to adjcncy list + ! + sdsz = 0 + do j=1, nadj + sdsz(adj(j)) = nidx + end do + !write(0,*)me,' Check on sizes into a2a:',adj(:),nadj,':',sdsz(:) + + call mpi_alltoall(sdsz,1,psb_mpi_mpk_,& + & rvsz,1,psb_mpi_mpk_,icomm,minfo) + hidx(0) = 0 + do i=0, np-1 + hidx(i+1) = hidx(i) + rvsz(i) + end do + hsize = hidx(np) + ! write(0,*)me,' Check on sizes from a2a:',hsize,rvsz(:) + ! + ! Second, allocate buffers and exchange data + ! + Allocate(rmtidx(hsize),lclidx(hsize),tproc(max(hsize,nidx)),stat=info) + + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate') + goto 9999 end if - end if - + do j=1, nadj + !write(0,*) me, ' First send to ',adj(j),nidx + if (nidx > 0) call psb_snd(ictxt,idx(1:nidx),adj(j)) + end do + do i = 0, np-1 + if (rvsz(i)>0) then + ! write(0,*) me, ' First receive from ',i,rvsz(i) + call psb_rcv(ictxt,rmtidx(hidx(i)+1:hidx(i)+rvsz(i)),i) + end if + end do + + ! + ! Third, compute local answers + ! + call idxmap%g2l(rmtidx(1:hsize),lclidx(1:hsize),info,owned=.true.) + do i=1, hsize + tproc(i) = -1 + if ((0 < lclidx(i)).and. (lclidx(i) <= n_row)) tproc(i) = me + end do + + ! + ! Fourth, send data back; + ! + do i = 0, np-1 + if (rvsz(i)>0) then + !write(0,*) me, ' Second send to ',i,rvsz(i) + call psb_snd(ictxt,tproc(hidx(i)+1:hidx(i)+rvsz(i)),i) + end if + end do + ! + ! Fifth: receive and combine. MAX works because default + ! answer is -1. Reuse tproc + ! + do j = 1, nadj + !write(0,*) me, ' Second receive from ',adj(j), nidx + if (nidx > 0) call psb_rcv(ictxt,tproc(1:nidx),adj(j)) + iprc(1:nidx) = max(iprc(1:nidx), tproc(1:nidx)) + end do + case default + info = psb_err_internal_error_ + call psb_errpush(info,name,a_err='invalid exchange alg choice') + goto 9999 + end select + call psb_erractionrestore(err_act) return diff --git a/base/internals/psi_crea_index.f90 b/base/internals/psi_crea_index.f90 index ec783899..126d54e2 100644 --- a/base/internals/psi_crea_index.f90 +++ b/base/internals/psi_crea_index.f90 @@ -54,6 +54,7 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) use psb_desc_mod use psb_error_mod use psb_penv_mod + use psb_timers_mod use psi_mod, psb_protect_name => psi_i_crea_index implicit none @@ -69,6 +70,9 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) integer(psb_ipk_),parameter :: root=psb_root_,no_comm=-1 integer(psb_ipk_) :: debug_level, debug_unit character(len=20) :: name + logical, parameter :: do_timings=.false. + integer(psb_ipk_), save :: idx_phase1=-1, idx_phase2=-1, idx_phase3=-1 + integer(psb_ipk_), save :: idx_phase11=-1, idx_phase12=-1, idx_phase13=-1 info = psb_success_ name='psi_crea_index' @@ -84,12 +88,26 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) call psb_errpush(info,name) goto 9999 endif + if ((do_timings).and.(idx_phase1==-1)) & + & idx_phase1 = psb_get_timer_idx("PSI_CREA_INDEX: phase1 ") + if ((do_timings).and.(idx_phase2==-1)) & + & idx_phase2 = psb_get_timer_idx("PSI_CREA_INDEX: phase2") + if ((do_timings).and.(idx_phase3==-1)) & + & idx_phase3 = psb_get_timer_idx("PSI_CREA_INDEX: phase3") +!!$ if ((do_timings).and.(idx_phase11==-1)) & +!!$ & idx_phase11 = psb_get_timer_idx("PSI_CREA_INDEX: phase11 ") +!!$ if ((do_timings).and.(idx_phase12==-1)) & +!!$ & idx_phase12 = psb_get_timer_idx("PSI_CREA_INDEX: phase12") +!!$ if ((do_timings).and.(idx_phase13==-1)) & +!!$ & idx_phase13 = psb_get_timer_idx("PSI_CREA_INDEX: phase13") + ! ...extract dependence list (ordered list of identifer process ! which every process must communcate with... if (debug_level >= psb_debug_inner_) & & write(debug_unit,*) me,' ',trim(name),': calling extract_dep_list' mode = 1 + if (do_timings) call psb_tic(idx_phase1) call psi_extract_dep_list(ictxt,& & desc_a%is_bld(), desc_a%is_upd(),& @@ -105,6 +123,8 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) ! ...now process root contains dependence list of all processes... if (debug_level >= psb_debug_inner_) & & write(debug_unit,*) me,' ',trim(name),': root sorting dep list' + if (do_timings) call psb_toc(idx_phase1) + if (do_timings) call psb_tic(idx_phase2) call psi_dl_check(dep_list,dl_lda,np,length_dl) @@ -114,6 +134,8 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) call psb_errpush(psb_err_from_subroutine_,name,a_err='psi_sort_dl') goto 9999 end if + if (do_timings) call psb_toc(idx_phase2) + if (do_timings) call psb_tic(idx_phase3) if(debug_level >= psb_debug_inner_)& & write(debug_unit,*) me,' ',trim(name),': calling psi_desc_index' @@ -128,6 +150,7 @@ subroutine psi_i_crea_index(desc_a,index_in,index_out,nxch,nsnd,nrcv,info) call psb_errpush(psb_err_from_subroutine_,name,a_err='psi_desc_index') goto 9999 end if + if (do_timings) call psb_toc(idx_phase3) deallocate(dep_list,length_dl) if(debug_level >= psb_debug_inner_) & diff --git a/base/internals/psi_desc_impl.f90 b/base/internals/psi_desc_impl.f90 index b552a8ad..43eae7bb 100644 --- a/base/internals/psi_desc_impl.f90 +++ b/base/internals/psi_desc_impl.f90 @@ -63,6 +63,7 @@ end subroutine psi_renum_index subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) use psi_mod, psi_protect_name => psi_i_cnv_dsc + use psb_timers_mod use psb_realloc_mod implicit none @@ -82,6 +83,9 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) integer(psb_ipk_) :: debug_level, debug_unit logical, parameter :: debug=.false. character(len=20) :: name + logical, parameter :: do_timings=.false. + integer(psb_ipk_), save :: idx_phase1=-1, idx_phase2=-1, idx_phase3=-1 + integer(psb_ipk_), save :: idx_phase11=-1, idx_phase12=-1, idx_phase13=-1 name='psi_cnv_desc' call psb_get_erraction(err_act) @@ -97,7 +101,22 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) call psb_errpush(info,name) goto 9999 endif - + if ((do_timings).and.(idx_phase1==-1)) & + & idx_phase1 = psb_get_timer_idx("PSI_CNV_DSC: phase1 ") + if ((do_timings).and.(idx_phase2==-1)) & + & idx_phase2 = psb_get_timer_idx("PSI_CNV_DSC: phase2") + if ((do_timings).and.(idx_phase3==-1)) & + & idx_phase3 = psb_get_timer_idx("PSI_CNV_DSC: phase3") + if ((do_timings).and.(idx_phase11==-1)) & + & idx_phase11 = psb_get_timer_idx("PSI_CNV_DSC: phase11 ") + if ((do_timings).and.(idx_phase12==-1)) & + & idx_phase12 = psb_get_timer_idx("PSI_CNV_DSC: phase12") + if ((do_timings).and.(idx_phase13==-1)) & + & idx_phase13 = psb_get_timer_idx("PSI_CNV_DSC: phase13") + + + if (do_timings) call psb_tic(idx_phase1) + if (do_timings) call psb_tic(idx_phase11) ! first the halo index if (debug_level>0) write(debug_unit,*) me,'Calling crea_index on halo',& @@ -111,6 +130,8 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) if (debug_level>0) write(debug_unit,*) me,'Done crea_index on halo' if (debug_level>0) write(debug_unit,*) me,'Calling crea_index on ext' + if (do_timings) call psb_toc(idx_phase11) + if (do_timings) call psb_tic(idx_phase12) ! then ext index @@ -124,6 +145,8 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) if (debug_level>0) write(debug_unit,*) me,'Done crea_index on ext' if (debug_level>0) write(debug_unit,*) me,'Calling crea_index on ovrlap' + if (do_timings) call psb_toc(idx_phase12) + if (do_timings) call psb_tic(idx_phase13) ! then the overlap index call psi_crea_index(cdesc,ovrlap_in, idx_out,nxch,nsnd,nrcv,info) @@ -136,6 +159,9 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_move_alloc') goto 9999 end if + if (do_timings) call psb_toc(idx_phase13) + if (do_timings) call psb_toc(idx_phase1) + if (do_timings) call psb_tic(idx_phase2) ! next ovrlap_elem @@ -161,6 +187,8 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) call psb_errpush(psb_err_from_subroutine_,name,a_err='psb_move_alloc') goto 9999 end if + if (do_timings) call psb_toc(idx_phase2) + if (do_timings) call psb_tic(idx_phase3) ! finally bnd_elem call psi_crea_bnd_elem(idx_out,cdesc,info) @@ -177,7 +205,8 @@ subroutine psi_i_cnv_dsc(halo_in,ovrlap_in,ext_in,cdesc, info, mold) goto 9999 end if if (debug_level>0) write(debug_unit,*) me,'Done crea_bnd_elem' - + if (do_timings) call psb_toc(idx_phase3) + call psb_erractionrestore(err_act) return diff --git a/base/internals/psi_desc_index.F90 b/base/internals/psi_desc_index.F90 index 7f36c6ea..f23662f1 100644 --- a/base/internals/psi_desc_index.F90 +++ b/base/internals/psi_desc_index.F90 @@ -128,11 +128,15 @@ subroutine psi_i_desc_index(desc,index_in,dep_list,& integer(psb_mpk_),allocatable :: brvindx(:),rvsz(:),& & bsdindx(:),sdsz(:) + integer(psb_mpk_) :: proc_to_comm, p2ptag, p2pstat(mpi_status_size),& + & iret, sz + integer(psb_mpk_), allocatable :: prcid(:), rvhd(:) + integer(psb_ipk_) :: ihinsz,ntot,k,err_act,nidx,& - & idxr, idxs, iszs, iszr, nesd, nerv + & idxr, idxs, iszs, iszr, nesd, nerv, ixp, idx integer(psb_mpk_) :: icomm, minfo - logical,parameter :: usempi=.true. + logical, parameter :: usempi=.false. integer(psb_ipk_) :: debug_level, debug_unit character(len=20) :: name @@ -255,12 +259,12 @@ subroutine psi_i_desc_index(desc,index_in,dep_list,& call desc%indxmap%l2g(index_in(i+1:i+nerv),& & sndbuf(bsdindx(proc+1)+1:bsdindx(proc+1)+nerv),& & info) - + if (info /= psb_success_) then call psb_errpush(psb_err_from_subroutine_,name,a_err='l2g') goto 9999 end if - + bsdindx(proc+1) = bsdindx(proc+1) + nerv i = i + nerv + 1 end do @@ -282,11 +286,76 @@ subroutine psi_i_desc_index(desc,index_in,dep_list,& idxr = idxr + rvsz(proc+1) end do - call mpi_alltoallv(sndbuf,sdsz,bsdindx,psb_mpi_lpk_,& - & rcvbuf,rvsz,brvindx,psb_mpi_lpk_,icomm,minfo) - if (minfo /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='mpi_alltoallv') - goto 9999 + if (usempi) then + call mpi_alltoallv(sndbuf,sdsz,bsdindx,psb_mpi_lpk_,& + & rcvbuf,rvsz,brvindx,psb_mpi_lpk_,icomm,minfo) + if (minfo /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='mpi_alltoallv') + goto 9999 + end if + else + if (.true.) then + allocate(prcid(length_dl),rvhd(length_dl)) + prcid = -1 + ixp = 1 + do i=1, length_dl + proc = dep_list(i) + prcid(ixp) = psb_get_mpi_rank(ictxt,proc) + sz = rvsz(proc+1) + if (sz > 0) then + p2ptag = psb_long_tag + idx = brvindx(proc+1) + call mpi_irecv(rcvbuf(idx+1:idx+sz),sz,& + & psb_mpi_lpk_, prcid(ixp), p2ptag, icomm,& + & rvhd(ixp),iret) + end if + ixp = ixp + 1 + end do + ixp = 1 + do i=1, length_dl + proc = dep_list(i) + prcid(ixp) = psb_get_mpi_rank(ictxt,proc) + sz = sdsz(proc+1) + if (sz > 0) then + p2ptag = psb_long_tag + idx = bsdindx(proc+1) + call mpi_send(sndbuf(idx+1:idx+sz),sz,& + & psb_mpi_lpk_, prcid(ixp), p2ptag, & + & icomm,iret) + end if + ixp = ixp + 1 + end do + ixp = 1 + do i=1, length_dl + proc = dep_list(i) + prcid(ixp) = psb_get_mpi_rank(ictxt,proc) + sz = rvsz(proc+1) + if (sz > 0) then + call mpi_wait(rvhd(ixp),p2pstat,iret) + end if + ixp = ixp + 1 + end do + else + + do i=1, length_dl + proc = dep_list(i) + sz = sdsz(proc+1) + idx = bsdindx(proc+1) + if (sz > 0) then + call psb_snd(ictxt,sndbuf(idx+1:idx+sz), proc) + end if + end do + + do i=1, length_dl + proc = dep_list(i) + sz = rvsz(proc+1) + idx = brvindx(proc+1) + if (sz > 0) then + call psb_rcv(ictxt,rcvbuf(idx+1:idx+sz),proc) + end if + end do + + end if end if ! @@ -327,7 +396,7 @@ subroutine psi_i_desc_index(desc,index_in,dep_list,& return 9999 call psb_error_handler(ictxt,err_act) - + return end subroutine psi_i_desc_index diff --git a/base/internals/psi_extrct_dl.F90 b/base/internals/psi_extrct_dl.F90 index f5fe3c58..95086408 100644 --- a/base/internals/psi_extrct_dl.F90 +++ b/base/internals/psi_extrct_dl.F90 @@ -266,7 +266,7 @@ subroutine psi_i_extract_dep_list(ictxt,is_bld,is_upd,desc_str,dep_list,& end if call psb_sum(iictxt,length_dl(0:np)) - icomm = psb_get_mpicomm(iictxt) + icomm = psb_get_mpi_comm(iictxt) call mpi_allgather(itmp,dl_lda,psb_mpi_ipk_,& & dep_list,dl_lda,psb_mpi_ipk_,icomm,minfo) info = minfo @@ -288,7 +288,7 @@ subroutine psi_i_extract_dep_list(ictxt,is_bld,is_upd,desc_str,dep_list,& goto 9999 end if call psb_sum(iictxt,length_dl(0:np)) - icomm = psb_get_mpicomm(iictxt) + icomm = psb_get_mpi_comm(iictxt) call mpi_allgather(itmp,dl_lda,psb_mpi_ipk_,& & dep_list,dl_lda,psb_mpi_ipk_,icomm,minfo) info = minfo diff --git a/base/internals/psi_graph_fnd_owner.F90 b/base/internals/psi_graph_fnd_owner.F90 index fa7fe47b..f87a5942 100644 --- a/base/internals/psi_graph_fnd_owner.F90 +++ b/base/internals/psi_graph_fnd_owner.F90 @@ -30,20 +30,50 @@ ! ! ! -! File: psi_fnd_owner.f90 ! -! Subroutine: psi_fnd_owner +! File: psi_graph_fnd_owner.f90 +! +! Subroutine: psi_graph_fnd_owner ! Figure out who owns global indices. ! ! Arguments: -! nv - integer Number of indices required on the calling -! process ! idx(:) - integer Required indices on the calling process. -! Note: the indices should be unique! +! ! iprc(:) - integer(psb_ipk_), allocatable Output: process identifiers for the corresponding ! indices -! desc_a - type(psb_desc_type). The communication descriptor. +! idxmap - class(psb_indx_map). The index map ! info - integer. return code. +! +! This is the method to find out who owns a set of indices. +! In principle we could do the following: +! 1. Do an allgatherv of IDX +! 2. For each of the collected indices figure if current proces owns it +! 3. Scatter the results +! 4. Loop through the answers +! This method is guaranteed to find the owner, unless an input index has +! an invalid value, however it could easily require too much additional space +! because each block of indices is replicated to all processes. +! Therefore the current routine takes a different approach: +! -1. Figure out a maximum size for a buffer to collect the IDX; the buffer +! should allow for at least one index from each process (i.e. min size NP); also +! check if we have an adjacency list of processes on input; +! 0. If the initial adjacency list is not empty, use psi_adj_fnd_sweep to go +! through all indices and use multiple calls to psi_adjcncy_fnd_owner +! (up to the buffer size) to see if the owning processes are in the +! initial neighbours list; +! 1. Extract a sample from IDX, up to the buffer size, and do a call +! to psi_a2a_fnd_owner. This is guaranteed to find the owners of all indices +! in the sample; +! 2. Build the list of processes that own the sample indices; these are +! (a subset of) the topological neighbours, and store the list in IDXMAP +! 3. Use psi_adj_fnd_sweep to go through all remaining indices and use +! multiple calls to psi_adjcncy_fnd_owner (up to the buffer size) +! to see if the owning processes are in the current neighbours list; +! 4. If the input indices IDX have not been exhausted, cycle to 1. +! +! Thus, we are alternating between asking all processes for a subset of indices, and +! asking a subset of processes for all the indices, thereby limiting the memory footprint to +! a predefined maximum (that the user can force with psb_cd_set_maxspace()). ! subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) use psb_serial_mod @@ -51,6 +81,7 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) use psb_error_mod use psb_penv_mod use psb_realloc_mod + use psb_timers_mod use psb_desc_mod, psb_protect_name => psi_graph_fnd_owner #ifdef MPI_MOD use mpi @@ -75,8 +106,9 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) integer(psb_lpk_) :: mglob, ih integer(psb_ipk_) :: ictxt,np,me, nresp integer(psb_ipk_), parameter :: nt=4 - integer(psb_ipk_) :: tmpv(2) - logical, parameter :: gettime=.false., trace=.false. + integer(psb_ipk_) :: tmpv(4) + logical, parameter :: do_timings=.false., trace=.false. + integer(psb_ipk_), save :: idx_sweep0=-1, idx_loop_a2a=-1, idx_loop_neigh=-1 real(psb_dpk_) :: t0, t1, t2, t3, t4 character(len=20) :: name @@ -90,6 +122,13 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) n_row = idxmap%get_lr() n_col = idxmap%get_lc() iictxt = ictxt + if ((do_timings).and.(idx_sweep0==-1)) & + & idx_sweep0 = psb_get_timer_idx("GRPH_FND_OWN: Outer sweep") + if ((do_timings).and.(idx_loop_a2a==-1)) & + & idx_loop_a2a = psb_get_timer_idx("GRPH_FND_OWN: Loop a2a") + if ((do_timings).and.(idx_loop_neigh==-1)) & + & idx_loop_neigh = psb_get_timer_idx("GRPH_FND_OWN: Loop neigh") + call psb_info(ictxt, me, np) @@ -104,17 +143,6 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) goto 9999 end if - ! - ! Choice of maxspace should be adjusted to account for a default - ! "sensible" size and/or a user-specified value - ! - tmpv(1) = n_row - tmpv(2) = psb_cd_get_maxspace() - call psb_max(ictxt,tmpv) - locr_max = tmpv(1) - maxspace = min(nt*locr_max,tmpv(2)) - maxspace = max(maxspace,np) - if (trace.and.(me == 0)) write(0,*) ' Through graph_fnd_owner with maxspace:',maxspace ! ! ! @@ -139,9 +167,21 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) n_rest = nv - n_answers nrest_max = n_rest + ! + ! Choice of maxspace should be adjusted to account for a default + ! "sensible" size and/or a user-specified value + ! tmpv(1) = nadj tmpv(2) = nrest_max + tmpv(3) = n_row + tmpv(4) = psb_cd_get_maxspace() call psb_max(ictxt,tmpv) + locr_max = tmpv(3) + maxspace = nt*locr_max + if (tmpv(4) > 0) maxspace = min(maxspace,tmpv(4)) + maxspace = max(maxspace,np) + if (trace.and.(me == 0)) write(0,*) ' Through graph_fnd_owner with maxspace:',maxspace + if (do_timings) call psb_tic(idx_sweep0) if ((tmpv(1) > 0).and.(tmpv(2) >0)) then ! ! Do a preliminary run on the user-defined adjacency lists @@ -155,9 +195,10 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) call psb_max(ictxt,nrest_max) if (trace.and.(me == 0)) write(0,*) ' After initial sweep:',nrest_max end if - + if (do_timings) call psb_toc(idx_sweep0) fnd_owner_loop: do while (nrest_max>0) + if (do_timings) call psb_tic(idx_loop_a2a) ! ! The basic idea of this loop is to alternate between ! searching through all processes and searching @@ -168,6 +209,7 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) ! ! if (trace.and.(me == 0)) write(0,*) 'Looping in graph_fnd_owner: ', nrest_max nsampl_in = min(n_rest,max(1,(maxspace+np-1)/np)) + !nsampl_in = min(n_rest,32) ! ! Choose a sample, should it be done in this simplistic way? ! Note: nsampl_in is a hint, not an absolute, hence nsampl_out @@ -195,7 +237,8 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) ladj = tprc(1:nsampl_in) call psb_msort_unique(ladj,nadj) call psb_realloc(nadj,ladj,info) - + if (do_timings) call psb_toc(idx_loop_a2a) + if (do_timings) call psb_tic(idx_loop_neigh) ! ! 4. Extract again a sample and do a neighbourhood search ! so that the total size is <= maxspace @@ -215,6 +258,7 @@ subroutine psi_graph_fnd_owner(idx,iprc,idxmap,info) nrest_max = n_rest call psb_max(ictxt,nrest_max) if (trace.and.(me == 0)) write(0,*) ' fnd_owner_loop remaining:',nrest_max + if (do_timings) call psb_toc(idx_loop_neigh) end do fnd_owner_loop call psb_erractionrestore(err_act) diff --git a/base/internals/psi_indx_map_fnd_owner.F90 b/base/internals/psi_indx_map_fnd_owner.F90 index 014306ff..0aee0806 100644 --- a/base/internals/psi_indx_map_fnd_owner.F90 +++ b/base/internals/psi_indx_map_fnd_owner.F90 @@ -30,20 +30,26 @@ ! ! ! -! File: psi_fnd_owner.f90 +! File: psi_indx_map_fnd_owner.f90 ! -! Subroutine: psi_fnd_owner +! Subroutine: psi_indx_map_fnd_owner ! Figure out who owns global indices. ! ! Arguments: -! nv - integer Number of indices required on the calling -! process ! idx(:) - integer Required indices on the calling process. ! Note: the indices should be unique! ! iprc(:) - integer(psb_ipk_), allocatable Output: process identifiers for the corresponding ! indices -! desc_a - type(psb_desc_type). The communication descriptor. +! idxmap - class(psb_indx_map). The index map ! info - integer. return code. +! +! This is the default implementation of the FND_OWNER method. +! If a particular index map class has additional information, it can override it +! (see e.g. the GEN_BLOCK_MAP class). +! +! 1. Check if IDXM%PARTS is available, and use it; or +! 2. Check if TEMPVG(:) is allocated, and use it; or +! 3. Call the general method PSI_GRAPH_FND_OWNER. ! subroutine psi_indx_map_fnd_owner(idx,iprc,idxmap,info) use psb_serial_mod diff --git a/base/internals/psi_symm_dep_list.F90 b/base/internals/psi_symm_dep_list.F90 index c3c4db84..cd2894c1 100644 --- a/base/internals/psi_symm_dep_list.F90 +++ b/base/internals/psi_symm_dep_list.F90 @@ -70,7 +70,7 @@ subroutine psi_symm_dep_list_inrv(rvsz,adj,ictxt,info) name = 'psi_symm_dep_list' call psb_erractionsave(err_act) - icomm = psb_get_mpicomm(ictxt) + icomm = psb_get_mpi_comm(ictxt) call psb_info(ictxt, me, np) @@ -151,7 +151,7 @@ subroutine psi_symm_dep_list_norv(adj,ictxt,info) name = 'psi_symm_dep_list' call psb_erractionsave(err_act) - icomm = psb_get_mpicomm(ictxt) + icomm = psb_get_mpi_comm(ictxt) call psb_info(ictxt, me, np) diff --git a/base/modules/desc/psb_desc_mod.F90 b/base/modules/desc/psb_desc_mod.F90 index 9728e970..fbc64c8c 100644 --- a/base/modules/desc/psb_desc_mod.F90 +++ b/base/modules/desc/psb_desc_mod.F90 @@ -310,7 +310,7 @@ module psb_desc_mod integer(psb_lpk_), private, save :: cd_large_threshold = psb_default_large_threshold - integer(psb_ipk_), private, save :: cd_maxspace = 1000*1000 + integer(psb_ipk_), private, save :: cd_maxspace = -1 contains diff --git a/base/modules/desc/psb_gen_block_map_mod.F90 b/base/modules/desc/psb_gen_block_map_mod.F90 index 258a69a6..255b05d1 100644 --- a/base/modules/desc/psb_gen_block_map_mod.F90 +++ b/base/modules/desc/psb_gen_block_map_mod.F90 @@ -2005,7 +2005,7 @@ contains idxmap%local_cols = nl idxmap%ictxt = ictxt idxmap%state = psb_desc_bld_ - idxmap%mpic = psb_get_mpicomm(ictxt) + idxmap%mpic = psb_get_mpi_comm(ictxt) idxmap%min_glob_row = vnl(iam)+1 idxmap%max_glob_row = vnl(iam+1) call move_alloc(vnl,idxmap%vnl) diff --git a/base/modules/desc/psb_glist_map_mod.f90 b/base/modules/desc/psb_glist_map_mod.f90 index e894d898..3298291a 100644 --- a/base/modules/desc/psb_glist_map_mod.f90 +++ b/base/modules/desc/psb_glist_map_mod.f90 @@ -126,7 +126,7 @@ contains idxmap%ictxt = ictxt idxmap%state = psb_desc_bld_ - idxmap%mpic = psb_get_mpicomm(ictxt) + idxmap%mpic = psb_get_mpi_comm(ictxt) nl = 0 do i=1, n diff --git a/base/modules/desc/psb_hash_map_mod.f90 b/base/modules/desc/psb_hash_map_mod.f90 index d6769fd5..02eff7a4 100644 --- a/base/modules/desc/psb_hash_map_mod.f90 +++ b/base/modules/desc/psb_hash_map_mod.f90 @@ -961,7 +961,7 @@ contains idxmap%local_cols = nl idxmap%ictxt = ictxt idxmap%state = psb_desc_bld_ - idxmap%mpic = psb_get_mpicomm(ictxt) + idxmap%mpic = psb_get_mpi_comm(ictxt) lc2 = int(1.5*nl) call psb_realloc(lc2,idxmap%loc_to_glob,info) diff --git a/base/modules/desc/psb_indx_map_mod.f90 b/base/modules/desc/psb_indx_map_mod.f90 index 378b38af..0f9d15c6 100644 --- a/base/modules/desc/psb_indx_map_mod.f90 +++ b/base/modules/desc/psb_indx_map_mod.f90 @@ -331,9 +331,40 @@ module psb_indx_map_mod end subroutine psi_symm_dep_list_norv end interface psi_symm_dep_list + integer(psb_mpk_), parameter :: psi_adj_fnd_irecv_ = 0 + integer(psb_mpk_), parameter :: psi_adj_fnd_a2av_ = 1 + integer(psb_mpk_), parameter :: psi_adj_fnd_pbrcv_ = 2 + integer(psb_mpk_), parameter :: psi_adj_alg_max_ = psi_adj_fnd_pbrcv_ + integer(psb_mpk_), save :: psi_adj_alg = psi_adj_fnd_irecv_ + contains + subroutine psi_set_adj_alg(ialg) + integer(psb_mpk_), intent(in) :: ialg + if ((ialg >=0) .and. (ialg <= psi_adj_alg_max_))& + & psi_adj_alg = ialg + end subroutine psi_set_adj_alg + function psi_get_adj_alg() result(val) + integer(psb_mpk_) :: val + val = psi_adj_alg + end function psi_get_adj_alg + + function psi_get_adj_alg_fmt() result(val) + character(len=20) :: val + select case(psi_adj_alg) + case(psi_adj_fnd_a2av_) + val = 'MPI_A2AV' + case(psi_adj_fnd_irecv_) + val = 'MPI_ISEND/IRECV' + case(psi_adj_fnd_pbrcv_) + val = 'PSB_SND/RCV' + case default + val = 'Unknown ?' + end select + end function psi_get_adj_alg_fmt + + !> !! \memberof psb_indx_map !! \brief Print a descriptive name diff --git a/base/modules/desc/psb_list_map_mod.f90 b/base/modules/desc/psb_list_map_mod.f90 index c3dd4154..68223682 100644 --- a/base/modules/desc/psb_list_map_mod.f90 +++ b/base/modules/desc/psb_list_map_mod.f90 @@ -1119,7 +1119,7 @@ contains idxmap%ictxt = ictxt idxmap%state = psb_desc_bld_ - idxmap%mpic = psb_get_mpicomm(ictxt) + idxmap%mpic = psb_get_mpi_comm(ictxt) do i=1, n idxmap%glob_to_loc(i) = -1 end do diff --git a/base/modules/desc/psb_repl_map_mod.f90 b/base/modules/desc/psb_repl_map_mod.f90 index 29a1eb4d..f262c8f5 100644 --- a/base/modules/desc/psb_repl_map_mod.f90 +++ b/base/modules/desc/psb_repl_map_mod.f90 @@ -746,7 +746,7 @@ contains idxmap%local_cols = nl idxmap%ictxt = ictxt idxmap%state = psb_desc_bld_ - idxmap%mpic = psb_get_mpicomm(ictxt) + idxmap%mpic = psb_get_mpi_comm(ictxt) call idxmap%set_state(psb_desc_bld_) end subroutine repl_init diff --git a/base/modules/penv/psi_penv_mod.F90 b/base/modules/penv/psi_penv_mod.F90 index f3f808bb..4d7be808 100644 --- a/base/modules/penv/psi_penv_mod.F90 +++ b/base/modules/penv/psi_penv_mod.F90 @@ -563,17 +563,30 @@ contains end subroutine psb_info_mpik - function psb_get_mpicomm(ictxt) result(comm) + function psb_get_mpi_comm(ictxt) result(comm) integer(psb_mpk_) :: ictxt, comm comm = ictxt - end function psb_get_mpicomm + end function psb_get_mpi_comm - function psb_get_rank(ictxt,id) result(rank) + function psb_get_mpi_rank(ictxt,id) result(rank) integer(psb_mpk_) :: rank,ictxt,id rank = id - end function psb_get_rank + end function psb_get_mpi_rank + + + subroutine psb_get_mpicomm(ictxt,comm) + integer(psb_mpk_) :: ictxt, comm + + comm = psb_get_mpi_comm(ictxt) + end subroutine psb_get_mpicomm + + subroutine psb_get_rank(rank,ictxt,id) + integer(psb_mpk_) :: rank,ictxt,id + + rank = psb_get_mpi_rank(ictxt,id) + end subroutine psb_get_rank ! !!!!!!!!!!!!!!!!!!!!!! diff --git a/base/modules/psb_const_mod.F90 b/base/modules/psb_const_mod.F90 index b0503e4e..92def010 100644 --- a/base/modules/psb_const_mod.F90 +++ b/base/modules/psb_const_mod.F90 @@ -309,5 +309,8 @@ module psb_const_mod integer(psb_ipk_), parameter, public :: psb_err_alloc_request_=4025 integer(psb_ipk_), parameter, public :: psb_err_from_subroutine_non_=4011 integer(psb_ipk_), parameter, public :: psb_err_invalid_istop_=5001 + integer(psb_ipk_), parameter, public :: psb_err_invalid_irst_ =5002 + integer(psb_ipk_), parameter, public :: psb_err_invalid_preci_=5003 + integer(psb_ipk_), parameter, public :: psb_err_invalid_preca_=5004 end module psb_const_mod diff --git a/base/modules/psb_error_mod.F90 b/base/modules/psb_error_mod.F90 index a2e37e84..05e42d35 100644 --- a/base/modules/psb_error_mod.F90 +++ b/base/modules/psb_error_mod.F90 @@ -1043,12 +1043,17 @@ contains achmsg(1) = tmpmsg write(achmsg(2),'("Invalid ISTOP: ",i0)')e_e_d(1) - case(5002) + case(psb_err_invalid_irst_) + allocate(achmsg(2)) + achmsg(1) = tmpmsg + write(achmsg(2),'("Invalid IRST: ",i0)')e_e_d(1) + + case(psb_err_invalid_preci_) allocate(achmsg(2)) achmsg(1) = tmpmsg write(achmsg(2),'("Invalid PREC: ",i0)')e_e_d(1) - case(5003) + case(psb_err_invalid_preca_) allocate(achmsg(2)) achmsg(1) = tmpmsg write(achmsg(2),'("Invalid PREC: ",a3)')a_e_d(1:3) diff --git a/base/modules/psi_i_mod.F90 b/base/modules/psi_i_mod.F90 index e8222753..ac2fcf06 100644 --- a/base/modules/psi_i_mod.F90 +++ b/base/modules/psi_i_mod.F90 @@ -118,11 +118,11 @@ module psi_i_mod & length_dl,dl_lda,mode,info) import implicit none - logical, intent(in) :: is_bld, is_upd - integer(psb_ipk_), intent(in) :: ictxt,mode + logical, intent(in) :: is_bld, is_upd + integer(psb_ipk_), intent(in) :: ictxt, mode integer(psb_ipk_), intent(out) :: dl_lda integer(psb_ipk_), intent(in) :: desc_str(*) - integer(psb_ipk_), allocatable, intent(out) :: dep_list(:,:),length_dl(:) + integer(psb_ipk_), allocatable, intent(out) :: dep_list(:,:), length_dl(:) integer(psb_ipk_), intent(out) :: info end subroutine psi_i_extract_dep_list end interface @@ -131,11 +131,11 @@ module psi_i_mod subroutine psi_i_fnd_owner(nv,idx,iprc,desc,info) import implicit none - integer(psb_ipk_), intent(in) :: nv - integer(psb_ipk_), intent(in) :: idx(:) + integer(psb_ipk_), intent(in) :: nv + integer(psb_ipk_), intent(in) :: idx(:) integer(psb_ipk_), allocatable, intent(out) :: iprc(:) - type(psb_desc_type), intent(inout) :: desc - integer(psb_ipk_), intent(out) :: info + type(psb_desc_type), intent(in) :: desc + integer(psb_ipk_), intent(out) :: info end subroutine psi_i_fnd_owner end interface psi_fnd_owner diff --git a/base/modules/tools/psb_c_tools_mod.f90 b/base/modules/tools/psb_c_tools_mod.f90 index cf838af4..bf02bdc5 100644 --- a/base/modules/tools/psb_c_tools_mod.f90 +++ b/base/modules/tools/psb_c_tools_mod.f90 @@ -37,13 +37,12 @@ Module psb_c_tools_mod use psb_c_multivect_mod, only : psb_c_base_multivect_type, psb_c_multivect_type interface psb_geall - subroutine psb_calloc_vect(x, desc_a,info,n) + subroutine psb_calloc_vect(x, desc_a,info) import implicit none type(psb_c_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_calloc_vect subroutine psb_calloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/modules/tools/psb_d_tools_mod.f90 b/base/modules/tools/psb_d_tools_mod.f90 index c88795b6..faf91045 100644 --- a/base/modules/tools/psb_d_tools_mod.f90 +++ b/base/modules/tools/psb_d_tools_mod.f90 @@ -37,13 +37,12 @@ Module psb_d_tools_mod use psb_d_multivect_mod, only : psb_d_base_multivect_type, psb_d_multivect_type interface psb_geall - subroutine psb_dalloc_vect(x, desc_a,info,n) + subroutine psb_dalloc_vect(x, desc_a,info) import implicit none type(psb_d_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_dalloc_vect subroutine psb_dalloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/modules/tools/psb_i_tools_mod.f90 b/base/modules/tools/psb_i_tools_mod.f90 index 8378dcfb..1faffd66 100644 --- a/base/modules/tools/psb_i_tools_mod.f90 +++ b/base/modules/tools/psb_i_tools_mod.f90 @@ -36,13 +36,12 @@ Module psb_i_tools_mod use psb_i_multivect_mod, only : psb_i_base_multivect_type, psb_i_multivect_type interface psb_geall - subroutine psb_ialloc_vect(x, desc_a,info,n) + subroutine psb_ialloc_vect(x, desc_a,info) import implicit none type(psb_i_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_ialloc_vect subroutine psb_ialloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/modules/tools/psb_l_tools_mod.f90 b/base/modules/tools/psb_l_tools_mod.f90 index 4eca54f3..96f44fd7 100644 --- a/base/modules/tools/psb_l_tools_mod.f90 +++ b/base/modules/tools/psb_l_tools_mod.f90 @@ -36,13 +36,12 @@ Module psb_l_tools_mod use psb_l_multivect_mod, only : psb_l_base_multivect_type, psb_l_multivect_type interface psb_geall - subroutine psb_lalloc_vect(x, desc_a,info,n) + subroutine psb_lalloc_vect(x, desc_a,info) import implicit none type(psb_l_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_lalloc_vect subroutine psb_lalloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/modules/tools/psb_s_tools_mod.f90 b/base/modules/tools/psb_s_tools_mod.f90 index 8a67ed5f..59c576a0 100644 --- a/base/modules/tools/psb_s_tools_mod.f90 +++ b/base/modules/tools/psb_s_tools_mod.f90 @@ -37,13 +37,12 @@ Module psb_s_tools_mod use psb_s_multivect_mod, only : psb_s_base_multivect_type, psb_s_multivect_type interface psb_geall - subroutine psb_salloc_vect(x, desc_a,info,n) + subroutine psb_salloc_vect(x, desc_a,info) import implicit none type(psb_s_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_salloc_vect subroutine psb_salloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/modules/tools/psb_z_tools_mod.f90 b/base/modules/tools/psb_z_tools_mod.f90 index 476dfd02..185aba04 100644 --- a/base/modules/tools/psb_z_tools_mod.f90 +++ b/base/modules/tools/psb_z_tools_mod.f90 @@ -37,13 +37,12 @@ Module psb_z_tools_mod use psb_z_multivect_mod, only : psb_z_base_multivect_type, psb_z_multivect_type interface psb_geall - subroutine psb_zalloc_vect(x, desc_a,info,n) + subroutine psb_zalloc_vect(x, desc_a,info) import implicit none type(psb_z_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n end subroutine psb_zalloc_vect subroutine psb_zalloc_vect_r2(x, desc_a,info,n,lb) import diff --git a/base/psblas/psb_camax.f90 b/base/psblas/psb_camax.f90 index 526c5e40..0de31a0c 100644 --- a/base/psblas/psb_camax.f90 +++ b/base/psblas/psb_camax.f90 @@ -32,7 +32,7 @@ ! File: psb_camax.f90 ! ! Function: psb_camax -! Searches the absolute max of X. +! Computes the maximum absolute value of X ! ! normi := max(abs(sub(X)(i)) ! @@ -164,7 +164,7 @@ end function psb_camax !!$ ! ! Function: psb_camaxv -! Searches the absolute max of X. +! Computes the maximum absolute value of X. ! ! normi := max(abs(X(i)) ! @@ -252,6 +252,17 @@ function psb_camaxv (x,desc_a, info,global) result(res) return end function psb_camaxv +! +! Function: psb_camax_vect +! Computes the maximum absolute value of X. +! +! normi := max(abs(X(i)) +! +! Arguments: +! x - type(psb_c_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! function psb_camax_vect(x, desc_a, info,global) result(res) use psb_penv_mod @@ -374,17 +385,16 @@ end function psb_camax_vect !!$ ! ! Subroutine: psb_camaxvs -! Searches the absolute max of X. +! Computes the maximum absolute value of X, subroutine version ! ! normi := max(abs(sub(X)(i)) ! -! where sub( X ) denotes X(1:N,JX:). +! where sub( X ) denotes X(1:N). ! ! Arguments: ! res - real The result. -! x(:,:) - complex The input vector. +! x(:) - complex The input vector. ! desc_a - type(psb_desc_type). The communication descriptor. -! info - integer. Return code ! jx - integer(optional). The column offset. ! subroutine psb_camaxvs(res,x,desc_a, info,global) diff --git a/base/psblas/psb_casum.f90 b/base/psblas/psb_casum.f90 index 2b0beda5..a0bf5262 100644 --- a/base/psblas/psb_casum.f90 +++ b/base/psblas/psb_casum.f90 @@ -135,6 +135,19 @@ function psb_casum (x,desc_a, info, jx,global) result(res) return end function psb_casum +! Function: psb_casum_vect +! Computes norm1 of X +! +! norm1 := sum(sub( X )(i)) +! +! where sub( X ) denotes X(1:N,JX:). +! +! Arguments: +! x - type(psb_c_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset. +! function psb_casum_vect(x, desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_casum_vect diff --git a/base/psblas/psb_caxpby.f90 b/base/psblas/psb_caxpby.f90 index ab00bd60..daa47829 100644 --- a/base/psblas/psb_caxpby.f90 +++ b/base/psblas/psb_caxpby.f90 @@ -31,6 +31,23 @@ ! ! File: psb_caxpby.f90 +! +! Subroutine: psb_caxpby_vect +! Adds one distributed vector to another, +! +! Y := beta * Y + alpha * X +! +! Arguments: +! alpha - complex,input The scalar used to multiply each component of X +! x - type(psb_c_vect_type) The input vector containing the entries of X +! beta - complex,input The scalar used to multiply each component of Y +! y - type(psb_c_vect_type) The input/output vector Y +! desc_a - type(psb_desc_type) The communication descriptor. +! info - integer Return code +! +! Note: from a functional point of view, X is input, but here +! it's declared INOUT because of the sync() methods. +! subroutine psb_caxpby_vect(alpha, x, beta, y,& & desc_a, info) use psb_base_mod, psb_protect_name => psb_caxpby_vect @@ -269,7 +286,7 @@ end subroutine psb_caxpby !!$ ! ! Subroutine: psb_caxpbyv -! Adds one distributed matrix to another, +! Adds one distributed vector to another, ! ! Y := beta * Y + alpha * X ! diff --git a/base/psblas/psb_cdot.f90 b/base/psblas/psb_cdot.f90 index 39cda431..5432eb32 100644 --- a/base/psblas/psb_cdot.f90 +++ b/base/psblas/psb_cdot.f90 @@ -31,22 +31,22 @@ ! ! File: psb_cdot.f90 ! -! Function: psb_cdot -! psb_cdot forms the dot product of two distributed vectors, +! Function: psb_cdot_vect +! psb_cdot computes the dot product of two distributed vectors, ! -! dot := sub( X )**C * sub( Y ) +! dot := ( X )**C * ( Y ) ! -! where sub( X ) denotes X(:,JX) -! -! sub( Y ) denotes Y(:,JY). ! ! Arguments: -! x(:,:) - complex The input vector containing the entries of sub( X ). -! y(:,:) - complex The input vector containing the entries of sub( Y ). +! x - type(psb_c_vect_type) The input vector containing the entries of sub( X ). +! y - type(psb_c_vect_type) The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code -! jx - integer(optional). The column offset for sub( X ). -! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! +! Note: from a functional point of view, X and Y are input, but here +! they are declared INOUT because of the sync() methods. +! ! function psb_cdot_vect(x, y, desc_a,info,global) result(res) use psb_desc_mod @@ -156,7 +156,25 @@ function psb_cdot_vect(x, y, desc_a,info,global) result(res) return end function psb_cdot_vect - +! +! Function: psb_cdot +! psb_cdot computes the dot product of two distributed vectors, +! +! dot := sub( X )**C * sub( Y ) +! +! where sub( X ) denotes X(:,JX) +! +! sub( Y ) denotes Y(:,JY). +! +! Arguments: +! x(:,:) - complex The input vector containing the entries of sub( X ). +! y(:,:) - complex The input vector containing the entries of sub( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset for sub( X ). +! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! function psb_cdot(x, y,desc_a, info, jx, jy,global) result(res) use psb_base_mod, psb_protect_name => psb_cdot implicit none @@ -298,7 +316,7 @@ end function psb_cdot !!$ ! ! Function: psb_cdotv -! psb_cdotv forms the dot product of two distributed vectors, +! psb_cdotv computes the dot product of two distributed vectors, ! ! dot := X**C * Y ! @@ -307,6 +325,7 @@ end function psb_cdot ! y(:) - complex The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! function psb_cdotv(x, y,desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_cdotv @@ -432,7 +451,7 @@ end function psb_cdotv !!$ ! ! Subroutine: psb_cdotvs -! psb_cdotvs forms the dot product of two distributed vectors, +! psb_cdotvs computes the dot product of two distributed vectors, ! ! res := X**C * Y ! @@ -442,6 +461,7 @@ end function psb_cdotv ! y(:) - complex The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_cdotvs(res, x, y,desc_a, info,global) use psb_base_mod, psb_protect_name => psb_cdotvs @@ -565,7 +585,7 @@ end subroutine psb_cdotvs !!$ ! ! Subroutine: psb_cmdots -! psb_cmdots forms the dot product of multiple distributed vectors, +! psb_cmdots computes the dot product of multiple distributed vectors, ! ! res(i) := ( X(:,i) )**C * ( Y(:,i) ) ! @@ -575,6 +595,7 @@ end subroutine psb_cdotvs ! y(:) - complex The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_cmdots(res, x, y, desc_a, info,global) use psb_base_mod, psb_protect_name => psb_cmdots diff --git a/base/psblas/psb_cnrm2.f90 b/base/psblas/psb_cnrm2.f90 index 43ab876c..1db5773a 100644 --- a/base/psblas/psb_cnrm2.f90 +++ b/base/psblas/psb_cnrm2.f90 @@ -32,9 +32,9 @@ ! File: psb_cnrm2.f90 ! ! Function: psb_cnrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( sub( X )**T * sub( X ) ) +! norm2 := sqrt ( sub( X )**C * sub( X ) ) ! ! where sub( X ) denotes X(:,JX). ! @@ -43,6 +43,7 @@ ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The column offset for sub( X ). +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_cnrm2(x, desc_a, info, jx,global) result(res) use psb_desc_mod @@ -170,14 +171,15 @@ end function psb_cnrm2 !!$ ! ! Function: psb_cnrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! x(:) - complex The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_cnrm2v(x, desc_a, info,global) result(res) use psb_desc_mod @@ -263,7 +265,17 @@ function psb_cnrm2v(x, desc_a, info,global) result(res) end function psb_cnrm2v - +! Function: psb_cnrm2_vect +! Computes the norm2 of a distributed vector, +! +! norm2 := sqrt ( X**C * X) +! +! Arguments: +! x - type(psb_c_vect_type) The input vector containing the entries of X. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. +! function psb_cnrm2_vect(x, desc_a, info,global) result(res) use psb_desc_mod use psb_check_mod @@ -344,7 +356,7 @@ function psb_cnrm2_vect(x, desc_a, info,global) result(res) res = res - sqrt(cone - dd*(abs(x%v%v(idx))/res)**2) end do end if - else + else res = szero end if @@ -392,15 +404,16 @@ end function psb_cnrm2_vect !!$ ! ! Subroutine: psb_cnrm2vs -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, subroutine version ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! res - real The result. ! x(:) - complex The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! subroutine psb_cnrm2vs(res, x, desc_a, info,global) use psb_desc_mod diff --git a/base/psblas/psb_cnrmi.f90 b/base/psblas/psb_cnrmi.f90 index 0ac0a04b..0abece53 100644 --- a/base/psblas/psb_cnrmi.f90 +++ b/base/psblas/psb_cnrmi.f90 @@ -32,14 +32,15 @@ ! File: psb_cnrmi.f90 ! ! Function: psb_cnrmi -! Forms the infinity norm of a sparse matrix, +! Computes the infinity norm of a sparse matrix, ! -! nrmi := max_i(abs(sum(A(i,:)))) +! nrmi := max_i(sum(abs(A(i,:)))) ! ! Arguments: ! a - type(psb_cspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_cnrmi(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_cnrmi diff --git a/base/psblas/psb_cspmm.f90 b/base/psblas/psb_cspmm.f90 index 3d1d3b7d..5a059647 100644 --- a/base/psblas/psb_cspmm.f90 +++ b/base/psblas/psb_cspmm.f90 @@ -31,6 +31,235 @@ ! ! File: psb_cspmm.f90 ! +! +! Subroutine: psb_cspm_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A' * Pr * X + beta * Y, +! +! alpha and beta are scalars, X and Y are distributed +! vectors and A is a M-by-N distributed matrix. +! +! Arguments: +! alpha - complex The scalar alpha. +! a - type(psb_cspmat_type). The sparse matrix containing A. +! x - type(psb_c_vect_type) The input vector containing the entries of ( X ). +! beta - complex The scalar beta. +! y - type(psb_c_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. Default: 'N' +! work(:) - complex,(optional). Working area. +! doswap - logical(optional). Whether to performe halo updates. +! +subroutine psb_cspmv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, work, doswap) + use psb_base_mod, psb_protect_name => psb_cspmv_vect + use psi_mod + implicit none + + complex(psb_spk_), intent(in) :: alpha, beta + type(psb_c_vect_type), intent(inout) :: x + type(psb_c_vect_type), intent(inout) :: y + type(psb_cspmat_type), intent(in) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + complex(psb_spk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans + logical, intent(in), optional :: doswap + + ! locals + integer(psb_ipk_) :: ictxt, np, me,& + & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & + & liwork, iiy, jjy, ib, ip, idx + integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja + integer(psb_ipk_), parameter :: nb=4 + complex(psb_spk_), pointer :: iwork(:), xp(:), yp(:) + complex(psb_spk_), allocatable :: xvsave(:) + character :: trans_ + character(len=20) :: name, ch_err + logical :: aliw, doswap_ + integer(psb_ipk_) :: debug_level, debug_unit + + name='psb_cspmv' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + debug_unit = psb_get_debug_unit() + debug_level = psb_get_debug_level() + + ictxt=desc_a%get_context() + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + if (present(doswap)) then + doswap_ = doswap + else + doswap_ = .true. + endif + + if (present(trans)) then + trans_ = psb_toupper(trans) + else + trans_ = 'N' + endif + if ( (trans_ == 'N').or.(trans_ == 'T')& + & .or.(trans_ == 'C')) then + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + + m = desc_a%get_global_rows() + n = desc_a%get_global_cols() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info + + if (trans_ == 'N') then + ! Matrix is not transposed + + if (doswap_) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & czero,x%v,desc_a,iwork,info,data=psb_comm_halo_) + end if + + call psb_csmm(alpha,a,x,beta,y,info) + + if(info /= psb_success_) then + info = psb_err_from_subroutine_non_ + call psb_errpush(info,name) + goto 9999 + end if + + else + ! Matrix is transposed + + ! + ! Non-empty overlap, need a buffer to hold + ! the entries updated with average operator. + ! Why the average? because in this way they will contribute + ! with a proper scale factor (1/np) to the overall product. + ! + call psi_ovrl_save(x%v,xvsave,desc_a,info) + if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) + + if (beta /= czero) call y%set(czero,nrow+1,ncol) + ! local Matrix-vector product + if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' csmm ', info + + if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) + if (info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='psb_csmm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + if (doswap_) then + call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& + & cone,y%v,desc_a,iwork,info) + if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & cone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' swaptran ', info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='PSI_SwapTran' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + end if + + end if + + if (aliw) deallocate(iwork,stat=info) + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='Deallocate iwork' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + nullify(iwork) + + call psb_erractionrestore(err_act) + if (debug_level >= psb_debug_comp_) then + call psb_barrier(ictxt) + write(debug_unit,*) me,' ',trim(name),' Returning ' + endif + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_cspmv_vect +! ! Subroutine: psb_cspmm ! Performs one of the distributed matrix-vector operations ! @@ -356,10 +585,6 @@ subroutine psb_cspmm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_cspmm - - - - !!$ !!$ Parallel Sparse BLAS version 3.5 !!$ (C) Copyright 2006-2018 @@ -670,211 +895,3 @@ subroutine psb_cspmv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_cspmv - - - -subroutine psb_cspmv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, work, doswap) - use psb_base_mod, psb_protect_name => psb_cspmv_vect - use psi_mod - implicit none - - complex(psb_spk_), intent(in) :: alpha, beta - type(psb_c_vect_type), intent(inout) :: x - type(psb_c_vect_type), intent(inout) :: y - type(psb_cspmat_type), intent(in) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - complex(psb_spk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans - logical, intent(in), optional :: doswap - - ! locals - integer(psb_ipk_) :: ictxt, np, me,& - & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & - & liwork, iiy, jjy, ib, ip, idx - integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja - integer(psb_ipk_), parameter :: nb=4 - complex(psb_spk_), pointer :: iwork(:), xp(:), yp(:) - complex(psb_spk_), allocatable :: xvsave(:) - character :: trans_ - character(len=20) :: name, ch_err - logical :: aliw, doswap_ - integer(psb_ipk_) :: debug_level, debug_unit - - name='psb_cspmv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - debug_unit = psb_get_debug_unit() - debug_level = psb_get_debug_level() - - ictxt=desc_a%get_context() - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - if (present(doswap)) then - doswap_ = doswap - else - doswap_ = .true. - endif - - if (present(trans)) then - trans_ = psb_toupper(trans) - else - trans_ = 'N' - endif - if ( (trans_ == 'N').or.(trans_ == 'T')& - & .or.(trans_ == 'C')) then - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - - m = desc_a%get_global_rows() - n = desc_a%get_global_cols() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='Allocate' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info - - if (trans_ == 'N') then - ! Matrix is not transposed - - if (doswap_) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & czero,x%v,desc_a,iwork,info,data=psb_comm_halo_) - end if - - call psb_csmm(alpha,a,x,beta,y,info) - - if(info /= psb_success_) then - info = psb_err_from_subroutine_non_ - call psb_errpush(info,name) - goto 9999 - end if - - else - ! Matrix is transposed - - ! - ! Non-empty overlap, need a buffer to hold - ! the entries updated with average operator. - ! Why the average? because in this way they will contribute - ! with a proper scale factor (1/np) to the overall product. - ! - call psi_ovrl_save(x%v,xvsave,desc_a,info) - if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) - - if (beta /= czero) call y%set(czero,nrow+1,ncol) - ! local Matrix-vector product - if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' csmm ', info - - if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) - if (info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='psb_csmm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - if (doswap_) then - call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& - & cone,y%v,desc_a,iwork,info) - if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & cone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' swaptran ', info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='PSI_SwapTran' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - end if - - end if - - if (aliw) deallocate(iwork,stat=info) - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='Deallocate iwork' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - nullify(iwork) - - call psb_erractionrestore(err_act) - if (debug_level >= psb_debug_comp_) then - call psb_barrier(ictxt) - write(debug_unit,*) me,' ',trim(name),' Returning ' - endif - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_cspmv_vect diff --git a/base/psblas/psb_cspnrm1.f90 b/base/psblas/psb_cspnrm1.f90 index a5076a0a..c49fdcc1 100644 --- a/base/psblas/psb_cspnrm1.f90 +++ b/base/psblas/psb_cspnrm1.f90 @@ -40,6 +40,7 @@ ! a - type(psb_cspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_cspnrm1(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_cspnrm1 diff --git a/base/psblas/psb_cspsm.f90 b/base/psblas/psb_cspsm.f90 index a8e0c570..3fc8138c 100644 --- a/base/psblas/psb_cspsm.f90 +++ b/base/psblas/psb_cspsm.f90 @@ -31,6 +31,203 @@ ! ! File: psb_cspsm.f90 ! +! +! Subroutine: psb_csps_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-1 * Pc * D * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * D * X + beta * Y, or +! +! X is a distributed +! vector and T is a M-by-M distributed triangular matrix. +! +! +! Arguments: +! alpha - complex. The scalar alpha. +! a - type(psb_cspmat_type). The sparse matrix containing A. +! x - type(psb_c_vect_type) The input vector containing the entries of ( X ). +! beta - complex The scalar beta. +! y - type(psb_c_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. If not present 'N' is assumed. +! scale - character(optional). Specify some type of operation with +! the diagonal matrix D. +! choice - integer(optional). The kind of update to perform on overlap elements. +! d(:) - complex, optional Matrix for diagonal scaling. +! work(:) - complex, optional Working area. +! +subroutine psb_cspsv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, scale, choice, diag, work) + use psb_base_mod, psb_protect_name => psb_cspsv_vect + use psi_mod + implicit none + + complex(psb_spk_), intent(in) :: alpha, beta + type(psb_c_vect_type), intent(inout) :: x + type(psb_c_vect_type), intent(inout) :: y + type(psb_cspmat_type), intent(inout) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + type(psb_c_vect_type), intent(inout), optional :: diag + complex(psb_spk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans, scale + integer(psb_ipk_), intent(in), optional :: choice + + ! locals + integer(psb_ipk_) :: ictxt, np, me, & + & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& + & ix, iy, ik, jx, jy, i, lld,& + & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm + + character :: lscale + integer(psb_ipk_), parameter :: nb=4 + complex(psb_spk_),pointer :: iwork(:), xp(:), yp(:) + character :: itrans + character(len=20) :: name, ch_err + logical :: aliw + + name='psb_cspsv_vect' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + + ictxt=desc_a%get_context() + + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + + if (present(choice)) then + choice_ = choice + else + choice_ = psb_avg_ + endif + + if (present(scale)) then + lscale = psb_toupper(scale) + else + lscale = 'U' + endif + + if (present(trans)) then + itrans = psb_toupper(trans) + if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then + ! Ok + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + else + itrans = 'N' + endif + + m = desc_a%get_global_rows() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + iwork(1)=0.d0 + + ! Perform local triangular system solve + if (present(diag)) then + call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) + else + call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) + end if + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='dcssm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + ! update overlap elements + if (choice_ > 0) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & cone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + + if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') + goto 9999 + end if + end if + + if (aliw) deallocate(iwork) + + call psb_erractionrestore(err_act) + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_cspsv_vect +! ! Subroutine: psb_cspsm ! Performs one of the distributed matrix-vector operations ! @@ -283,38 +480,6 @@ subroutine psb_cspsm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_cspsm - -!!$ -!!$ Parallel Sparse BLAS version 3.5 -!!$ (C) Copyright 2006-2018 -!!$ Salvatore Filippone University of Rome Tor Vergata -!!$ Alfredo Buttari -!!$ -!!$ Redistribution and use in source and binary forms, with or without -!!$ modification, are permitted provided that the following conditions -!!$ are met: -!!$ 1. Redistributions of source code must retain the above copyright -!!$ notice, this list of conditions and the following disclaimer. -!!$ 2. Redistributions in binary form must reproduce the above copyright -!!$ notice, this list of conditions, and the following disclaimer in the -!!$ documentation and/or other materials provided with the distribution. -!!$ 3. The name of the PSBLAS group or the names of its contributors may -!!$ not be used to endorse or promote products derived from this -!!$ software without specific written permission. -!!$ -!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED -!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS -!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR -!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF -!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS -!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN -!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) -!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -!!$ POSSIBILITY OF SUCH DAMAGE. -!!$ -!!$ ! ! Subroutine: psb_cspsv ! Performs one of the distributed matrix-vector operations @@ -545,166 +710,3 @@ subroutine psb_cspsv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_cspsv - -subroutine psb_cspsv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, scale, choice, diag, work) - use psb_base_mod, psb_protect_name => psb_cspsv_vect - use psi_mod - implicit none - - complex(psb_spk_), intent(in) :: alpha, beta - type(psb_c_vect_type), intent(inout) :: x - type(psb_c_vect_type), intent(inout) :: y - type(psb_cspmat_type), intent(inout) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - type(psb_c_vect_type), intent(inout), optional :: diag - complex(psb_spk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans, scale - integer(psb_ipk_), intent(in), optional :: choice - - ! locals - integer(psb_ipk_) :: ictxt, np, me, & - & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& - & ix, iy, ik, jx, jy, i, lld,& - & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm - - character :: lscale - integer(psb_ipk_), parameter :: nb=4 - complex(psb_spk_),pointer :: iwork(:), xp(:), yp(:) - character :: itrans - character(len=20) :: name, ch_err - logical :: aliw - - name='psb_sspsv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - - ictxt=desc_a%get_context() - - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - - if (present(choice)) then - choice_ = choice - else - choice_ = psb_avg_ - endif - - if (present(scale)) then - lscale = psb_toupper(scale) - else - lscale = 'U' - endif - - if (present(trans)) then - itrans = psb_toupper(trans) - if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then - ! Ok - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - else - itrans = 'N' - endif - - m = desc_a%get_global_rows() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - iwork(1)=0.d0 - - ! Perform local triangular system solve - if (present(diag)) then - call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) - else - call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) - end if - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='dcssm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - ! update overlap elements - if (choice_ > 0) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & cone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - - if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') - goto 9999 - end if - end if - - if (aliw) deallocate(iwork) - - call psb_erractionrestore(err_act) - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_cspsv_vect - diff --git a/base/psblas/psb_damax.f90 b/base/psblas/psb_damax.f90 index 33dd2dc9..0f3ea0b6 100644 --- a/base/psblas/psb_damax.f90 +++ b/base/psblas/psb_damax.f90 @@ -32,7 +32,7 @@ ! File: psb_damax.f90 ! ! Function: psb_damax -! Searches the absolute max of X. +! Computes the maximum absolute value of X ! ! normi := max(abs(sub(X)(i)) ! @@ -164,7 +164,7 @@ end function psb_damax !!$ ! ! Function: psb_damaxv -! Searches the absolute max of X. +! Computes the maximum absolute value of X. ! ! normi := max(abs(X(i)) ! @@ -252,6 +252,17 @@ function psb_damaxv (x,desc_a, info,global) result(res) return end function psb_damaxv +! +! Function: psb_damax_vect +! Computes the maximum absolute value of X. +! +! normi := max(abs(X(i)) +! +! Arguments: +! x - type(psb_d_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! function psb_damax_vect(x, desc_a, info,global) result(res) use psb_penv_mod @@ -374,17 +385,16 @@ end function psb_damax_vect !!$ ! ! Subroutine: psb_damaxvs -! Searches the absolute max of X. +! Computes the maximum absolute value of X, subroutine version ! ! normi := max(abs(sub(X)(i)) ! -! where sub( X ) denotes X(1:N,JX:). +! where sub( X ) denotes X(1:N). ! ! Arguments: ! res - real The result. -! x(:,:) - real The input vector. +! x(:) - real The input vector. ! desc_a - type(psb_desc_type). The communication descriptor. -! info - integer. Return code ! jx - integer(optional). The column offset. ! subroutine psb_damaxvs(res,x,desc_a, info,global) diff --git a/base/psblas/psb_dasum.f90 b/base/psblas/psb_dasum.f90 index cf2d8fe3..5de367f7 100644 --- a/base/psblas/psb_dasum.f90 +++ b/base/psblas/psb_dasum.f90 @@ -135,6 +135,19 @@ function psb_dasum (x,desc_a, info, jx,global) result(res) return end function psb_dasum +! Function: psb_dasum_vect +! Computes norm1 of X +! +! norm1 := sum(sub( X )(i)) +! +! where sub( X ) denotes X(1:N,JX:). +! +! Arguments: +! x - type(psb_d_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset. +! function psb_dasum_vect(x, desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_dasum_vect diff --git a/base/psblas/psb_daxpby.f90 b/base/psblas/psb_daxpby.f90 index b1c83d3a..73f62881 100644 --- a/base/psblas/psb_daxpby.f90 +++ b/base/psblas/psb_daxpby.f90 @@ -31,6 +31,23 @@ ! ! File: psb_daxpby.f90 +! +! Subroutine: psb_daxpby_vect +! Adds one distributed vector to another, +! +! Y := beta * Y + alpha * X +! +! Arguments: +! alpha - real,input The scalar used to multiply each component of X +! x - type(psb_d_vect_type) The input vector containing the entries of X +! beta - real,input The scalar used to multiply each component of Y +! y - type(psb_d_vect_type) The input/output vector Y +! desc_a - type(psb_desc_type) The communication descriptor. +! info - integer Return code +! +! Note: from a functional point of view, X is input, but here +! it's declared INOUT because of the sync() methods. +! subroutine psb_daxpby_vect(alpha, x, beta, y,& & desc_a, info) use psb_base_mod, psb_protect_name => psb_daxpby_vect @@ -269,7 +286,7 @@ end subroutine psb_daxpby !!$ ! ! Subroutine: psb_daxpbyv -! Adds one distributed matrix to another, +! Adds one distributed vector to another, ! ! Y := beta * Y + alpha * X ! diff --git a/base/psblas/psb_ddot.f90 b/base/psblas/psb_ddot.f90 index c2231d8a..ba1d9619 100644 --- a/base/psblas/psb_ddot.f90 +++ b/base/psblas/psb_ddot.f90 @@ -31,22 +31,22 @@ ! ! File: psb_ddot.f90 ! -! Function: psb_ddot -! psb_ddot forms the dot product of two distributed vectors, +! Function: psb_ddot_vect +! psb_ddot computes the dot product of two distributed vectors, ! -! dot := sub( X )**C * sub( Y ) +! dot := ( X )**C * ( Y ) ! -! where sub( X ) denotes X(:,JX) -! -! sub( Y ) denotes Y(:,JY). ! ! Arguments: -! x(:,:) - complex The input vector containing the entries of sub( X ). -! y(:,:) - complex The input vector containing the entries of sub( Y ). +! x - type(psb_d_vect_type) The input vector containing the entries of sub( X ). +! y - type(psb_d_vect_type) The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code -! jx - integer(optional). The column offset for sub( X ). -! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! +! Note: from a functional point of view, X and Y are input, but here +! they are declared INOUT because of the sync() methods. +! ! function psb_ddot_vect(x, y, desc_a,info,global) result(res) use psb_desc_mod @@ -156,7 +156,25 @@ function psb_ddot_vect(x, y, desc_a,info,global) result(res) return end function psb_ddot_vect - +! +! Function: psb_ddot +! psb_ddot computes the dot product of two distributed vectors, +! +! dot := sub( X )**C * sub( Y ) +! +! where sub( X ) denotes X(:,JX) +! +! sub( Y ) denotes Y(:,JY). +! +! Arguments: +! x(:,:) - real The input vector containing the entries of sub( X ). +! y(:,:) - real The input vector containing the entries of sub( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset for sub( X ). +! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! function psb_ddot(x, y,desc_a, info, jx, jy,global) result(res) use psb_base_mod, psb_protect_name => psb_ddot implicit none @@ -298,7 +316,7 @@ end function psb_ddot !!$ ! ! Function: psb_ddotv -! psb_ddotv forms the dot product of two distributed vectors, +! psb_ddotv computes the dot product of two distributed vectors, ! ! dot := X**C * Y ! @@ -307,6 +325,7 @@ end function psb_ddot ! y(:) - real The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! function psb_ddotv(x, y,desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_ddotv @@ -432,7 +451,7 @@ end function psb_ddotv !!$ ! ! Subroutine: psb_ddotvs -! psb_ddotvs forms the dot product of two distributed vectors, +! psb_ddotvs computes the dot product of two distributed vectors, ! ! res := X**C * Y ! @@ -442,6 +461,7 @@ end function psb_ddotv ! y(:) - real The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_ddotvs(res, x, y,desc_a, info,global) use psb_base_mod, psb_protect_name => psb_ddotvs @@ -565,7 +585,7 @@ end subroutine psb_ddotvs !!$ ! ! Subroutine: psb_dmdots -! psb_dmdots forms the dot product of multiple distributed vectors, +! psb_dmdots computes the dot product of multiple distributed vectors, ! ! res(i) := ( X(:,i) )**C * ( Y(:,i) ) ! @@ -575,6 +595,7 @@ end subroutine psb_ddotvs ! y(:) - real The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_dmdots(res, x, y, desc_a, info,global) use psb_base_mod, psb_protect_name => psb_dmdots diff --git a/base/psblas/psb_dnrm2.f90 b/base/psblas/psb_dnrm2.f90 index b72a72ee..0845aac4 100644 --- a/base/psblas/psb_dnrm2.f90 +++ b/base/psblas/psb_dnrm2.f90 @@ -32,9 +32,9 @@ ! File: psb_dnrm2.f90 ! ! Function: psb_dnrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( sub( X )**T * sub( X ) ) +! norm2 := sqrt ( sub( X )**C * sub( X ) ) ! ! where sub( X ) denotes X(:,JX). ! @@ -43,6 +43,7 @@ ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The column offset for sub( X ). +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_dnrm2(x, desc_a, info, jx,global) result(res) use psb_desc_mod @@ -170,14 +171,15 @@ end function psb_dnrm2 !!$ ! ! Function: psb_dnrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! x(:) - real The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_dnrm2v(x, desc_a, info,global) result(res) use psb_desc_mod @@ -263,7 +265,17 @@ function psb_dnrm2v(x, desc_a, info,global) result(res) end function psb_dnrm2v - +! Function: psb_dnrm2_vect +! Computes the norm2 of a distributed vector, +! +! norm2 := sqrt ( X**C * X) +! +! Arguments: +! x - type(psb_d_vect_type) The input vector containing the entries of X. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. +! function psb_dnrm2_vect(x, desc_a, info,global) result(res) use psb_desc_mod use psb_check_mod @@ -344,7 +356,7 @@ function psb_dnrm2_vect(x, desc_a, info,global) result(res) res = res - sqrt(done - dd*(abs(x%v%v(idx))/res)**2) end do end if - else + else res = dzero end if @@ -392,15 +404,16 @@ end function psb_dnrm2_vect !!$ ! ! Subroutine: psb_dnrm2vs -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, subroutine version ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! res - real The result. ! x(:) - real The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! subroutine psb_dnrm2vs(res, x, desc_a, info,global) use psb_desc_mod diff --git a/base/psblas/psb_dnrmi.f90 b/base/psblas/psb_dnrmi.f90 index 6d585981..a6a97751 100644 --- a/base/psblas/psb_dnrmi.f90 +++ b/base/psblas/psb_dnrmi.f90 @@ -32,14 +32,15 @@ ! File: psb_dnrmi.f90 ! ! Function: psb_dnrmi -! Forms the infinity norm of a sparse matrix, +! Computes the infinity norm of a sparse matrix, ! -! nrmi := max_i(abs(sum(A(i,:)))) +! nrmi := max_i(sum(abs(A(i,:)))) ! ! Arguments: ! a - type(psb_dspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_dnrmi(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_dnrmi diff --git a/base/psblas/psb_dspmm.f90 b/base/psblas/psb_dspmm.f90 index bf262541..1fdf6171 100644 --- a/base/psblas/psb_dspmm.f90 +++ b/base/psblas/psb_dspmm.f90 @@ -31,6 +31,235 @@ ! ! File: psb_dspmm.f90 ! +! +! Subroutine: psb_dspm_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A' * Pr * X + beta * Y, +! +! alpha and beta are scalars, X and Y are distributed +! vectors and A is a M-by-N distributed matrix. +! +! Arguments: +! alpha - real The scalar alpha. +! a - type(psb_dspmat_type). The sparse matrix containing A. +! x - type(psb_d_vect_type) The input vector containing the entries of ( X ). +! beta - real The scalar beta. +! y - type(psb_d_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. Default: 'N' +! work(:) - real,(optional). Working area. +! doswap - logical(optional). Whether to performe halo updates. +! +subroutine psb_dspmv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, work, doswap) + use psb_base_mod, psb_protect_name => psb_dspmv_vect + use psi_mod + implicit none + + real(psb_dpk_), intent(in) :: alpha, beta + type(psb_d_vect_type), intent(inout) :: x + type(psb_d_vect_type), intent(inout) :: y + type(psb_dspmat_type), intent(in) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + real(psb_dpk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans + logical, intent(in), optional :: doswap + + ! locals + integer(psb_ipk_) :: ictxt, np, me,& + & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & + & liwork, iiy, jjy, ib, ip, idx + integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja + integer(psb_ipk_), parameter :: nb=4 + real(psb_dpk_), pointer :: iwork(:), xp(:), yp(:) + real(psb_dpk_), allocatable :: xvsave(:) + character :: trans_ + character(len=20) :: name, ch_err + logical :: aliw, doswap_ + integer(psb_ipk_) :: debug_level, debug_unit + + name='psb_dspmv' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + debug_unit = psb_get_debug_unit() + debug_level = psb_get_debug_level() + + ictxt=desc_a%get_context() + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + if (present(doswap)) then + doswap_ = doswap + else + doswap_ = .true. + endif + + if (present(trans)) then + trans_ = psb_toupper(trans) + else + trans_ = 'N' + endif + if ( (trans_ == 'N').or.(trans_ == 'T')& + & .or.(trans_ == 'C')) then + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + + m = desc_a%get_global_rows() + n = desc_a%get_global_cols() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info + + if (trans_ == 'N') then + ! Matrix is not transposed + + if (doswap_) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & dzero,x%v,desc_a,iwork,info,data=psb_comm_halo_) + end if + + call psb_csmm(alpha,a,x,beta,y,info) + + if(info /= psb_success_) then + info = psb_err_from_subroutine_non_ + call psb_errpush(info,name) + goto 9999 + end if + + else + ! Matrix is transposed + + ! + ! Non-empty overlap, need a buffer to hold + ! the entries updated with average operator. + ! Why the average? because in this way they will contribute + ! with a proper scale factor (1/np) to the overall product. + ! + call psi_ovrl_save(x%v,xvsave,desc_a,info) + if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) + + if (beta /= dzero) call y%set(dzero,nrow+1,ncol) + ! local Matrix-vector product + if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' csmm ', info + + if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) + if (info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='psb_csmm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + if (doswap_) then + call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& + & done,y%v,desc_a,iwork,info) + if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & done,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' swaptran ', info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='PSI_SwapTran' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + end if + + end if + + if (aliw) deallocate(iwork,stat=info) + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='Deallocate iwork' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + nullify(iwork) + + call psb_erractionrestore(err_act) + if (debug_level >= psb_debug_comp_) then + call psb_barrier(ictxt) + write(debug_unit,*) me,' ',trim(name),' Returning ' + endif + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_dspmv_vect +! ! Subroutine: psb_dspmm ! Performs one of the distributed matrix-vector operations ! @@ -356,10 +585,6 @@ subroutine psb_dspmm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_dspmm - - - - !!$ !!$ Parallel Sparse BLAS version 3.5 !!$ (C) Copyright 2006-2018 @@ -670,211 +895,3 @@ subroutine psb_dspmv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_dspmv - - - -subroutine psb_dspmv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, work, doswap) - use psb_base_mod, psb_protect_name => psb_dspmv_vect - use psi_mod - implicit none - - real(psb_dpk_), intent(in) :: alpha, beta - type(psb_d_vect_type), intent(inout) :: x - type(psb_d_vect_type), intent(inout) :: y - type(psb_dspmat_type), intent(in) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - real(psb_dpk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans - logical, intent(in), optional :: doswap - - ! locals - integer(psb_ipk_) :: ictxt, np, me,& - & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & - & liwork, iiy, jjy, ib, ip, idx - integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja - integer(psb_ipk_), parameter :: nb=4 - real(psb_dpk_), pointer :: iwork(:), xp(:), yp(:) - real(psb_dpk_), allocatable :: xvsave(:) - character :: trans_ - character(len=20) :: name, ch_err - logical :: aliw, doswap_ - integer(psb_ipk_) :: debug_level, debug_unit - - name='psb_dspmv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - debug_unit = psb_get_debug_unit() - debug_level = psb_get_debug_level() - - ictxt=desc_a%get_context() - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - if (present(doswap)) then - doswap_ = doswap - else - doswap_ = .true. - endif - - if (present(trans)) then - trans_ = psb_toupper(trans) - else - trans_ = 'N' - endif - if ( (trans_ == 'N').or.(trans_ == 'T')& - & .or.(trans_ == 'C')) then - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - - m = desc_a%get_global_rows() - n = desc_a%get_global_cols() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='Allocate' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info - - if (trans_ == 'N') then - ! Matrix is not transposed - - if (doswap_) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & dzero,x%v,desc_a,iwork,info,data=psb_comm_halo_) - end if - - call psb_csmm(alpha,a,x,beta,y,info) - - if(info /= psb_success_) then - info = psb_err_from_subroutine_non_ - call psb_errpush(info,name) - goto 9999 - end if - - else - ! Matrix is transposed - - ! - ! Non-empty overlap, need a buffer to hold - ! the entries updated with average operator. - ! Why the average? because in this way they will contribute - ! with a proper scale factor (1/np) to the overall product. - ! - call psi_ovrl_save(x%v,xvsave,desc_a,info) - if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) - - if (beta /= dzero) call y%set(dzero,nrow+1,ncol) - ! local Matrix-vector product - if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' csmm ', info - - if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) - if (info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='psb_csmm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - if (doswap_) then - call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& - & done,y%v,desc_a,iwork,info) - if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & done,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' swaptran ', info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='PSI_SwapTran' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - end if - - end if - - if (aliw) deallocate(iwork,stat=info) - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='Deallocate iwork' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - nullify(iwork) - - call psb_erractionrestore(err_act) - if (debug_level >= psb_debug_comp_) then - call psb_barrier(ictxt) - write(debug_unit,*) me,' ',trim(name),' Returning ' - endif - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_dspmv_vect diff --git a/base/psblas/psb_dspnrm1.f90 b/base/psblas/psb_dspnrm1.f90 index 01a7de96..9d367615 100644 --- a/base/psblas/psb_dspnrm1.f90 +++ b/base/psblas/psb_dspnrm1.f90 @@ -40,6 +40,7 @@ ! a - type(psb_dspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_dspnrm1(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_dspnrm1 diff --git a/base/psblas/psb_dspsm.f90 b/base/psblas/psb_dspsm.f90 index 4efad6b7..f1a019ad 100644 --- a/base/psblas/psb_dspsm.f90 +++ b/base/psblas/psb_dspsm.f90 @@ -31,6 +31,203 @@ ! ! File: psb_dspsm.f90 ! +! +! Subroutine: psb_dsps_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-1 * Pc * D * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * D * X + beta * Y, or +! +! X is a distributed +! vector and T is a M-by-M distributed triangular matrix. +! +! +! Arguments: +! alpha - real. The scalar alpha. +! a - type(psb_dspmat_type). The sparse matrix containing A. +! x - type(psb_d_vect_type) The input vector containing the entries of ( X ). +! beta - real The scalar beta. +! y - type(psb_d_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. If not present 'N' is assumed. +! scale - character(optional). Specify some type of operation with +! the diagonal matrix D. +! choice - integer(optional). The kind of update to perform on overlap elements. +! d(:) - real, optional Matrix for diagonal scaling. +! work(:) - real, optional Working area. +! +subroutine psb_dspsv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, scale, choice, diag, work) + use psb_base_mod, psb_protect_name => psb_dspsv_vect + use psi_mod + implicit none + + real(psb_dpk_), intent(in) :: alpha, beta + type(psb_d_vect_type), intent(inout) :: x + type(psb_d_vect_type), intent(inout) :: y + type(psb_dspmat_type), intent(inout) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + type(psb_d_vect_type), intent(inout), optional :: diag + real(psb_dpk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans, scale + integer(psb_ipk_), intent(in), optional :: choice + + ! locals + integer(psb_ipk_) :: ictxt, np, me, & + & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& + & ix, iy, ik, jx, jy, i, lld,& + & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm + + character :: lscale + integer(psb_ipk_), parameter :: nb=4 + real(psb_dpk_),pointer :: iwork(:), xp(:), yp(:) + character :: itrans + character(len=20) :: name, ch_err + logical :: aliw + + name='psb_dspsv_vect' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + + ictxt=desc_a%get_context() + + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + + if (present(choice)) then + choice_ = choice + else + choice_ = psb_avg_ + endif + + if (present(scale)) then + lscale = psb_toupper(scale) + else + lscale = 'U' + endif + + if (present(trans)) then + itrans = psb_toupper(trans) + if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then + ! Ok + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + else + itrans = 'N' + endif + + m = desc_a%get_global_rows() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + iwork(1)=0.d0 + + ! Perform local triangular system solve + if (present(diag)) then + call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) + else + call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) + end if + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='dcssm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + ! update overlap elements + if (choice_ > 0) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & done,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + + if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') + goto 9999 + end if + end if + + if (aliw) deallocate(iwork) + + call psb_erractionrestore(err_act) + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_dspsv_vect +! ! Subroutine: psb_dspsm ! Performs one of the distributed matrix-vector operations ! @@ -283,38 +480,6 @@ subroutine psb_dspsm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_dspsm - -!!$ -!!$ Parallel Sparse BLAS version 3.5 -!!$ (C) Copyright 2006-2018 -!!$ Salvatore Filippone University of Rome Tor Vergata -!!$ Alfredo Buttari -!!$ -!!$ Redistribution and use in source and binary forms, with or without -!!$ modification, are permitted provided that the following conditions -!!$ are met: -!!$ 1. Redistributions of source code must retain the above copyright -!!$ notice, this list of conditions and the following disclaimer. -!!$ 2. Redistributions in binary form must reproduce the above copyright -!!$ notice, this list of conditions, and the following disclaimer in the -!!$ documentation and/or other materials provided with the distribution. -!!$ 3. The name of the PSBLAS group or the names of its contributors may -!!$ not be used to endorse or promote products derived from this -!!$ software without specific written permission. -!!$ -!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED -!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS -!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR -!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF -!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS -!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN -!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) -!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -!!$ POSSIBILITY OF SUCH DAMAGE. -!!$ -!!$ ! ! Subroutine: psb_dspsv ! Performs one of the distributed matrix-vector operations @@ -545,166 +710,3 @@ subroutine psb_dspsv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_dspsv - -subroutine psb_dspsv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, scale, choice, diag, work) - use psb_base_mod, psb_protect_name => psb_dspsv_vect - use psi_mod - implicit none - - real(psb_dpk_), intent(in) :: alpha, beta - type(psb_d_vect_type), intent(inout) :: x - type(psb_d_vect_type), intent(inout) :: y - type(psb_dspmat_type), intent(inout) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - type(psb_d_vect_type), intent(inout), optional :: diag - real(psb_dpk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans, scale - integer(psb_ipk_), intent(in), optional :: choice - - ! locals - integer(psb_ipk_) :: ictxt, np, me, & - & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& - & ix, iy, ik, jx, jy, i, lld,& - & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm - - character :: lscale - integer(psb_ipk_), parameter :: nb=4 - real(psb_dpk_),pointer :: iwork(:), xp(:), yp(:) - character :: itrans - character(len=20) :: name, ch_err - logical :: aliw - - name='psb_sspsv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - - ictxt=desc_a%get_context() - - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - - if (present(choice)) then - choice_ = choice - else - choice_ = psb_avg_ - endif - - if (present(scale)) then - lscale = psb_toupper(scale) - else - lscale = 'U' - endif - - if (present(trans)) then - itrans = psb_toupper(trans) - if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then - ! Ok - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - else - itrans = 'N' - endif - - m = desc_a%get_global_rows() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - iwork(1)=0.d0 - - ! Perform local triangular system solve - if (present(diag)) then - call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) - else - call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) - end if - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='dcssm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - ! update overlap elements - if (choice_ > 0) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & done,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - - if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') - goto 9999 - end if - end if - - if (aliw) deallocate(iwork) - - call psb_erractionrestore(err_act) - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_dspsv_vect - diff --git a/base/psblas/psb_samax.f90 b/base/psblas/psb_samax.f90 index ee70314f..174c7a28 100644 --- a/base/psblas/psb_samax.f90 +++ b/base/psblas/psb_samax.f90 @@ -32,7 +32,7 @@ ! File: psb_samax.f90 ! ! Function: psb_samax -! Searches the absolute max of X. +! Computes the maximum absolute value of X ! ! normi := max(abs(sub(X)(i)) ! @@ -164,7 +164,7 @@ end function psb_samax !!$ ! ! Function: psb_samaxv -! Searches the absolute max of X. +! Computes the maximum absolute value of X. ! ! normi := max(abs(X(i)) ! @@ -252,6 +252,17 @@ function psb_samaxv (x,desc_a, info,global) result(res) return end function psb_samaxv +! +! Function: psb_samax_vect +! Computes the maximum absolute value of X. +! +! normi := max(abs(X(i)) +! +! Arguments: +! x - type(psb_s_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! function psb_samax_vect(x, desc_a, info,global) result(res) use psb_penv_mod @@ -374,17 +385,16 @@ end function psb_samax_vect !!$ ! ! Subroutine: psb_samaxvs -! Searches the absolute max of X. +! Computes the maximum absolute value of X, subroutine version ! ! normi := max(abs(sub(X)(i)) ! -! where sub( X ) denotes X(1:N,JX:). +! where sub( X ) denotes X(1:N). ! ! Arguments: ! res - real The result. -! x(:,:) - real The input vector. +! x(:) - real The input vector. ! desc_a - type(psb_desc_type). The communication descriptor. -! info - integer. Return code ! jx - integer(optional). The column offset. ! subroutine psb_samaxvs(res,x,desc_a, info,global) diff --git a/base/psblas/psb_sasum.f90 b/base/psblas/psb_sasum.f90 index 2abf254d..a61f1851 100644 --- a/base/psblas/psb_sasum.f90 +++ b/base/psblas/psb_sasum.f90 @@ -135,6 +135,19 @@ function psb_sasum (x,desc_a, info, jx,global) result(res) return end function psb_sasum +! Function: psb_sasum_vect +! Computes norm1 of X +! +! norm1 := sum(sub( X )(i)) +! +! where sub( X ) denotes X(1:N,JX:). +! +! Arguments: +! x - type(psb_s_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset. +! function psb_sasum_vect(x, desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_sasum_vect diff --git a/base/psblas/psb_saxpby.f90 b/base/psblas/psb_saxpby.f90 index 26cecd30..d3f573dc 100644 --- a/base/psblas/psb_saxpby.f90 +++ b/base/psblas/psb_saxpby.f90 @@ -31,6 +31,23 @@ ! ! File: psb_saxpby.f90 +! +! Subroutine: psb_saxpby_vect +! Adds one distributed vector to another, +! +! Y := beta * Y + alpha * X +! +! Arguments: +! alpha - real,input The scalar used to multiply each component of X +! x - type(psb_s_vect_type) The input vector containing the entries of X +! beta - real,input The scalar used to multiply each component of Y +! y - type(psb_s_vect_type) The input/output vector Y +! desc_a - type(psb_desc_type) The communication descriptor. +! info - integer Return code +! +! Note: from a functional point of view, X is input, but here +! it's declared INOUT because of the sync() methods. +! subroutine psb_saxpby_vect(alpha, x, beta, y,& & desc_a, info) use psb_base_mod, psb_protect_name => psb_saxpby_vect @@ -269,7 +286,7 @@ end subroutine psb_saxpby !!$ ! ! Subroutine: psb_saxpbyv -! Adds one distributed matrix to another, +! Adds one distributed vector to another, ! ! Y := beta * Y + alpha * X ! diff --git a/base/psblas/psb_sdot.f90 b/base/psblas/psb_sdot.f90 index 2c8bea51..cce9e15c 100644 --- a/base/psblas/psb_sdot.f90 +++ b/base/psblas/psb_sdot.f90 @@ -31,22 +31,22 @@ ! ! File: psb_sdot.f90 ! -! Function: psb_sdot -! psb_sdot forms the dot product of two distributed vectors, +! Function: psb_sdot_vect +! psb_sdot computes the dot product of two distributed vectors, ! -! dot := sub( X )**C * sub( Y ) +! dot := ( X )**C * ( Y ) ! -! where sub( X ) denotes X(:,JX) -! -! sub( Y ) denotes Y(:,JY). ! ! Arguments: -! x(:,:) - complex The input vector containing the entries of sub( X ). -! y(:,:) - complex The input vector containing the entries of sub( Y ). +! x - type(psb_s_vect_type) The input vector containing the entries of sub( X ). +! y - type(psb_s_vect_type) The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code -! jx - integer(optional). The column offset for sub( X ). -! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! +! Note: from a functional point of view, X and Y are input, but here +! they are declared INOUT because of the sync() methods. +! ! function psb_sdot_vect(x, y, desc_a,info,global) result(res) use psb_desc_mod @@ -156,7 +156,25 @@ function psb_sdot_vect(x, y, desc_a,info,global) result(res) return end function psb_sdot_vect - +! +! Function: psb_sdot +! psb_sdot computes the dot product of two distributed vectors, +! +! dot := sub( X )**C * sub( Y ) +! +! where sub( X ) denotes X(:,JX) +! +! sub( Y ) denotes Y(:,JY). +! +! Arguments: +! x(:,:) - real The input vector containing the entries of sub( X ). +! y(:,:) - real The input vector containing the entries of sub( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset for sub( X ). +! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! function psb_sdot(x, y,desc_a, info, jx, jy,global) result(res) use psb_base_mod, psb_protect_name => psb_sdot implicit none @@ -298,7 +316,7 @@ end function psb_sdot !!$ ! ! Function: psb_sdotv -! psb_sdotv forms the dot product of two distributed vectors, +! psb_sdotv computes the dot product of two distributed vectors, ! ! dot := X**C * Y ! @@ -307,6 +325,7 @@ end function psb_sdot ! y(:) - real The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! function psb_sdotv(x, y,desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_sdotv @@ -432,7 +451,7 @@ end function psb_sdotv !!$ ! ! Subroutine: psb_sdotvs -! psb_sdotvs forms the dot product of two distributed vectors, +! psb_sdotvs computes the dot product of two distributed vectors, ! ! res := X**C * Y ! @@ -442,6 +461,7 @@ end function psb_sdotv ! y(:) - real The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_sdotvs(res, x, y,desc_a, info,global) use psb_base_mod, psb_protect_name => psb_sdotvs @@ -565,7 +585,7 @@ end subroutine psb_sdotvs !!$ ! ! Subroutine: psb_smdots -! psb_smdots forms the dot product of multiple distributed vectors, +! psb_smdots computes the dot product of multiple distributed vectors, ! ! res(i) := ( X(:,i) )**C * ( Y(:,i) ) ! @@ -575,6 +595,7 @@ end subroutine psb_sdotvs ! y(:) - real The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_smdots(res, x, y, desc_a, info,global) use psb_base_mod, psb_protect_name => psb_smdots diff --git a/base/psblas/psb_snrm2.f90 b/base/psblas/psb_snrm2.f90 index d182a2cd..35260ef7 100644 --- a/base/psblas/psb_snrm2.f90 +++ b/base/psblas/psb_snrm2.f90 @@ -32,9 +32,9 @@ ! File: psb_snrm2.f90 ! ! Function: psb_snrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( sub( X )**T * sub( X ) ) +! norm2 := sqrt ( sub( X )**C * sub( X ) ) ! ! where sub( X ) denotes X(:,JX). ! @@ -43,6 +43,7 @@ ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The column offset for sub( X ). +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_snrm2(x, desc_a, info, jx,global) result(res) use psb_desc_mod @@ -170,14 +171,15 @@ end function psb_snrm2 !!$ ! ! Function: psb_snrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! x(:) - real The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_snrm2v(x, desc_a, info,global) result(res) use psb_desc_mod @@ -263,7 +265,17 @@ function psb_snrm2v(x, desc_a, info,global) result(res) end function psb_snrm2v - +! Function: psb_snrm2_vect +! Computes the norm2 of a distributed vector, +! +! norm2 := sqrt ( X**C * X) +! +! Arguments: +! x - type(psb_s_vect_type) The input vector containing the entries of X. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. +! function psb_snrm2_vect(x, desc_a, info,global) result(res) use psb_desc_mod use psb_check_mod @@ -344,7 +356,7 @@ function psb_snrm2_vect(x, desc_a, info,global) result(res) res = res - sqrt(sone - dd*(abs(x%v%v(idx))/res)**2) end do end if - else + else res = szero end if @@ -392,15 +404,16 @@ end function psb_snrm2_vect !!$ ! ! Subroutine: psb_snrm2vs -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, subroutine version ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! res - real The result. ! x(:) - real The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! subroutine psb_snrm2vs(res, x, desc_a, info,global) use psb_desc_mod diff --git a/base/psblas/psb_snrmi.f90 b/base/psblas/psb_snrmi.f90 index 07b88de2..9fc41073 100644 --- a/base/psblas/psb_snrmi.f90 +++ b/base/psblas/psb_snrmi.f90 @@ -32,14 +32,15 @@ ! File: psb_snrmi.f90 ! ! Function: psb_snrmi -! Forms the infinity norm of a sparse matrix, +! Computes the infinity norm of a sparse matrix, ! -! nrmi := max_i(abs(sum(A(i,:)))) +! nrmi := max_i(sum(abs(A(i,:)))) ! ! Arguments: ! a - type(psb_sspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_snrmi(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_snrmi diff --git a/base/psblas/psb_sspmm.f90 b/base/psblas/psb_sspmm.f90 index a84962dc..56b881b8 100644 --- a/base/psblas/psb_sspmm.f90 +++ b/base/psblas/psb_sspmm.f90 @@ -31,6 +31,235 @@ ! ! File: psb_sspmm.f90 ! +! +! Subroutine: psb_sspm_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A' * Pr * X + beta * Y, +! +! alpha and beta are scalars, X and Y are distributed +! vectors and A is a M-by-N distributed matrix. +! +! Arguments: +! alpha - real The scalar alpha. +! a - type(psb_sspmat_type). The sparse matrix containing A. +! x - type(psb_s_vect_type) The input vector containing the entries of ( X ). +! beta - real The scalar beta. +! y - type(psb_s_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. Default: 'N' +! work(:) - real,(optional). Working area. +! doswap - logical(optional). Whether to performe halo updates. +! +subroutine psb_sspmv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, work, doswap) + use psb_base_mod, psb_protect_name => psb_sspmv_vect + use psi_mod + implicit none + + real(psb_spk_), intent(in) :: alpha, beta + type(psb_s_vect_type), intent(inout) :: x + type(psb_s_vect_type), intent(inout) :: y + type(psb_sspmat_type), intent(in) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + real(psb_spk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans + logical, intent(in), optional :: doswap + + ! locals + integer(psb_ipk_) :: ictxt, np, me,& + & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & + & liwork, iiy, jjy, ib, ip, idx + integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja + integer(psb_ipk_), parameter :: nb=4 + real(psb_spk_), pointer :: iwork(:), xp(:), yp(:) + real(psb_spk_), allocatable :: xvsave(:) + character :: trans_ + character(len=20) :: name, ch_err + logical :: aliw, doswap_ + integer(psb_ipk_) :: debug_level, debug_unit + + name='psb_sspmv' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + debug_unit = psb_get_debug_unit() + debug_level = psb_get_debug_level() + + ictxt=desc_a%get_context() + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + if (present(doswap)) then + doswap_ = doswap + else + doswap_ = .true. + endif + + if (present(trans)) then + trans_ = psb_toupper(trans) + else + trans_ = 'N' + endif + if ( (trans_ == 'N').or.(trans_ == 'T')& + & .or.(trans_ == 'C')) then + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + + m = desc_a%get_global_rows() + n = desc_a%get_global_cols() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info + + if (trans_ == 'N') then + ! Matrix is not transposed + + if (doswap_) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & szero,x%v,desc_a,iwork,info,data=psb_comm_halo_) + end if + + call psb_csmm(alpha,a,x,beta,y,info) + + if(info /= psb_success_) then + info = psb_err_from_subroutine_non_ + call psb_errpush(info,name) + goto 9999 + end if + + else + ! Matrix is transposed + + ! + ! Non-empty overlap, need a buffer to hold + ! the entries updated with average operator. + ! Why the average? because in this way they will contribute + ! with a proper scale factor (1/np) to the overall product. + ! + call psi_ovrl_save(x%v,xvsave,desc_a,info) + if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) + + if (beta /= szero) call y%set(szero,nrow+1,ncol) + ! local Matrix-vector product + if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' csmm ', info + + if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) + if (info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='psb_csmm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + if (doswap_) then + call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& + & sone,y%v,desc_a,iwork,info) + if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & sone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' swaptran ', info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='PSI_SwapTran' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + end if + + end if + + if (aliw) deallocate(iwork,stat=info) + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='Deallocate iwork' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + nullify(iwork) + + call psb_erractionrestore(err_act) + if (debug_level >= psb_debug_comp_) then + call psb_barrier(ictxt) + write(debug_unit,*) me,' ',trim(name),' Returning ' + endif + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_sspmv_vect +! ! Subroutine: psb_sspmm ! Performs one of the distributed matrix-vector operations ! @@ -356,10 +585,6 @@ subroutine psb_sspmm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_sspmm - - - - !!$ !!$ Parallel Sparse BLAS version 3.5 !!$ (C) Copyright 2006-2018 @@ -670,211 +895,3 @@ subroutine psb_sspmv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_sspmv - - - -subroutine psb_sspmv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, work, doswap) - use psb_base_mod, psb_protect_name => psb_sspmv_vect - use psi_mod - implicit none - - real(psb_spk_), intent(in) :: alpha, beta - type(psb_s_vect_type), intent(inout) :: x - type(psb_s_vect_type), intent(inout) :: y - type(psb_sspmat_type), intent(in) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - real(psb_spk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans - logical, intent(in), optional :: doswap - - ! locals - integer(psb_ipk_) :: ictxt, np, me,& - & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & - & liwork, iiy, jjy, ib, ip, idx - integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja - integer(psb_ipk_), parameter :: nb=4 - real(psb_spk_), pointer :: iwork(:), xp(:), yp(:) - real(psb_spk_), allocatable :: xvsave(:) - character :: trans_ - character(len=20) :: name, ch_err - logical :: aliw, doswap_ - integer(psb_ipk_) :: debug_level, debug_unit - - name='psb_sspmv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - debug_unit = psb_get_debug_unit() - debug_level = psb_get_debug_level() - - ictxt=desc_a%get_context() - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - if (present(doswap)) then - doswap_ = doswap - else - doswap_ = .true. - endif - - if (present(trans)) then - trans_ = psb_toupper(trans) - else - trans_ = 'N' - endif - if ( (trans_ == 'N').or.(trans_ == 'T')& - & .or.(trans_ == 'C')) then - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - - m = desc_a%get_global_rows() - n = desc_a%get_global_cols() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='Allocate' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info - - if (trans_ == 'N') then - ! Matrix is not transposed - - if (doswap_) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & szero,x%v,desc_a,iwork,info,data=psb_comm_halo_) - end if - - call psb_csmm(alpha,a,x,beta,y,info) - - if(info /= psb_success_) then - info = psb_err_from_subroutine_non_ - call psb_errpush(info,name) - goto 9999 - end if - - else - ! Matrix is transposed - - ! - ! Non-empty overlap, need a buffer to hold - ! the entries updated with average operator. - ! Why the average? because in this way they will contribute - ! with a proper scale factor (1/np) to the overall product. - ! - call psi_ovrl_save(x%v,xvsave,desc_a,info) - if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) - - if (beta /= szero) call y%set(szero,nrow+1,ncol) - ! local Matrix-vector product - if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' csmm ', info - - if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) - if (info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='psb_csmm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - if (doswap_) then - call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& - & sone,y%v,desc_a,iwork,info) - if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & sone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' swaptran ', info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='PSI_SwapTran' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - end if - - end if - - if (aliw) deallocate(iwork,stat=info) - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='Deallocate iwork' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - nullify(iwork) - - call psb_erractionrestore(err_act) - if (debug_level >= psb_debug_comp_) then - call psb_barrier(ictxt) - write(debug_unit,*) me,' ',trim(name),' Returning ' - endif - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_sspmv_vect diff --git a/base/psblas/psb_sspnrm1.f90 b/base/psblas/psb_sspnrm1.f90 index 391d60ee..9d2afeb8 100644 --- a/base/psblas/psb_sspnrm1.f90 +++ b/base/psblas/psb_sspnrm1.f90 @@ -40,6 +40,7 @@ ! a - type(psb_sspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_sspnrm1(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_sspnrm1 diff --git a/base/psblas/psb_sspsm.f90 b/base/psblas/psb_sspsm.f90 index 8bcfdcad..1cbbd6d2 100644 --- a/base/psblas/psb_sspsm.f90 +++ b/base/psblas/psb_sspsm.f90 @@ -31,6 +31,203 @@ ! ! File: psb_sspsm.f90 ! +! +! Subroutine: psb_ssps_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-1 * Pc * D * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * D * X + beta * Y, or +! +! X is a distributed +! vector and T is a M-by-M distributed triangular matrix. +! +! +! Arguments: +! alpha - real. The scalar alpha. +! a - type(psb_sspmat_type). The sparse matrix containing A. +! x - type(psb_s_vect_type) The input vector containing the entries of ( X ). +! beta - real The scalar beta. +! y - type(psb_s_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. If not present 'N' is assumed. +! scale - character(optional). Specify some type of operation with +! the diagonal matrix D. +! choice - integer(optional). The kind of update to perform on overlap elements. +! d(:) - real, optional Matrix for diagonal scaling. +! work(:) - real, optional Working area. +! +subroutine psb_sspsv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, scale, choice, diag, work) + use psb_base_mod, psb_protect_name => psb_sspsv_vect + use psi_mod + implicit none + + real(psb_spk_), intent(in) :: alpha, beta + type(psb_s_vect_type), intent(inout) :: x + type(psb_s_vect_type), intent(inout) :: y + type(psb_sspmat_type), intent(inout) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + type(psb_s_vect_type), intent(inout), optional :: diag + real(psb_spk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans, scale + integer(psb_ipk_), intent(in), optional :: choice + + ! locals + integer(psb_ipk_) :: ictxt, np, me, & + & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& + & ix, iy, ik, jx, jy, i, lld,& + & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm + + character :: lscale + integer(psb_ipk_), parameter :: nb=4 + real(psb_spk_),pointer :: iwork(:), xp(:), yp(:) + character :: itrans + character(len=20) :: name, ch_err + logical :: aliw + + name='psb_sspsv_vect' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + + ictxt=desc_a%get_context() + + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + + if (present(choice)) then + choice_ = choice + else + choice_ = psb_avg_ + endif + + if (present(scale)) then + lscale = psb_toupper(scale) + else + lscale = 'U' + endif + + if (present(trans)) then + itrans = psb_toupper(trans) + if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then + ! Ok + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + else + itrans = 'N' + endif + + m = desc_a%get_global_rows() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + iwork(1)=0.d0 + + ! Perform local triangular system solve + if (present(diag)) then + call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) + else + call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) + end if + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='dcssm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + ! update overlap elements + if (choice_ > 0) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & sone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + + if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') + goto 9999 + end if + end if + + if (aliw) deallocate(iwork) + + call psb_erractionrestore(err_act) + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_sspsv_vect +! ! Subroutine: psb_sspsm ! Performs one of the distributed matrix-vector operations ! @@ -283,38 +480,6 @@ subroutine psb_sspsm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_sspsm - -!!$ -!!$ Parallel Sparse BLAS version 3.5 -!!$ (C) Copyright 2006-2018 -!!$ Salvatore Filippone University of Rome Tor Vergata -!!$ Alfredo Buttari -!!$ -!!$ Redistribution and use in source and binary forms, with or without -!!$ modification, are permitted provided that the following conditions -!!$ are met: -!!$ 1. Redistributions of source code must retain the above copyright -!!$ notice, this list of conditions and the following disclaimer. -!!$ 2. Redistributions in binary form must reproduce the above copyright -!!$ notice, this list of conditions, and the following disclaimer in the -!!$ documentation and/or other materials provided with the distribution. -!!$ 3. The name of the PSBLAS group or the names of its contributors may -!!$ not be used to endorse or promote products derived from this -!!$ software without specific written permission. -!!$ -!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED -!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS -!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR -!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF -!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS -!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN -!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) -!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -!!$ POSSIBILITY OF SUCH DAMAGE. -!!$ -!!$ ! ! Subroutine: psb_sspsv ! Performs one of the distributed matrix-vector operations @@ -545,166 +710,3 @@ subroutine psb_sspsv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_sspsv - -subroutine psb_sspsv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, scale, choice, diag, work) - use psb_base_mod, psb_protect_name => psb_sspsv_vect - use psi_mod - implicit none - - real(psb_spk_), intent(in) :: alpha, beta - type(psb_s_vect_type), intent(inout) :: x - type(psb_s_vect_type), intent(inout) :: y - type(psb_sspmat_type), intent(inout) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - type(psb_s_vect_type), intent(inout), optional :: diag - real(psb_spk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans, scale - integer(psb_ipk_), intent(in), optional :: choice - - ! locals - integer(psb_ipk_) :: ictxt, np, me, & - & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& - & ix, iy, ik, jx, jy, i, lld,& - & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm - - character :: lscale - integer(psb_ipk_), parameter :: nb=4 - real(psb_spk_),pointer :: iwork(:), xp(:), yp(:) - character :: itrans - character(len=20) :: name, ch_err - logical :: aliw - - name='psb_sspsv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - - ictxt=desc_a%get_context() - - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - - if (present(choice)) then - choice_ = choice - else - choice_ = psb_avg_ - endif - - if (present(scale)) then - lscale = psb_toupper(scale) - else - lscale = 'U' - endif - - if (present(trans)) then - itrans = psb_toupper(trans) - if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then - ! Ok - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - else - itrans = 'N' - endif - - m = desc_a%get_global_rows() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - iwork(1)=0.d0 - - ! Perform local triangular system solve - if (present(diag)) then - call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) - else - call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) - end if - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='dcssm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - ! update overlap elements - if (choice_ > 0) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & sone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - - if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') - goto 9999 - end if - end if - - if (aliw) deallocate(iwork) - - call psb_erractionrestore(err_act) - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_sspsv_vect - diff --git a/base/psblas/psb_zamax.f90 b/base/psblas/psb_zamax.f90 index 21a82b39..5e768023 100644 --- a/base/psblas/psb_zamax.f90 +++ b/base/psblas/psb_zamax.f90 @@ -32,7 +32,7 @@ ! File: psb_zamax.f90 ! ! Function: psb_zamax -! Searches the absolute max of X. +! Computes the maximum absolute value of X ! ! normi := max(abs(sub(X)(i)) ! @@ -164,7 +164,7 @@ end function psb_zamax !!$ ! ! Function: psb_zamaxv -! Searches the absolute max of X. +! Computes the maximum absolute value of X. ! ! normi := max(abs(X(i)) ! @@ -252,6 +252,17 @@ function psb_zamaxv (x,desc_a, info,global) result(res) return end function psb_zamaxv +! +! Function: psb_zamax_vect +! Computes the maximum absolute value of X. +! +! normi := max(abs(X(i)) +! +! Arguments: +! x - type(psb_z_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! function psb_zamax_vect(x, desc_a, info,global) result(res) use psb_penv_mod @@ -374,17 +385,16 @@ end function psb_zamax_vect !!$ ! ! Subroutine: psb_zamaxvs -! Searches the absolute max of X. +! Computes the maximum absolute value of X, subroutine version ! ! normi := max(abs(sub(X)(i)) ! -! where sub( X ) denotes X(1:N,JX:). +! where sub( X ) denotes X(1:N). ! ! Arguments: ! res - real The result. -! x(:,:) - complex The input vector. +! x(:) - complex The input vector. ! desc_a - type(psb_desc_type). The communication descriptor. -! info - integer. Return code ! jx - integer(optional). The column offset. ! subroutine psb_zamaxvs(res,x,desc_a, info,global) diff --git a/base/psblas/psb_zasum.f90 b/base/psblas/psb_zasum.f90 index 6bfd01ca..9b6fddd7 100644 --- a/base/psblas/psb_zasum.f90 +++ b/base/psblas/psb_zasum.f90 @@ -135,6 +135,19 @@ function psb_zasum (x,desc_a, info, jx,global) result(res) return end function psb_zasum +! Function: psb_zasum_vect +! Computes norm1 of X +! +! norm1 := sum(sub( X )(i)) +! +! where sub( X ) denotes X(1:N,JX:). +! +! Arguments: +! x - type(psb_z_vect_type) The input vector. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset. +! function psb_zasum_vect(x, desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_zasum_vect diff --git a/base/psblas/psb_zaxpby.f90 b/base/psblas/psb_zaxpby.f90 index 273aa882..b48bb5ff 100644 --- a/base/psblas/psb_zaxpby.f90 +++ b/base/psblas/psb_zaxpby.f90 @@ -31,6 +31,23 @@ ! ! File: psb_zaxpby.f90 +! +! Subroutine: psb_zaxpby_vect +! Adds one distributed vector to another, +! +! Y := beta * Y + alpha * X +! +! Arguments: +! alpha - complex,input The scalar used to multiply each component of X +! x - type(psb_z_vect_type) The input vector containing the entries of X +! beta - complex,input The scalar used to multiply each component of Y +! y - type(psb_z_vect_type) The input/output vector Y +! desc_a - type(psb_desc_type) The communication descriptor. +! info - integer Return code +! +! Note: from a functional point of view, X is input, but here +! it's declared INOUT because of the sync() methods. +! subroutine psb_zaxpby_vect(alpha, x, beta, y,& & desc_a, info) use psb_base_mod, psb_protect_name => psb_zaxpby_vect @@ -269,7 +286,7 @@ end subroutine psb_zaxpby !!$ ! ! Subroutine: psb_zaxpbyv -! Adds one distributed matrix to another, +! Adds one distributed vector to another, ! ! Y := beta * Y + alpha * X ! diff --git a/base/psblas/psb_zdot.f90 b/base/psblas/psb_zdot.f90 index 8f673c02..ad21b1d8 100644 --- a/base/psblas/psb_zdot.f90 +++ b/base/psblas/psb_zdot.f90 @@ -31,22 +31,22 @@ ! ! File: psb_zdot.f90 ! -! Function: psb_zdot -! psb_zdot forms the dot product of two distributed vectors, +! Function: psb_zdot_vect +! psb_zdot computes the dot product of two distributed vectors, ! -! dot := sub( X )**C * sub( Y ) +! dot := ( X )**C * ( Y ) ! -! where sub( X ) denotes X(:,JX) -! -! sub( Y ) denotes Y(:,JY). ! ! Arguments: -! x(:,:) - complex The input vector containing the entries of sub( X ). -! y(:,:) - complex The input vector containing the entries of sub( Y ). +! x - type(psb_z_vect_type) The input vector containing the entries of sub( X ). +! y - type(psb_z_vect_type) The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code -! jx - integer(optional). The column offset for sub( X ). -! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! +! Note: from a functional point of view, X and Y are input, but here +! they are declared INOUT because of the sync() methods. +! ! function psb_zdot_vect(x, y, desc_a,info,global) result(res) use psb_desc_mod @@ -156,7 +156,25 @@ function psb_zdot_vect(x, y, desc_a,info,global) result(res) return end function psb_zdot_vect - +! +! Function: psb_zdot +! psb_zdot computes the dot product of two distributed vectors, +! +! dot := sub( X )**C * sub( Y ) +! +! where sub( X ) denotes X(:,JX) +! +! sub( Y ) denotes Y(:,JY). +! +! Arguments: +! x(:,:) - complex The input vector containing the entries of sub( X ). +! y(:,:) - complex The input vector containing the entries of sub( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! jx - integer(optional). The column offset for sub( X ). +! jy - integer(optional). The column offset for sub( Y ). +! global - logical(optional) Whether to perform the global sum, default: .true. +! function psb_zdot(x, y,desc_a, info, jx, jy,global) result(res) use psb_base_mod, psb_protect_name => psb_zdot implicit none @@ -298,7 +316,7 @@ end function psb_zdot !!$ ! ! Function: psb_zdotv -! psb_zdotv forms the dot product of two distributed vectors, +! psb_zdotv computes the dot product of two distributed vectors, ! ! dot := X**C * Y ! @@ -307,6 +325,7 @@ end function psb_zdot ! y(:) - complex The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! function psb_zdotv(x, y,desc_a, info,global) result(res) use psb_base_mod, psb_protect_name => psb_zdotv @@ -432,7 +451,7 @@ end function psb_zdotv !!$ ! ! Subroutine: psb_zdotvs -! psb_zdotvs forms the dot product of two distributed vectors, +! psb_zdotvs computes the dot product of two distributed vectors, ! ! res := X**C * Y ! @@ -442,6 +461,7 @@ end function psb_zdotv ! y(:) - complex The input vector containing the entries of Y. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_zdotvs(res, x, y,desc_a, info,global) use psb_base_mod, psb_protect_name => psb_zdotvs @@ -565,7 +585,7 @@ end subroutine psb_zdotvs !!$ ! ! Subroutine: psb_zmdots -! psb_zmdots forms the dot product of multiple distributed vectors, +! psb_zmdots computes the dot product of multiple distributed vectors, ! ! res(i) := ( X(:,i) )**C * ( Y(:,i) ) ! @@ -575,6 +595,7 @@ end subroutine psb_zdotvs ! y(:) - complex The input vector containing the entries of sub( Y ). ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global sum, default: .true. ! subroutine psb_zmdots(res, x, y, desc_a, info,global) use psb_base_mod, psb_protect_name => psb_zmdots diff --git a/base/psblas/psb_znrm2.f90 b/base/psblas/psb_znrm2.f90 index 1e1cac26..9f327773 100644 --- a/base/psblas/psb_znrm2.f90 +++ b/base/psblas/psb_znrm2.f90 @@ -32,9 +32,9 @@ ! File: psb_znrm2.f90 ! ! Function: psb_znrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( sub( X )**T * sub( X ) ) +! norm2 := sqrt ( sub( X )**C * sub( X ) ) ! ! where sub( X ) denotes X(:,JX). ! @@ -43,6 +43,7 @@ ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code ! jx - integer(optional). The column offset for sub( X ). +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_znrm2(x, desc_a, info, jx,global) result(res) use psb_desc_mod @@ -170,14 +171,15 @@ end function psb_znrm2 !!$ ! ! Function: psb_znrm2 -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! x(:) - complex The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_znrm2v(x, desc_a, info,global) result(res) use psb_desc_mod @@ -263,7 +265,17 @@ function psb_znrm2v(x, desc_a, info,global) result(res) end function psb_znrm2v - +! Function: psb_znrm2_vect +! Computes the norm2 of a distributed vector, +! +! norm2 := sqrt ( X**C * X) +! +! Arguments: +! x - type(psb_z_vect_type) The input vector containing the entries of X. +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. +! function psb_znrm2_vect(x, desc_a, info,global) result(res) use psb_desc_mod use psb_check_mod @@ -344,7 +356,7 @@ function psb_znrm2_vect(x, desc_a, info,global) result(res) res = res - sqrt(zone - dd*(abs(x%v%v(idx))/res)**2) end do end if - else + else res = dzero end if @@ -392,15 +404,16 @@ end function psb_znrm2_vect !!$ ! ! Subroutine: psb_znrm2vs -! Forms the norm2 of a distributed vector, +! Computes the norm2 of a distributed vector, subroutine version ! -! norm2 := sqrt ( X**T * X) +! norm2 := sqrt ( X**C * X) ! ! Arguments: ! res - real The result. ! x(:) - complex The input vector containing the entries of X. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! subroutine psb_znrm2vs(res, x, desc_a, info,global) use psb_desc_mod diff --git a/base/psblas/psb_znrmi.f90 b/base/psblas/psb_znrmi.f90 index 9e0440ff..19b071e4 100644 --- a/base/psblas/psb_znrmi.f90 +++ b/base/psblas/psb_znrmi.f90 @@ -32,14 +32,15 @@ ! File: psb_znrmi.f90 ! ! Function: psb_znrmi -! Forms the infinity norm of a sparse matrix, +! Computes the infinity norm of a sparse matrix, ! -! nrmi := max_i(abs(sum(A(i,:)))) +! nrmi := max_i(sum(abs(A(i,:)))) ! ! Arguments: ! a - type(psb_zspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_znrmi(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_znrmi diff --git a/base/psblas/psb_zspmm.f90 b/base/psblas/psb_zspmm.f90 index 83c42bc0..add3205b 100644 --- a/base/psblas/psb_zspmm.f90 +++ b/base/psblas/psb_zspmm.f90 @@ -31,6 +31,235 @@ ! ! File: psb_zspmm.f90 ! +! +! Subroutine: psb_zspm_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A' * Pr * X + beta * Y, +! +! alpha and beta are scalars, X and Y are distributed +! vectors and A is a M-by-N distributed matrix. +! +! Arguments: +! alpha - complex The scalar alpha. +! a - type(psb_zspmat_type). The sparse matrix containing A. +! x - type(psb_z_vect_type) The input vector containing the entries of ( X ). +! beta - complex The scalar beta. +! y - type(psb_z_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. Default: 'N' +! work(:) - complex,(optional). Working area. +! doswap - logical(optional). Whether to performe halo updates. +! +subroutine psb_zspmv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, work, doswap) + use psb_base_mod, psb_protect_name => psb_zspmv_vect + use psi_mod + implicit none + + complex(psb_dpk_), intent(in) :: alpha, beta + type(psb_z_vect_type), intent(inout) :: x + type(psb_z_vect_type), intent(inout) :: y + type(psb_zspmat_type), intent(in) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + complex(psb_dpk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans + logical, intent(in), optional :: doswap + + ! locals + integer(psb_ipk_) :: ictxt, np, me,& + & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & + & liwork, iiy, jjy, ib, ip, idx + integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja + integer(psb_ipk_), parameter :: nb=4 + complex(psb_dpk_), pointer :: iwork(:), xp(:), yp(:) + complex(psb_dpk_), allocatable :: xvsave(:) + character :: trans_ + character(len=20) :: name, ch_err + logical :: aliw, doswap_ + integer(psb_ipk_) :: debug_level, debug_unit + + name='psb_zspmv' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + debug_unit = psb_get_debug_unit() + debug_level = psb_get_debug_level() + + ictxt=desc_a%get_context() + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + if (present(doswap)) then + doswap_ = doswap + else + doswap_ = .true. + endif + + if (present(trans)) then + trans_ = psb_toupper(trans) + else + trans_ = 'N' + endif + if ( (trans_ == 'N').or.(trans_ == 'T')& + & .or.(trans_ == 'C')) then + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + + m = desc_a%get_global_rows() + n = desc_a%get_global_cols() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='Allocate' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info + + if (trans_ == 'N') then + ! Matrix is not transposed + + if (doswap_) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & zzero,x%v,desc_a,iwork,info,data=psb_comm_halo_) + end if + + call psb_csmm(alpha,a,x,beta,y,info) + + if(info /= psb_success_) then + info = psb_err_from_subroutine_non_ + call psb_errpush(info,name) + goto 9999 + end if + + else + ! Matrix is transposed + + ! + ! Non-empty overlap, need a buffer to hold + ! the entries updated with average operator. + ! Why the average? because in this way they will contribute + ! with a proper scale factor (1/np) to the overall product. + ! + call psi_ovrl_save(x%v,xvsave,desc_a,info) + if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) + + if (beta /= zzero) call y%set(zzero,nrow+1,ncol) + ! local Matrix-vector product + if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' csmm ', info + + if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) + if (info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='psb_csmm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + if (doswap_) then + call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& + & zone,y%v,desc_a,iwork,info) + if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & zone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' swaptran ', info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='PSI_SwapTran' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + end if + + end if + + if (aliw) deallocate(iwork,stat=info) + if (debug_level >= psb_debug_comp_) & + & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='Deallocate iwork' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + nullify(iwork) + + call psb_erractionrestore(err_act) + if (debug_level >= psb_debug_comp_) then + call psb_barrier(ictxt) + write(debug_unit,*) me,' ',trim(name),' Returning ' + endif + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_zspmv_vect +! ! Subroutine: psb_zspmm ! Performs one of the distributed matrix-vector operations ! @@ -356,10 +585,6 @@ subroutine psb_zspmm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_zspmm - - - - !!$ !!$ Parallel Sparse BLAS version 3.5 !!$ (C) Copyright 2006-2018 @@ -670,211 +895,3 @@ subroutine psb_zspmv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_zspmv - - - -subroutine psb_zspmv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, work, doswap) - use psb_base_mod, psb_protect_name => psb_zspmv_vect - use psi_mod - implicit none - - complex(psb_dpk_), intent(in) :: alpha, beta - type(psb_z_vect_type), intent(inout) :: x - type(psb_z_vect_type), intent(inout) :: y - type(psb_zspmat_type), intent(in) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - complex(psb_dpk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans - logical, intent(in), optional :: doswap - - ! locals - integer(psb_ipk_) :: ictxt, np, me,& - & err_act, iix, jjx, iia, jja, nrow, ncol, lldx, lldy, & - & liwork, iiy, jjy, ib, ip, idx - integer(psb_lpk_) :: ix, ijx, iy, ijy, m, n, ia, ja - integer(psb_ipk_), parameter :: nb=4 - complex(psb_dpk_), pointer :: iwork(:), xp(:), yp(:) - complex(psb_dpk_), allocatable :: xvsave(:) - character :: trans_ - character(len=20) :: name, ch_err - logical :: aliw, doswap_ - integer(psb_ipk_) :: debug_level, debug_unit - - name='psb_zspmv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - debug_unit = psb_get_debug_unit() - debug_level = psb_get_debug_level() - - ictxt=desc_a%get_context() - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - if (present(doswap)) then - doswap_ = doswap - else - doswap_ = .true. - endif - - if (present(trans)) then - trans_ = psb_toupper(trans) - else - trans_ = 'N' - endif - if ( (trans_ == 'N').or.(trans_ == 'T')& - & .or.(trans_ == 'C')) then - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - - m = desc_a%get_global_rows() - n = desc_a%get_global_cols() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='Allocate' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' Allocated work ', info - - if (trans_ == 'N') then - ! Matrix is not transposed - - if (doswap_) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & zzero,x%v,desc_a,iwork,info,data=psb_comm_halo_) - end if - - call psb_csmm(alpha,a,x,beta,y,info) - - if(info /= psb_success_) then - info = psb_err_from_subroutine_non_ - call psb_errpush(info,name) - goto 9999 - end if - - else - ! Matrix is transposed - - ! - ! Non-empty overlap, need a buffer to hold - ! the entries updated with average operator. - ! Why the average? because in this way they will contribute - ! with a proper scale factor (1/np) to the overall product. - ! - call psi_ovrl_save(x%v,xvsave,desc_a,info) - if (info == psb_success_) call psi_ovrl_upd(x%v,desc_a,psb_avg_,info) - - if (beta /= zzero) call y%set(zzero,nrow+1,ncol) - ! local Matrix-vector product - if (info == psb_success_) call psb_csmm(alpha,a,x,beta,y,info,trans=trans_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' csmm ', info - - if (info == psb_success_) call psi_ovrl_restore(x%v,xvsave,desc_a,info) - if (info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='psb_csmm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - if (doswap_) then - call psi_swaptran(ior(psb_swap_send_,psb_swap_recv_),& - & zone,y%v,desc_a,iwork,info) - if (info == psb_success_) call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & zone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' swaptran ', info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='PSI_SwapTran' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - end if - - end if - - if (aliw) deallocate(iwork,stat=info) - if (debug_level >= psb_debug_comp_) & - & write(debug_unit,*) me,' ',trim(name),' deallocat ',aliw, info - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='Deallocate iwork' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - nullify(iwork) - - call psb_erractionrestore(err_act) - if (debug_level >= psb_debug_comp_) then - call psb_barrier(ictxt) - write(debug_unit,*) me,' ',trim(name),' Returning ' - endif - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_zspmv_vect diff --git a/base/psblas/psb_zspnrm1.f90 b/base/psblas/psb_zspnrm1.f90 index 3c292a74..7bc5fa15 100644 --- a/base/psblas/psb_zspnrm1.f90 +++ b/base/psblas/psb_zspnrm1.f90 @@ -40,6 +40,7 @@ ! a - type(psb_zspmat_type). The sparse matrix containing A. ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. Return code +! global - logical(optional) Whether to perform the global reduction, default: .true. ! function psb_zspnrm1(a,desc_a,info,global) result(res) use psb_base_mod, psb_protect_name => psb_zspnrm1 diff --git a/base/psblas/psb_zspsm.f90 b/base/psblas/psb_zspsm.f90 index 13e00d3f..63cbe783 100644 --- a/base/psblas/psb_zspsm.f90 +++ b/base/psblas/psb_zspsm.f90 @@ -31,6 +31,203 @@ ! ! File: psb_zspsm.f90 ! +! +! Subroutine: psb_zsps_vect +! Performs one of the distributed matrix-vector operations +! +! Y := alpha * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-1 * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-1 * Pc * D * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * D * Pr * A-T * Pc * X + beta * Y, or +! +! Y := alpha * Pr * A-T * Pc * D * X + beta * Y, or +! +! X is a distributed +! vector and T is a M-by-M distributed triangular matrix. +! +! +! Arguments: +! alpha - complex. The scalar alpha. +! a - type(psb_zspmat_type). The sparse matrix containing A. +! x - type(psb_z_vect_type) The input vector containing the entries of ( X ). +! beta - complex The scalar beta. +! y - type(psb_z_vect_type) The input vector containing the entries of ( Y ). +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. Return code +! trans - character(optional). Whether A or A'. If not present 'N' is assumed. +! scale - character(optional). Specify some type of operation with +! the diagonal matrix D. +! choice - integer(optional). The kind of update to perform on overlap elements. +! d(:) - complex, optional Matrix for diagonal scaling. +! work(:) - complex, optional Working area. +! +subroutine psb_zspsv_vect(alpha,a,x,beta,y,desc_a,info,& + & trans, scale, choice, diag, work) + use psb_base_mod, psb_protect_name => psb_zspsv_vect + use psi_mod + implicit none + + complex(psb_dpk_), intent(in) :: alpha, beta + type(psb_z_vect_type), intent(inout) :: x + type(psb_z_vect_type), intent(inout) :: y + type(psb_zspmat_type), intent(inout) :: a + type(psb_desc_type), intent(in) :: desc_a + integer(psb_ipk_), intent(out) :: info + type(psb_z_vect_type), intent(inout), optional :: diag + complex(psb_dpk_), optional, target, intent(inout) :: work(:) + character, intent(in), optional :: trans, scale + integer(psb_ipk_), intent(in), optional :: choice + + ! locals + integer(psb_ipk_) :: ictxt, np, me, & + & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& + & ix, iy, ik, jx, jy, i, lld,& + & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm + + character :: lscale + integer(psb_ipk_), parameter :: nb=4 + complex(psb_dpk_),pointer :: iwork(:), xp(:), yp(:) + character :: itrans + character(len=20) :: name, ch_err + logical :: aliw + + name='psb_zspsv_vect' + info=psb_success_ + call psb_erractionsave(err_act) + if (psb_errstatus_fatal()) then + info = psb_err_internal_error_ ; goto 9999 + end if + + ictxt=desc_a%get_context() + + call psb_info(ictxt, me, np) + if (np == -1) then + info = psb_err_context_error_ + call psb_errpush(info,name) + goto 9999 + endif + + if (.not.allocated(x%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + if (.not.allocated(y%v)) then + info = psb_err_invalid_vect_state_ + call psb_errpush(info,name) + goto 9999 + endif + + + if (present(choice)) then + choice_ = choice + else + choice_ = psb_avg_ + endif + + if (present(scale)) then + lscale = psb_toupper(scale) + else + lscale = 'U' + endif + + if (present(trans)) then + itrans = psb_toupper(trans) + if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then + ! Ok + else + info = psb_err_iarg_invalid_value_ + call psb_errpush(info,name) + goto 9999 + end if + else + itrans = 'N' + endif + + m = desc_a%get_global_rows() + nrow = desc_a%get_local_rows() + ncol = desc_a%get_local_cols() + lldx = x%get_nrows() + lldy = y%get_nrows() + if ((info == 0).and.(lldx null() + ! check for presence/size of a work area + liwork= 2*ncol + + if (present(work)) then + if (size(work) >= liwork) then + aliw =.false. + else + aliw=.true. + endif + else + aliw=.true. + end if + + if (aliw) then + allocate(iwork(liwork),stat=info) + if(info /= psb_success_) then + info=psb_err_from_subroutine_ + ch_err='psb_realloc' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + else + iwork => work + endif + + iwork(1)=0.d0 + + ! Perform local triangular system solve + if (present(diag)) then + call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) + else + call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) + end if + if(info /= psb_success_) then + info = psb_err_from_subroutine_ + ch_err='dcssm' + call psb_errpush(info,name,a_err=ch_err) + goto 9999 + end if + + ! update overlap elements + if (choice_ > 0) then + call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& + & zone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) + + + if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) + if (info /= psb_success_) then + call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') + goto 9999 + end if + end if + + if (aliw) deallocate(iwork) + + call psb_erractionrestore(err_act) + return + +9999 call psb_error_handler(ictxt,err_act) + + return +end subroutine psb_zspsv_vect +! ! Subroutine: psb_zspsm ! Performs one of the distributed matrix-vector operations ! @@ -283,38 +480,6 @@ subroutine psb_zspsm(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_zspsm - -!!$ -!!$ Parallel Sparse BLAS version 3.5 -!!$ (C) Copyright 2006-2018 -!!$ Salvatore Filippone University of Rome Tor Vergata -!!$ Alfredo Buttari -!!$ -!!$ Redistribution and use in source and binary forms, with or without -!!$ modification, are permitted provided that the following conditions -!!$ are met: -!!$ 1. Redistributions of source code must retain the above copyright -!!$ notice, this list of conditions and the following disclaimer. -!!$ 2. Redistributions in binary form must reproduce the above copyright -!!$ notice, this list of conditions, and the following disclaimer in the -!!$ documentation and/or other materials provided with the distribution. -!!$ 3. The name of the PSBLAS group or the names of its contributors may -!!$ not be used to endorse or promote products derived from this -!!$ software without specific written permission. -!!$ -!!$ THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS -!!$ ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED -!!$ TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR -!!$ PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE PSBLAS GROUP OR ITS CONTRIBUTORS -!!$ BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR -!!$ CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF -!!$ SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS -!!$ INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN -!!$ CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) -!!$ ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE -!!$ POSSIBILITY OF SUCH DAMAGE. -!!$ -!!$ ! ! Subroutine: psb_zspsv ! Performs one of the distributed matrix-vector operations @@ -545,166 +710,3 @@ subroutine psb_zspsv(alpha,a,x,beta,y,desc_a,info,& return end subroutine psb_zspsv - -subroutine psb_zspsv_vect(alpha,a,x,beta,y,desc_a,info,& - & trans, scale, choice, diag, work) - use psb_base_mod, psb_protect_name => psb_zspsv_vect - use psi_mod - implicit none - - complex(psb_dpk_), intent(in) :: alpha, beta - type(psb_z_vect_type), intent(inout) :: x - type(psb_z_vect_type), intent(inout) :: y - type(psb_zspmat_type), intent(inout) :: a - type(psb_desc_type), intent(in) :: desc_a - integer(psb_ipk_), intent(out) :: info - type(psb_z_vect_type), intent(inout), optional :: diag - complex(psb_dpk_), optional, target, intent(inout) :: work(:) - character, intent(in), optional :: trans, scale - integer(psb_ipk_), intent(in), optional :: choice - - ! locals - integer(psb_ipk_) :: ictxt, np, me, & - & err_act, iix, jjx, ia, ja, iia, jja, lldx,lldy, choice_,& - & ix, iy, ik, jx, jy, i, lld,& - & m, nrow, ncol, liwork, llwork, iiy, jjy, idx, ndm - - character :: lscale - integer(psb_ipk_), parameter :: nb=4 - complex(psb_dpk_),pointer :: iwork(:), xp(:), yp(:) - character :: itrans - character(len=20) :: name, ch_err - logical :: aliw - - name='psb_sspsv' - info=psb_success_ - call psb_erractionsave(err_act) - if (psb_errstatus_fatal()) then - info = psb_err_internal_error_ ; goto 9999 - end if - - ictxt=desc_a%get_context() - - call psb_info(ictxt, me, np) - if (np == -1) then - info = psb_err_context_error_ - call psb_errpush(info,name) - goto 9999 - endif - - if (.not.allocated(x%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - if (.not.allocated(y%v)) then - info = psb_err_invalid_vect_state_ - call psb_errpush(info,name) - goto 9999 - endif - - - if (present(choice)) then - choice_ = choice - else - choice_ = psb_avg_ - endif - - if (present(scale)) then - lscale = psb_toupper(scale) - else - lscale = 'U' - endif - - if (present(trans)) then - itrans = psb_toupper(trans) - if((itrans == 'N').or.(itrans == 'T').or.(itrans == 'C')) then - ! Ok - else - info = psb_err_iarg_invalid_value_ - call psb_errpush(info,name) - goto 9999 - end if - else - itrans = 'N' - endif - - m = desc_a%get_global_rows() - nrow = desc_a%get_local_rows() - ncol = desc_a%get_local_cols() - lldx = x%get_nrows() - lldy = y%get_nrows() - if ((info == 0).and.(lldx null() - ! check for presence/size of a work area - liwork= 2*ncol - - if (present(work)) then - if (size(work) >= liwork) then - aliw =.false. - else - aliw=.true. - endif - else - aliw=.true. - end if - - if (aliw) then - allocate(iwork(liwork),stat=info) - if(info /= psb_success_) then - info=psb_err_from_subroutine_ - ch_err='psb_realloc' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - else - iwork => work - endif - - iwork(1)=0.d0 - - ! Perform local triangular system solve - if (present(diag)) then - call a%spsm(alpha,x,beta,y,info,scale=scale,d=diag,trans=trans) - else - call a%spsm(alpha,x,beta,y,info,scale=scale,trans=trans) - end if - if(info /= psb_success_) then - info = psb_err_from_subroutine_ - ch_err='dcssm' - call psb_errpush(info,name,a_err=ch_err) - goto 9999 - end if - - ! update overlap elements - if (choice_ > 0) then - call psi_swapdata(ior(psb_swap_send_,psb_swap_recv_),& - & zone,y%v,desc_a,iwork,info,data=psb_comm_ovr_) - - - if (info == psb_success_) call psi_ovrl_upd(y%v,desc_a,choice_,info) - if (info /= psb_success_) then - call psb_errpush(psb_err_from_subroutine_,name,a_err='Inner updates') - goto 9999 - end if - end if - - if (aliw) deallocate(iwork) - - call psb_erractionrestore(err_act) - return - -9999 call psb_error_handler(ictxt,err_act) - - return -end subroutine psb_zspsv_vect - diff --git a/base/serial/psb_camax_s.f90 b/base/serial/psb_camax_s.f90 index 7e608c8e..d9073d0f 100644 --- a/base/serial/psb_camax_s.f90 +++ b/base/serial/psb_camax_s.f90 @@ -31,7 +31,7 @@ ! ! ! Function: psb_camax_s -! Searches the absolute max of X. +! Computes the max absolute value of X. ! ! normi := max(abs(X(i)) ! diff --git a/base/serial/psb_casum_s.f90 b/base/serial/psb_casum_s.f90 index cf799cdc..1c357cc8 100644 --- a/base/serial/psb_casum_s.f90 +++ b/base/serial/psb_casum_s.f90 @@ -31,9 +31,9 @@ ! ! ! Function: psb_casum_s -! Searches the absolute max of X. +! Computes the sum of absolute values of X. ! -! normi := max(abs(X(i)) +! asum := sum(abs(X(:)) ! ! Arguments: ! n - integer size of X diff --git a/base/serial/psb_damax_s.f90 b/base/serial/psb_damax_s.f90 index f376f0ba..66aef288 100644 --- a/base/serial/psb_damax_s.f90 +++ b/base/serial/psb_damax_s.f90 @@ -31,7 +31,7 @@ ! ! ! Function: psb_damax_s -! Searches the absolute max of X. +! Computes the max absolute value of X. ! ! normi := max(abs(X(i)) ! diff --git a/base/serial/psb_dasum_s.f90 b/base/serial/psb_dasum_s.f90 index 6fb6e4f6..1ab42614 100644 --- a/base/serial/psb_dasum_s.f90 +++ b/base/serial/psb_dasum_s.f90 @@ -31,9 +31,9 @@ ! ! ! Function: psb_dasum_s -! Searches the absolute max of X. +! Computes the sum of absolute values of X. ! -! normi := max(abs(X(i)) +! asum := sum(abs(X(:)) ! ! Arguments: ! n - integer size of X diff --git a/base/serial/psb_samax_s.f90 b/base/serial/psb_samax_s.f90 index da7fc93e..f2b1fee2 100644 --- a/base/serial/psb_samax_s.f90 +++ b/base/serial/psb_samax_s.f90 @@ -31,7 +31,7 @@ ! ! ! Function: psb_samax_s -! Searches the absolute max of X. +! Computes the max absolute value of X. ! ! normi := max(abs(X(i)) ! diff --git a/base/serial/psb_sasum_s.f90 b/base/serial/psb_sasum_s.f90 index 7a3b44e2..c692cbd4 100644 --- a/base/serial/psb_sasum_s.f90 +++ b/base/serial/psb_sasum_s.f90 @@ -31,9 +31,9 @@ ! ! ! Function: psb_sasum_s -! Searches the absolute max of X. +! Computes the sum of absolute values of X. ! -! normi := max(abs(X(i)) +! asum := sum(abs(X(:)) ! ! Arguments: ! n - integer size of X diff --git a/base/serial/psb_zamax_s.f90 b/base/serial/psb_zamax_s.f90 index 8cac2e2e..4a408566 100644 --- a/base/serial/psb_zamax_s.f90 +++ b/base/serial/psb_zamax_s.f90 @@ -31,7 +31,7 @@ ! ! ! Function: psb_zamax_s -! Searches the absolute max of X. +! Computes the max absolute value of X. ! ! normi := max(abs(X(i)) ! diff --git a/base/serial/psb_zasum_s.f90 b/base/serial/psb_zasum_s.f90 index f00e4347..35a043ed 100644 --- a/base/serial/psb_zasum_s.f90 +++ b/base/serial/psb_zasum_s.f90 @@ -31,9 +31,9 @@ ! ! ! Function: psb_zasum_s -! Searches the absolute max of X. +! Computes the sum of absolute values of X. ! -! normi := max(abs(X(i)) +! asum := sum(abs(X(:)) ! ! Arguments: ! n - integer size of X diff --git a/base/tools/psb_callc.f90 b/base/tools/psb_callc.f90 index 6464ab3b..19924fbe 100644 --- a/base/tools/psb_callc.f90 +++ b/base/tools/psb_callc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_callc.f90 ! -! Function: psb_calloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_calloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_calloc_vect(x, desc_a,info,n) +subroutine psb_calloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_calloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_calloc_vect(x, desc_a,info,n) type(psb_c_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_calloc_vect(x, desc_a,info,n) return end subroutine psb_calloc_vect +! Function: psb_calloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_calloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_calloc_vect_r2 diff --git a/base/tools/psb_casb.f90 b/base/tools/psb_casb.f90 index 5c6b7dc2..b7e57549 100644 --- a/base/tools/psb_casb.f90 +++ b/base/tools/psb_casb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_casb.f90 ! -! Subroutine: psb_casb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_casb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - complex, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_c_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_c_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_casb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_casb_vect implicit none diff --git a/base/tools/psb_cins.f90 b/base/tools/psb_cins.f90 index a069c33b..cfb82b88 100644 --- a/base/tools/psb_cins.f90 +++ b/base/tools/psb_cins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_cinsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_cins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - complex The source dense submatrix. -! x(:) - complex The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - complex The source vector +! x - type(psb_c_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_cins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_cins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_cins_vect +! Subroutine: psb_cins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_c_vect_type) The source vector +! x - type(psb_c_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_cins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_cins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_cins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_cins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_cins_vect_r2 - - subroutine psb_cins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_cins_multivect use psi_mod diff --git a/base/tools/psb_csphalo.F90 b/base/tools/psb_csphalo.F90 index 2393bed6..f0432cc6 100644 --- a/base/tools/psb_csphalo.F90 +++ b/base/tools/psb_csphalo.F90 @@ -1208,7 +1208,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - prcid(ip+1) = psb_get_rank(ictxt,ip) + prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = rvsz(ip+1) if (sz > 0) then idx = brvindx(ip+1) @@ -1235,7 +1235,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - if (prcid(ip+1)<0) prcid(ip+1) = psb_get_rank(ictxt,ip) + if (prcid(ip+1)<0) prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = sdsz(ip+1) if (sz > 0) then idx = bsdindx(ip+1) diff --git a/base/tools/psb_dallc.f90 b/base/tools/psb_dallc.f90 index ac812ca7..73611ad7 100644 --- a/base/tools/psb_dallc.f90 +++ b/base/tools/psb_dallc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_dallc.f90 ! -! Function: psb_dalloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_dalloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_dalloc_vect(x, desc_a,info,n) +subroutine psb_dalloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_dalloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_dalloc_vect(x, desc_a,info,n) type(psb_d_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_dalloc_vect(x, desc_a,info,n) return end subroutine psb_dalloc_vect +! Function: psb_dalloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_dalloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_dalloc_vect_r2 diff --git a/base/tools/psb_dasb.f90 b/base/tools/psb_dasb.f90 index 3a022b1c..1d141cdf 100644 --- a/base/tools/psb_dasb.f90 +++ b/base/tools/psb_dasb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_dasb.f90 ! -! Subroutine: psb_dasb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_dasb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - real, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_d_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_d_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_dasb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_dasb_vect implicit none diff --git a/base/tools/psb_dins.f90 b/base/tools/psb_dins.f90 index 84d5a015..ad7f8d90 100644 --- a/base/tools/psb_dins.f90 +++ b/base/tools/psb_dins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_dinsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_dins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - real The source dense submatrix. -! x(:) - real The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - real The source vector +! x - type(psb_d_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_dins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_dins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_dins_vect +! Subroutine: psb_dins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_d_vect_type) The source vector +! x - type(psb_d_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_dins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_dins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_dins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_dins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_dins_vect_r2 - - subroutine psb_dins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_dins_multivect use psi_mod diff --git a/base/tools/psb_dsphalo.F90 b/base/tools/psb_dsphalo.F90 index 4da40e96..032a139c 100644 --- a/base/tools/psb_dsphalo.F90 +++ b/base/tools/psb_dsphalo.F90 @@ -1208,7 +1208,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - prcid(ip+1) = psb_get_rank(ictxt,ip) + prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = rvsz(ip+1) if (sz > 0) then idx = brvindx(ip+1) @@ -1235,7 +1235,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - if (prcid(ip+1)<0) prcid(ip+1) = psb_get_rank(ictxt,ip) + if (prcid(ip+1)<0) prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = sdsz(ip+1) if (sz > 0) then idx = bsdindx(ip+1) diff --git a/base/tools/psb_iallc.f90 b/base/tools/psb_iallc.f90 index 8f0ab312..65f5f1da 100644 --- a/base/tools/psb_iallc.f90 +++ b/base/tools/psb_iallc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_iallc.f90 ! -! Function: psb_ialloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_ialloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_ialloc_vect(x, desc_a,info,n) +subroutine psb_ialloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_ialloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_ialloc_vect(x, desc_a,info,n) type(psb_i_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_ialloc_vect(x, desc_a,info,n) return end subroutine psb_ialloc_vect +! Function: psb_ialloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_ialloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_ialloc_vect_r2 diff --git a/base/tools/psb_iasb.f90 b/base/tools/psb_iasb.f90 index 11bf80d7..52fbe165 100644 --- a/base/tools/psb_iasb.f90 +++ b/base/tools/psb_iasb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_iasb.f90 ! -! Subroutine: psb_iasb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_iasb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - integer, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_i_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_i_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_iasb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_iasb_vect implicit none diff --git a/base/tools/psb_icdasb.F90 b/base/tools/psb_icdasb.F90 index 7176d185..6b2ba199 100644 --- a/base/tools/psb_icdasb.F90 +++ b/base/tools/psb_icdasb.F90 @@ -65,6 +65,10 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) integer(psb_ipk_) :: i, n_col, dectype, err_act, n_row integer(psb_mpk_) :: np,me, icomm, ictxt logical :: ext_hv_ + logical, parameter :: do_timings=.false. + integer(psb_ipk_), save :: idx_phase1=-1, idx_phase2=-1, idx_phase3=-1 + integer(psb_ipk_), save :: idx_phase11=-1, idx_phase12=-1, idx_phase13=-1 + integer(psb_ipk_), save :: idx_total=-1 integer(psb_ipk_) :: debug_level, debug_unit character(len=20) :: name @@ -81,7 +85,22 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) n_row = desc%get_local_rows() n_col = desc%get_local_cols() icomm = desc%get_mpic() - + if ((do_timings).and.(idx_total==-1)) & + & idx_total = psb_get_timer_idx("ICDASB: total ") + if ((do_timings).and.(idx_phase1==-1)) & + & idx_phase1 = psb_get_timer_idx("ICDASB: phase1 ") + if ((do_timings).and.(idx_phase2==-1)) & + & idx_phase2 = psb_get_timer_idx("ICDASB: phase2") + if ((do_timings).and.(idx_phase3==-1)) & + & idx_phase3 = psb_get_timer_idx("ICDASB: phase3") +!!$ if ((do_timings).and.(idx_phase11==-1)) & +!!$ & idx_phase11 = psb_get_timer_idx("ICDASB: phase11 ") +!!$ if ((do_timings).and.(idx_phase12==-1)) & +!!$ & idx_phase12 = psb_get_timer_idx("ICDASB: phase12") +!!$ if ((do_timings).and.(idx_phase13==-1)) & +!!$ & idx_phase13 = psb_get_timer_idx("ICDASB: phase13") + + call psb_tic(idx_total) ! check on blacs grid call psb_info(ictxt, me, np) if (np == -1) then @@ -115,6 +134,7 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) & write(debug_unit, *) me,' ',trim(name),': start' if (allocated(desc%indxmap)) then + if (do_timings) call psb_tic(idx_phase1) if (.not.ext_hv_) then call psi_bld_tmphalo(desc,info) if (info /= psb_success_) then @@ -122,7 +142,8 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) goto 9999 end if end if - + if (do_timings) call psb_toc(idx_phase1) + if (do_timings) call psb_tic(idx_phase2) ! Take out the lists for ovrlap, halo and ext... call psb_move_alloc(desc%ovrlap_index,ovrlap_index,info) call psb_move_alloc(desc%halo_index,halo_index,info) @@ -144,6 +165,8 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) call psb_errpush(info,name) goto 9999 end if + if (do_timings) call psb_toc(idx_phase2) + if (do_timings) call psb_tic(idx_phase3) call desc%indxmap%asb(info) if (info == psb_success_) then @@ -154,14 +177,14 @@ subroutine psb_icdasb(desc,info,ext_hv,mold) write(0,*) 'Error from internal indxmap asb ',info info = psb_success_ end if - + if (do_timings) call psb_toc(idx_phase3) else info = psb_err_invalid_cd_state_ call psb_errpush(info,name) goto 9999 endif - + call psb_toc(idx_total) if (debug_level >= psb_debug_ext_) & & write(debug_unit,*) me,' ',trim(name),': Done' diff --git a/base/tools/psb_iins.f90 b/base/tools/psb_iins.f90 index 8b8eea7e..48aa97fb 100644 --- a/base/tools/psb_iins.f90 +++ b/base/tools/psb_iins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_iinsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_iins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - integer The source dense submatrix. -! x(:) - integer The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - integer The source vector +! x - type(psb_i_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_iins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_iins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_iins_vect +! Subroutine: psb_iins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_i_vect_type) The source vector +! x - type(psb_i_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_iins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_iins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_iins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_iins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_iins_vect_r2 - - subroutine psb_iins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_iins_multivect use psi_mod diff --git a/base/tools/psb_lallc.f90 b/base/tools/psb_lallc.f90 index 66731177..e397f7cb 100644 --- a/base/tools/psb_lallc.f90 +++ b/base/tools/psb_lallc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_lallc.f90 ! -! Function: psb_lalloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_lalloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_lalloc_vect(x, desc_a,info,n) +subroutine psb_lalloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_lalloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_lalloc_vect(x, desc_a,info,n) type(psb_l_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_lalloc_vect(x, desc_a,info,n) return end subroutine psb_lalloc_vect +! Function: psb_lalloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_lalloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_lalloc_vect_r2 diff --git a/base/tools/psb_lasb.f90 b/base/tools/psb_lasb.f90 index 8d3c7a97..c1835b05 100644 --- a/base/tools/psb_lasb.f90 +++ b/base/tools/psb_lasb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_lasb.f90 ! -! Subroutine: psb_lasb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_lasb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - integer, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_l_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_l_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_lasb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_lasb_vect implicit none diff --git a/base/tools/psb_lins.f90 b/base/tools/psb_lins.f90 index b0d02018..d7c044d1 100644 --- a/base/tools/psb_lins.f90 +++ b/base/tools/psb_lins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_linsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_lins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - integer The source dense submatrix. -! x(:) - integer The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - integer The source vector +! x - type(psb_l_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_lins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_lins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_lins_vect +! Subroutine: psb_lins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_l_vect_type) The source vector +! x - type(psb_l_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_lins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_lins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_lins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_lins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_lins_vect_r2 - - subroutine psb_lins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_lins_multivect use psi_mod diff --git a/base/tools/psb_sallc.f90 b/base/tools/psb_sallc.f90 index 9cbb6f8f..6e20f82e 100644 --- a/base/tools/psb_sallc.f90 +++ b/base/tools/psb_sallc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_sallc.f90 ! -! Function: psb_salloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_salloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_salloc_vect(x, desc_a,info,n) +subroutine psb_salloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_salloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_salloc_vect(x, desc_a,info,n) type(psb_s_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_salloc_vect(x, desc_a,info,n) return end subroutine psb_salloc_vect +! Function: psb_salloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_salloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_salloc_vect_r2 diff --git a/base/tools/psb_sasb.f90 b/base/tools/psb_sasb.f90 index b0aa03a5..67d4ac92 100644 --- a/base/tools/psb_sasb.f90 +++ b/base/tools/psb_sasb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_sasb.f90 ! -! Subroutine: psb_sasb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_sasb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - real, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_s_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_s_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_sasb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_sasb_vect implicit none diff --git a/base/tools/psb_sins.f90 b/base/tools/psb_sins.f90 index 95803319..85b68322 100644 --- a/base/tools/psb_sins.f90 +++ b/base/tools/psb_sins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_sinsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_sins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - real The source dense submatrix. -! x(:) - real The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - real The source vector +! x - type(psb_s_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_sins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_sins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_sins_vect +! Subroutine: psb_sins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_s_vect_type) The source vector +! x - type(psb_s_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_sins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_sins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_sins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_sins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_sins_vect_r2 - - subroutine psb_sins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_sins_multivect use psi_mod diff --git a/base/tools/psb_ssphalo.F90 b/base/tools/psb_ssphalo.F90 index 51e3a973..1cd942f1 100644 --- a/base/tools/psb_ssphalo.F90 +++ b/base/tools/psb_ssphalo.F90 @@ -1208,7 +1208,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - prcid(ip+1) = psb_get_rank(ictxt,ip) + prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = rvsz(ip+1) if (sz > 0) then idx = brvindx(ip+1) @@ -1235,7 +1235,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - if (prcid(ip+1)<0) prcid(ip+1) = psb_get_rank(ictxt,ip) + if (prcid(ip+1)<0) prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = sdsz(ip+1) if (sz > 0) then idx = bsdindx(ip+1) diff --git a/base/tools/psb_zallc.f90 b/base/tools/psb_zallc.f90 index e01f0af2..1bf67e74 100644 --- a/base/tools/psb_zallc.f90 +++ b/base/tools/psb_zallc.f90 @@ -32,17 +32,15 @@ ! ! File: psb_zallc.f90 ! -! Function: psb_zalloc -! Allocates dense matrix for PSBLAS routines. +! Function: psb_zalloc_vect +! Allocates dense vector for PSBLAS routines. ! The descriptor may be in either the build or assembled state. ! ! Arguments: -! x - the matrix to be allocated. +! x - the vector to be allocated. ! desc_a - the communication descriptor. ! info - Return code -! n - optional number of columns. -! lb - optional lower bound on column indices -subroutine psb_zalloc_vect(x, desc_a,info,n) +subroutine psb_zalloc_vect(x, desc_a,info) use psb_base_mod, psb_protect_name => psb_zalloc_vect use psi_mod implicit none @@ -51,7 +49,6 @@ subroutine psb_zalloc_vect(x, desc_a,info,n) type(psb_z_vect_type), intent(out) :: x type(psb_desc_type), intent(in) :: desc_a integer(psb_ipk_),intent(out) :: info - integer(psb_ipk_), optional, intent(in) :: n !locals integer(psb_ipk_) :: np,me,nr,i,err_act @@ -113,6 +110,16 @@ subroutine psb_zalloc_vect(x, desc_a,info,n) return end subroutine psb_zalloc_vect +! Function: psb_zalloc_vect_r2 +! Allocates a vector of dense vectors for PSBLAS routines. +! The descriptor may be in either the build or assembled state. +! +! Arguments: +! x - the vector to be allocated. +! desc_a - the communication descriptor. +! info - Return code +! n - optional number of columns. +! lb - optional lower bound on column indices subroutine psb_zalloc_vect_r2(x, desc_a,info,n,lb) use psb_base_mod, psb_protect_name => psb_zalloc_vect_r2 diff --git a/base/tools/psb_zasb.f90 b/base/tools/psb_zasb.f90 index 5d6127c9..6ebf4281 100644 --- a/base/tools/psb_zasb.f90 +++ b/base/tools/psb_zasb.f90 @@ -31,17 +31,26 @@ ! ! File: psb_zasb.f90 ! -! Subroutine: psb_zasb -! Assembles a dense matrix for PSBLAS routines +! Subroutine: psb_zasb_vect, _vect_r2 and _multivect +! Assembles a dense vector, an array of vectors or a multivector +! for PSBLAS routines. ! Since the allocation may have been called with the desciptor ! in the build state we make sure that X has a number of rows ! allowing for the halo indices, reallocating if necessary. ! We also call the halo routine for good measure. +! However, sometimes we need to create temporary vectors whose contents +! will be initialized through some subsequent call to geaxpby or similar; +! for this situation we provide the SCRATCH flag. +! ! ! Arguments: -! x(:,:) - complex, allocatable The matrix to be assembled. -! desc_a - type(psb_desc_type). The communication descriptor. +! x - type(psb_z_vect_type) The matrix to be assembled. +! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code +! mold - type(psb_z_base_vect_type), optional A mold for the inner storage format +! scratch - logical, optional If true, allocate without checking/zeroing contents. +! default: .false. +! subroutine psb_zasb_vect(x, desc_a, info, mold, scratch) use psb_base_mod, psb_protect_name => psb_zasb_vect implicit none diff --git a/base/tools/psb_zins.f90 b/base/tools/psb_zins.f90 index e87f3a11..8307434b 100644 --- a/base/tools/psb_zins.f90 +++ b/base/tools/psb_zins.f90 @@ -29,17 +29,17 @@ ! POSSIBILITY OF SUCH DAMAGE. ! ! -! Subroutine: psb_zinsvi -! Insert dense submatrix to dense matrix. Note: the row indices in IRW +! Subroutine: psb_zins_vect +! Insert entries into a dense vector. Note: the row indices in IRW ! are assumed to be in global numbering and are converted on the fly. ! Row indices not belonging to the current process are silently discarded. ! ! Arguments: ! m - integer. Number of rows of submatrix belonging to ! val to be inserted. -! irw(:) - integer Row indices of rows of val (global numbering) -! val(:) - complex The source dense submatrix. -! x(:) - complex The destination dense matrix. +! irw(:) - integer(psb_lpk_) Row indices of rows of val (global numbering) +! val(:) - complex The source vector +! x - type(psb_z_vect_type) The destination vector ! desc_a - type(psb_desc_type). The communication descriptor. ! info - integer. return code ! dupl - integer What to do with duplicates: @@ -50,10 +50,6 @@ subroutine psb_zins_vect(m, irw, val, x, desc_a, info, dupl,local) use psi_mod implicit none - ! m rows number of submatrix belonging to val to be inserted - ! ix x global-row corresponding to position at which val submatrix - ! must be inserted - !....parameters... integer(psb_ipk_), intent(in) :: m integer(psb_lpk_), intent(in) :: irw(:) @@ -155,6 +151,23 @@ subroutine psb_zins_vect(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_zins_vect +! Subroutine: psb_zins_vect_v +! Insert entries into a vector from another encapsulated vector. +! Note: the row indices in IRW +! are assumed to be in global numbering and are converted on the fly. +! Row indices not belonging to the current process are silently discarded. +! +! Arguments: +! m - integer. Number of rows of submatrix belonging to +! val to be inserted. +! irw - type(psb_l_vect_type) Row indices of rows of val (global numbering) +! val - type(psb_z_vect_type) The source vector +! x - type(psb_z_vect_type) The destination vector +! desc_a - type(psb_desc_type). The communication descriptor. +! info - integer. return code +! dupl - integer What to do with duplicates: +! psb_dupl_ovwrt_ overwrite +! psb_dupl_add_ add subroutine psb_zins_vect_v(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_zins_vect_v use psi_mod @@ -329,7 +342,6 @@ subroutine psb_zins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) mglob = desc_a%get_global_rows() - n = min(size(x),size(val,2)) allocate(irl(m),stat=info) if (info /= psb_success_) then @@ -375,8 +387,6 @@ subroutine psb_zins_vect_r2(m, irw, val, x, desc_a, info, dupl,local) end subroutine psb_zins_vect_r2 - - subroutine psb_zins_multivect(m, irw, val, x, desc_a, info, dupl,local) use psb_base_mod, psb_protect_name => psb_zins_multivect use psi_mod diff --git a/base/tools/psb_zsphalo.F90 b/base/tools/psb_zsphalo.F90 index 16ee45b4..6dc1d82b 100644 --- a/base/tools/psb_zsphalo.F90 +++ b/base/tools/psb_zsphalo.F90 @@ -1208,7 +1208,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - prcid(ip+1) = psb_get_rank(ictxt,ip) + prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = rvsz(ip+1) if (sz > 0) then idx = brvindx(ip+1) @@ -1235,7 +1235,7 @@ contains n_el_recv = ipdxv(counter+psb_n_elem_recv_) counter = counter+n_el_recv n_el_send = ipdxv(counter+psb_n_elem_send_) - if (prcid(ip+1)<0) prcid(ip+1) = psb_get_rank(ictxt,ip) + if (prcid(ip+1)<0) prcid(ip+1) = psb_get_mpi_rank(ictxt,ip) sz = sdsz(ip+1) if (sz > 0) then idx = bsdindx(ip+1) diff --git a/docs/html/cmsy10-42.png b/docs/html/cmsy10-42.png new file mode 100644 index 00000000..3e3ff34f Binary files /dev/null and b/docs/html/cmsy10-42.png differ diff --git a/docs/html/cmsy10-48.png b/docs/html/cmsy10-48.png new file mode 100644 index 00000000..b5d0fbf1 Binary files /dev/null and b/docs/html/cmsy10-48.png differ diff --git a/docs/html/cmsy10-49.png b/docs/html/cmsy10-49.png new file mode 100644 index 00000000..b44b91b4 Binary files /dev/null and b/docs/html/cmsy10-49.png differ diff --git a/docs/html/contents.png b/docs/html/contents.png deleted file mode 100644 index 0c752c66..00000000 Binary files a/docs/html/contents.png and /dev/null differ diff --git a/docs/html/footnode.html b/docs/html/footnode.html deleted file mode 100644 index 9b6f0db5..00000000 --- a/docs/html/footnode.html +++ /dev/null @@ -1,218 +0,0 @@ - - - - - -Footnotes - - - - - - - - - - - - - - - - -
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... -explicitly1
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In our prototype implementation we provide -sample scatter/gather routines. - -
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... domain2
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This is - the normal situation when the pattern of the sparse matrix is - symmetric, which is equivalent to say that the interaction between - two variables is reciprocal. If the matrix pattern is non-symmetric - we may have one-way interactions, and these could cause a situation - in which a boundary point is not a halo point for its neighbour. - -
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... prec%build3
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The subroutine style psb_precinit and psb_precbl are still supported for - backward compatibility - -
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... follows4
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The string is case-insensitive - -
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... method5
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Note: - the implementation is for $FCG(1)$. - -
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PSBLAS
User’s and Reference Guide
A reference guide for the Parallel Sparse BLAS library
Salvatore Filippone
Alfredo Buttari
Software version: 3.7.0
Jan 7th, 2020 + - - - -userhtml - - - - + + - - + +

+ Contents +
1 Introduction +
2 General overview +
 2.1 Basic Nomenclature +
 2.2 Library contents +
 2.3 Application structure +
 2.4 Programming model +
3 Data Structures and Classes +
 3.1 Descriptor data structure +
 3.2 Sparse Matrix class +
 3.3 Dense Vector Data Structure +
 3.4 Preconditioner data structure +
 3.5 Heap data structure +
4 Computational routines +
 4.1 psb_geaxpby — General Dense Matrix Sum +
 4.2 psb_gedot — Dot Product +
 4.3 psb_gedots — Generalized Dot Product +
 4.4 psb_normi — Infinity-Norm of Vector +
 4.5 psb_geamaxs — Generalized Infinity Norm +
 4.6 psb_norm1 — 1-Norm of Vector +
 4.7 psb_geasums — Generalized 1-Norm of Vector +
 4.8 psb_norm2 — 2-Norm of Vector +
 4.9 psb_genrm2s — Generalized 2-Norm of Vector +
 4.10 psb_norm1 — 1-Norm of Sparse Matrix +
 4.11 psb_normi — Infinity Norm of Sparse Matrix +
 4.12 psb_spmm — Sparse Matrix by Dense Matrix Product +
 4.13 psb_spsm — Triangular System Solve +
 4.14 psb_gemlt — Entrywise Product +
 4.15 psb_gediv — Entrywise Division +
 4.16 psb_geinv — Entrywise Inversion +
5 Communication routines +
 5.1 psb_halo — Halo Data Communication +
 5.2 psb_ovrl — Overlap Update +
 5.3 psb_gather — Gather Global Dense Matrix +
 5.4 psb_scatter — Scatter Global Dense Matrix +
6 Data management routines +
 6.1 psb_cdall — Allocates a communication descriptor +
 6.2 psb_cdins — Communication descriptor insert routine +
 6.3 psb_cdasb — Communication descriptor assembly routine +
 6.4 psb_cdcpy — Copies a communication descriptor +
 6.5 psb_cdfree — Frees a communication descriptor +
 6.6 psb_cdbldext — Build an extended communication descriptor +
 6.7 psb_spall — Allocates a sparse matrix +
 6.8 psb_spins — Insert a set of coefficients into a sparse matrix +
 6.9 psb_spasb — Sparse matrix assembly routine +
 6.10 psb_spfree — Frees a sparse matrix +
 6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. +
 6.12 psb_geall — Allocates a dense matrix + - + +
 6.13 psb_geins — Dense matrix insertion routine +
 6.14 psb_geasb — Assembly a dense matrix +
 6.15 psb_gefree — Frees a dense matrix +
 6.16 psb_gelp — Applies a left permutation to a dense matrix +
 6.17 psb_glob_to_loc — Global to local indices convertion +
 6.18 psb_loc_to_glob — Local to global indices conversion +
 6.19 psb_is_owned — +
 6.20 psb_owned_index — +
 6.21 psb_is_local — +
 6.22 psb_local_index — +
 6.23 psb_get_boundary — Extract list of boundary elements +
 6.24 psb_get_overlap — Extract list of overlap elements +
 6.25 psb_sp_getrow — Extract row(s) from a sparse matrix +
 6.26 psb_sizeof — Memory occupation +
 6.27 Sorting utilities — +
7 Parallel environment routines +
 7.1 psb_init — Initializes PSBLAS parallel environment +
 7.2 psb_info — Return information about PSBLAS parallel environment +
 7.3 psb_exit — Exit from PSBLAS parallel environment +
 7.4 psb_get_mpi_comm — Get the MPI communicator +
 7.5 psb_get_mpi_rank — Get the MPI rank +
 7.6 psb_wtime — Wall clock timing +
 7.7 psb_barrier — Sinchronization point parallel environment +
 7.8 psb_abort — Abort a computation +
 7.9 psb_bcast — Broadcast data +
 7.10 psb_sum — Global sum +
 7.11 psb_max — Global maximum +
 7.12 psb_min — Global minimum +
 7.13 psb_amx — Global maximum absolute value +
 7.14 psb_amn — Global minimum absolute value +
 7.15 psb_nrm2 — Global 2-norm reduction +
 7.16 psb_snd — Send data +
 7.17 psb_rcv — Receive data +
8 Error handling +
 8.1 psb_errpush — Pushes an error code onto the error stack +
 8.2 psb_error — Prints the error stack content and aborts execution +
 8.3 psb_set_errverbosity — Sets the verbosity of error messages +
 8.4 psb_set_erraction — Set the type of action to be taken upon error condition +
9 Utilities +
 9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format +
 9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format +
 9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format +
 9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format +
 9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format +
 9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format +
10 Preconditioner routines +
 10.1 init — Initialize a preconditioner +
 10.2 build — Builds a preconditioner +
 10.3 apply — Preconditioner application routine +
 10.4 descr — Prints a description of current preconditioner + - - + +
 10.5 clone — clone current preconditioner +
 10.6 free — Free a preconditioner +
11 Iterative Methods +
 11.1 psb_krylov — Krylov Methods Driver Routine +
References +
- -
- -next -up -previous - -contents -
- Next: Contents -   Contents -
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- -language=Fortran -

-PSBLAS -
-
-User's and Reference - Guide -
A reference guide for the Parallel Sparse BLAS library -
-
-
-
Salvatore Filippone -
-Alfredo Buttari -
-Software version: 3.6.0 -
-Dec 1st, 2018 -

- - - - -
- - + + + + + + + + + + + diff --git a/docs/html/next.png b/docs/html/next.png deleted file mode 100644 index 1628652a..00000000 Binary files a/docs/html/next.png and /dev/null differ diff --git a/docs/html/next_g.png b/docs/html/next_g.png deleted file mode 100644 index 9d3f5912..00000000 Binary files a/docs/html/next_g.png and /dev/null differ diff --git a/docs/html/node1.html b/docs/html/node1.html deleted file mode 100644 index 5acc7f7d..00000000 --- a/docs/html/node1.html +++ /dev/null @@ -1,111 +0,0 @@ - - - - - -Contents - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous -
- Next: Introduction - Up: userhtml - Previous: userhtml -
-
- -
- -

-Contents -

- - - - -

- -

- -

-

- - - diff --git a/docs/html/node10.html b/docs/html/node10.html deleted file mode 100644 index ce622a01..00000000 --- a/docs/html/node10.html +++ /dev/null @@ -1,298 +0,0 @@ - - - - - -Descriptor data structure - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Descriptor Methods - Up: Data Structures and Classes - Previous: Data Structures and Classes -   Contents -
-
- - -

- -
-Descriptor data structure -

-All the general matrix informations and elements to be -exchanged among processes are stored within a data structure of the -type descdatapsb_desc_type. -Every structure of this type is associated with a discretization -pattern and enables data communications and other operations that are -necessary for implementing the various algorithms of interest to us. - -

-The data structure itself psb_desc_type can be treated as an -opaque object handled via the tools routines of -Sec. 6 or the query routines detailed below; -nevertheless we include here a description for the curious -reader. - -

-First we describe the psb_indx_map type. This is a data -structure that keeps track of a certain number of basic issues such -as: - -

    -
  • The value of the communication/MPI context; -
    • -
  • The number of indices in the index space, i.e. global number of - rows and columns of a sparse matrix; -
    • -
  • The local set of indices, including: - -
      -
    • The number of local indices (and local rows); -
      • -
    • The number of halo indices (and therefore local columns); -
      • -
    • The global indices corresponding to the local ones. -
      • -
    -
    • -
-There are many different schemes for storing these data; therefore -there are a number of types extending the base one, and the descriptor -structure holds a polymorphic object whose dynamic type can be any of -the extended types. -The methods associated with this data type answer the following -queries: - -
    -
  • For a given set of local indices, find the corresponding indices - in the global numbering; -
    • -
  • For a given set of global indices, find the corresponding - indices in the local numbering, if any, or return an invalid -
    • -
  • Add a global index to the set of halo indices; -
    • -
  • Find the process owner of each member of a set of global - indices. -
    • -
-All methods but the last are purely local; the last method potentially -requires communication among processes, and thus is a synchronous -method. The choice of a specific dynamic type for the index map is -made at the time the descriptor is initially allocated, according to -the mode of initialization (see also 6). - -

-The descriptor contents are as follows: -

-
indxmap
-
A polymorphic variable of a type that is any - extension of the indx_map type described above. -
-
halo_index
-
A list of the halo and boundary elements for -the current process to be exchanged with other processes; for each -processes with which it is necessary to communicate: - -
    -
  1. Process identifier; -
    2. -
  2. Number of points to be received; -
    3. -
  3. Indices of points to be received; -
    4. -
  4. Number of points to be sent; -
    5. -
  5. Indices of points to be sent; -
    6. -
-Specified as: a vector of integer type, see 3.3. -
-
ext_index
-
A list of element indices to be exchanged to - implement the mapping between a base descriptor and a descriptor - with overlap. -
-Specified as: a vector of integer type, see 3.3. -
-
ovrlap_index
-
A list of the overlap elements for the -current process, organized in groups like the previous vector: - -
    -
  1. Process identifier; -
    2. -
  2. Number of points to be received; -
    3. -
  3. Indices of points to be received; -
    4. -
  4. Number of points to be sent; -
    5. -
  5. Indices of points to be sent; -
    6. -
-Specified as: a vector of integer type, see 3.3. -
-
ovr_mst_idx
-
A list to retrieve the value of each - overlap element from the respective master process. -
-Specified as: a vector of integer type, see 3.3. -
-
ovrlap_elem
-
For all overlap points belonging to th -ecurrent process: - -
    -
  1. Overlap point index; -
    2. -
  2. Number of processes sharing that overlap points; -
    3. -
  3. Index of a “master” process: -
    4. -
-Specified as: an allocatable integer array of rank two. -
-
bnd_elem
-
A list of all boundary points, i.e. points - that have a connection with other processes. -
-
-The Fortran 2003 declaration for psb_desc_type structures is -as follows: - -
- - - -
Figure 3: -The PSBLAS defined data type that - contains the communication descriptor.
-
- -
-
 
-type psb_desc_type 
-    class(psb_indx_map), allocatable :: indxmap
-    type(psb_i_vect_type) :: v_halo_index
-    type(psb_i_vect_type) :: v_ext_index
-    type(psb_i_vect_type) :: v_ovrlap_index
-    type(psb_i_vect_type) :: v_ovr_mst_idx 
-    integer, allocatable  :: ovrlap_elem(:,:)
-    integer, allocatable  :: bnd_elem(:)
-end type psb_desc_type
-
-
-
-
-A communication descriptor associated with a sparse matrix has a -state, which can take the following values: -
-
Build:
-
State entered after the first allocation, and before the - first assembly; in this state it is possible to add communication - requirements among different processes. -
-
Assembled:
-
State entered after the assembly; computations using - the associated sparse matrix, such as matrix-vector products, are - only possible in this state. -
-
- -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: Descriptor Methods - Up: Data Structures and Classes - Previous: Data Structures and Classes -   Contents
- - - - diff --git a/docs/html/node100.html b/docs/html/node100.html deleted file mode 100644 index 1f5586b7..00000000 --- a/docs/html/node100.html +++ /dev/null @@ -1,177 +0,0 @@ - - - - - -psb_init -- Initializes PSBLAS parallel environment - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_info Return - Up: Parallel environment routines - Previous: Parallel environment routines -   Contents -
-
- - -

-psb_init -- Initializes PSBLAS parallel - environment -

- -

-

-call psb_init(icontxt, np, basectxt, ids)
-
- -

-This subroutine initializes the PSBLAS parallel environment, defining -a virtual parallel machine. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
np
-
Number of processes in the PSBLAS virtual parallel machine. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value. Default: use all available processes. -
-
basectxt
-
the initial communication context. The new context - will be defined from the processes participating in the initial one. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value. Default: use MPI_COMM_WORLD. -
-
ids
-
Identities of the processes to use for the new context; the - argument is ignored when np is not specified. This allows the - processes in the new environment to be in an order different from the - original one. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer array. Default: use the indices $(0\dots np-1)$. -
-
- -

-

-
On Return
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. Note that this is always a duplicate of - basectxt, so that library communications are completely - separated from other communication operations. -
-Scope: global. -
-Type: required. -
-Intent: out. -
-Specified as: an integer variable. -
-
- -

-Notes - -

    -
  1. A call to this routine must precede any other PSBLAS call. -
    2. -
  2. It is an error to specify a value for $np$ greater than the - number of processes available in the underlying base parallel - environment. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_info Return - Up: Parallel environment routines - Previous: Parallel environment routines -   Contents
- - - - diff --git a/docs/html/node101.html b/docs/html/node101.html deleted file mode 100644 index 81e42059..00000000 --- a/docs/html/node101.html +++ /dev/null @@ -1,146 +0,0 @@ - - - - - -psb_info -- Return information about PSBLAS parallel environment - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_exit Exit - Up: Parallel environment routines - Previous: psb_init Initializes -   Contents -
-
- - -

-psb_info -- Return information about PSBLAS parallel - environment -

- -

-

-call psb_info(icontxt, iam, np)
-
- -

-This subroutine returns information about the PSBLAS parallel environment, defining -a virtual parallel machine. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
- -

-

-
On Return
-
-
-
iam
-
Identifier of current process in the PSBLAS virtual parallel machine. -
-Scope: local. -
-Type: required. -
-Intent: out. -
-Specified as: an integer value. -$-1 \le iam \le np-1$
-
np
-
Number of processes in the PSBLAS virtual parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: out. -
-Specified as: an integer variable.
-
- -

-Notes - -

    -
  1. For processes in the virtual parallel machine the identifier - will satisfy -$0 \le iam \le np-1$; -
    2. -
  2. If the user has requested on psb_init a number of - processes less than the total available in the parallel execution - environment, the remaining processes will have on return $iam=-1$; - the only call involving icontxt that any such process may - execute is to psb_exit. -
    3. -
- -

-

- - - diff --git a/docs/html/node102.html b/docs/html/node102.html deleted file mode 100644 index ef55917c..00000000 --- a/docs/html/node102.html +++ /dev/null @@ -1,149 +0,0 @@ - - - - - -psb_exit -- Exit from PSBLAS parallel environment - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_get_mpicomm Get - Up: Parallel environment routines - Previous: psb_info Return -   Contents -
-
- - -

-psb_exit -- Exit from PSBLAS parallel - environment -

- -

-

-call psb_exit(icontxt)
-call psb_exit(icontxt,close)
-
- -

-This subroutine exits from the PSBLAS parallel virtual machine. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
close
-
Whether to close all data structures related to the - virtual parallel machine, besides those associated with icontxt. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: a logical variable, default value: true. -
-
- -

-Notes - -

    -
  1. This routine may be called even if a previous call to - psb_info has returned with $iam=-1$; indeed, it it is the only - routine that may be called with argument icontxt in this - situation. -
    2. -
  2. A call to this routine with close=.true. implies a call - to MPI_Finalize, after which no parallel routine may be called. -
    3. -
  3. If the user whishes to use multiple communication contexts in the - same program, or to enter and exit multiple times into the parallel - environment, this routine may be called to - selectively close the contexts with close=.false., while on - the last call it should be called with close=.true. to - shutdown in a clean way the entire parallel environment. -
    4. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_get_mpicomm Get - Up: Parallel environment routines - Previous: psb_info Return -   Contents
- - - - diff --git a/docs/html/node103.html b/docs/html/node103.html deleted file mode 100644 index 561d6988..00000000 --- a/docs/html/node103.html +++ /dev/null @@ -1,103 +0,0 @@ - - - - - -psb_get_mpicomm -- Get the MPI communicator - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_get_rank Get - Up: Parallel environment routines - Previous: psb_exit Exit -   Contents -
-
- - -

-psb_get_mpicomm -- Get the MPI communicator -

- -

-

-icomm = psb_get_mpicomm(icontxt)
-
- -

-This subroutine returns the MPI communicator associated with a PSBLAS context -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
- -

-

-
On Return
-
-
-
Function value
-
The MPI communicator associated with the PSBLAS virtual parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: out. -
-
- -

-

- - - diff --git a/docs/html/node104.html b/docs/html/node104.html deleted file mode 100644 index 99879bc0..00000000 --- a/docs/html/node104.html +++ /dev/null @@ -1,125 +0,0 @@ - - - - - -psb_get_rank -- Get the MPI rank - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_wtime Wall - Up: Parallel environment routines - Previous: psb_get_mpicomm Get -   Contents -
-
- - -

-psb_get_rank -- Get the MPI rank -

- -

-

-rank = psb_get_rank(icontxt, id)
-
- -

-This subroutine returns the MPI rank of the PSBLAS process $id$ -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
id
-
Identifier of a process in the PSBLAS virtual parallel machine. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value. -$0 \le id \le np-1$
-
- -

-

-
On Return
-
-
-
Funciton value
-
The MPI rank associated with the PSBLAS process $id$. -
-Scope: local. -
-Type: required. -
-Intent: out. -
-
- -

-

- - - diff --git a/docs/html/node105.html b/docs/html/node105.html deleted file mode 100644 index a93ed542..00000000 --- a/docs/html/node105.html +++ /dev/null @@ -1,81 +0,0 @@ - - - - - -psb_wtime -- Wall clock timing - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_barrier Sinchronization - Up: Parallel environment routines - Previous: psb_get_rank Get -   Contents -
-
- - -

-psb_wtime -- Wall clock timing -

- -

-

-time = psb_wtime()
-
- -

-This function returns a wall clock timer. The resolution of the timer -is dependent on the underlying parallel environment implementation. -

-
Type:
-
Asynchronous. -
-
On Exit
-
-
-
Function value
-
the elapsed time in seconds. -
-Returned as: a real(psb_dpk_) variable. -
-
- -

-

- - - diff --git a/docs/html/node106.html b/docs/html/node106.html deleted file mode 100644 index 74bd3f51..00000000 --- a/docs/html/node106.html +++ /dev/null @@ -1,89 +0,0 @@ - - - - - -psb_barrier -- Sinchronization point parallel environment - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_abort Abort - Up: Parallel environment routines - Previous: psb_wtime Wall -   Contents -
-
- - -

-psb_barrier -- Sinchronization point parallel - environment -

- -

-

-call psb_barrier(icontxt)
-
- -

-This subroutine acts as an explicit synchronization point for the PSBLAS -parallel virtual machine. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
- -

-

- - - diff --git a/docs/html/node107.html b/docs/html/node107.html deleted file mode 100644 index 0f37acf3..00000000 --- a/docs/html/node107.html +++ /dev/null @@ -1,87 +0,0 @@ - - - - - -psb_abort -- Abort a computation - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_bcast Broadcast - Up: Parallel environment routines - Previous: psb_barrier Sinchronization -   Contents -
-
- - -

-psb_abort -- Abort a computation -

- -

-

-call psb_abort(icontxt)
-
- -

-This subroutine aborts computation on the parallel virtual machine. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
- -

-

- - - diff --git a/docs/html/node108.html b/docs/html/node108.html deleted file mode 100644 index cada5b11..00000000 --- a/docs/html/node108.html +++ /dev/null @@ -1,136 +0,0 @@ - - - - - -psb_bcast -- Broadcast data - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_sum Global - Up: Parallel environment routines - Previous: psb_abort Abort -   Contents -
-
- - -

-psb_bcast -- Broadcast data -

- -

-

-call psb_bcast(icontxt, dat, root)
-
- -

-This subroutine implements a broadcast operation based on the -underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
On the root process, the data to be broadcast. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical variable, -which may be a scalar or rank 1 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Root process holding data to be broadcast. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$0<= root <= np-1$, default 0
-
- -

-

-
On Return
-
-
-
dat
-
On processes other than root, the data to be broadcast. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind, rank and size must agree on all processes. -
-
- -

-

- - - diff --git a/docs/html/node109.html b/docs/html/node109.html deleted file mode 100644 index c023b27a..00000000 --- a/docs/html/node109.html +++ /dev/null @@ -1,177 +0,0 @@ - - - - - -psb_sum -- Global sum - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_max Global - Up: Parallel environment routines - Previous: psb_bcast Broadcast -   Contents -
-
- - -

-psb_sum -- Global sum -

- -

-

-call psb_sum(icontxt, dat, root)
-
- -

-This subroutine implements a sum reduction operation based on the -underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global sum. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final sum, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1.
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the sum operation. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. -
-Type, kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    2. -
  2. The dat argument may also be a long integer scalar. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_max Global - Up: Parallel environment routines - Previous: psb_bcast Broadcast -   Contents
- - - - diff --git a/docs/html/node11.html b/docs/html/node11.html deleted file mode 100644 index c3adba33..00000000 --- a/docs/html/node11.html +++ /dev/null @@ -1,59 +0,0 @@ - - - - - -Descriptor Methods - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_local_rows Get - Up: Descriptor data structure - Previous: Descriptor data structure -   Contents -
-
- - -

-Descriptor Methods -

- -

-

- - - diff --git a/docs/html/node110.html b/docs/html/node110.html deleted file mode 100644 index 06883b02..00000000 --- a/docs/html/node110.html +++ /dev/null @@ -1,176 +0,0 @@ - - - - - -psb_max -- Global maximum - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_min Global - Up: Parallel environment routines - Previous: psb_sum Global -   Contents -
-
- - -

-psb_max -- Global maximum -

- -

-

-call psb_max(icontxt, dat, root)
-
- -

-This subroutine implements a maximum valuereduction -operation based on the underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global maximum. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer or real variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final maximum, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1. -
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the maximum operation. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer or real variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    2. -
  2. The dat argument may also be a long integer scalar. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_min Global - Up: Parallel environment routines - Previous: psb_sum Global -   Contents
- - - - diff --git a/docs/html/node111.html b/docs/html/node111.html deleted file mode 100644 index 76e40bd5..00000000 --- a/docs/html/node111.html +++ /dev/null @@ -1,178 +0,0 @@ - - - - - -psb_min -- Global minimum - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_amx Global - Up: Parallel environment routines - Previous: psb_max Global -   Contents -
-
- - -

-psb_min -- Global minimum -

- -

-

-call psb_min(icontxt, dat, root)
-
- -

-This subroutine implements a minimum value reduction -operation based on the underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global minimum. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer or real variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final value, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1. -
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the minimum operation. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer or real variable, which may be a -scalar, or a rank 1 or 2 array. -
-Type, kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    2. -
  2. The dat argument may also be a long integer scalar. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_amx Global - Up: Parallel environment routines - Previous: psb_max Global -   Contents
- - - - diff --git a/docs/html/node112.html b/docs/html/node112.html deleted file mode 100644 index 36e57ef8..00000000 --- a/docs/html/node112.html +++ /dev/null @@ -1,176 +0,0 @@ - - - - - -psb_amx -- Global maximum absolute value - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_amn Global - Up: Parallel environment routines - Previous: psb_min Global -   Contents -
-
- - -

-psb_amx -- Global maximum absolute value -

- -

-

-call psb_amx(icontxt, dat, root)
-
- -

-This subroutine implements a maximum absolute value reduction -operation based on the underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global maximum. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final value, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1. -
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the maximum operation. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    2. -
  2. The dat argument may also be a long integer scalar. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_amn Global - Up: Parallel environment routines - Previous: psb_min Global -   Contents
- - - - diff --git a/docs/html/node113.html b/docs/html/node113.html deleted file mode 100644 index 587b7431..00000000 --- a/docs/html/node113.html +++ /dev/null @@ -1,178 +0,0 @@ - - - - - -psb_amn -- Global minimum absolute value - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_nrm2 Global - Up: Parallel environment routines - Previous: psb_amx Global -   Contents -
-
- - -

-psb_amn -- Global minimum absolute value -

- -

-

-call psb_amn(icontxt, dat, root)
-
- -

-This subroutine implements a minimum absolute value reduction -operation based on the underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global minimum. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. Type, kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final value, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1. -
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the minimum operation. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array. -
-Type, kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    2. -
  2. The dat argument may also be a long integer scalar. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_nrm2 Global - Up: Parallel environment routines - Previous: psb_amx Global -   Contents
- - - - diff --git a/docs/html/node114.html b/docs/html/node114.html deleted file mode 100644 index 0f1bd184..00000000 --- a/docs/html/node114.html +++ /dev/null @@ -1,210 +0,0 @@ - - - - - -psb_nrm2 -- Global 2-norm reduction - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_snd Send - Up: Parallel environment routines - Previous: psb_amn Global -   Contents -
-
- - -

-psb_nrm2 -- Global 2-norm reduction -

- -

-

-call psb_nrm2(icontxt, dat, root)
-
- -

-This subroutine implements a 2-norm value reduction -operation based on the underlying communication library. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The local contribution to the global minimum. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: a real variable, which may be a -scalar, or a rank 1 array. Kind, rank and size must agree on all processes. -
-
root
-
Process to hold the final value, or $-1$ to make it available - on all processes. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value -$-1<= root <= np-1$, default -1. -
-
- -

-

-
On Return
-
-
-
dat
-
On destination process(es), the result of the 2-norm reduction. -
-Scope: global. -
-Type: required. -
-Intent: inout. -
-Specified as: a real variable, which may be a -scalar, or a rank 1 array. -
-Kind, rank and size must agree on all processes. -
-
- -

-Notes - -

    -
  1. This reduction is appropriate to compute the results of multiple - (local) NRM2 operations at the same time. -
    2. -
  2. Denoting by $dat_i$ the value of the variable $dat$ on process - $i$, the output $res$ is equivalent to the computation of -

    -
    - - -\begin{displaymath}res = \sqrt{\sum_i dat_i^2},\end{displaymath} -
    -
    -

    -with care taken to avoid unnecessary overflow. -
    3. -
  3. The dat argument is both input and output, and its - value may be changed even on processes different from the final - result destination. -
    4. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_snd Send - Up: Parallel environment routines - Previous: psb_amn Global -   Contents
- - - - diff --git a/docs/html/node115.html b/docs/html/node115.html deleted file mode 100644 index 2da350d6..00000000 --- a/docs/html/node115.html +++ /dev/null @@ -1,190 +0,0 @@ - - - - - -psb_snd -- Send data - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_rcv Receive - Up: Parallel environment routines - Previous: psb_nrm2 Global -   Contents -
-
- - -

-psb_snd -- Send data -

- -

-

-call psb_snd(icontxt, dat, dst, m)
-
- -

-This subroutine sends a packet of data to a destination. -

-
Type:
-
Synchronous: see usage notes. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
dat
-
The data to be sent. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is -not specified, size must agree as well. -
-
dst
-
Destination process. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value -$0<= dst <= np-1$. -
-
m
-
Number of rows. -
-Scope: global. -
-Type: Optional. -
-Intent: in. -
-Specified as: an integer value -$0<= m <= size(dat,1)$. -
-When $dat$ is a rank 2 array, specifies the number of rows to be sent -independently of the leading dimension $size(dat,1)$; must have the -same value on sending and receiving processes. -
-
- -

-

-
On Return
-
-
-
- -

-Notes - -

    -
  1. This subroutine implies a synchronization, but only between the - calling process and the destination process $dst$. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_rcv Receive - Up: Parallel environment routines - Previous: psb_nrm2 Global -   Contents
- - - - diff --git a/docs/html/node116.html b/docs/html/node116.html deleted file mode 100644 index 6f0eaa1e..00000000 --- a/docs/html/node116.html +++ /dev/null @@ -1,189 +0,0 @@ - - - - - -psb_rcv -- Receive data - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Error handling - Up: Parallel environment routines - Previous: psb_snd Send -   Contents -
-
- - -

-psb_rcv -- Receive data -

- -

-

-call psb_rcv(icontxt, dat, src, m)
-
- -

-This subroutine receives a packet of data to a destination. -

-
Type:
-
Synchronous: see usage notes. -
-
On Entry
-
-
-
icontxt
-
the communication context identifying the virtual - parallel machine. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer variable. -
-
src
-
Source process. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value -$0<= src <= np-1$. -
-
m
-
Number of rows. -
-Scope: global. -
-Type: Optional. -
-Intent: in. -
-Specified as: an integer value -$0<= m <= size(dat,1)$. -
-When $dat$ is a rank 2 array, specifies the number of rows to be sent -independently of the leading dimension $size(dat,1)$; must have the -same value on sending and receiving processes. -
-
- -

-

-
On Return
-
-
-
dat
-
The data to be received. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: an integer, real or complex variable, which may be a -scalar, or a rank 1 or 2 array, or a character or logical scalar. Type, kind and rank must agree on sender and receiver process; if $m$ is -not specified, size must agree as well. -
-
- -

-Notes - -

    -
  1. This subroutine implies a synchronization, but only between the - calling process and the source process $src$. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: Error handling - Up: Parallel environment routines - Previous: psb_snd Send -   Contents
- - - - diff --git a/docs/html/node117.html b/docs/html/node117.html deleted file mode 100644 index 3f350078..00000000 --- a/docs/html/node117.html +++ /dev/null @@ -1,342 +0,0 @@ - - - - - -Error handling - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Utilities - Up: userhtml - Previous: psb_rcv Receive -   Contents -
-
- - -

-Error handling -

- -

-The PSBLAS library error handling policy has been completely rewritten -in version 2.0. The idea behind the design of this new error handling -strategy is to keep error messages on a stack allowing the user to -trace back up to the point where the first error message has been -generated. Every routine in the PSBLAS-2.0 library has, as last -non-optional argument, an integer info variable; whenever, -inside the routine, an error is detected, this variable is set to a -value corresponding to a specific error code. Then this error code is -also pushed on the error stack and then either control is returned to -the caller routine or the execution is aborted, depending on the users -choice. At the time when the execution is aborted, an error message is -printed on standard output with a level of verbosity than can be -chosen by the user. If the execution is not aborted, then, the caller -routine checks the value returned in the info variable and, if -not zero, an error condition is raised. This process continues on all the -levels of nested calls until the level where the user decides to abort -the program execution. - -

-Figure 9 shows the layout of a generic psb_foo -routine with respect to the PSBLAS-2.0 error handling policy. It is -possible to see how, whenever an error condition is detected, the -info variable is set to the corresponding error code which is, -then, pushed on top of the stack by means of the -psb_errpush. An error condition may be directly detected inside -a routine or indirectly checking the error code returned returned by a -called routine. Whenever an error is encountered, after it has been -pushed on stack, the program execution skips to a point where the -error condition is handled; the error condition is handled either by -returning control to the caller routine or by calling the -psb\_error routine which prints the content of the error stack -and aborts the program execution, according to the choice made by the -user with psb_set_erraction. The default is to print the error -and terminate the program, but the user may choose to handle the error -explicitly. - -

- -

- - - -
Figure 9: -The layout of a generic psb_foo - routine with respect to PSBLAS-2.0 error handling policy.
-
- -
- -\fbox{\TheSbox} -
-
- -

-Figure 10 reports a sample error message generated by -the PSBLAS-2.0 library. This error has been generated by the fact that -the user has chosen the invalid “FOO” storage format to represent -the sparse matrix. From this error message it is possible to see that -the error has been detected inside the psb_cest subroutine -called by psb_spasb ... by process 0 (i.e. the root process). - -

- -

- - - -
Figure 10: -A sample PSBLAS-2.0 error - message. Process 0 detected an error condition inside the psb_cest subroutine
-
- -
- -\fbox{\TheSbox} -
-
- -

-ifstarsubroutinesubroutinepsb_errpushPushes an error code onto the error - stack - -

-
-\begin{lstlisting} -call psb_errpush(err_c, r_name, i_err, a_err) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
err_c
-
the error code -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an integer. -
-
r_name
-
the soutine where the error has been caught. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a string. -
-
i_err
-
addional info for error code -
-Scope: local -
-Type: optional -
-Specified as: an integer array -
-
a_err
-
addional info for error code -
-Scope: local -
-Type: optional -
-Specified as: a string. -
-
- -

-ifstarsubroutinesubroutinepsb_errorPrints the error stack content and aborts - execution - -

-
-\begin{lstlisting} -call psb_error(icontxt) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: an integer. -
-
- -

-ifstarsubroutinesubroutinepsb_set_errverbositySets the verbosity of error - messages. - -

-
-\begin{lstlisting} -call psb_set_errverbosity(v) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
v
-
the verbosity level -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: an integer. -
-
- -

-ifstarsubroutinesubroutinepsb_set_erractionSet the type of action to be - taken upon error condition. - -

-
-\begin{lstlisting} -call psb_set_erraction(err_act) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
err_act
-
the type of action. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: an integer. Possible values: psb_act_ret, -psb_act_abort. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: Utilities - Up: userhtml - Previous: psb_rcv Receive -   Contents
- - - - diff --git a/docs/html/node118.html b/docs/html/node118.html deleted file mode 100644 index 9e19b009..00000000 --- a/docs/html/node118.html +++ /dev/null @@ -1,91 +0,0 @@ - - - - - -Utilities - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: hb_read Read - Up: userhtml - Previous: Error handling -   Contents -
-
- - -

- -
-Utilities -

- -

-We have some utilities available for input and output of -sparse matrices; the interfaces to these routines are available in the -module psb_util_mod. - -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node119.html b/docs/html/node119.html deleted file mode 100644 index 31f1fbaf..00000000 --- a/docs/html/node119.html +++ /dev/null @@ -1,159 +0,0 @@ - - - - - -hb_read -- Read a sparse matrix from a file in the Harwell-Boeing format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: hb_write Write - Up: Utilities - Previous: Utilities -   Contents -
-
- - -

- hb_read -- Read a sparse matrix from a file in the - Harwell-Boeing format -

- -

-
-\begin{lstlisting} -call hb_read(a, iret, iunit, filename, b, mtitle) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
filename
-
The name of the file to be read. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
- -

-

-
On Return
-
-
-
a
-
the sparse matrix read from file. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
b
-
Rigth hand side(s). -
-Type: Optional -
-An array of type real or complex, rank 2 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side, otherwise will be left in the UNALLOCATED state. -
-
mtitle
-
Matrix title. -
-Type: Optional -
-A charachter variable of length 72 holding a copy of the -matrix title as specified by the Harwell-Boeing format and contained -in the input file. -
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: hb_write Write - Up: Utilities - Previous: Utilities -   Contents
- - - - diff --git a/docs/html/node12.html b/docs/html/node12.html deleted file mode 100644 index 165f326d..00000000 --- a/docs/html/node12.html +++ /dev/null @@ -1,98 +0,0 @@ - - - - - -get_local_rows -- Get number of local rows - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_local_cols Get - Up: Descriptor data structure - Previous: Descriptor Methods -   Contents -
-
- - -

-get_local_rows -- Get number of local rows -

- -

-

-nr = desc%get_local_rows()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of local rows, i.e. the number of - rows owned by the current process; as explained in 1, - it is equal to -$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$. The returned value is - specific to the calling process. -
-
- -

-

- - - diff --git a/docs/html/node120.html b/docs/html/node120.html deleted file mode 100644 index 11e1a5b6..00000000 --- a/docs/html/node120.html +++ /dev/null @@ -1,168 +0,0 @@ - - - - - -hb_write -- Write a sparse matrix to a file in the Harwell-Boeing format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: mm_mat_read Read - Up: Utilities - Previous: hb_read Read -   Contents -
-
- - -

-hb_write -- Write a sparse matrix to a file - in the Harwell-Boeing format -

- -

-
-\begin{lstlisting} -call hb_write(a, iret, iunit, filename, key, rhs, mtitle) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix to be written. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
b
-
Rigth hand side. -
-Type: Optional -
-An array of type real or complex, rank 1 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side. -
-
filename
-
The name of the file to be written to. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default output unit 6 (i.e. standard output -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
key
-
Matrix key. -
-Type: Optional -
-A charachter variable of length 8 holding the -matrix key as specified by the Harwell-Boeing format and to be -written to file. -
-
mtitle
-
Matrix title. -
-Type: Optional -
-A charachter variable of length 72 holding the -matrix title as specified by the Harwell-Boeing format and to be -written to file. -
-
- -

-

-
On Return
-
-
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: mm_mat_read Read - Up: Utilities - Previous: hb_read Read -   Contents
- - - - diff --git a/docs/html/node121.html b/docs/html/node121.html deleted file mode 100644 index 2854dbbe..00000000 --- a/docs/html/node121.html +++ /dev/null @@ -1,117 +0,0 @@ - - - - - -mm_mat_read -- Read a sparse matrix from a file in the MatrixMarket format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: mm_array_read Read - Up: Utilities - Previous: hb_write Write -   Contents -
-
- - -

-mm_mat_read -- Read a sparse matrix from a - file in the MatrixMarket format -

- -

-
-\begin{lstlisting} -call mm_mat_read(a, iret, iunit, filename) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
filename
-
The name of the file to be read. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
- -

-

-
On Return
-
-
-
a
-
the sparse matrix read from file. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node122.html b/docs/html/node122.html deleted file mode 100644 index 5a57cd34..00000000 --- a/docs/html/node122.html +++ /dev/null @@ -1,119 +0,0 @@ - - - - - -mm_array_read -- Read a dense array from a file in the MatrixMarket format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: mm_mat_write Write - Up: Utilities - Previous: mm_mat_read Read -   Contents -
-
- - -

-mm_array_read -- Read a dense array from a - file in the MatrixMarket format -

- -

-
-\begin{lstlisting} -call mm_array_read(b, iret, iunit, filename) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
filename
-
The name of the file to be read. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
- -

-

-
On Return
-
-
-
b
-
Rigth hand side(s). -
-Type: required -
-An array of type real or complex, rank 1 or 2 and having the ALLOCATABLE -attribute; will be allocated and filled in if the input file contains -a right hand side, otherwise will be left in the UNALLOCATED state. -
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node123.html b/docs/html/node123.html deleted file mode 100644 index 4dd5f34e..00000000 --- a/docs/html/node123.html +++ /dev/null @@ -1,123 +0,0 @@ - - - - - -mm_mat_write -- Write a sparse matrix to a file in the MatrixMarket format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: mm_array_write Write - Up: Utilities - Previous: mm_array_read Read -   Contents -
-
- - -

-mm_mat_write -- Write a sparse matrix to a - file in the MatrixMarket format -

- -

-
-\begin{lstlisting} -call mm_mat_write(a, mtitle, iret, iunit, filename) -\end{lstlisting} -
-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix to be written. -
-Type:required. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
mtitle
-
Matrix title. -
-Type: required -
-A charachter variable holding a descriptive title for the matrix to be - written to file. -
-
filename
-
The name of the file to be written to. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default output unit 6 (i.e. standard output -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
- -

-

-
On Return
-
-
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node124.html b/docs/html/node124.html deleted file mode 100644 index e7e3f85f..00000000 --- a/docs/html/node124.html +++ /dev/null @@ -1,115 +0,0 @@ - - - - - -mm_array_write -- Write a dense array from a file in the MatrixMarket format - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Preconditioner routines - Up: Utilities - Previous: mm_mat_write Write -   Contents -
-
- - -

-mm_array_write -- Write a dense array from a - file in the MatrixMarket format -

- -

-
-\begin{lstlisting} -call mm_array_write(b, iret, iunit, filename) -\end{lstlisting} -
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
b
-
Rigth hand side(s). -
-Type: required -
-An array of type real or complex, rank 1 or 2; will be written..
-
filename
-
The name of the file to be written. -
-Type:optional. -
-Specified as: a character variable containing a valid file name, or --, in which case the default input unit 5 (i.e. standard input -in Unix jargon) is used. Default: -. -
-
iunit
-
The Fortran file unit number. -
-Type:optional. -
-Specified as: an integer value. Only meaningful if filename is not -. -
-
- -

-

-
On Return
-
-
-
iret
-
Error code. -
-Type: required -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node125.html b/docs/html/node125.html deleted file mode 100644 index 0b67b710..00000000 --- a/docs/html/node125.html +++ /dev/null @@ -1,98 +0,0 @@ - - - - - -Preconditioner routines - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: init Initialize - Up: userhtml - Previous: mm_array_write Write -   Contents -
-
- - -

- -
-Preconditioner routines -

- -

-The base PSBLAS library contains the implementation of two simple -preconditioning techniques: - -

    -
  • Diagonal Scaling -
    • -
  • Block Jacobi with ILU(0) factorization -
    • -
-The supporting data type and subroutine interfaces are defined in the -module psb_prec_mod. -The old interfaces psb_precinit and psb_precbld are still supported for -backward compatibility - -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node126.html b/docs/html/node126.html deleted file mode 100644 index aa0d47e7..00000000 --- a/docs/html/node126.html +++ /dev/null @@ -1,150 +0,0 @@ - - - - - -init -- Initialize a preconditioner - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: build Builds - Up: Preconditioner routines - Previous: Preconditioner routines -   Contents -
-
- - -

-init -- Initialize a preconditioner -

- -

-

-call prec%init(icontxt,ptype, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
icontxt
-
the communication context. -
-Scope:global. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value. -
-
ptype
-
the type of preconditioner. -Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a character string, see usage notes. -
-
On Exit
-

-

-
prec
-
Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
info
-
Scope: global -
-Type: required -
-Intent: out. -
-Error code: if no error, 0 is returned. -
-
-Notes -Legal inputs to this subroutine are interpreted depending on the -$ptype$ string as follows4: -
-
NONE
-
No preconditioning, i.e. the preconditioner is just a copy - operator. -
-
DIAG
-
Diagonal scaling; each entry of the input vector is - multiplied by the reciprocal of the sum of the absolute values of - the coefficients in the corresponding row of matrix $A$; -
-
BJAC
-
Precondition by a factorization of the - block-diagonal of matrix $A$, where block boundaries are determined - by the data allocation boundaries for each process; requires no - communication. Only the incomplete factorization $ILU(0)$ is - currently implemented. -
-
- -

-

- - - diff --git a/docs/html/node127.html b/docs/html/node127.html deleted file mode 100644 index e6a55901..00000000 --- a/docs/html/node127.html +++ /dev/null @@ -1,194 +0,0 @@ - - - - - -build -- Builds a preconditioner - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: apply Preconditioner - Up: Preconditioner routines - Previous: init Initialize -   Contents -
-
- - -

-build -- Builds a preconditioner -

- -

-

-call prec%build(a, desc_a, info[,amold,vmold,imold])
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
the system sparse matrix. -Scope: local -
-Type: required -
-Intent: in, target. -
-Specified as: a sparse matrix data structure spdatapsb_Tspmat_type. -
-
prec
-
the preconditioner. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: an already initialized precondtioner data structure precdatapsb_prec_type -
-
desc_a
-
the problem communication descriptor. -Scope: local -
-Type: required -
-Intent: in, target. -
-Specified as: a communication descriptor data structure descdatapsb_desc_type. -
-
amold
-
The desired dynamic type for the internal matrix storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from spbasedatapsb_T_base_sparse_mat. -
-
vmold
-
The desired dynamic type for the internal vector storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from vbasedatapsb_T_base_vect_type. -
-
imold
-
The desired dynamic type for the internal integer vector storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from (integer) vbasedatapsb_T_base_vect_type. -
-
- -

-

-
On Return
-
-
-
prec
-
the preconditioner. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a precondtioner data structure precdatapsb_prec_type -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
-The amold, vmold and imold arguments may be -employed to interface with special devices, such as GPUs and other -accelerators. - -

- -

- - -next - -up - -previous - -contents -
- Next: apply Preconditioner - Up: Preconditioner routines - Previous: init Initialize -   Contents
- - - - diff --git a/docs/html/node128.html b/docs/html/node128.html deleted file mode 100644 index d6071c08..00000000 --- a/docs/html/node128.html +++ /dev/null @@ -1,153 +0,0 @@ - - - - - -apply -- Preconditioner application routine - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: descr Prints - Up: Preconditioner routines - Previous: build Builds -   Contents -
-
- - -

-apply -- Preconditioner application - routine -

- -

-

-call prec%apply(x,y,desc_a,info,trans,work)
-call prec%apply(x,desc_a,info,trans)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
prec
-
the preconditioner. -Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
x
-
the source vector. -Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array or an object of type vdatapsb_T_vect_type. -
-
desc_a
-
the problem communication descriptor. -Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a communication data structure descdatapsb_desc_type. -
-
trans
-
Scope: -
-Type: optional -
-Intent: in. -
-Specified as: a character. -
-
work
-
an optional work space -Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a double precision array. -
-
- -

-

-
On Return
-
-
-
y
-
the destination vector. -Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array or an object of type vdatapsb_T_vect_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node129.html b/docs/html/node129.html deleted file mode 100644 index de6f38ea..00000000 --- a/docs/html/node129.html +++ /dev/null @@ -1,114 +0,0 @@ - - - - - -descr -- Prints a description of current preconditioner - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: clone clone - Up: Preconditioner routines - Previous: apply Preconditioner -   Contents -
-
- - -

-descr -- Prints a description of current - preconditioner -

- -

-

-call prec%descr()
-call prec%descr(iout, root)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
prec
-
the preconditioner. -Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
iout
-
output unit. -Scope: local -
-Type: optional -
-Intent: in. -
-Specified as: an integer number. Default: default output unit. -
-
root
-
Process from which to print -Scope: local -
-Type: optional -
-Intent: in. -
-Specified as: an integer number between 0 and $np-1$, in which case -the specified process will print the description, or $-1$, in which case -all processes will print. Default: 0. -
-
- -

-

- - - diff --git a/docs/html/node13.html b/docs/html/node13.html deleted file mode 100644 index 0fdc4242..00000000 --- a/docs/html/node13.html +++ /dev/null @@ -1,99 +0,0 @@ - - - - - -get_local_cols -- Get number of local cols - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_global_rows Get - Up: Descriptor data structure - Previous: get_local_rows Get -   Contents -
-
- - -

-get_local_cols -- Get number of local cols -

- -

-

-nc = desc%get_local_cols()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of local cols, i.e. the number of - indices used by the current process, including both local and halo - indices; as explained in 1, - it is equal to -$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$. The - returned value is specific to the calling process. -
-
- -

-

- - - diff --git a/docs/html/node130.html b/docs/html/node130.html deleted file mode 100644 index 8cad168c..00000000 --- a/docs/html/node130.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -clone -- clone current preconditioner - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: free Free - Up: Preconditioner routines - Previous: descr Prints -   Contents -
-
- - -

-clone -- clone current - preconditioner -

- -
-call  prec%clone(precout,info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
prec
-
the preconditioner. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
precout
-
A copy of the input object. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node131.html b/docs/html/node131.html deleted file mode 100644 index 2c00d6de..00000000 --- a/docs/html/node131.html +++ /dev/null @@ -1,107 +0,0 @@ - - - - - -free -- Free a preconditioner - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Iterative Methods - Up: Preconditioner routines - Previous: clone clone -   Contents -
-
- - -

-free -- Free a preconditioner -

- -

-

-call prec%free(info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
prec
-
the preconditioner. -
-Scope: local. -
-Type: required -
-Intent: inout. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
On Exit
-

-

-
prec
-
Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
info
-
Scope: global -
-Type: required -
-Intent: out. -
-Error code: if no error, 0 is returned. -
-
-Notes -Releases all internal storage. - -

-

- - - diff --git a/docs/html/node132.html b/docs/html/node132.html deleted file mode 100644 index 9c42bbe2..00000000 --- a/docs/html/node132.html +++ /dev/null @@ -1,76 +0,0 @@ - - - - - -Iterative Methods - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_krylov Krylov - Up: userhtml - Previous: free Free -   Contents -
-
- - -

- -
-Iterative Methods -

- -

-In this chapter we provide routines for preconditioners and iterative -methods. The interfaces for Krylov subspace methods are available in -the module psb_krylov_mod. - -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node133.html b/docs/html/node133.html deleted file mode 100644 index ba43c36f..00000000 --- a/docs/html/node133.html +++ /dev/null @@ -1,440 +0,0 @@ - - - - - -psb_krylov -- Krylov Methods Driver Routine - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Bibliography - Up: Iterative Methods - Previous: Iterative Methods -   Contents -
-
- - -

-
-psb_krylov -- Krylov Methods Driver - Routine -

- -

-This subroutine is a driver that provides a general interface for all -the Krylov-Subspace family methods implemented in PSBLAS version 2. - -

-The stopping criterion can take the following values: -

-
1
-
normwise backward error in the infinity -norm; the iteration is stopped when -

-
- - -\begin{displaymath}err = \frac{\Vert r_i\Vert}{(\Vert A\Vert\Vert x_i\Vert+\Vert b\Vert)} < eps \end{displaymath} -
-
-

-
-
2
-
Relative residual in the 2-norm; the iteration is stopped -when -

-
- - -\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert b\Vert _2} < eps \end{displaymath} -
-
-

-
-
3
-
Relative residual reduction in the 2-norm; the iteration is stopped -when -

-
- - -\begin{displaymath}err = \frac{\Vert r_i\Vert}{\Vert r_0\Vert _2} < eps \end{displaymath} -
-
-

-
-
-The behaviour is controlled by the istop argument (see -later). In the above formulae, $x_i$ is the tentative solution and -$r_i=b-Ax_i$ the corresponding residual at the $i$-th iteration. - -

-
-\begin{lstlisting} -call psb_krylov(method,a,prec,b,x,eps,desc_a,info,& -& itmax,iter,err,itrace,irst,istop,cond) -\end{lstlisting} -
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
method
-
a string that defines the iterative method to be - used. Supported values are: -
-
CG:
-
the Conjugate Gradient method; - -
-
CGS:
-
the Conjugate Gradient Stabilized method; - -

-

-
GCR:
-
the Generalized Conjugate Residual method; - -
-
FCG:
-
the Flexible Conjugate Gradient method5; - -

-

-
BICG:
-
the Bi-Conjugate Gradient method; - -
-
BICGSTAB:
-
the Bi-Conjugate Gradient Stabilized method; - -
-
BICGSTABL:
-
the Bi-Conjugate Gradient Stabilized method with restarting; - -
-
RGMRES:
-
the Generalized Minimal Residual method with restarting. - -
-
-
-
a
-
the local portion of global sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
prec
-
The data structure containing the preconditioner. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type precdatapsb_prec_type. -
-
b
-
The RHS vector. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one array or an object of type vdatapsb_T_vect_type. -
-
x
-
The initial guess. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array or an object of type vdatapsb_T_vect_type. -
-
eps
-
The stopping tolerance. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a real number. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
itmax
-
The maximum number of iterations to perform. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $itmax = 1000$. -
-Specified as: an integer variable $itmax \ge 1$. -
-
itrace
-
If $>0$ print out an informational message about - convergence every $itrace$ iterations. If $=0$ print a message in - case of convergence failure. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $itrace = -1$. -
-
irst
-
An integer specifying the restart parameter. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Values: $irst>0$. This is employed for the BiCGSTABL or RGMRES -methods, otherwise it is ignored. - -

-

-
istop
-
An integer specifying the stopping criterion. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Values: 1: use the normwise backward error, 2: use the scaled 2-norm -of the residual, 3: use the residual reduction in the 2-norm. Default: 2. -
-
On Return
-
-
-
x
-
The computed solution. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one array or an object of type vdatapsb_T_vect_type. -
-
iter
-
The number of iterations performed. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: an integer variable. -
-
err
-
The convergence estimate on exit. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: a real number. -
-
cond
-
An estimate of the condition number of matrix $A$; only - available with the $CG$ method on real data. -
-Scope: global -
-Type: optional -
-Intent: out. -
-Returned as: a real number. A correct result will be greater than or -equal to one; if specified for non-real data, or an error occurred, -zero is returned. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- -

- -

- -

- - -next - -up - -previous - -contents -
- Next: Bibliography - Up: Iterative Methods - Previous: Iterative Methods -   Contents
- - - - diff --git a/docs/html/node134.html b/docs/html/node134.html deleted file mode 100644 index fa6197a5..00000000 --- a/docs/html/node134.html +++ /dev/null @@ -1,180 +0,0 @@ - - - - - -Bibliography - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: About this document ... - Up: userhtml - Previous: psb_krylov Krylov -   Contents -

- - -

-Bibliography -

1 -
- D. Barbieri, V. Cardellini, S. Filippone and D. Rouson -Design Patterns for Scientific Computations on Sparse Matrices, - HPSS 2011, Algorithms and Programming Tools for Next-Generation High-Performance Scientific Software, Bordeaux, Sep. 2011 - -

-

2 -
-G. Bella, S. Filippone, A. De Maio and M. Testa, -A Simulation Model for Forest Fires, -in J. Dongarra, K. Madsen, J. Wasniewski, editors, -Proceedings of PARA 04 Workshop on State of the Art -in Scientific Computing, pp. 546-553, Lecture Notes in Computer Science, -Springer, 2005. -

3 -
A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,
-2LEV-D2P4: a package of high-performance preconditioners,
-Applicable Algebra in Engineering, Communications and Computing, -Volume 18, Number 3, May, 2007, pp. 223-239 -

4 -
P. D'Ambra, S. Filippone, D. Di Serafino
-On the Development of PSBLAS-based Parallel Two-level Schwarz Preconditioners -
-Applied Numerical Mathematics, Elsevier Science, -Volume 57, Issues 11-12, November-December 2007, Pages 1181-1196. - -

-

5 -
- Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., -An Extended Set of Fortran Basic Linear Algebra Subprograms, -ACM Trans. Math. Softw. vol. 14, 1-17, 1988. -

6 -
- Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., -A Set of level 3 Basic Linear Algebra Subprograms, -ACM Trans. Math. Softw. vol. 16, 1-17, 1990. -

7 -
-J. J. Dongarra and R. C. Whaley, -A User's Guide to the BLACS v. 1.1, -Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of -Tennessee, March 1995 (updated May 1997). -

8 -
-I. Duff, M. Marrone, G. Radicati and C. Vittoli, -Level 3 Basic Linear Algebra Subprograms for Sparse Matrices: -a User Level Interface, -ACM Transactions on Mathematical Software, 23(3), pp. 379-401, 1997. -

9 -
-I. Duff, M. Heroux and R. Pozo, -An Overview of the Sparse Basic Linear -Algebra Subprograms: the New Standard from the BLAS Technical Forum, -ACM Transactions on Mathematical Software, 28(2), pp. 239-267, 2002. -

10 -
-S. Filippone and M. Colajanni, -PSBLAS: A Library for Parallel Linear Algebra -Computation on Sparse Matrices, -
-ACM Transactions on Mathematical Software, 26(4), pp. 527-550, 2000. -

11 -
-S. Filippone and A. Buttari, -Object-Oriented Techniques for Sparse Matrix Computations in Fortran 2003, -
-ACM Transactions on Mathematical Software, 38(4), 2012. -

12 -
-S. Filippone, P. D'Ambra, M. Colajanni, -Using a Parallel Library of Sparse Linear Algebra in a Fluid Dynamics -Applications Code on Linux Clusters, -in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors, -Parallel Computing - Advances & Current Issues, -pp. 441-448, Imperial College Press, 2002. -

13 -
- Gamma, E., Helm, R., Johnson, R., and Vlissides, - J. 1995. - Design Patterns: Elements of Reusable Object-Oriented Software. - Addison-Wesley. - -

-

14 -
-Karypis, G. and Kumar, V., -METIS: Unstructured Graph Partitioning and Sparse Matrix - Ordering System. -Minneapolis, MN 55455: University of Minnesota, Department of - Computer Science, 1995. -Internet Address: http://www.cs.umn.edu/~karypis. -

15 -
-Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., - Basic Linear Algebra Subprograms for Fortran usage, -ACM Trans. Math. Softw. vol. 5, 38-329, 1979. - -

-

16 -
-Machiels, L. and Deville, M. -Fortran 90: An entry to object-oriented programming for the solution - of partial differential equations. -ACM Trans. Math. Softw. vol. 23, 32-49. -

17 -
-Metcalf, M., Reid, J. and Cohen, M. -Fortran 95/2003 explained. -Oxford University Press, 2004. -

18 -
-Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The - Object-Oriented Way. Cambridge University Press (2011) - -

-

19 -
-M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra, -MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, -MIT Press, 1998. -
- -

-

- - - diff --git a/docs/html/node135.html b/docs/html/node135.html deleted file mode 100644 index 003af8ea..00000000 --- a/docs/html/node135.html +++ /dev/null @@ -1,67 +0,0 @@ - - - - - -About this document ... - - - - - - - - - - - - - - - - -
-next - -up - -previous - -contents -
- Up: userhtml - Previous: Bibliography -   Contents -
-
- - -

-About this document ... -

-

-This document was generated using the -LaTeX2HTML translator Version 2018 (Released Feb 1, 2018) -

-Copyright © 1993, 1994, 1995, 1996, -Nikos Drakos, -Computer Based Learning Unit, University of Leeds. -
-Copyright © 1997, 1998, 1999, -Ross Moore, -Mathematics Department, Macquarie University, Sydney. -

-The command line arguments were:
- latex2html -local_icons -noaddress -dir ../../html userhtml.tex -

-The translation was initiated on 2019-11-20 -

- - - diff --git a/docs/html/node14.html b/docs/html/node14.html deleted file mode 100644 index df52c1c4..00000000 --- a/docs/html/node14.html +++ /dev/null @@ -1,90 +0,0 @@ - - - - - -get_global_rows -- Get number of global rows - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_global_cols Get - Up: Descriptor data structure - Previous: get_local_cols Get -   Contents -
-
- - -

-get_global_rows -- Get number of global rows -

- -

-

-nr = desc%get_global_rows()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of global rows, i.e. the size of the - global index space. -
-
- -

-

- - - diff --git a/docs/html/node15.html b/docs/html/node15.html deleted file mode 100644 index 32983a8e..00000000 --- a/docs/html/node15.html +++ /dev/null @@ -1,90 +0,0 @@ - - - - - -get_global_cols -- Get number of global cols - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_global_indices Get - Up: Descriptor data structure - Previous: get_global_rows Get -   Contents -
-
- - -

-get_global_cols -- Get number of global cols -

- -

-

-nr = desc%get_global_cols()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of global cols; usually this is equal - to the number of global rows. -
-
- -

-

- - - diff --git a/docs/html/node16.html b/docs/html/node16.html deleted file mode 100644 index d7a1001d..00000000 --- a/docs/html/node16.html +++ /dev/null @@ -1,99 +0,0 @@ - - - - - -get_global_indices -- Get vector of global indices - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_context Get - Up: Descriptor data structure - Previous: get_global_cols Get -   Contents -
-
- - -

-get_global_indices -- Get vector of global indices -

- -

-

-myidx = desc%get_global_indices([owned])
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-Type: required. -
-
owned
-
Choose if you only want owned indices - (owned=.true.) or also halo indices (owned=.false.). -Scope: local. -
-Type: optional; default: .true.. -
-
- -

-

-
On Return
-
-
-
Function value
-
The global indices, returned as an allocatable - integer array of rank 1. -
-
- -

-

- - - diff --git a/docs/html/node17.html b/docs/html/node17.html deleted file mode 100644 index c432cd85..00000000 --- a/docs/html/node17.html +++ /dev/null @@ -1,89 +0,0 @@ - - - - - -get_context -- Get communication context - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Clone clone - Up: Descriptor data structure - Previous: get_global_indices Get -   Contents -
-
- - -

-get_context -- Get communication context -

- -

-

-ictxt = desc%get_context()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
Function value
-
The communication context. -
-
- -

-

- - - diff --git a/docs/html/node18.html b/docs/html/node18.html deleted file mode 100644 index 42ebe881..00000000 --- a/docs/html/node18.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -Clone -- clone current object - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: CNV convert - Up: Descriptor data structure - Previous: get_context Get -   Contents -
-
- - -

-Clone -- clone current object -

- -

-

-call  desc%clone(descout,info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
descout
-
A copy of the input object. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node19.html b/docs/html/node19.html deleted file mode 100644 index 35a0d5cb..00000000 --- a/docs/html/node19.html +++ /dev/null @@ -1,89 +0,0 @@ - - - - - -CNV -- convert internal storage format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cd_get_large_threshold Get - Up: Descriptor data structure - Previous: Clone clone -   Contents -
-
- - -

-CNV -- convert internal storage format -

- -

-

-call  desc%cnv(mold)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope: local. -
-
mold
-
the desred integer storage format. -
-Scope: local. -
-Specified as: a object of type derived from (integer) vbasedatapsb_T_base_vect_type. -
-
-The mold arguments may be -employed to interface with special devices, such as GPUs and other -accelerators. - -

-

- - - diff --git a/docs/html/node2.html b/docs/html/node2.html deleted file mode 100644 index 3f09ef74..00000000 --- a/docs/html/node2.html +++ /dev/null @@ -1,169 +0,0 @@ - - - - - -Introduction - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: General overview - Up: userhtml - Previous: Contents -   Contents -
-
- - -

-
-Introduction -

- -

-The PSBLAS library, developed with the aim to facilitate the -parallelization of computationally intensive scientific applications, -is designed to address parallel implementation of iterative solvers -for sparse linear systems through the distributed memory paradigm. It -includes routines for multiplying sparse matrices by dense matrices, -solving block diagonal systems with triangular diagonal entries, -preprocessing sparse matrices, and contains additional routines for -dense matrix operations. The current implementation of PSBLAS -addresses a distributed memory execution model operating with message -passing. - -

-The PSBLAS library version 3 is implemented in - the Fortran 2003 [17] programming language, with reuse and/or - adaptation of existing Fortran 77 and Fortran 95 software, plus a - handful of C routines. - -

-The use of Fortran 2003 offers a number of advantages over Fortran 95, -mostly in the handling of requirements for evolution and adaptation of -the library to new computing architectures and integration of -new algorithms. -For a detailed discussion of our design see [11]; other -works discussing advanced programming in Fortran 2003 -include [1,18]; sufficient support for -Fortran 2003 is now available from many compilers, including the GNU -Fortran compiler from the Free Software Foundation (as of version 4.8). - -

-Previous approaches have been based on mixing Fortran 95, with its -support for object-based design, with other languages; these have -been advocated by a number of authors, -e.g. [16]. Moreover, the Fortran 95 facilities for dynamic -memory management and interface overloading greatly enhance the -usability of the PSBLAS -subroutines. In this way, the library can take care of runtime memory -requirements that are quite difficult or even impossible to predict at -implementation or compilation time. - -

-The presentation of the -PSBLAS library follows the general structure of the proposal for -serial Sparse BLAS [8,9], which in its turn is based on the -proposal for BLAS on dense matrices [15,5,6]. - -

-The applicability of sparse iterative solvers to many different areas -causes some terminology problems because the same concept may be -denoted through different names depending on the application area. The -PSBLAS features presented in this document will be discussed referring -to a finite difference discretization of a Partial Differential -Equation (PDE). However, the scope of the library is wider than -that: for example, it can be applied to finite element discretizations -of PDEs, and even to different classes of problems such as nonlinear -optimization, for example in optimal control problems. - -

-The design of a solver for sparse linear systems is driven by many -conflicting objectives, such as limiting occupation of storage -resources, exploiting regularities in the input data, exploiting -hardware characteristics of the parallel platform. To achieve an -optimal communication to computation ratio on distributed memory -machines it is essential to keep the data locality as high as -possible; this can be done through an appropriate data allocation -strategy. The choice of the preconditioner is another very important -factor that affects efficiency of the implemented application. Optimal -data distribution requirements for a given preconditioner may conflict -with distribution requirements of the rest of the solver. Finding the -optimal trade-off may be very difficult because it is application -dependent. Possible solutions to these problems and other important -inputs to the development of the PSBLAS software package have come from -an established experience in applying the PSBLAS solvers to -computational fluid dynamics applications. - -

- -

- - -next - -up - -previous - -contents -
- Next: General overview - Up: userhtml - Previous: Contents -   Contents
- - - - diff --git a/docs/html/node20.html b/docs/html/node20.html deleted file mode 100644 index 905f54a5..00000000 --- a/docs/html/node20.html +++ /dev/null @@ -1,80 +0,0 @@ - - - - - -psb_cd_get_large_threshold -- Get threshold for index mapping switch - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cd_set_large_threshold Set - Up: Descriptor data structure - Previous: CNV convert -   Contents -
-
- - -

-psb_cd_get_large_threshold -- Get threshold for - index mapping switch -

- -

-

-ith = psb_cd_get_large_threshold()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Return
-
-
-
Function value
-
The current value for the size threshold. - -

-

-
- -

-

- - - diff --git a/docs/html/node21.html b/docs/html/node21.html deleted file mode 100644 index 3478b03a..00000000 --- a/docs/html/node21.html +++ /dev/null @@ -1,91 +0,0 @@ - - - - - -psb_cd_set_large_threshold -- Set threshold for index mapping switch - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Named Constants - Up: Descriptor data structure - Previous: psb_cd_get_large_threshold Get -   Contents -
-
- - -

-psb_cd_set_large_threshold -- Set threshold for - index mapping switch -

- -

-

-call psb_cd_set_large_threshold(ith)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
ith
-
the new threshold for communication descriptors. -
-Scope: global. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value greater than zero. -
-
-Note: the threshold value is only queried by the library at the time a -call to psb_cdall is executed, therefore changing the threshold -has no effect on communication descriptors that have already been -initialized. Moreover the threshold must have the same value on all -processes. - -

-

- - - diff --git a/docs/html/node22.html b/docs/html/node22.html deleted file mode 100644 index b733e044..00000000 --- a/docs/html/node22.html +++ /dev/null @@ -1,98 +0,0 @@ - - - - - -Named Constants - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Sparse Matrix class - Up: Descriptor data structure - Previous: psb_cd_set_large_threshold Set -   Contents -
-
- - -

- -
-Named Constants -

-
-
psb_none_
-
Generic no-op; -
-
psb_root_
-
Default root process for broadcast and scatter operations; -
-
psb_nohalo_
-
Do not fetch halo elements; -
-
psb_halo_
-
Fetch halo elements from neighbouring processes; -
-
psb_sum_
-
Sum overlapped elements -
-
psb_avg_
-
Average overlapped elements -
-
psb_comm_halo_
-
Exchange data based on the halo_index - list; -
-
psb_comm_ext_
-
Exchange data based on the ext_index - list; -
-
psb_comm_ovr_
-
Exchange data based on the ovrlap_index - list; -
-
psb_comm_mov_
-
Exchange data based on the ovr_mst_idx - list; - -

-

-
- -

-

- - - diff --git a/docs/html/node23.html b/docs/html/node23.html deleted file mode 100644 index ecc0e565..00000000 --- a/docs/html/node23.html +++ /dev/null @@ -1,216 +0,0 @@ - - - - - -Sparse Matrix class - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Sparse Matrix Methods - Up: Data Structures and Classes - Previous: Named Constants -   Contents -
-
- - -

- -
-Sparse Matrix class -

-The spdatapsb_Tspmat_type class -contains all information about the local portion of the sparse matrix and -its storage mode. Its design is -based on the STATE design pattern [13] as detailed -in [11]; the type declaration is shown in -figure 4 where T is a placeholder for the -data type and precision variants -
-
S
-
Single precision real; -
-
D
-
Double precision real; -
-
C
-
Single precision complex; -
-
Z
-
Double precision complex. -
-
-The actual data is contained in the polymorphic component a%a -of type spbasedatapsb_T_base_sparse_mat; its -specific layout can be chosen dynamically among the predefined types, -or an entirely new storage layout can be implemented and passed to the -library at runtime via the psb_spasb routine. - -
- - - -
Figure 4: - The PSBLAS defined data type that - contains a sparse matrix.
-
- -
-
-  type :: psb_Tspmat_type
-    class(psb_T_base_sparse_mat), allocatable  :: a 
-  end type  psb_Tspmat_type
-
-
-
-
-The following very common formats are precompiled in PSBLAS and thus -are always available: -
-
psb_T_coo_sparse_mat
-
Coordinate storage; -
-
psb_T_csr_sparse_mat
-
Compressed storage by rows; -
-
psb_T_csc_sparse_mat
-
Compressed storage by columns; -
-
-The inner sparse matrix has an associated state, which can take the -following values: -
-
Build:
-
State entered after the first allocation, and before the - first assembly; in this state it is possible to add nonzero entries. -
-
Assembled:
-
State entered after the assembly; computations using - the sparse matrix, such as matrix-vector products, are only possible - in this state; -
-
Update:
-
State entered after a reinitalization; this is used to - handle applications in which the same sparsity pattern is used - multiple times with different coefficients. In this state it is only - possible to enter coefficients for already existing nonzero entries. -
-
-The only storage variant supporting the build state is COO; all other -variants are obtained by conversion to/from it. - -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: Sparse Matrix Methods - Up: Data Structures and Classes - Previous: Named Constants -   Contents
- - - - diff --git a/docs/html/node24.html b/docs/html/node24.html deleted file mode 100644 index 660dda42..00000000 --- a/docs/html/node24.html +++ /dev/null @@ -1,59 +0,0 @@ - - - - - -Sparse Matrix Methods - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_nrows Get - Up: Sparse Matrix class - Previous: Sparse Matrix class -   Contents -
-
- - -

-Sparse Matrix Methods -

- -

-

- - - diff --git a/docs/html/node25.html b/docs/html/node25.html deleted file mode 100644 index 4e11b66d..00000000 --- a/docs/html/node25.html +++ /dev/null @@ -1,89 +0,0 @@ - - - - - -get_nrows -- Get number of rows in a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_ncols Get - Up: Sparse Matrix class - Previous: Sparse Matrix Methods -   Contents -
-
- - -

-get_nrows -- Get number of rows in a sparse matrix -

- -

-

-nr = a%get_nrows()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of rows of sparse matrix a. -
-
- -

-

- - - diff --git a/docs/html/node26.html b/docs/html/node26.html deleted file mode 100644 index c22ddd4c..00000000 --- a/docs/html/node26.html +++ /dev/null @@ -1,90 +0,0 @@ - - - - - -get_ncols -- Get number of columns in a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_nnzeros Get - Up: Sparse Matrix class - Previous: get_nrows Get -   Contents -
-
- - -

-get_ncols -- Get number of columns in a sparse - matrix -

- -

-

-nc = a%get_ncols()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of columns of sparse matrix a. -
-
- -

-

- - - diff --git a/docs/html/node27.html b/docs/html/node27.html deleted file mode 100644 index a7b464d0..00000000 --- a/docs/html/node27.html +++ /dev/null @@ -1,100 +0,0 @@ - - - - - -get_nnzeros -- Get number of nonzero elements in a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_size Get - Up: Sparse Matrix class - Previous: get_ncols Get -   Contents -
-
- - -

-get_nnzeros -- Get number of nonzero elements - in a sparse matrix -

- -

-

-nz = a%get_nnzeros()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of nonzero elements stored in sparse matrix a. -
-
- -

-Notes - -

    -
  1. The function value is specific to the storage format of matrix - a; some storage formats employ padding, thus the returned - value for the same matrix may be different for different storage choices. -
    2. -
- -

-

- - - diff --git a/docs/html/node28.html b/docs/html/node28.html deleted file mode 100644 index c7f4130f..00000000 --- a/docs/html/node28.html +++ /dev/null @@ -1,91 +0,0 @@ - - - - - -get_size -- Get maximum number of nonzero elements in a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: sizeof Get - Up: Sparse Matrix class - Previous: get_nnzeros Get -   Contents -
-
- - -

-get_size -- Get maximum number of nonzero elements - in a sparse matrix -

- -

-

-maxnz = a%get_size()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The maximum number of nonzero elements that can - be stored in sparse matrix a using its current memory allocation. -
-
- -

-

- - - diff --git a/docs/html/node29.html b/docs/html/node29.html deleted file mode 100644 index bd2a7410..00000000 --- a/docs/html/node29.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -sizeof -- Get memory occupation in bytes -of a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_fmt Short - Up: Sparse Matrix class - Previous: get_size Get -   Contents -
-
- - -

-sizeof -- Get memory occupation in bytes -of a sparse matrix -

- -

-

-memory_size = a%sizeof()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The memory occupation in bytes. -
-
- -

-

- - - diff --git a/docs/html/node3.html b/docs/html/node3.html deleted file mode 100644 index 9d55ff44..00000000 --- a/docs/html/node3.html +++ /dev/null @@ -1,196 +0,0 @@ - - - - - -General overview - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Basic Nomenclature - Up: userhtml - Previous: Introduction -   Contents -
-
- - -

- -
-General overview -

-The PSBLAS library is designed to handle the implementation of -iterative solvers for sparse linear systems on distributed memory -parallel computers. The system coefficient matrix $A$ must be square; -it may be real or complex, nonsymmetric, and its sparsity pattern -needs not to be symmetric. The serial computation parts are based on -the serial sparse BLAS, so that any extension made to the data -structures of the serial kernels is available to the parallel -version. The overall design and parallelization strategy have been -influenced by the structure of the ScaLAPACK parallel -library. The layered structure of the PSBLAS library -is shown in figure 1; lower layers of the library -indicate an encapsulation relationship with upper layers. The ongoing -discussion focuses on the Fortran 2003 layer immediately below the -application layer. -The serial parts of the computation on each process are executed through -calls to the serial sparse BLAS subroutines. -In a similar way, the inter-process message exchanges are encapsulated -in an applicaiton layer that has been strongly inspired by the Basic -Linear Algebra Communication Subroutines (BLACS) library [7]. -Usually there is no need to deal directly with MPI; however, in some -cases, MPI routines are used directly to improve efficiency. For -further details on our communication layer see Sec. 7. - -

- -

- - - -
Figure 1: -PSBLAS library components hierarchy.
-
-\includegraphics[scale=0.65]{figures/psblas.eps} - -\includegraphics[scale=0.65]{figures/psblas} - -
-
- -

-The type of linear system matrices that we address typically arise in the -numerical solution of PDEs; in such a context, -it is necessary to pay special attention to the -structure of the problem from which the application originates. -The nonzero pattern of a matrix arising from the -discretization of a PDE is influenced by various factors, such as the -shape of the domain, the discretization strategy, and -the equation/unknown ordering. The matrix itself can be interpreted as -the adjacency matrix of the graph associated with the discretization -mesh. - -

-The distribution of the coefficient matrix for the linear system is -based on the “owner computes” rule: -the variable associated to each mesh point is assigned to a process -that will own the corresponding row in the coefficient matrix and -will carry out all related computations. This allocation strategy -is equivalent to a partition of the discretization mesh into sub-domains. -Our library supports any distribution that keeps together -the coefficients of each matrix row; there are no other constraints on -the variable assignment. -This choice is consistent with simple data distributions -such as CYCLIC(N) and BLOCK, -as well as completely arbitrary assignments of -equation indices to processes. -In particular it is consistent with the -usage of graph partitioning tools commonly available in the -literature, e.g. METIS [14]. -Dense vectors conform to sparse -matrices, that is, the entries of a vector follow the same distribution -of the matrix rows. - -

-We assume that the sparse matrix is built in parallel, where each -process generates its own portion. We never require that the entire -matrix be available on a single node. However, it is possible -to hold the entire matrix in one process and distribute it -explicitly1, even though the resulting memory -bottleneck would make this option unattractive in most cases. - -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: Basic Nomenclature - Up: userhtml - Previous: Introduction -   Contents
- - - - diff --git a/docs/html/node30.html b/docs/html/node30.html deleted file mode 100644 index abfd6eca..00000000 --- a/docs/html/node30.html +++ /dev/null @@ -1,91 +0,0 @@ - - - - - -get_fmt -- Short description of the dynamic type - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: is_bld, is_upd, is_asb - Up: Sparse Matrix class - Previous: sizeof Get -   Contents -
-
- - -

-get_fmt -- Short description of the dynamic type -

- -

-

-write(*,*) a%get_fmt()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
A short string describing the dynamic type of - the matrix. Predefined values include NULL, COO, - CSR and CSC. -
-
- -

-

- - - diff --git a/docs/html/node31.html b/docs/html/node31.html deleted file mode 100644 index d12946dd..00000000 --- a/docs/html/node31.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -is_bld, is_upd, is_asb -- Status check - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: is_lower, is_upper, is_triangle, is_unit - Up: Sparse Matrix class - Previous: get_fmt Short -   Contents -
-
- - -

-is_bld, is_upd, is_asb -- Status check -

- -

-

-if (a%is_bld()) then 
-if (a%is_upd()) then 
-if (a%is_asb()) then 
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
A logical value indicating whether the - matrix is in the Build, Update or Assembled state, respectively. -
-
- -

-

- - - diff --git a/docs/html/node32.html b/docs/html/node32.html deleted file mode 100644 index e799406e..00000000 --- a/docs/html/node32.html +++ /dev/null @@ -1,96 +0,0 @@ - - - - - -is_lower, is_upper, is_triangle, is_unit -- Format check - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: cscnv Convert - Up: Sparse Matrix class - Previous: is_bld, is_upd, is_asb -   Contents -
-
- - -

-is_lower, is_upper, is_triangle, is_unit -- - Format check -

- -

-

-if (a%is_triangle()) then 
-if (a%is_upper()) then 
-if (a%is_lower()) then 
-if (a%is_unit()) then 
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
A logical value indicating whether the - matrix is triangular; if is_triangle() returns .true. - check also if it is lower, upper and with a unit (i.e. assumed) - diagonal. -
-
- -

-

- - - diff --git a/docs/html/node33.html b/docs/html/node33.html deleted file mode 100644 index 09fdf104..00000000 --- a/docs/html/node33.html +++ /dev/null @@ -1,114 +0,0 @@ - - - - - -cscnv -- Convert to a different storage format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: csclip Reduce - Up: Sparse Matrix class - Previous: is_lower, is_upper, is_triangle, is_unit -   Contents -
-
- - -

-cscnv -- Convert to a different storage format -

- -

-

-call  a%cscnv(b,info [, type, mold, dupl])
-call  a%cscnv(info [, type, mold, dupl])
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
type
-
a string requesting a new format. -
-Type: optional. -
-
mold
-
a variable of class(psb_T_base_sparse_mat) requesting a new format. -
-Type: optional. -
-
dupl
-
an integer value specifing how to handle duplicates (see - Named Constants below) -
-
- -

-

-
On Return
-
-
-
b,a
-
A copy of a with a new storage format. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
-The mold arguments may be -employed to interface with special devices, such as GPUs and other -accelerators. - -

-

- - - diff --git a/docs/html/node34.html b/docs/html/node34.html deleted file mode 100644 index c5b9402d..00000000 --- a/docs/html/node34.html +++ /dev/null @@ -1,106 +0,0 @@ - - - - - -csclip -- Reduce to a submatrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: clean_zeros Eliminate - Up: Sparse Matrix class - Previous: cscnv Convert -   Contents -
-
- - -

-csclip -- Reduce to a submatrix -

- -
-    call a%csclip(b,info[,&
-       & imin,imax,jmin,jmax,rscale,cscale])
-
- -

-Returns the submatrix A(imin:imax,jmin:jmax), optionally -rescaling row/col indices to the range -1:imax-imin+1,1:jmax-jmin+1. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
imin,imax,jmin,jmax
-
Minimum and maximum row and column indices. -
-Type: optional. -
-
rscale,cscale
-
Whether to rescale row/column indices. -Type: optional. -
-
-
-
On Return
-
-
-
b
-
A copy of a submatrix of a. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node35.html b/docs/html/node35.html deleted file mode 100644 index 027817f2..00000000 --- a/docs/html/node35.html +++ /dev/null @@ -1,98 +0,0 @@ - - - - - -clean_zeros -- Eliminate zero coefficients - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_diag Get - Up: Sparse Matrix class - Previous: csclip Reduce -   Contents -
-
- - -

-clean_zeros -- Eliminate zero coefficients -

- -
-    call a%clean_zeros(info)
-
- -

-Eliminates zero coefficients in the input matrix. Note that depending -on the internal storage format, there may still be some amount of -zero padding in the output. - -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
-
-
On Return
-
-
-
a
-
The matrix a without zero coefficients. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node36.html b/docs/html/node36.html deleted file mode 100644 index 4768938d..00000000 --- a/docs/html/node36.html +++ /dev/null @@ -1,94 +0,0 @@ - - - - - -get_diag -- Get main diagonal - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: clip_diag Cut - Up: Sparse Matrix class - Previous: clean_zeros Eliminate -   Contents -
-
- - -

-get_diag -- Get main diagonal -

- -
-    call a%get_diag(d,info)
-
- -

-Returns a copy of the main diagonal. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
-
-
On Return
-
-
-
d
-
A copy of the main diagonal. -
-A one-dimensional array of the appropriate type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node37.html b/docs/html/node37.html deleted file mode 100644 index 6cc088c9..00000000 --- a/docs/html/node37.html +++ /dev/null @@ -1,94 +0,0 @@ - - - - - -clip_diag -- Cut out main diagonal - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: tril Return - Up: Sparse Matrix class - Previous: get_diag Get -   Contents -
-
- - -

-clip_diag -- Cut out main diagonal -

- -
-    call a%clip_diag(b,info)
-
- -

-Returns a copy of a without the main diagonal. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
-
-
On Return
-
-
-
b
-
A copy of a without the main diagonal. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node38.html b/docs/html/node38.html deleted file mode 100644 index a718ea45..00000000 --- a/docs/html/node38.html +++ /dev/null @@ -1,117 +0,0 @@ - - - - - -tril -- Return the lower triangle - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: triu Return - Up: Sparse Matrix class - Previous: clip_diag Cut -   Contents -
-
- - -

-tril -- Return the lower triangle -

- -
-    call a%tril(l,info[,&
-       & diag,imin,imax,jmin,jmax,rscale,cscale,u])
-
- -

-Returns the lower triangular part of submatrix -A(imin:imax,jmin:jmax), optionally rescaling row/col indices to -the range 1:imax-imin+1,1:jmax-jmin+1 and returing the -complementary upper triangle. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
diag
-
Include diagonals up to this one; diag=1 means the - first superdiagonal, diag=-1 means the first subdiagonal. -Default 0. -
-
imin,imax,jmin,jmax
-
Minimum and maximum row and column indices. -
-Type: optional. -
-
rscale,cscale
-
Whether to rescale row/column indices. -Type: optional. -
-
-
-
On Return
-
-
-
l
-
A copy of the lower triangle of a. -
-A variable of type psb_Tspmat_type. -
-
u
-
(optional) A copy of the upper triangle of a. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node39.html b/docs/html/node39.html deleted file mode 100644 index 685de000..00000000 --- a/docs/html/node39.html +++ /dev/null @@ -1,117 +0,0 @@ - - - - - -triu -- Return the upper triangle - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_set_mat_default Set - Up: Sparse Matrix class - Previous: tril Return -   Contents -
-
- - -

-triu -- Return the upper triangle -

- -
-    call a%triu(u,info[,&
-       & diag,imin,imax,jmin,jmax,rscale,cscale,l])
-
- -

-Returns the upper triangular part of submatrix -A(imin:imax,jmin:jmax), optionally rescaling row/col indices to -the range 1:imax-imin+1,1:jmax-jmin+1, and returing the -complementary lower triangle. -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-A variable of type psb_Tspmat_type. -
-Scope: local. -
-
diag
-
Include diagonals up to this one; diag=1 means the - first superdiagonal, diag=-1 means the first subdiagonal. -Default 0. -
-
imin,imax,jmin,jmax
-
Minimum and maximum row and column indices. -
-Type: optional. -
-
rscale,cscale
-
Whether to rescale row/column indices. -Type: optional. -
-
-
-
On Return
-
-
-
u
-
A copy of the upper triangle of a. -
-A variable of type psb_Tspmat_type. -
-
l
-
(optional) A copy of the lower triangle of a. -
-A variable of type psb_Tspmat_type. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node4.html b/docs/html/node4.html deleted file mode 100644 index 1fd13393..00000000 --- a/docs/html/node4.html +++ /dev/null @@ -1,222 +0,0 @@ - - - - - -Basic Nomenclature - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Library contents - Up: General overview - Previous: General overview -   Contents -
-
- - -

-Basic Nomenclature -

- -

-Our computational model implies that the data allocation on the -parallel distributed memory machine is guided by the structure of the -physical model, and specifically by the discretization mesh of the -PDE. - -

-Each point of the discretization mesh will have (at least) one -associated equation/variable, and therefore one index. We say that -point $i$ depends on point $j$ if the equation for a -variable associated with $i$ contains a term in $j$, or equivalently -if $a_{ij} \ne0$. -After the partition of the discretization mesh into sub-domains -assigned to the parallel processes, -we classify the points of a given sub-domain as following. -

-
Internal.
-
An internal point of - a given domain depends only on points of the -same domain. -If all points of a domain are assigned to one -process, then a computational step (e.g., a -matrix-vector product) of the -equations associated with the internal points requires no data -items from other domains and no communications. - -

-

-
Boundary.
-
A point of -a given domain is a boundary point if it depends on points -belonging to other domains. - -

-

-
Halo.
-
A halo point for a given domain is a point belonging to -another domain such that there is a boundary point which depends -on it. Whenever performing a computational step, such as a -matrix-vector product, the values associated with halo points are -requested from other domains. A boundary point of a given -domain is usually a halo point for some other domain2; therefore -the cardinality of the boundary points set denotes the amount of data - sent to other domains. -
-
Overlap.
-
An overlap point is a boundary point assigned to -multiple domains. Any operation that involves an overlap point -has to be replicated for each assignment. -
-
-Overlap points do not usually exist in the basic data -distributions; however they are a feature of Domain Decomposition -Schwarz preconditioners which are the subject of related research -work [4,3]. - -

-We denote the sets of internal, boundary and halo points for a given -subdomain by $\cal I$, $\cal B$ and $\cal H$. -Each subdomain is assigned to one process; each process usually -owns one subdomain, although the user may choose to assign more than -one subdomain to a process. If each process $i$ owns one -subdomain, the number of rows in the local sparse matrix is - -$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert$, and the number of local columns -(i.e. those for which there exists at least one non-zero entry in the -local rows) is -$\vert{\cal I}_i\vert + \vert{\cal B}_i\vert +\vert{\cal H}_i\vert$. - -

- -

- - - -
Figure 2: -Point classfication.
-
-\includegraphics[scale=0.65]{figures/points.eps} - -\rotatebox{-90}{\includegraphics[scale=0.65]{figures/points}} - -
-
- -

-This classification of mesh points guides the naming scheme that we -adopted in the library internals and in the data structures. We -explicitly note that “Halo” points are also often called “ghost” -points in the literature. - -

- -

- - -next - -up - -previous - -contents -
- Next: Library contents - Up: General overview - Previous: General overview -   Contents
- - - - diff --git a/docs/html/node40.html b/docs/html/node40.html deleted file mode 100644 index 33021ee9..00000000 --- a/docs/html/node40.html +++ /dev/null @@ -1,80 +0,0 @@ - - - - - -psb_set_mat_default -- Set default storage format - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: clone Clone - Up: Sparse Matrix class - Previous: triu Return -   Contents -
-
- - -

-psb_set_mat_default -- Set default storage format -

- -

-

-call  psb_set_mat_default(a)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
a variable of class(psb_T_base_sparse_mat) requesting - a new default storage format. -
-Type: required. -
-
- -

-

- - - diff --git a/docs/html/node41.html b/docs/html/node41.html deleted file mode 100644 index b76f447c..00000000 --- a/docs/html/node41.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -clone -- Clone current object - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Named Constants - Up: Sparse Matrix class - Previous: psb_set_mat_default Set -   Contents -
-
- - -

-clone -- Clone current object -

- -

-

-call  a%clone(b,info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
the sparse matrix. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
b
-
A copy of the input object. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node42.html b/docs/html/node42.html deleted file mode 100644 index 0810e2ec..00000000 --- a/docs/html/node42.html +++ /dev/null @@ -1,82 +0,0 @@ - - - - - -Named Constants - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Dense Vector Data Structure - Up: Sparse Matrix class - Previous: clone Clone -   Contents -
-
- - -

- -
-Named Constants -

-
-
psb_dupl_ovwrt_
-
Duplicate coefficients should be overwritten - (i.e. ignore duplications) -
-
psb_dupl_add_
-
Duplicate coefficients should be added; -
-
psb_dupl_err_
-
Duplicate coefficients should trigger an error conditino -
-
psb_upd_dflt_
-
Default update strategy for matrix coefficients; -
-
psb_upd_srch_
-
Update strategy based on search into the data structure; -
-
psb_upd_perm_
-
Update strategy based on additional - permutation data (see tools routine description). -
-
- -

-

- - - diff --git a/docs/html/node43.html b/docs/html/node43.html deleted file mode 100644 index 74f930ba..00000000 --- a/docs/html/node43.html +++ /dev/null @@ -1,164 +0,0 @@ - - - - - -Dense Vector Data Structure - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Vector Methods - Up: Data Structures and Classes - Previous: Named Constants -   Contents -
-
- - -

- -
-Dense Vector Data Structure -

-The vdatapsb_T_vect_type data structure -encapsulates the dense vectors in a way similar to sparse matrices, -i.e. including a base type vbasedata psb_T_base_vect_type. -The user will not, in general, access the vector components directly, -but rather via the routines of sec. 6. Among other -simple things, we define here an extraction method that can be used to -get a full copy of the part of the vector stored on the local -process. - -

-The type declaration is shown in -figure 5 where T is a placeholder for the -data type and precision variants -

-
I
-
Integer; -
-
S
-
Single precision real; -
-
D
-
Double precision real; -
-
C
-
Single precision complex; -
-
Z
-
Double precision complex. -
-
-The actual data is contained in the polymorphic component v%v; -the separation between the application and the actual data is -essential for cases where it is necessary to link to data storage made -available elsewhere outside the direct control of the -compiler/application, e.g. data stored in a graphics accelerator's -private memory. - -
- - - -
Figure 5: - The PSBLAS defined data type that - contains a dense vector.
-
- -
-
-  type psb_T_base_vect_type
-    TYPE(KIND_), allocatable :: v(:)
-  end type psb_T_base_vect_type
-
-  type psb_T_vect_type
-    class(psb_T_base_vect_type), allocatable :: v 
-  end type  psb_T_vect_type
-
-
-
-
- -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: Vector Methods - Up: Data Structures and Classes - Previous: Named Constants -   Contents
- - - - diff --git a/docs/html/node44.html b/docs/html/node44.html deleted file mode 100644 index d7ea4154..00000000 --- a/docs/html/node44.html +++ /dev/null @@ -1,57 +0,0 @@ - - - - - -Vector Methods - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_nrows Get - Up: Dense Vector Data Structure - Previous: Dense Vector Data Structure -   Contents -
-
- - -

-Vector Methods -

-
- - - diff --git a/docs/html/node45.html b/docs/html/node45.html deleted file mode 100644 index 967d15c6..00000000 --- a/docs/html/node45.html +++ /dev/null @@ -1,89 +0,0 @@ - - - - - -get_nrows -- Get number of rows in a dense vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: sizeof Get - Up: Dense Vector Data Structure - Previous: Vector Methods -   Contents -
-
- - -

-get_nrows -- Get number of rows in a dense vector -

- -

-

-nr = v%get_nrows()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
v
-
the dense vector -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The number of rows of dense vector v. -
-
- -

-

- - - diff --git a/docs/html/node46.html b/docs/html/node46.html deleted file mode 100644 index 85e38867..00000000 --- a/docs/html/node46.html +++ /dev/null @@ -1,92 +0,0 @@ - - - - - -sizeof -- Get memory occupation in bytes -of a dense vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: set Set - Up: Dense Vector Data Structure - Previous: get_nrows Get -   Contents -
-
- - -

-sizeof -- Get memory occupation in bytes -of a dense vector -

- -

-

-memory_size = v%sizeof()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
v
-
the dense vector -
-Scope: local -
-
- -

-

-
On Return
-
-
-
Function value
-
The memory occupation in bytes. -
-
- -

-

- - - diff --git a/docs/html/node47.html b/docs/html/node47.html deleted file mode 100644 index b14e02f9..00000000 --- a/docs/html/node47.html +++ /dev/null @@ -1,134 +0,0 @@ - - - - - -set -- Set contents of the vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: get_vect Get - Up: Dense Vector Data Structure - Previous: sizeof Get -   Contents -
-
- - -

-set -- Set contents of the vector -

- -

-

- call  v%set(alpha[,first,last])
- call  v%set(vect[,first,last])
- call  v%zero()
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
v
-
the dense vector -
-Scope: local -
-
alpha
-
A scalar value. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a number of the data -type indicated in Table 1. - -

-

-
first,last
-
Boundaries for setting in the vector. -
-Scope: local -
-Type: optional -
-Intent: in. -
-Specified - as: integers. -
-
vect
-
An array -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a number of the data -type indicated in Table 1. -
-
-Note that a call to v%zero() is provided as a shorthand, but -is equivalent to a call to v%set(zero) with the zero -constant having the appropriate type and kind. - -

-

-
On Return
-
-
-
v
-
the dense vector, with updated entries -
-Scope: local -
-
- -

-

- - - diff --git a/docs/html/node48.html b/docs/html/node48.html deleted file mode 100644 index e8c5cf98..00000000 --- a/docs/html/node48.html +++ /dev/null @@ -1,111 +0,0 @@ - - - - - -get_vect -- Get a copy of the vector contents - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: clone Clone - Up: Dense Vector Data Structure - Previous: set Set -   Contents -
-
- - -

-get_vect -- Get a copy of the vector contents -

- -

-

-extv = v%get_vect([n])
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
v
-
the dense vector -
-Scope: local -
-
n
-
Size to be returned -
-Scope: local. -
-Type: optional; default: entire vector. -
-

-

-
- -

-

-
On Return
-
-
-
Function value
-
An allocatable array holding a copy of the dense - vector contents. If the argument $n$ is specified, the size of the - returned array equals the minimum between $n$ and the internal size - of the vector, or 0 if $n$ is negative; otherwise, the size of the - array is the same as the internal size of the vector. -
-
- -

-

- - - diff --git a/docs/html/node49.html b/docs/html/node49.html deleted file mode 100644 index 08d0b52c..00000000 --- a/docs/html/node49.html +++ /dev/null @@ -1,90 +0,0 @@ - - - - - -clone -- Clone current object - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Preconditioner data structure - Up: Dense Vector Data Structure - Previous: get_vect Get -   Contents -
-
- - -

-clone -- Clone current object -

- -
-call  x%clone(y,info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
the dense vector. -
-Scope: local. -
-
- -

-

-
On Return
-
-
-
y
-
A copy of the input object. -
-
info
-
Return code. -
-
- -

-

- - - diff --git a/docs/html/node5.html b/docs/html/node5.html deleted file mode 100644 index a2f0e2b8..00000000 --- a/docs/html/node5.html +++ /dev/null @@ -1,194 +0,0 @@ - - - - - -Library contents - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Application structure - Up: General overview - Previous: Basic Nomenclature -   Contents -
-
- - -

-Library contents -

- -

-The PSBLAS library consists of various classes of subroutines: -

-
Computational routines
-
comprising: - -
    -
  • Sparse matrix by dense matrix product; -
    • -
  • Sparse triangular -systems solution for block diagonal matrices; -
    • -
  • Vector and matrix norms; -
    • -
  • Dense matrix sums; -
    • -
  • Dot products. -
    • -
-
-
Communication routines
-
handling halo and overlap - communications; -
-
Data management and auxiliary routines
-
including: - -
    -
  • Parallel environment management -
    • -
  • Communication descriptors allocation; -
    • -
  • Dense and sparse matrix allocation; -
    • -
  • Dense and sparse matrix build and update; -
    • -
  • Sparse matrix and data distribution preprocessing. -
    • -
-
-
Preconditioner routines
-
-
-
Iterative methods
-
a subset of Krylov subspace iterative - methods -
-
-The following naming scheme has been adopted for all the symbols -internally defined in the PSBLAS software package: - -
    -
  • all symbols (i.e. subroutine names, data types...) are - prefixed by psb_ -
    • -
  • all data type names are suffixed by _type -
    • -
  • all constants are suffixed by _ -
    • -
  • all top-level subroutine names follow the rule psb_xxname where - xx can be either: - -
      -
    • ge: the routine is related to dense data, -
      • -
    • sp: the routine is related to sparse data, -
      • -
    • cd: the routine is related to communication descriptor - (see 3). - -
      • -
    - For example the psb_geins, psb_spins and - psb_cdins perform the same action (see 6) on - dense matrices, sparse matrices and communication descriptors - respectively. - Interface overloading allows the usage of the same subroutine - names for both real and complex data. -
    • -
-In the description of the subroutines, arguments or argument entries -are classified as: -
-
global
-
For input arguments, the value must be the same on all processes - participating in the subroutine call; for output arguments the value - is guaranteed to be the same. -
-
local
-
Each process has its own value(s) independently. -
-
-To finish our general description, we define a version string with the -constant -

-
- - -\begin{displaymath}\verb\vert psb_version_string_\vert\end{displaymath} -
-
-

-whose current value is 3.4.0 - -

- -

- - -next - -up - -previous - -contents -
- Next: Application structure - Up: General overview - Previous: Basic Nomenclature -   Contents
- - - - diff --git a/docs/html/node50.html b/docs/html/node50.html deleted file mode 100644 index 3b2fcc2e..00000000 --- a/docs/html/node50.html +++ /dev/null @@ -1,88 +0,0 @@ - - - - - -Preconditioner data structure - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Heap data structure - Up: Data Structures and Classes - Previous: clone Clone -   Contents -
-
- - -

- -
-Preconditioner data structure -

-Our base library offers support for simple well known preconditioners -like Diagonal Scaling or Block Jacobi with incomplete -factorization ILU(0). - -

-A preconditioner is held in the precdata psb_prec_type data structure reported in -figure 6. The psb_prec_type -data type may contain a simple preconditioning matrix with the -associated communication descriptor.The internal preconditioner is allocated appropriately with the -dynamic type corresponding to the desired preconditioner. - -

- - - -
Figure 6: -The PSBLAS defined data type that contains a preconditioner.
-
- -
-
-  type psb_Tprec_type
-    class(psb_T_base_prec_type), allocatable :: prec
-  end type psb_Tprec_type
-
-
-
- -

-

- - - diff --git a/docs/html/node51.html b/docs/html/node51.html deleted file mode 100644 index d7f55d82..00000000 --- a/docs/html/node51.html +++ /dev/null @@ -1,97 +0,0 @@ - - - - - -Heap data structure - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Computational routines - Up: Data Structures and Classes - Previous: Preconditioner data structure -   Contents -
-
- - -

-Heap data structure -

- -

-Among the tools routines of sec. 6, we have a number -of sorting utilities; the heap sort is implemented in terms of heaps -having the following signatures: -

-
psb_T_heap
-
: a heap containing elements of type T, where T - can be i,s,c,d,z for integer, real and complex data; -
-
psb_T_idx_heap
-
: a heap containing elements of type T, as - above, together with an integer index. -
-
-Given a heap object, the following methods are defined on it: -
-
init
-
Initialize memory; also choose ascending or descending - order; -
-
howmany
-
Current heap occupancy; -
-
insert
-
Add an item (or an item and its index); -
-
get_first
-
Remove and return the first element; -
-
dump
-
Print on file; -
-
free
-
Release memory. -
-
-These objects are used in MLD2P4 to implement the factorization -algorithms. - -

-

- - - diff --git a/docs/html/node52.html b/docs/html/node52.html deleted file mode 100644 index deb3c842..00000000 --- a/docs/html/node52.html +++ /dev/null @@ -1,93 +0,0 @@ - - - - - -Computational routines - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geaxpby General - Up: userhtml - Previous: Heap data structure -   Contents -
-
- - -

-Computational routines -

- -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node53.html b/docs/html/node53.html deleted file mode 100644 index 6df5a187..00000000 --- a/docs/html/node53.html +++ /dev/null @@ -1,280 +0,0 @@ - - - - - -psb_geaxpby -- General Dense Matrix Sum - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_gedot Dot - Up: Computational routines - Previous: Computational routines -   Contents -
-
- - -

-psb_geaxpby -- General Dense Matrix Sum -

- -

-This subroutine is an interface to the computational kernel for -dense matrix sum: -

-
- - -\begin{displaymath}y \leftarrow \alpha\> x+ \beta y \end{displaymath} -
-
-

- -

-

-call psb_geaxpby(alpha, x, beta, y, desc_a, info)
-
- -

-

-
- - - -
Table 1: -Data types
-
- - - - - - - - - - - - - - - - -
$x$, $y$, $\alpha$, $\beta$Subroutine
Short Precision Realpsb_geaxpby
Long Precision Realpsb_geaxpby
Short Precision Complexpsb_geaxpby
Long Precision Complexpsb_geaxpby
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
alpha
-
the scalar $\alpha$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data -type indicated in Table 1. -
-
x
-
the local portion of global dense matrix -$x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type -specified in Table 1. The rank of $x$ must be the same of $y$. -
-
beta
-
the scalar $\beta$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 1. -
-
y
-
the local portion of the global dense matrix -$y$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type containing numbers of the type -indicated in Table 1. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. - -

-

-
- -

-

-
On Return
-
-
-
y
-
the local portion of result submatrix $y$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type containing numbers of the type -indicated in Table 1. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_gedot Dot - Up: Computational routines - Previous: Computational routines -   Contents
- - - - diff --git a/docs/html/node54.html b/docs/html/node54.html deleted file mode 100644 index 1cfefa4f..00000000 --- a/docs/html/node54.html +++ /dev/null @@ -1,317 +0,0 @@ - - - - - -psb_gedot -- Dot Product - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_gedots Generalized - Up: Computational routines - Previous: psb_geaxpby General -   Contents -
-
- - -

-psb_gedot -- Dot Product -

- -

-This function computes dot product between two vectors $x$ and -$y$. -
-If $x$ and $y$ are real vectors -it computes dot-product as: -

-
- - -\begin{displaymath}dot \leftarrow x^T y\end{displaymath} -
-
-

-Else if $x$ and $y$ are complex vectors then it computes dot-product as: -

-
- - -\begin{displaymath}dot \leftarrow x^H y\end{displaymath} -
-
-

- -

-

-psb_gedot(x, y, desc_a, info [,global])
-
-

-
- - - -
Table 2: -Data types
-
- - - - - - - - - - - - - - - - -
$dot$, $x$, $y$Function
Short Precision Realpsb_gedot
Long Precision Realpsb_gedot
Short Precision Complexpsb_gedot
Long Precision Complexpsb_gedot
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 2. The rank of $x$ must be the same of $y$. -
-
y
-
the local portion of global dense matrix -$y$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 2. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
global
-
Specifies whether the computation should include the - global reduction across all processes. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Specified as: a logical scalar. -Default: global=.true. -
-

-

-
On Return
-
-
-
Function value
-
is the dot product of vectors $x$ and $y$. -
-Scope: global unless the optional variable -global=.false. has been specified -
-Specified as: a number of the data type indicated in Table 2. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. The computation of a global result requires a global - communication, which entails a significant overhead. It may be - necessary and/or advisable to compute multiple dot products at the same - time; in this case, it is possible to improve the runtime efficiency - by using the following scheme: -
    -\begin{lstlisting} -vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.) -vres(... -...,y3,desc_a,info,global=.false.) -call psb_sum(ictxt,vres(1:3)) -\end{lstlisting} -
    -In this way the global communication, which for small sizes is a - latency-bound operation, is invoked only once. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_gedots Generalized - Up: Computational routines - Previous: psb_geaxpby General -   Contents
- - - - diff --git a/docs/html/node55.html b/docs/html/node55.html deleted file mode 100644 index f14e7e64..00000000 --- a/docs/html/node55.html +++ /dev/null @@ -1,264 +0,0 @@ - - - - - -psb_gedots -- Generalized Dot Product - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_normi Infinity-Norm - Up: Computational routines - Previous: psb_gedot Dot -   Contents -
-
- - -

-psb_gedots -- Generalized Dot Product -

- -

-This subroutine computes a series of dot products among the columns of -two dense matrices $x$ and $y$: -

-
- - -\begin{displaymath}res(i) \leftarrow x(:,i)^T y(:,i)\end{displaymath} -
-
-

-If the matrices are complex, then the -usual convention applies, i.e. the conjugate transpose of $x$ is -used. If $x$ and $y$ are of rank one, then $res$ is a scalar, else it -is a rank one array. - -

-

-call psb_gedots(res, x, y, desc_a, info)
-
-

-
- - - -
Table 3: -Data types
-
- - - - - - - - - - - - - - - - -
$res$, $x$, $y$Subroutine
Short Precision Realpsb_gedots
Long Precision Realpsb_gedots
Short Precision Complexpsb_gedots
Long Precision Complexpsb_gedots
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 3. The rank of $x$ must be the same of $y$. -
-
y
-
the local portion of global dense matrix -$y$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 3. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
On Return
-
-
-
res
-
is the dot product of vectors $x$ and $y$. -
-Scope: global -
-Intent: out. -
-Specified as: a number or a rank-one array of the data type indicated -in Table 2. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_normi Infinity-Norm - Up: Computational routines - Previous: psb_gedot Dot -   Contents
- - - - diff --git a/docs/html/node56.html b/docs/html/node56.html deleted file mode 100644 index d626f7f6..00000000 --- a/docs/html/node56.html +++ /dev/null @@ -1,283 +0,0 @@ - - - - - -psb_normi -- Infinity-Norm of Vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geamaxs Generalized - Up: Computational routines - Previous: psb_gedots Generalized -   Contents -
-
- - -

-psb_normi -- Infinity-Norm of Vector -

- -

-This function computes - the infinity-norm of a vector $x$. -
-If $x$ is a real vector -it computes infinity norm as: -

-
- - -\begin{displaymath}amax \leftarrow \max_i \vert x_i\vert\end{displaymath} -
-
-

-else if $x$ is a complex vector then it computes the infinity-norm as: -

-
- - -\begin{displaymath}amax \leftarrow \max_i {(\vert re(x_i)\vert + \vert im(x_i)\vert)}\end{displaymath} -
-
-

- -

-

-psb_geamax(x, desc_a, info [,global])
-psb_normi(x, desc_a, info [,global])
-
- -

-

-
- - - -
Table 4: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$amax$$x$Function
Short Precision RealShort Precision Realpsb_geamax
Long Precision RealLong Precision Realpsb_geamax
Short Precision RealShort Precision Complexpsb_geamax
Long Precision RealLong Precision Complexpsb_geamax
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 4. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
global
-
Specifies whether the computation should include the - global reduction across all processes. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Specified as: a logical scalar. -Default: global=.true. -
- -

-

-
On Return
-
-
-
Function value
-
is the infinity norm of vector $x$. -
-Scope: global unless the optional variable -global=.false. has been specified -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. The computation of a global result requires a global - communication, which entails a significant overhead. It may be - necessary and/or advisable to compute multiple norms at the same - time; in this case, it is possible to improve the runtime efficiency - by using the following scheme: -
    -\begin{lstlisting} -vres(1) = psb_geamax(x1,desc_a,info,global=.false.) -vres(2)... -...(x3,desc_a,info,global=.false.) -call psb_amx(ictxt,vres(1:3)) -\end{lstlisting} -
    -In this way the global communication, which for small sizes is a - latency-bound operation, is invoked only once. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_geamaxs Generalized - Up: Computational routines - Previous: psb_gedots Generalized -   Contents
- - - - diff --git a/docs/html/node57.html b/docs/html/node57.html deleted file mode 100644 index fdd2f842..00000000 --- a/docs/html/node57.html +++ /dev/null @@ -1,216 +0,0 @@ - - - - - -psb_geamaxs -- Generalized Infinity Norm - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_norm1 1-Norm - Up: Computational routines - Previous: psb_normi Infinity-Norm -   Contents -
-
- - -

-psb_geamaxs -- Generalized Infinity Norm -

- -

-This subroutine computes a series of infinity norms on the columns of -a dense matrix $x$: -

-
- - -\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath} -
-
-

- -

-

-call psb_geamaxs(res, x, desc_a, info)
-
- -

-

-
- - - -
Table 5: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$res$$x$Subroutine
Short Precision RealShort Precision Realpsb_geamaxs
Long Precision RealLong Precision Realpsb_geamaxs
Short Precision RealShort Precision Complexpsb_geamaxs
Long Precision RealLong Precision Complexpsb_geamaxs
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 5. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
On Return
-
-
-
res
-
is the infinity norm of the columns of $x$. -
-Scope: global -
-Intent: out. -
-Specified as: a number or a rank-one array of long precision real numbers. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_norm1 1-Norm - Up: Computational routines - Previous: psb_normi Infinity-Norm -   Contents
- - - - diff --git a/docs/html/node58.html b/docs/html/node58.html deleted file mode 100644 index c4fd28f7..00000000 --- a/docs/html/node58.html +++ /dev/null @@ -1,281 +0,0 @@ - - - - - -psb_norm1 -- 1-Norm of Vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geasums Generalized - Up: Computational routines - Previous: psb_geamaxs Generalized -   Contents -
-
- - -

-psb_norm1 -- 1-Norm of Vector -

- -

-This function computes the 1-norm of a vector $x$. -
-If $x$ is a real vector -it computes 1-norm as: -

-
- - -\begin{displaymath}asum \leftarrow \Vert x_i\Vert\end{displaymath} -
-
-

-else if $x$ is a complex vector then it computes 1-norm as: -

-
- - -\begin{displaymath}asum \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath} -
-
-

- -

-

-psb_geasum(x, desc_a, info [,global])
-psb_norm1(x, desc_a, info [,global])
-
- -

-

-
- - - -
Table 6: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$asum$$x$Function
Short Precision RealShort Precision Realpsb_geasum
Long Precision RealLong Precision Realpsb_geasum
Short Precision RealShort Precision Complexpsb_geasum
Long Precision RealLong Precision Complexpsb_geasum
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 6. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
global
-
Specifies whether the computation should include the - global reduction across all processes. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Specified as: a logical scalar. -Default: global=.true. -
-

-

-
On Return
-
-
-
Function value
-
is the 1-norm of vector $x$. -
-Scope: global unless the optional variable -global=.false. has been specified -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. The computation of a global result requires a global - communication, which entails a significant overhead. It may be - necessary and/or advisable to compute multiple norms at the same - time; in this case, it is possible to improve the runtime efficiency - by using the following scheme: -
    -\begin{lstlisting} -vres(1) = psb_geasum(x1,desc_a,info,global=.false.) -vres(2)... -...(x3,desc_a,info,global=.false.) -call psb_sum(ictxt,vres(1:3)) -\end{lstlisting} -
    -In this way the global communication, which for small sizes is a - latency-bound operation, is invoked only once. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_geasums Generalized - Up: Computational routines - Previous: psb_geamaxs Generalized -   Contents
- - - - diff --git a/docs/html/node59.html b/docs/html/node59.html deleted file mode 100644 index 4ab320ea..00000000 --- a/docs/html/node59.html +++ /dev/null @@ -1,264 +0,0 @@ - - - - - -psb_geasums -- Generalized 1-Norm of Vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_norm2 2-Norm - Up: Computational routines - Previous: psb_norm1 1-Norm -   Contents -
-
- - -

-psb_geasums -- Generalized 1-Norm of Vector -

- -

-This subroutine computes a series of 1-norms on the columns of -a dense matrix $x$: -

-
- - -\begin{displaymath}res(i) \leftarrow \max_k \vert x(k,i)\vert \end{displaymath} -
-
-

-This function computes the 1-norm of a vector $x$. -
-If $x$ is a real vector -it computes 1-norm as: -

-
- - -\begin{displaymath}res(i) \leftarrow \Vert x_i\Vert\end{displaymath} -
-
-

-else if $x$ is a complex vector then it computes 1-norm as: -

-
- - -\begin{displaymath}res(i) \leftarrow \Vert re(x)\Vert _1 + \Vert im(x)\Vert _1\end{displaymath} -
-
-

- -

-

-call psb_geasums(res, x, desc_a, info)
-
- -

-

-
- - - -
Table 7: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$res$$x$Subroutine
Short Precision RealShort Precision Realpsb_geasums
Long Precision RealLong Precision Realpsb_geasums
Short Precision RealShort Precision Complexpsb_geasums
Long Precision RealLong Precision Complexpsb_geasums
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 7. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. - -

-

-
On Return
-
-
-
res
-
contains the 1-norm of (the columns of) $x$. -
-Scope: global -
-Intent: out. -
-Short as: a long precision real number. -Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_norm2 2-Norm - Up: Computational routines - Previous: psb_norm1 1-Norm -   Contents
- - - - diff --git a/docs/html/node6.html b/docs/html/node6.html deleted file mode 100644 index 91707813..00000000 --- a/docs/html/node6.html +++ /dev/null @@ -1,281 +0,0 @@ - - - - - -Application structure - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: User-defined index mappings - Up: General overview - Previous: Library contents -   Contents -
-
- - -

- -
-Application structure -

- -

-The main underlying principle of the PSBLAS library is that the -library objects are created and exist with reference to a discretized -space to which there corresponds an index space and a matrix sparsity -pattern. As an example, consider a cell-centered finite-volume -discretization of the Navier-Stokes equations on a simulation domain; -the index space $1\dots n$ is isomorphic to the set of cell centers, -whereas the pattern of the associated linear system matrix is -isomorphic to the adjacency graph imposed on the discretization mesh -by the discretization stencil. - -

-Thus the first order of business is to establish an index space, and -this is done with a call to psb_cdall in which we specify the -size of the index space $n$ and the allocation of the elements of the -index space to the various processes making up the MPI (virtual) -parallel machine. - -

-The index space is partitioned among processes, and this creates a -mapping from the “global” numbering $1\dots n$ to a numbering -“local” to each process; each process $i$ will own a certain subset - -$1\dots n_{\hbox{row}_i}$, each element of which corresponds to a certain -element of $1\dots n$. The user does not set explicitly this mapping; -when the application needs to indicate to which element of the index -space a certain item is related, such as the row and column index of a -matrix coefficient, it does so in the “global” numbering, and the -library will translate into the appropriate “local” numbering. - -

-For a given index space $1\dots n$ there are many possible associated -topologies, i.e. many different discretization stencils; thus the -description of the index space is not completed until the user has -defined a sparsity pattern, either explicitly through psb_cdins -or implicitly through psb_spins. The descriptor is finalized -with a call to psb_cdasb and a sparse matrix with a call to -psb_spasb. After psb_cdasb each process $i$ will have -defined a set of “halo” (or “ghost”) indices - -$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$, denoting elements of the index -space that are not assigned to process $i$; however the -variables associated with them are needed to complete computations -associated with the sparse matrix $A$, and thus they have to be -fetched from (neighbouring) processes. The descriptor of the index -space is built exactly for the purpose of properly sequencing the -communication steps required to achieve this objective. - -

-A simple application structure will walk through the index space -allocation, matrix/vector creation and linear system solution as -follows: - -

    -
  1. Initialize parallel environment with psb_init -
    2. -
  2. Initialize index space with psb_cdall -
    3. -
  3. Allocate sparse matrix and dense vectors with psb_spall - and psb_geall -
    4. -
  4. Loop over all local rows, generate matrix and vector entries, - and insert them with psb_spins and psb_geins -
    5. -
  5. Assemble the various entities: - -
      -
    1. psb_cdasb -
      2. -
    2. psb_spasb -
      3. -
    3. psb_geasb -
      4. -
    -
    6. -
  6. Choose the preconditioner to be used with prec%init and - build it with prec%build3. -
    7. -
  7. Call the iterative method of choice, e.g. psb_bicgstab -
    8. -
-This is the structure of the sample programs in the directory -test/pargen/. - -

-For a simulation in which the same discretization mesh is used over -multiple time steps, the following structure may be more appropriate: - -

    -
  1. Initialize parallel environment with psb_init -
    2. -
  2. Initialize index space with psb_cdall -
    3. -
  3. Loop over the topology of the discretization mesh and build the - descriptor with psb_cdins -
    4. -
  4. Assemble the descriptor with psb_cdasb -
    5. -
  5. Allocate the sparse matrices and dense vectors with - psb_spall and psb_geall -
    6. -
  6. Loop over the time steps: - -
      -
    1. If after first time step, - reinitialize the sparse matrix with psb_sprn; also zero out - the dense vectors; -
      2. -
    2. Loop over the mesh, generate the coefficients and insert/update - them with psb_spins and psb_geins -
      3. -
    3. Assemble with psb_spasb and psb_geasb -
      4. -
    4. Choose and build preconditioner with prec%init and - prec%build -
      5. -
    5. Call the iterative method of choice, e.g. psb_bicgstab - -
      6. -
    -
    7. -
-The insertion routines will be called as many times as needed; -they only need to be called on the data that is actually -allocated to the current process, i.e. each process generates its own -data. - -

-In principle there is no specific order in the calls to -psb_spins, nor is there a requirement to build a matrix row in -its entirety before calling the routine; this allows the application -programmer to walk through the discretization mesh element by element, -generating the main part of a given matrix row but also contributions -to the rows corresponding to neighbouring elements. - -

-From a functional point of view it is even possible to execute one -call for each nonzero coefficient; however this would have a -substantial computational overhead. It is therefore advisable to pack -a certain amount of data into each call to the insertion routine, say -touching on a few tens of rows; the best performng value would depend -on both the architecture of the computer being used and on the problem -structure. -At the opposite extreme, it would be possible to generate the entire -part of a coefficient matrix residing on a process and pass it in a -single call to psb_spins; this, however, would entail a -doubling of memory occupation, and thus would be almost always far -from optimal. - -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: User-defined index mappings - Up: General overview - Previous: Library contents -   Contents
- - - - diff --git a/docs/html/node60.html b/docs/html/node60.html deleted file mode 100644 index f663ca4c..00000000 --- a/docs/html/node60.html +++ /dev/null @@ -1,283 +0,0 @@ - - - - - -psb_norm2 -- 2-Norm of Vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_genrm2s Generalized - Up: Computational routines - Previous: psb_geasums Generalized -   Contents -
-
- - -

-psb_norm2 -- 2-Norm of Vector -

- -

-This function computes the 2-norm of a vector $x$. -
-If $x$ is a real vector -it computes 2-norm as: -

-
- - -\begin{displaymath}nrm2 \leftarrow \sqrt{x^T x}\end{displaymath} -
-
-

-else if $x$ is a complex vector then it computes 2-norm as: -

-
- - -\begin{displaymath}nrm2 \leftarrow \sqrt{x^H x}\end{displaymath} -
-
-

- -

-

-
- - - -
Table 8: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$nrm2$$x$Function
Short Precision RealShort Precision Realpsb_genrm2
Long Precision RealLong Precision Realpsb_genrm2
Short Precision RealShort Precision Complexpsb_genrm2
Long Precision RealLong Precision Complexpsb_genrm2
-
-
-

-
- -

-

-psb_genrm2(x, desc_a, info [,global])
-psb_norm2(x, desc_a, info [,global])
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 8. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
global
-
Specifies whether the computation should include the - global reduction across all processes. -
-Scope: global -
-Type: optional. -
-Intent: in. -
-Specified as: a logical scalar. -Default: global=.true. -
- -

-

-
On Return
-
-
-
Function Value
-
is the 2-norm of vector $x$. -
-Scope: global unless the optional variable -global=.false. has been specified -
-Type: required -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. The computation of a global result requires a global - communication, which entails a significant overhead. It may be - necessary and/or advisable to compute multiple norms at the same - time; in this case, it is possible to improve the runtime efficiency - by using the following scheme: -
    -\begin{lstlisting} -vres(1) = psb_genrm2(x1,desc_a,info,global=.false.) -vres(2)... -...x3,desc_a,info,global=.false.) -call psb_nrm2(ictxt,vres(1:3)) -\end{lstlisting} -
    -In this way the global communication, which for small sizes is a - latency-bound operation, is invoked only once. -
    2. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_genrm2s Generalized - Up: Computational routines - Previous: psb_geasums Generalized -   Contents
- - - - diff --git a/docs/html/node61.html b/docs/html/node61.html deleted file mode 100644 index 867d4545..00000000 --- a/docs/html/node61.html +++ /dev/null @@ -1,219 +0,0 @@ - - - - - -psb_genrm2s -- Generalized 2-Norm of Vector - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_norm1 1-Norm - Up: Computational routines - Previous: psb_norm2 2-Norm -   Contents -
-
- - -

-psb_genrm2s -- Generalized 2-Norm of Vector -

- -

-This subroutine computes a series of 2-norms on the columns of -a dense matrix $x$: -

-
- - -\begin{displaymath}res(i) \leftarrow \Vert x(:,i)\Vert _2 \end{displaymath} -
-
-

- -

-

-call psb_genrm2s(res, x, desc_a, info)
-
- -

-

-
- - - -
Table 9: -Data types
-
- - - - - - - - - - - - - - - - - - - - - -
$res$$x$Subroutine
Short Precision RealShort Precision Realpsb_genrm2s
Long Precision RealLong Precision Realpsb_genrm2s
Short Precision RealShort Precision Complexpsb_genrm2s
Long Precision RealLong Precision Complexpsb_genrm2s
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 9. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. - -

-

-
On Return
-
-
-
res
-
contains the 1-norm of (the columns of) $x$. -
-Scope: global -
-Intent: out. -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_norm1 1-Norm - Up: Computational routines - Previous: psb_norm2 2-Norm -   Contents
- - - - diff --git a/docs/html/node62.html b/docs/html/node62.html deleted file mode 100644 index 6ef4e36d..00000000 --- a/docs/html/node62.html +++ /dev/null @@ -1,194 +0,0 @@ - - - - - -psb_norm1 -- 1-Norm of Sparse Matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_normi Infinity - Up: Computational routines - Previous: psb_genrm2s Generalized -   Contents -
-
- - -

-psb_norm1 -- 1-Norm of Sparse Matrix -

- -

-This function computes the 1-norm of a matrix $A$: -
-

-

-
- - -\begin{displaymath}nrm1 \leftarrow \Vert A\Vert _1 \end{displaymath} -
-
-

-where: -
-
$A$
-
represents the global matrix $A$ -
-
- -

-

-
- - - -
Table 10: -Data types
-
- - - - - - - - - - - - - - - - -
$A$Function
Short Precision Realpsb_spnrm1
Long Precision Realpsb_spnrm1
Short Precision Complexpsb_spnrm1
Long Precision Complexpsb_spnrm1
-
-
-

-
- -

-

-psb_spnrm1(A, desc_a, info)
-psb_norm1(A, desc_a, info)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
the local portion of the global sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type spdatapsb_Tspmat_type. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
On Return
-
-
-
Function value
-
is the 1-norm of sparse submatrix $A$. -
-Scope: global -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node63.html b/docs/html/node63.html deleted file mode 100644 index d084adad..00000000 --- a/docs/html/node63.html +++ /dev/null @@ -1,194 +0,0 @@ - - - - - -psb_normi -- Infinity Norm of Sparse Matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spmm Sparse - Up: Computational routines - Previous: psb_norm1 1-Norm -   Contents -
-
- - -

-psb_normi -- Infinity Norm of Sparse Matrix -

- -

-This function computes the infinity-norm of a matrix $A$: -
-

-

-
- - -\begin{displaymath}nrmi \leftarrow \Vert A\Vert _\infty \end{displaymath} -
-
-

-where: -
-
$A$
-
represents the global matrix $A$ -
-
- -

-

-
- - - -
Table 11: -Data types
-
- - - - - - - - - - - - - - - - -
$A$Function
Short Precision Realpsb_spnrmi
Long Precision Realpsb_spnrmi
Short Precision Complexpsb_spnrmi
Long Precision Complexpsb_spnrmi
-
-
-

-
- -

-

-psb_spnrmi(A, desc_a, info)
-psb_normi(A, desc_a, info)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
the local portion of the global sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type spdatapsb_Tspmat_type. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
On Return
-
-
-
Function value
-
is the infinity-norm of sparse submatrix $A$. -
-Scope: global -
-Specified as: a long precision real number. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node64.html b/docs/html/node64.html deleted file mode 100644 index 9f15d14c..00000000 --- a/docs/html/node64.html +++ /dev/null @@ -1,427 +0,0 @@ - - - - - -psb_spmm -- Sparse Matrix by Dense Matrix Product - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spsm Triangular - Up: Computational routines - Previous: psb_normi Infinity -   Contents -
-
- - -

-psb_spmm -- Sparse Matrix by Dense Matrix - Product -

- -

-This subroutine computes the Sparse Matrix by Dense Matrix Product: - -

-
-

- - - - - - -
\begin{displaymath} -y \leftarrow \alpha A x + \beta y -\end{displaymath} -(1)
-

-
-
- - - - - - -
\begin{displaymath} -y \leftarrow \alpha A^T x + \beta y -\end{displaymath} -(2)
-

-
-
- - - - - - -
\begin{displaymath} -y \leftarrow \alpha A^H x + \beta y -\end{displaymath} -(3)
-

- -

-where: -

-
$x$
-
is the global dense matrix $x_{:, :}$ -
-
$y$
-
is the global dense matrix $y_{:, :}$ -
-
$A$
-
is the global sparse matrix $A$ -
-
- -

-

-
- - - -
Table 12: -Data types
-
- - - - - - - - - - - - - - - - -
$A$, $x$, $y$, $\alpha$, $\beta$Subroutine
Short Precision Realpsb_spmm
Long Precision Realpsb_spmm
Short Precision Complexpsb_spmm
Long Precision Complexpsb_spmm
-
-
-

-
- -

-

-call psb_spmm(alpha, a, x, beta, y, desc_a, info)
-call psb_spmm(alpha, a, x, beta, y,desc_a, info, &
-             & trans, work)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
alpha
-
the scalar $\alpha$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in -Table 12. -
-
a
-
the local portion of the sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type spdatapsb_Tspmat_type. -
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 12. The rank of $x$ must be the same of $y$. -
-
beta
-
the scalar $\beta$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 12. -
-
y
-
the local portion of global dense matrix -$y$. - -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 12. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
trans
-
indicates what kind of operation to perform. -
-
trans = N
-
the operation is specified by equation 1 -
-
trans = T
-
the operation is specified by equation -2 -
-
trans = C
-
the operation is specified by equation -3 -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $trans = N$ -
-Specified as: a character variable. - -

-

-
work
-
work array. -
-Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a rank one array of the same type of $x$ and $y$ with -the TARGET attribute. - -

-

-
On Return
-
-
-
y
-
the local portion of result matrix $y$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 12. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_spsm Triangular - Up: Computational routines - Previous: psb_normi Infinity -   Contents
- - - - diff --git a/docs/html/node65.html b/docs/html/node65.html deleted file mode 100644 index 7617d650..00000000 --- a/docs/html/node65.html +++ /dev/null @@ -1,469 +0,0 @@ - - - - - -psb_spsm -- Triangular System Solve - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Communication routines - Up: Computational routines - Previous: psb_spmm Sparse -   Contents -
-
- - -

-psb_spsm -- Triangular System Solve -

- -

-This subroutine computes the Triangular System Solve: - -

-

-
- -\begin{eqnarray*} -y &\leftarrow& \alpha T^{-1} x + \beta y\\ -y &\leftarrow& \al... -...-H} x + \beta y\\ -y &\leftarrow& \alpha T^{-H} D x + \beta y\\ -\end{eqnarray*}
-

-

- -

-where: -

-
$x$
-
is the global dense matrix $x_{:, :}$ -
-
$y$
-
is the global dense matrix $y_{:, :}$ -
-
$T$
-
is the global sparse block triangular submatrix $T$ -
-
$D$
-
is the scaling diagonal matrix. -
-
- -

-

-call psb_spsm(alpha, t, x, beta, y, desc_a, info)
-call psb_spsm(alpha, t, x, beta, y, desc_a, info,&
-             & trans, unit, choice, diag, work)
-
- -

-

-
- - - -
Table 13: -Data types
-
- - - - - - - - - - - - - - - - -
$T$, $x$, $y$, $D$, $\alpha$, $\beta$Subroutine
Short Precision Realpsb_spsm
Long Precision Realpsb_spsm
Short Precision Complexpsb_spsm
Long Precision Complexpsb_spsm
-
-
-

-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
alpha
-
the scalar $\alpha$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in -Table 13. -
-
t
-
the global portion of the sparse matrix -$T$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object type specified in -§ 3. -
-
x
-
the local portion of global dense matrix -$x$. - -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 13. The rank of $x$ must be the same of $y$. -
-
beta
-
the scalar $\beta$. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a number of the data type indicated in Table 13. -
-
y
-
the local portion of global dense matrix -$y$. - -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 13. The rank of $y$ must be the same of $x$. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an object of type descdatapsb_desc_type. -
-
trans
-
specify with unitd the operation to perform. -
-
trans = 'N'
-
the operation is with no transposed matrix -
-
trans = 'T'
-
the operation is with transposed matrix. -
-
trans = 'C'
-
the operation is with conjugate transposed matrix. -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $trans = N$ -
-Specified as: a character variable. -
-
unitd
-
specify with trans the operation to perform. -
-
unitd = 'U'
-
the operation is with no scaling -
-
unitd = 'L'
-
the operation is with left scaling -
-
unitd = 'R'
-
the operation is with right scaling. -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: $unitd = U$ -
-Specified as: a character variable. -
-
choice
-
specifies the update of overlap elements to be performed - on exit: -
-
-
psb_none_ -
-
-
psb_sum_ -
-
-
psb_avg_ -
-
-
psb_square_root_ -
-
-Scope: global -
-Type: optional -
-Intent: in. -
-Default: psb_avg_ -
-Specified as: an integer variable. -
-
diag
-
the diagonal scaling matrix. -
-Scope: local -
-Type: optional -
-Intent: in. -
-Default: -$diag(1) = 1 (no scaling)$ -
-Specified as: a rank one array containing numbers of the type -indicated in Table 13. -
-
work
-
a work array. -
-Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a rank one array of the same type of $x$ with the -TARGET attribute. - -

-

-
On Return
-
-
-
y
-
the local portion of global dense matrix -$y$. - -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 13. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: Communication routines - Up: Computational routines - Previous: psb_spmm Sparse -   Contents
- - - - diff --git a/docs/html/node66.html b/docs/html/node66.html deleted file mode 100644 index e73a47eb..00000000 --- a/docs/html/node66.html +++ /dev/null @@ -1,77 +0,0 @@ - - - - - -Communication routines - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_halo Halo - Up: userhtml - Previous: psb_spsm Triangular -   Contents -
-
- - -

-Communication routines -

-The routines in this chapter implement various global communication operators -on vectors associated with a discretization mesh. For auxiliary communication -routines not tied to a discretization space see 6. - -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node67.html b/docs/html/node67.html deleted file mode 100644 index 1ab4ea30..00000000 --- a/docs/html/node67.html +++ /dev/null @@ -1,633 +0,0 @@ - - - - - -psb_halo -- Halo Data Communication - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_ovrl Overlap - Up: Communication routines - Previous: Communication routines -   Contents -
-
- - -

-psb_halo -- Halo Data Communication -

- -

-These subroutines gathers the values of the halo -elements: - -

-

-
- - -\begin{displaymath}x \leftarrow x \end{displaymath} -
-
-

-where: -
-
$x$
-
is a global dense submatrix. -
-
- -

-

-
- - - -
Table 14: -Data types
-
- - - - - - - - - - - - - - - - - - - -
$\alpha$, $x$Subroutine
Integerpsb_halo
Short Precision Realpsb_halo
Long Precision Realpsb_halo
Short Precision Complexpsb_halo
Long Precision Complexpsb_halo
-
-
-

-
- -

-
-\begin{lstlisting} -call psb_halo(x, desc_a, info) -call psb_halo(x, desc_a, info, work, data) -\end{lstlisting} -
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
global dense matrix $x$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 14. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
work
-
the work array. -
-Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a rank one array of the same type of $x$. -
-
data
-
index list selector. -
-Scope: global -
-Type: optional -
-Specified as: an integer. Values:psb_comm_halo_,psb_comm_mov_, -psb_comm_ext_, default: psb_comm_halo_. Chooses the -index list on which to base the data exchange. - -

-

-
On Return
-
-
-
x
-
global dense result matrix $x$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Returned as: a rank one or two array -containing numbers of type specified in -Table 14. -
-
info
-
the local portion of result submatrix $y$. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value that contains an error code. -
-
- -
- - - -
Figure 7: -Sample discretization mesh.
-
-\includegraphics[scale=0.45]{figures/try8x8.eps} - -\includegraphics[scale=0.45]{figures/try8x8} - -
-
- -

-Usage Example -Consider the discretization mesh depicted in fig. 7, -partitioned among two processes as shown by the dashed line; the data -distribution is such that each process will own 32 entries in the -index space, with a halo made of 8 entries placed at local indices 33 -through 40. If process 0 assigns an initial value of 1 to its entries -in the $x$ vector, and process 1 assigns a value of 2, then after a -call to psb_halo the contents of the local vectors will be the -following: -
-

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Process 0  -Process 1
- I GLOB(I) X(I)   I GLOB(I) X(I)
- 1 1 1.0   1 33 2.0
- 2 2 1.0   2 34 2.0
- 3 3 1.0   3 35 2.0
- 4 4 1.0   4 36 2.0
- 5 5 1.0   5 37 2.0
- 6 6 1.0   6 38 2.0
- 7 7 1.0   7 39 2.0
- 8 8 1.0   8 40 2.0
- 9 9 1.0   9 41 2.0
- 10 10 1.0   10 42 2.0
- 11 11 1.0   11 43 2.0
- 12 12 1.0   12 44 2.0
- 13 13 1.0   13 45 2.0
- 14 14 1.0   14 46 2.0
- 15 15 1.0   15 47 2.0
- 16 16 1.0   16 48 2.0
- 17 17 1.0   17 49 2.0
- 18 18 1.0   18 50 2.0
- 19 19 1.0   19 51 2.0
- 20 20 1.0   20 52 2.0
-21 21 1.0   21 53 2.0
-22 22 1.0   22 54 2.0
-23 23 1.0   23 55 2.0
-24 24 1.0   24 56 2.0
-25 25 1.0   25 57 2.0
-26 26 1.0   26 58 2.0
-27 27 1.0   27 59 2.0
-28 28 1.0   28 60 2.0
-29 29 1.0   29 61 2.0
-30 30 1.0   30 62 2.0
-31 31 1.0   31 63 2.0
-32 32 1.0   32 64 2.0
-33 33 2.0   33 25 1.0
-34 34 2.0   34 26 1.0
-35 35 2.0   35 27 1.0
-36 36 2.0   36 28 1.0
-37 37 2.0   37 29 1.0
-38 38 2.0   38 30 1.0
-39 39 2.0   39 31 1.0
-40 40 2.0   40 32 1.0
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_ovrl Overlap - Up: Communication routines - Previous: Communication routines -   Contents
- - - - diff --git a/docs/html/node68.html b/docs/html/node68.html deleted file mode 100644 index eff574f4..00000000 --- a/docs/html/node68.html +++ /dev/null @@ -1,761 +0,0 @@ - - - - - -psb_ovrl -- Overlap Update - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_gather Gather - Up: Communication routines - Previous: psb_halo Halo -   Contents -
-
- - -

-psb_ovrl -- Overlap Update -

- -

-These subroutines applies an overlap operator to the input vector: - -

-

-
- - -\begin{displaymath}x \leftarrow Q x \end{displaymath} -
-
-

-where: -
-
$x$
-
is the global dense submatrix $x$ -
-
$Q$
-
is the overlap operator; it is the composition of two -operators $P_a$ and $P^{T}$. -
-
- -

-

-
- - - -
Table 15: -Data types
-
- - - - - - - - - - - - - - - - -
$x$Subroutine
Short Precision Realpsb_ovrl
Long Precision Realpsb_ovrl
Short Precision Complexpsb_ovrl
Long Precision Complexpsb_ovrl
-
-
-

-
- -

-
-\begin{lstlisting} -call psb_ovrl(x, desc_a, info) -call psb_ovrl(x, desc_a, info, update=update_type, work=work) -\end{lstlisting} -
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
global dense matrix $x$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -containing numbers of type specified in -Table 15. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
update
-
Update operator. -
-
update = psb_none_
-
Do nothing; -
-
update = psb_add_
-
Sum overlap entries, i.e. apply $P^T$; -
-
update = psb_avg_
-
Average overlap entries, i.e. apply $P_aP^T$; -
-
-Scope: global -
-Intent: in. -
-Default: -$update\_type = psb\_avg\_ $ -
-Scope: global -
-Specified as: a integer variable. -
-
work
-
the work array. -
-Scope: local -
-Type: optional -
-Intent: inout. -
-Specified as: a one dimensional array of the same type of $x$. - -

-

-
On Return
-
-
-
x
-
global dense result matrix $x$. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: an array of rank one or two -containing numbers of type specified in -Table 15. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. If there is no overlap in the data distribution associated with - the descriptor, no operations are performed; -
    2. -
  2. The operator $P^{T}$ performs the reduction sum of overlap -elements; it is a “prolongation” operator $P^T$ that -replicates overlap elements, accounting for the physical replication -of data; -
    3. -
  3. The operator $P_a$ performs a scaling on the overlap elements by -the amount of replication; thus, when combined with the reduction -operator, it implements the average of replicated elements over all of -their instances. -
    4. -
- -

- -

- - - -
Figure 8: -Sample discretization mesh.
-
-\includegraphics[scale=0.65]{figures/try8x8_ov.eps} - -\includegraphics[scale=0.65]{figures/try8x8_ov} - -
-
- -Example of use -Consider the discretization mesh depicted in fig. 8, -partitioned among two processes as shown by the dashed lines, with an -overlap of 1 extra layer with respect to the partition of -fig. 7; the data -distribution is such that each process will own 40 entries in the -index space, with an overlap of 16 entries placed at local indices 25 -through 40; the halo will run from local index 41 through local index 48.. If process 0 assigns an initial value of 1 to its entries -in the $x$ vector, and process 1 assigns a value of 2, then after a -call to psb_ovrl with psb_avg_ and a call to -psb_halo_ the contents of the local vectors will be the -following (showing a transition among the two subdomains) - -

-
-

- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -
-Process 0  -Process 1
- I GLOB(I) X(I)   I GLOB(I) X(I)
- 1 1 1.0   1 33 1.5
- 2 2 1.0   2 34 1.5
- 3 3 1.0   3 35 1.5
- 4 4 1.0   4 36 1.5
- 5 5 1.0   5 37 1.5
- 6 6 1.0   6 38 1.5
- 7 7 1.0   7 39 1.5
- 8 8 1.0   8 40 1.5
- 9 9 1.0   9 41 2.0
- 10 10 1.0   10 42 2.0
- 11 11 1.0   11 43 2.0
- 12 12 1.0   12 44 2.0
- 13 13 1.0   13 45 2.0
- 14 14 1.0   14 46 2.0
- 15 15 1.0   15 47 2.0
- 16 16 1.0   16 48 2.0
- 17 17 1.0   17 49 2.0
- 18 18 1.0   18 50 2.0
- 19 19 1.0   19 51 2.0
- 20 20 1.0   20 52 2.0
- 21 21 1.0   21 53 2.0
- 22 22 1.0   22 54 2.0
- 23 23 1.0   23 55 2.0
- 24 24 1.0   24 56 2.0
- 25 25 1.5   25 57 2.0
- 26 26 1.5   26 58 2.0
- 27 27 1.5   27 59 2.0
- 28 28 1.5   28 60 2.0
- 29 29 1.5   29 61 2.0
- 30 30 1.5   30 62 2.0
- 31 31 1.5   31 63 2.0
- 32 32 1.5   32 64 2.0
- 33 33 1.5   33 25 1.5
- 34 34 1.5   34 26 1.5
- 35 35 1.5   35 27 1.5
- 36 36 1.5   36 28 1.5
- 37 37 1.5   37 29 1.5
- 38 38 1.5   38 30 1.5
- 39 39 1.5   39 31 1.5
- 40 40 1.5   40 32 1.5
- 41 41 2.0   41 17 1.0
- 42 42 2.0   42 18 1.0
- 43 43 2.0   43 19 1.0
- 44 44 2.0   44 20 1.0
- 45 45 2.0   45 21 1.0
- 46 46 2.0   46 22 1.0
- 47 47 2.0   47 23 1.0
- 48 48 2.0   48 24 1.0
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_gather Gather - Up: Communication routines - Previous: psb_halo Halo -   Contents
- - - - diff --git a/docs/html/node69.html b/docs/html/node69.html deleted file mode 100644 index 79a9d84c..00000000 --- a/docs/html/node69.html +++ /dev/null @@ -1,270 +0,0 @@ - - - - - -psb_gather -- Gather Global Dense Matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_scatter Scatter - Up: Communication routines - Previous: psb_ovrl Overlap -   Contents -
-
- - -

-psb_gather -- Gather Global Dense Matrix -

- -

-These subroutines collect the portions of global dense matrix -distributed over all process into one single array stored on one -process. - -

-

-
- - -\begin{displaymath}glob\_x \leftarrow collect(loc\_x_i) \end{displaymath} -
-
-

-where: -
-
$glob\_x$
-
is the global submatrix -$glob\_x_{1:m,1:n}$ -
-
$loc\_x_i$
-
is the local portion of global dense matrix on -process $i$. -
-
$collect$
-
is the collect function. -
-
- -

-

-
- - - -
Table 16: -Data types
-
- - - - - - - - - - - - - - - - - - - -
$x_i, y$Subroutine
Integerpsb_gather
Short Precision Realpsb_gather
Long Precision Realpsb_gather
Short Precision Complexpsb_gather
Long Precision Complexpsb_gather
-
-
-

-
- -

-
-\begin{lstlisting} -call psb_gather(glob_x, loc_x, desc_a, info, root) -call psb_gather(glob_x, loc_x, desc_a, info, root) -\end{lstlisting} -
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
loc_x
-
the local portion of global dense matrix -$glob\_x$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type -indicated in Table 16. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
root
-
The process that holds the global copy. If $root=-1$ all - the processes will have a copy of the global vector. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: an integer variable -$-1\le root\le np-1$, default $-1$. -
-
On Return
-
-
-
glob_x
-
The array where the local parts must be gathered. -
-Scope: global -
-Type: required -
-Intent: out. -
-Specified as: a rank one or two array with the ALLOCATABLE attribute. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_scatter Scatter - Up: Communication routines - Previous: psb_ovrl Overlap -   Contents
- - - - diff --git a/docs/html/node7.html b/docs/html/node7.html deleted file mode 100644 index 155a14f7..00000000 --- a/docs/html/node7.html +++ /dev/null @@ -1,108 +0,0 @@ - - - - - -User-defined index mappings - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Programming model - Up: Application structure - Previous: Application structure -   Contents -
-
- - -

- -
-User-defined index mappings -

-PSBLAS supports user-defined global to local index mappings, subject -to the constraints outlined in sec. 2.3: - -
    -
  1. The set of indices owned locally must be mapped to the set - -$1\dots n_{\hbox{row}_i}$; -
    2. -
  2. The set of halo points must be mapped to the set - -$n_{\hbox{row}_i}+1\dots n_{\hbox{col}_i}$; -
    3. -
-but otherwise the mapping is arbitrary. The user application is -responsible to ensure consistency of this mapping; some errors may be -caught by the library, but this is not guaranteed. -The application structure to -support this usage is as follows: - -
    -
  1. Initialize index space with - psb_cdall(ictx,desc,info,vl=vl,lidx=lidx) passing the vectors - vl(:) containing the set of global indices owned by the - current process and lidx(:) containing the corresponding - local indices; -
    2. -
  2. Add the halo points ja(:) and their associated local - indices lidx(:) with a(some) call(s) to - psb_cdins(nz,ja,desc,info,lidx=lidx); -
    3. -
  3. Assemble the descriptor with psb_cdasb; -
    4. -
  4. Build the sparse matrices and vectors, optionally making use in - psb_spins and psb_geins of the local argument - specifying that the indices in ia, ja and irw, - respectively, are already local indices. -
    5. -
- -

-

- - - diff --git a/docs/html/node70.html b/docs/html/node70.html deleted file mode 100644 index d16ab510..00000000 --- a/docs/html/node70.html +++ /dev/null @@ -1,277 +0,0 @@ - - - - - -psb_scatter -- Scatter Global Dense Matrix - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Data management routines - Up: Communication routines - Previous: psb_gather Gather -   Contents -
-
- - -

-psb_scatter -- Scatter Global Dense Matrix -

- -

-These subroutines scatters the portions of global dense matrix owned -by a process to all the processes in the processes grid. - -

-

-
- - -\begin{displaymath}loc\_x_i \leftarrow scatter(glob\_x) \end{displaymath} -
-
-

-where: -
-
$glob\_x$
-
is the global matrix -$glob\_x_{1:m,1:n}$ -
-
$loc\_x_i$
-
is the local portion of global dense matrix on -process $i$. -
-
$scatter$
-
is the scatter function. -
-
- -

-

-
- - - -
Table 17: -Data types
-
- - - - - - - - - - - - - - - - - - - -
$x_i, y$Subroutine
Integerpsb_scatter
Short Precision Realpsb_scatter
Long Precision Realpsb_scatter
Short Precision Complexpsb_scatter
Long Precision Complexpsb_scatter
-
-
-

-
- -

-
-\begin{lstlisting} -call psb_scatter(glob_x, loc_x, desc_a, info, root, mold) -\end{lstlisting} -
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
glob_x
-
The array that must be scattered into local pieces. -
-Scope: global -
-Type: required -
-Intent: in. -
-Specified as: a rank one or two array. -
-
desc_a
-
contains data structures for communications. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
root
-
The process that holds the global copy. If $root=-1$ all - the processes have a copy of the global vector. -
-Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: an integer variable -$-1\le root\le np-1$, default -psb_root_, i.e. process 0. -
-
mold
-
The desired dynamic type for the internal vector storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from vbasedatapsb_T_base_vect_type; this is -only allowed when loc_x is of type vdatapsb_T_vect_type. -
-
On Return
-
-
-
loc_x
-
the local portion of global dense matrix -$glob\_x$. -
-Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a rank one or two ALLOCATABLE array or an object of type vdatapsb_T_vect_type containing numbers of the type -indicated in Table 17. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: Data management routines - Up: Communication routines - Previous: psb_gather Gather -   Contents
- - - - diff --git a/docs/html/node71.html b/docs/html/node71.html deleted file mode 100644 index ae405046..00000000 --- a/docs/html/node71.html +++ /dev/null @@ -1,133 +0,0 @@ - - - - - -Data management routines - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdall Allocates - Up: userhtml - Previous: psb_scatter Scatter -   Contents -
-
- - -

- -
-Data management routines -

- -

-

- -Subsections - - - -
- - - diff --git a/docs/html/node72.html b/docs/html/node72.html deleted file mode 100644 index 6277372e..00000000 --- a/docs/html/node72.html +++ /dev/null @@ -1,450 +0,0 @@ - - - - - -psb_cdall -- Allocates a communication descriptor - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdins Communication - Up: Data management routines - Previous: Data management routines -   Contents -
-
- - -

-psb_cdall -- Allocates a communication descriptor -

- -

-

-call psb_cdall(icontxt, desc_a, info,mg=mg,parts=parts)
-call psb_cdall(icontxt, desc_a, info,vg=vg,[mg=mg,flag=flag])
-call psb_cdall(icontxt, desc_a, info,vl=vl,[nl=nl,globalcheck=.false.,lidx=lidx])
-call psb_cdall(icontxt, desc_a, info,nl=nl)
-call psb_cdall(icontxt, desc_a, info,mg=mg,repl=.true.)
-
- -

-This subroutine initializes the communication descriptor associated -with an index space. One of the optional arguments -parts, vg, vl, nl or repl -must be specified, thereby choosing -the specific initialization strategy. -

-
On Entry
-
-
-
Type:
-
Synchronous. -
-
icontxt
-
the communication context. -
-Scope:global. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value. -
-
vg
-
Data allocation: each index -$i\in \{1\dots mg\}$ is allocated - to process $vg(i)$. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer array. -
-
flag
-
Specifies whether entries in $vg$ are zero- or one-based. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer value $0,1$, default $0$. - -

-

-
mg
-
the (global) number of rows of the problem. -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer value. It is required if parts or -repl is specified, it is optional if vg is specified. -
-
parts
-
the subroutine that defines the partitioning scheme. -
-Scope:global. -
-Type:required. -
-Specified as: a subroutine. -
-
vl
-
Data allocation: the set of global indices - $vl(1:nl)$ belonging to the calling process. -
-Scope:local. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer array. -
-
nl
-
Data allocation: in a generalized block-row distribution the - number of indices belonging to the current process. -
-Scope:local. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer value. May be specified together with -vl. -
-
repl
-
Data allocation: build a replicated index space - (i.e. all processes own all indices). -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: the logical value .true. -
-
globalcheck
-
Data allocation: do global checks on the local - index lists vl -
-Scope:global. -
-Type:optional. -
-Intent: in. -
-Specified as: a logical value, default: .false. -
-
lidx
-
Data allocation: the set of local indices - $lidx(1:nl)$ to be assigned to the global indices $vl$. -
-Scope:local. -
-Type:optional. -
-Intent: in. -
-Specified as: an integer array. -
-
- -

-

-
On Return
-
-
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: out. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. One of the optional arguments parts, vg, - vl, nl or repl must be specified, thereby choosing the - initialization strategy as follows: -
    -
    parts
    -
    In this case we have a subroutine specifying the mapping - between global indices and process/local index pairs. If this - optional argument is specified, then it is mandatory to - specify the argument mg as well. - The subroutine must conform to the following interface: -
    -  interface 
-     subroutine psb_parts(glob_index,mg,np,pv,nv)
-       integer, intent (in)  :: glob_index,np,mg
-       integer, intent (out) :: nv, pv(*)
-     end subroutine psb_parts
-  end interface
-
    - The input arguments are: -
    -
    glob_index
    -
    The global index to be mapped; - -
    -
    np
    -
    The number of processes in the mapping; - -
    -
    mg
    -
    The total number of global rows in the mapping; - -
    -
    - The output arguments are: -
    -
    nv
    -
    The number of entries in pv; - -
    -
    pv
    -
    A vector containing the indices of the processes to - which the global index should be assigend; each entry must satisfy - -$0\le pv(i) < np$; if $nv>1$ we have an index assigned to multiple - processes, i.e. we have an overlap among the subdomains. - -
    -
    -
    -
    vg
    -
    In this case the association between an index and a process - is specified via an integer vector vg(1:mg); - each index -$i\in \{1\dots mg\}$ is assigned to process $vg(i)$. - The vector vg must be identical on all - calling processes; its entries may have the ranges $(0\dots np-1)$ - or $(1\dots np)$ according to the value of flag. - The size $mg$ may be specified via the optional argument mg; - the default is to use the entire vector vg, thus having - mg=size(vg). -
    -
    vl
    -
    In this case we are specifying the list of indices - vl(1:nl) assigned to the current process; thus, the global - problem size $mg$ is given by - the range of the aggregate of the individual vectors vl specified - in the calling processes. The size may be specified via the optional - argument nl; the default is to use the entire vector - vl, thus having nl=size(vl). - If globalcheck=.true. the subroutine will check how many - times each entry in the global index space $(1\dots mg)$ is - specified in the input lists vl, thus allowing for the - presence of overlap in the input, and checking for “orphan” - indices. If globalcheck=.false., the subroutine will not - check for overlap, and may be significantly faster, but the user - is implicitly guaranteeing that there are neither orphan nor - overlap indices. -
    -
    lidx
    -
    The optional argument lidx is available for - those cases in which the user has already established a - global-to-local mapping; if it is specified, each index in - vl(i) will be mapped to the corresponding local index - lidx(i). When specifying the argument lidx the user - would also likely employ lidx in calls to psb_cdins - and local in calls to psb_spins and psb_geins; - see also sec. 2.3.1. -
    -
    nl
    -
    If this argument is specified alone (i.e. without vl) - the result is a generalized row-block distribution in which each - process $I$ gets assigned a consecutive chunk of $N_I=nl$ global - indices. -
    -
    repl
    -
    This arguments specifies to replicate all indices on - all processes. This is a special purpose data allocation that is - useful in the construction of some multilevel preconditioners. -
    -
    -
    2. -
  2. On exit from this routine the descriptor is in the build - state. -
    3. -
  3. Calling the routine with vg or parts implies that - every process will scan the entire index space to figure out the - local indices. -
    4. -
  4. Overlapped indices are possible with both parts and - vl invocations. -
    5. -
  5. When the subroutine is invoked with vl in - conjunction with globalcheck=.true., it will perform a scan - of the index space to search for overlap or orphan indices. -
    6. -
  6. When the subroutine is invoked with vl in - conjunction with globalcheck=.false., no index space scan - will take place. Thus it is the responsibility of the user to make - sure that the indices specified in vl have neither orphans nor - overlaps; if this assumption fails, results will be - unpredictable. -
    7. -
  7. Orphan and overlap indices are - impossible by construction when the subroutine is invoked with - nl (alone), or vg. -
    8. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_cdins Communication - Up: Data management routines - Previous: Data management routines -   Contents
- - - - diff --git a/docs/html/node73.html b/docs/html/node73.html deleted file mode 100644 index 364e18a0..00000000 --- a/docs/html/node73.html +++ /dev/null @@ -1,259 +0,0 @@ - - - - - -psb_cdins -- Communication descriptor insert routine - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdasb Communication - Up: Data management routines - Previous: psb_cdall Allocates -   Contents -
-
- - -

-psb_cdins -- Communication descriptor insert - routine -

- -

-

-call psb_cdins(nz, ia, ja, desc_a, info [,ila,jla])
-call psb_cdins(nz,ja,desc,info[,jla,mask,lidx])
-
- -

-This subroutine examines the edges of the graph associated with the -discretization mesh (and isomorphic to the sparsity pattern of a -linear system coefficient matrix), storing them as necessary into the -communication descriptor. In the first form the edges are specified as -pairs of indices $ia(i),ja(i)$; the starting index $ia(i)$ should -belong to the current process. -In the second form only the remote indices $ja(i)$ are specified. - -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
nz
-
the number of points being inserted. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer value. -
-
ia
-
the indices of the starting vertex of the edges being inserted. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer array of length $nz$. -
-
ja
-
the indices of the end vertex of the edges being inserted. -
-Scope: local. -
-Type: required. -
-Intent: in. -
-Specified as: an integer array of length $nz$. -
-
mask
-
Mask entries in ja, they are inserted only when the - corresponding mask entries are .true. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: a logical array of length $nz$, default .true.. -
-
lidx
-
User defined local indices for ja. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer array of length $nz$. -
-
- -

-

-
On Return
-
-
-
desc_a
-
the updated communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
ila
-
the local indices of the starting vertex of the edges being inserted. -
-Scope: local. -
-Type: optional. -
-Intent: out. -
-Specified as: an integer array of length $nz$. -
-
jla
-
the local indices of the end vertex of the edges being inserted. -
-Scope: local. -
-Type: optional. -
-Intent: out. -
-Specified as: an integer array of length $nz$. - -

-

-
-Notes - -
    -
  1. This routine may only be called if the descriptor is in the - build state; -
    2. -
  2. This routine automatically ignores edges that do not -insist on the current process, i.e. edges for which neither the starting -nor the end vertex belong to the current process. -
    3. -
  3. The second form of this routine will be useful when dealing with - user-specified index mappings; see also 2.3.1. -
    4. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_cdasb Communication - Up: Data management routines - Previous: psb_cdall Allocates -   Contents
- - - - diff --git a/docs/html/node74.html b/docs/html/node74.html deleted file mode 100644 index dce0fc24..00000000 --- a/docs/html/node74.html +++ /dev/null @@ -1,133 +0,0 @@ - - - - - -psb_cdasb -- Communication descriptor assembly routine - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdcpy Copies - Up: Data management routines - Previous: psb_cdins Communication -   Contents -
-
- - -

-psb_cdasb -- Communication descriptor assembly - routine -

- -

-

-call psb_cdasb(desc_a, info [, mold])
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
mold
-
The desired dynamic type for the internal index storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: a object of type derived from (integer) vbasedatapsb_T_base_vect_type. -
-
- -

-

-
On Return
-
-
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
-Notes - -
    -
  1. On exit from this routine the descriptor is in the assembled - state. -
    2. -
- -

-

- - - diff --git a/docs/html/node75.html b/docs/html/node75.html deleted file mode 100644 index 508603a4..00000000 --- a/docs/html/node75.html +++ /dev/null @@ -1,116 +0,0 @@ - - - - - -psb_cdcpy -- Copies a communication descriptor - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdfree Frees - Up: Data management routines - Previous: psb_cdasb Communication -   Contents -
-
- - -

-psb_cdcpy -- Copies a communication descriptor -

- -

-

-call psb_cdcpy(desc_in, desc_out, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc_in
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. - -

-

-
- -

-

-
On Return
-
-
-
desc_out
-
the communication descriptor copy. -
-Scope:local. -
-Type:required. -
-Intent: out. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node76.html b/docs/html/node76.html deleted file mode 100644 index 6a43fb9f..00000000 --- a/docs/html/node76.html +++ /dev/null @@ -1,103 +0,0 @@ - - - - - -psb_cdfree -- Frees a communication descriptor - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_cdbldext Build - Up: Data management routines - Previous: psb_cdcpy Copies -   Contents -
-
- - -

-psb_cdfree -- Frees a communication descriptor -

- -

-

-call psb_cdfree(desc_a, info)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
the communication descriptor to be freed. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node77.html b/docs/html/node77.html deleted file mode 100644 index 9716704a..00000000 --- a/docs/html/node77.html +++ /dev/null @@ -1,198 +0,0 @@ - - - - - -psb_cdbldext -- Build an extended communication descriptor - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spall Allocates - Up: Data management routines - Previous: psb_cdfree Frees -   Contents -
-
- - -

-psb_cdbldext -- Build an extended communication - descriptor -

- -

-

-call psb_cdbldext(a,desc_a,nl,desc_out, info, extype)
-
- -

-This subroutine builds an extended communication descriptor, based on -the input descriptor desc_a and on the stencil specified -through the input sparse matrix a. -

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
A sparse matrix -Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data type. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
nl
-
the number of additional layers desired. -
-Scope:global. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value $nl\ge 0$. -
-
extype
-
the kind of estension required. -
-Scope:global. -
-Type:optional . -
-Intent: in. -
-Specified as: an integer value -psb_ovt_xhal_, psb_ovt_asov_, default: psb_ovt_xhal_ - -

-

-
- -

-

-
On Return
-
-
-
desc_out
-
the extended communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. Specifying psb_ovt_xhal_ for the extype argument - the user will obtain a descriptor for a domain partition in which - the additional layers are fetched as part of an (extended) halo; - however the index-to-process mapping is identical to that of the - base descriptor; -
    2. -
  2. Specifying psb_ovt_asov_ for the extype argument - the user will obtain a descriptor with an overlapped decomposition: - the additional layer is aggregated to the local subdomain (and thus - is an overlap), and a new halo extending beyond the last additional - layer is formed. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_spall Allocates - Up: Data management routines - Previous: psb_cdfree Frees -   Contents
- - - - diff --git a/docs/html/node78.html b/docs/html/node78.html deleted file mode 100644 index 42ebd801..00000000 --- a/docs/html/node78.html +++ /dev/null @@ -1,143 +0,0 @@ - - - - - -psb_spall -- Allocates a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spins Insert - Up: Data management routines - Previous: psb_cdbldext Build -   Contents -
-
- - -

-psb_spall -- Allocates a sparse matrix -

- -

-

-call psb_spall(a, desc_a, info, nnz)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
nnz
-
An estimate of the number of nonzeroes in the local - part of the assembled matrix. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: an integer value. -
-
- -

-

-
On Return
-
-
-
a
-
the matrix to be allocated. -
-Scope:local -
-Type:required -
-Intent: out. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
-Notes - -
    -
  1. On exit from this routine the sparse matrix is in the build - state. -
    2. -
  2. The descriptor may be in either the build or assembled state. -
    3. -
  3. Providing a good estimate for the number of nonzeroes $nnz$ in - the assembled matrix may substantially improve performance in the - matrix build phase, as it will reduce or eliminate the need for - (potentially multiple) data reallocations. -
    4. -
- -

-

- - - diff --git a/docs/html/node79.html b/docs/html/node79.html deleted file mode 100644 index 562a80b0..00000000 --- a/docs/html/node79.html +++ /dev/null @@ -1,320 +0,0 @@ - - - - - -psb_spins -- Insert a set of coefficients into a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spasb Sparse - Up: Data management routines - Previous: psb_spall Allocates -   Contents -
-
- - -

-psb_spins -- Insert a set of coefficients into a sparse - matrix -

- -

-

-call psb_spins(nz, ia, ja, val, a, desc_a, info [,local])
-call psb_spins(nr, irw, irp, ja, val, a, desc_a, info [,local])
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
nz
-
the number of coefficients to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer scalar. -
-
nr
-
the number of rows to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer scalar. -
-
irw
-
the first row to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer scalar. -
-
ia
-
the row indices of the coefficients to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer array of size $nz$. -
-
irp
-
the row pointers of the coefficients to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer array of size . -
-
ja
-
the column indices of the coefficients to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer array of size $nz$. -
-
val
-
the coefficients to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an array of size $nz$. Must be of the same type and kind -of the coefficients of the sparse matrix $a$. -
-
desc_a
-
The communication descriptor. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: a variable of type descdatapsb_desc_type. -
-
local
-
Whether the entries in the indices vectors ia, - ja are already in local numbering. -
-Scope:local. -
-Type:optional. -
-Specified as: a logical value; default: .false.. - -

-

-
- -

-

-
On Return
-
-
-
a
-
the matrix into which coefficients will be inserted. -
-Scope:local -
-Type:required -
-Intent: inout. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
desc_a
-
The communication descriptor. -
-Scope: local. -
-Type: required. -
-Intent: inout. -
-Specified as: a variable of type descdatapsb_desc_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. On entry to this routine the descriptor may be in either the - build or assembled state. -
    2. -
  2. On entry to this routine the sparse matrix may be in either the - build or update state. -
    3. -
  3. If the descriptor is in the build state, then the sparse matrix - must also be in the build state; the action of the routine is to - (implicitly) call psb_cdins to add entries to the sparsity - pattern; each sparse matrix entry implicitly defines a graph edge, - that is passed to the descriptor routine for the appropriate - processing; -
    4. -
  4. The input data can be passed in either COO or CSR formats; -
    5. -
  5. In COO format the coefficients to be inserted are represented by - the ordered triples -$ia(i),ja(i),val(i)$, for $i=1,\dots,nz$; - these triples should belong to the current process, i.e. $ia(i)$ - should be one of the local indices, but are otherwise arbitrary; -
    6. -
  6. In CSR format the coefficients to be inserted for each input row - are represented by the ordered triples -, for - -; - these triples should belong to the current process, i.e. - should be one of the local indices, but are otherwise arbitrary; -
    7. -
  7. There is no requirement that a given row must be passed in its - entirety to a single call to this routine: the buildup of a row - may be split into as many calls as desired (even in the CSR format); -
    8. -
  8. Coefficients from different rows may also be mixed up freely - in a single call, according to the application needs; -
    9. -
  9. Any coefficients from matrix rows not owned by the calling - process are silently ignored; -
    10. -
  10. If the descriptor is in the assembled state, then any entries in - the sparse matrix that would generate additional communication - requirements are ignored; -
    11. -
  11. If the matrix is in the update state, any entries in positions - that were not present in the original matrix are ignored. -
    12. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_spasb Sparse - Up: Data management routines - Previous: psb_spall Allocates -   Contents
- - - - diff --git a/docs/html/node8.html b/docs/html/node8.html deleted file mode 100644 index df750f2a..00000000 --- a/docs/html/node8.html +++ /dev/null @@ -1,121 +0,0 @@ - - - - - -Programming model - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Data Structures and Classes - Up: General overview - Previous: User-defined index mappings -   Contents -
-
- - -

-Programming model -

- -

-The PSBLAS librarary is based on the Single Program Multiple Data -(SPMD) programming model: each process participating in the -computation performs the same actions on a chunk of data. Parallelism -is thus data-driven. - -

-Because of this structure, many subroutines coordinate their action -across the various processes, thus providing an implicit -synchronization point, and therefore must be -called simultaneously by all processes participating in the -computation. This is certainly true for the data allocation and -assembly routines, for all the computational routines and for some of -the tools routines. - -

-However there are many cases where no synchronization, and indeed no -communication among processes, is implied; for instance, all the routines in -sec. 3 are only acting on the local data structures, -and thus may be called independently. The most important case is that -of the coefficient insertion routines: since the number of -coefficients in the sparse and dense matrices varies among the -processors, and since the user is free to choose an arbitrary order in -builiding the matrix entries, these routines cannot imply a -synchronization. - -

-Throughout this user's guide each subroutine will be clearly indicated -as: -

-
Synchronous:
-
must be called simultaneously by all the - processes in the relevant communication context; -
-
Asynchronous:
-
may be called in a totally independent manner. -
-
- -

- -

- - -next - -up - -previous - -contents -
- Next: Data Structures and Classes - Up: General overview - Previous: User-defined index mappings -   Contents
- - - - diff --git a/docs/html/node80.html b/docs/html/node80.html deleted file mode 100644 index 295e944c..00000000 --- a/docs/html/node80.html +++ /dev/null @@ -1,209 +0,0 @@ - - - - - -psb_spasb -- Sparse matrix assembly routine - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_spfree Frees - Up: Data management routines - Previous: psb_spins Insert -   Contents -
-
- - -

-psb_spasb -- Sparse matrix assembly routine -

- -

-

-call psb_spasb(a, desc_a, info, afmt, upd, dupl, mold)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
afmt
-
the storage format for the sparse matrix. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an array of characters. Defalt: 'CSR'. -
-
upd
-
Provide for updates to the matrix coefficients. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: integer, possible values: psb_upd_srch_, psb_upd_perm_ -
-
dupl
-
How to handle duplicate coefficients. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: integer, possible values: psb_dupl_ovwrt_, -psb_dupl_add_, psb_dupl_err_. -
-
mold
-
The desired dynamic type for the internal matrix storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from spbasedatapsb_T_base_sparse_mat. -
-
- -

-

-
On Return
-
-
-
a
-
the matrix to be assembled. -
-Scope:local -
-Type:required -
-Intent: inout. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. On entry to this routine the descriptor must be in the - assembled state, i.e. psb_cdasb must already have been called. -
    2. -
  2. The sparse matrix may be in either the build or update state; -
    3. -
  3. Duplicate entries are detected and handled in both build and - update state, with the exception of the error action that is only - taken in the build state, i.e. on the first assembly; -
    4. -
  4. If the update choice is psb_upd_perm_, then subsequent - calls to psb_spins to update the matrix must be arranged in - such a way as to produce exactly the same sequence of coefficient - values as encountered at the first assembly; -
    5. -
  5. The output storage format need not be the same on all - processes; -
    6. -
  6. On exit from this routine the matrix is in the assembled state, - and thus is suitable for the computational routines. -
    7. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_spfree Frees - Up: Data management routines - Previous: psb_spins Insert -   Contents
- - - - diff --git a/docs/html/node81.html b/docs/html/node81.html deleted file mode 100644 index 7320ea14..00000000 --- a/docs/html/node81.html +++ /dev/null @@ -1,114 +0,0 @@ - - - - - -psb_spfree -- Frees a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_sprn Reinit - Up: Data management routines - Previous: psb_spasb Sparse -   Contents -
-
- - -

-psb_spfree -- Frees a sparse matrix -

- -

-

-call psb_spfree(a, desc_a, info)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
the matrix to be freed. -
-Scope:local -
-Type:required -
-Intent: inout. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node82.html b/docs/html/node82.html deleted file mode 100644 index e966ada4..00000000 --- a/docs/html/node82.html +++ /dev/null @@ -1,133 +0,0 @@ - - - - - -psb_sprn -- Reinit sparse matrix structure for psblas routines. - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geall Allocates - Up: Data management routines - Previous: psb_spfree Frees -   Contents -
-
- - -

-psb_sprn -- Reinit sparse matrix structure for psblas - routines. -

- -

-

-call psb_sprn(a, decsc_a, info, clear)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
a
-
the matrix to be reinitialized. -
-Scope:local -
-Type:required -
-Intent: inout. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
clear
-
Choose whether to zero out matrix coefficients -
-Scope:local. -
-Type:optional. -
-Intent: in. -
-Default: true. -
-
- -

-

-
On Return
-
-
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
-Notes - -
    -
  1. On exit from this routine the sparse matrix is in the update - state. -
    2. -
- -

-

- - - diff --git a/docs/html/node83.html b/docs/html/node83.html deleted file mode 100644 index 65e4c10e..00000000 --- a/docs/html/node83.html +++ /dev/null @@ -1,151 +0,0 @@ - - - - - -psb_geall -- Allocates a dense matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geins Dense - Up: Data management routines - Previous: psb_sprn Reinit -   Contents -
-
- - -

-psb_geall -- Allocates a dense matrix -

- -

-

-call psb_geall(x, desc_a, info, n, lb)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
The communication descriptor. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a variable of type descdatapsb_desc_type. -
-
n
-
The number of columns of the dense matrix to be allocated. -
-Scope: local -
-Type: optional -
-Intent: in. -
-Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a -rank-1 array. -
-
lb
-
The lower bound for the column index range of the dense matrix to be allocated. -
-Scope: local -
-Type: optional -
-Intent: in. -
-Specified as: Integer scalar, default $1$. It is not a valid argument if $x$ is a -rank-1 array. -
-
- -

-

-
On Return
-
-
-
x
-
The dense matrix to be allocated. -
-Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a rank one or two array with the ALLOCATABLE attribute -or an object of type vdatapsb_T_vect_type, of type real, complex or integer. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node84.html b/docs/html/node84.html deleted file mode 100644 index 26821fda..00000000 --- a/docs/html/node84.html +++ /dev/null @@ -1,221 +0,0 @@ - - - - - -psb_geins -- Dense matrix insertion routine - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_geasb Assembly - Up: Data management routines - Previous: psb_geall Allocates -   Contents -
-
- - -

-psb_geins -- Dense matrix insertion routine -

- -

-

-call psb_geins(m, irw, val, x, desc_a, info [,dupl,local])
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
m
-
Number of rows in $val$ to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer value. -
-
irw
-
Indices of the rows to be inserted. Specifically, row $i$ - of $val$ will be inserted into the local row corresponding to the - global row index $irw(i)$. -Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: an integer array. -
-
val
-
the dense submatrix to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a rank 1 or 2 array. -Specified as: an integer value. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
dupl
-
How to handle duplicate coefficients. -
-Scope: global. -
-Type: optional. -
-Intent: in. -
-Specified as: integer, possible values: psb_dupl_ovwrt_, -psb_dupl_add_. -
-
local
-
Whether the entries in the index vector irw, - are already in local numbering. -
-Scope:local. -
-Type:optional. -
-Specified as: a logical value; default: .false.. - -

-

-
- -

-

-
On Return
-
-
-
x
-
the output dense matrix. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array or an object of type vdatapsb_T_vect_type, of -type real, complex or integer. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. Dense vectors/matrices do not have an associated state; -
    2. -
  2. Duplicate entries are either overwritten or added, there is no - provision for raising an error condition. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_geasb Assembly - Up: Data management routines - Previous: psb_geall Allocates -   Contents
- - - - diff --git a/docs/html/node85.html b/docs/html/node85.html deleted file mode 100644 index 3a23b931..00000000 --- a/docs/html/node85.html +++ /dev/null @@ -1,128 +0,0 @@ - - - - - -psb_geasb -- Assembly a dense matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_gefree Frees - Up: Data management routines - Previous: psb_geins Dense -   Contents -
-
- - -

-psb_geasb -- Assembly a dense matrix -

- -

-

-call psb_geasb(x, desc_a, info, mold)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
desc_a
-
The communication descriptor. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a variable of type descdatapsb_desc_type. -
-
mold
-
The desired dynamic type for the internal vector storage. -
-Scope: local. -
-Type: optional. -
-Intent: in. -
-Specified as: an object of a class derived from vbasedatapsb_T_base_vect_type; this is -only allowed when $x$ is of type vdatapsb_T_vect_type. -
-
- -

-

-
On Return
-
-
-
x
-
The dense matrix to be assembled. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array with the ALLOCATABLE or an -object of type vdatapsb_T_vect_type, of type real, complex or integer. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
-
- - - diff --git a/docs/html/node86.html b/docs/html/node86.html deleted file mode 100644 index e1744ccb..00000000 --- a/docs/html/node86.html +++ /dev/null @@ -1,118 +0,0 @@ - - - - - -psb_gefree -- Frees a dense matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_gelp Applies - Up: Data management routines - Previous: psb_geasb Assembly -   Contents -
-
- - -

-psb_gefree -- Frees a dense matrix -

- -

-

-call psb_gefree(x, desc_a, info)
-
- -

-

-
Type:
-
Synchronous. -
-
On Entry
-
-
-
x
-
The dense matrix to - be freed. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a rank one or two array with the ALLOCATABLE or an -object of type vdatapsb_T_vect_type, of type real, complex or integer. -
-

-

-
desc_a
-
The communication descriptor. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a variable of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node87.html b/docs/html/node87.html deleted file mode 100644 index dbb80998..00000000 --- a/docs/html/node87.html +++ /dev/null @@ -1,138 +0,0 @@ - - - - - -psb_gelp -- Applies a left permutation to a dense matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_glob_to_loc Global - Up: Data management routines - Previous: psb_gefree Frees -   Contents -
-
- - -

-psb_gelp -- Applies a left permutation to a dense - matrix -

- -

-

-call psb_gelp(trans, iperm, x, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
trans
-
A character that specifies whether to permute $A$ or $A^T$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a single character with value 'N' for $A$ or 'T' for $A^T$. -
-
iperm
-
An integer array containing permutation information. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: an integer one-dimensional array. -
-
x
-
The dense matrix to be permuted. -
-Scope: local -
-Type: required -
-Intent: inout. -
-Specified as: a one or two dimensional array. -
-
- -

-

-
On Return
-
-
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node88.html b/docs/html/node88.html deleted file mode 100644 index 56205478..00000000 --- a/docs/html/node88.html +++ /dev/null @@ -1,213 +0,0 @@ - - - - - -psb_glob_to_loc -- Global to local indices convertion - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_loc_to_glob Local - Up: Data management routines - Previous: psb_gelp Applies -   Contents -
-
- - -

-psb_glob_to_loc -- Global to local indices - convertion -

- -

-

-call psb_glob_to_loc(x, y, desc_a, info, iact,owned)
-call psb_glob_to_loc(x, desc_a, info, iact,owned)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
An integer vector of indices to be converted. -
-Scope: local -
-Type: required -
-Intent: in, inout. -
-Specified as: a rank one integer array. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -
-
owned
-
Specfies valid range of input -Scope: global -
-Type: optional -
-Intent: in. -
-If true, then only indices strictly owned by the current process are -considered valid, if false then halo indices are also -accepted. Default: false. -
-
- -

-

-
On Return
-
-
-
x
-
If $y$ is not present, - then $x$ is overwritten with the translated integer indices. -Scope: global -
-Type: required -
-Intent: inout. -
-Specified as: a rank one integer array. -
-
y
-
If $y$ is present, - then $y$ is overwritten with the translated integer indices, and $x$ - is left unchanged. -Scope: global -
-Type: optional -
-Intent: out. -
-Specified as: a rank one integer array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. If an input index is out of range, then the corresponding output - index is set to a negative number; -
    2. -
  2. The default Ignore means that the negative output is the - only action taken on an out-of-range input. -
    3. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_loc_to_glob Local - Up: Data management routines - Previous: psb_gelp Applies -   Contents
- - - - diff --git a/docs/html/node89.html b/docs/html/node89.html deleted file mode 100644 index ac275095..00000000 --- a/docs/html/node89.html +++ /dev/null @@ -1,165 +0,0 @@ - - - - - -psb_loc_to_glob -- Local to global indices conversion - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_is_owned - Up: Data management routines - Previous: psb_glob_to_loc Global -   Contents -
-
- - -

-psb_loc_to_glob -- Local to global indices - conversion -

- -

-

-call psb_loc_to_glob(x, y, desc_a, info, iact)
-call psb_loc_to_glob(x, desc_a, info, iact)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
An integer vector of indices to be converted. -
-Scope: local -
-Type: required -
-Intent: in, inout. -
-Specified as: a rank one integer array. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -
-
- -

-

-
On Return
-
-
-
x
-
If $y$ is not present, - then $x$ is overwritten with the translated integer indices. -Scope: global -
-Type: required -
-Intent: inout. -
-Specified as: a rank one integer array. -
-
y
-
If $y$ is not present, - then $y$ is overwritten with the translated integer indices, and $x$ - is left unchanged. -Scope: global -
-Type: optional -
-Intent: out. -
-Specified as: a rank one integer array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-

- - - diff --git a/docs/html/node9.html b/docs/html/node9.html deleted file mode 100644 index b60f74d3..00000000 --- a/docs/html/node9.html +++ /dev/null @@ -1,247 +0,0 @@ - - - - - -Data Structures and Classes - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Descriptor data structure - Up: userhtml - Previous: Programming model -   Contents -
-
- - -

- -
-Data Structures and Classes -

- -

-In this chapter we illustrate the data structures used for definition of -routines interfaces. They include data structures for sparse matrices, -communication descriptors and preconditioners. -

-All the data types and the basic subroutine interfaces related to -descriptors and sparse matrices are defined in -the module psb_base_mod; this will have to be included by every -user subroutine that makes use of the library. The preconditioners are -defined in the module psb_prec_mod - -

-Integer, real and complex data types are parametrized with a kind type -defined in the library as follows: -

-
psb_spk_
-
Kind parameter for short precision real and complex - data; corresponds to a REAL declaration and is - normally 4 bytes; -
-
psb_dpk_
-
Kind parameter for long precision real and complex - data; corresponds to a DOUBLE PRECISION declaration and is - normally 8 bytes; -
-
psb_mpk_
-
Kind parameter for 4-bytes integer data, as is - always used by MPI; -
-
psb_epk_
-
Kind parameter for 8-bytes integer data, as is - always used by the sizeof methods; -
-
psb_ipk_
-
Kind parameter for “local” integer indices and data; - with default build options this is a 4 bytes integer; -
-
psb_lpk_
-
Kind parameter for “global” integer indices and data; - with default build options this is an 8 bytes integer; -
-
-The integer kinds for local and global indices can be chosen at -configure time to hold 4 or 8 bytes, with the global indices at least -as large as the local ones. -Together with the classes attributes we also discuss their -methods. Most methods detailed here only act on the local variable, -i.e. their action is purely local and asynchronous unless otherwise -stated. -The list of methods here is not completely exhaustive; many methods, -especially those that alter the contents of the various objects, are -usually not needed by the end-user, and therefore are described in the -developer's documentation. - -

-

- -Subsections - - - - -
- - -next - -up - -previous - -contents -
- Next: Descriptor data structure - Up: userhtml - Previous: Programming model -   Contents
- - - - diff --git a/docs/html/node90.html b/docs/html/node90.html deleted file mode 100644 index aaf6d3e3..00000000 --- a/docs/html/node90.html +++ /dev/null @@ -1,125 +0,0 @@ - - - - - -psb_is_owned -- - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_owned_index - Up: Data management routines - Previous: psb_loc_to_glob Local -   Contents -
-
- - -

-psb_is_owned -- -

- -

-

-call psb_is_owned(x, desc_a)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
Integer index. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a scalar integer. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
Function value
-
A logical mask which is true if - $x$ is owned by the current process -Scope: local -
-Type: required -
-Intent: out. -
-
- -

-Notes - -

    -
  1. This routine returns a .true. value for an index - that is strictly owned by the current process, excluding the halo - indices -
    2. -
- -

-

- - - diff --git a/docs/html/node91.html b/docs/html/node91.html deleted file mode 100644 index d2bd979c..00000000 --- a/docs/html/node91.html +++ /dev/null @@ -1,149 +0,0 @@ - - - - - -psb_owned_index -- - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_is_local - Up: Data management routines - Previous: psb_is_owned -   Contents -
-
- - -

-psb_owned_index -- -

- -

-

-call psb_owned_index(y, x, desc_a, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
Integer indices. -
-Scope: local -
-Type: required -
-Intent: in, inout. -
-Specified as: a scalar or a rank one integer array. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -
-
- -

-

-
On Return
-
-
-
y
-
A logical mask which is true for all corresponding entries of - $x$ that are owned by the current process -Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a scalar or rank one logical array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. This routine returns a .true. value for those indices - that are strictly owned by the current process, excluding the halo - indices -
    2. -
- -

-

- - - diff --git a/docs/html/node92.html b/docs/html/node92.html deleted file mode 100644 index a3c4d4b6..00000000 --- a/docs/html/node92.html +++ /dev/null @@ -1,125 +0,0 @@ - - - - - -psb_is_local -- - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_local_index - Up: Data management routines - Previous: psb_owned_index -   Contents -
-
- - -

-psb_is_local -- -

- -

-

-call psb_is_local(x, desc_a)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
Integer index. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a scalar integer. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
Function value
-
A logical mask which is true if - $x$ is local to the current process -Scope: local -
-Type: required -
-Intent: out. -
-
- -

-Notes - -

    -
  1. This routine returns a .true. value for an index - that is local to the current process, including the halo - indices -
    2. -
- -

-

- - - diff --git a/docs/html/node93.html b/docs/html/node93.html deleted file mode 100644 index 3a12cab9..00000000 --- a/docs/html/node93.html +++ /dev/null @@ -1,149 +0,0 @@ - - - - - -psb_local_index -- - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_get_boundary Extract - Up: Data management routines - Previous: psb_is_local -   Contents -
-
- - -

-psb_local_index -- -

- -

-

-call psb_local_index(y, x, desc_a, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
Integer indices. -
-Scope: local -
-Type: required -
-Intent: in, inout. -
-Specified as: a scalar or a rank one integer array. -
-
desc_a
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
iact
-
specifies action to be taken in case of range errors. -Scope: global -
-Type: optional -
-Intent: in. -
-Specified as: a character variable Ignore, Warning or -Abort, default Ignore. -
-
- -

-

-
On Return
-
-
-
y
-
A logical mask which is true for all corresponding entries of - $x$ that are local to the current process -Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a scalar or rank one logical array. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. This routine returns a .true. value for those indices - that are local to the current process, including the halo - indices. -
    2. -
- -

-

- - - diff --git a/docs/html/node94.html b/docs/html/node94.html deleted file mode 100644 index 41a1b858..00000000 --- a/docs/html/node94.html +++ /dev/null @@ -1,130 +0,0 @@ - - - - - -psb_get_boundary -- Extract list of boundary elements - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_get_overlap Extract - Up: Data management routines - Previous: psb_local_index -   Contents -
-
- - -

-psb_get_boundary -- Extract list of boundary - elements -

- -

-

-call psb_get_boundary(bndel, desc, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
bndel
-
The list of boundary elements on the calling process, in - local numbering. -
-Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a rank one array with the ALLOCATABLE -attribute, of type integer. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. If there are no boundary elements (i.e., if the local part of - the connectivity graph is self-contained) the output vector is set - to the “not allocated” state. -
    2. -
  2. Otherwise the size of bndel will be exactly equal to the - number of boundary elements. -
    3. -
- -

-

- - - diff --git a/docs/html/node95.html b/docs/html/node95.html deleted file mode 100644 index 07d57981..00000000 --- a/docs/html/node95.html +++ /dev/null @@ -1,129 +0,0 @@ - - - - - -psb_get_overlap -- Extract list of overlap elements - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_sp_getrow Extract - Up: Data management routines - Previous: psb_get_boundary Extract -   Contents -
-
- - -

-psb_get_overlap -- Extract list of overlap - elements -

- -

-

-call psb_get_overlap(ovrel, desc, info)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
desc
-
the communication descriptor. -
-Scope:local. -
-Type:required. -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
- -

-

-
On Return
-
-
-
ovrel
-
The list of overlap elements on the calling process, in - local numbering. -
-Scope: local -
-Type: required -
-Intent: out. -
-Specified as: a rank one array with the ALLOCATABLE -attribute, of type integer. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. If there are no overlap elements the output vector is set - to the “not allocated” state. -
    2. -
  2. Otherwise the size of ovrel will be exactly equal to the - number of overlap elements. -
    3. -
- -

-

- - - diff --git a/docs/html/node96.html b/docs/html/node96.html deleted file mode 100644 index 2736fbfb..00000000 --- a/docs/html/node96.html +++ /dev/null @@ -1,256 +0,0 @@ - - - - - -psb_sp_getrow -- Extract row(s) from a sparse matrix - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: psb_sizeof Memory - Up: Data management routines - Previous: psb_get_overlap Extract -   Contents -
-
- - -

-psb_sp_getrow -- Extract row(s) from a sparse - matrix -

- -

-

-call psb_sp_getrow(row, a, nz, ia, ja, val, info, &
-              & append, nzin, lrw)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
row
-
The (first) row to be extracted. -
-Scope:local -
-Type:required -
-Intent: in. -
-Specified as: an integer $>0$. -
-
a
-
the matrix from which to get rows. -
-Scope:local -
-Type:required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
append
-
Whether to append or overwrite existing output. -
-Scope:local -
-Type:optional -
-Intent: in. -
-Specified as: a logical value default: false (overwrite). -
-
nzin
-
Input size to be appended to. -
-Scope:local -
-Type:optional -
-Intent: in. -
-Specified as: an integer $>0$. When append is true, specifies how many -entries in the output vectors are already filled. -
-
lrw
-
The last row to be extracted. -
-Scope:local -
-Type:optional -
-Intent: in. -
-Specified as: an integer $>0$, default: $row$. - -

-

-
- -

-

-
On Return
-
-
-
nz
-
the number of elements returned by this call. -
-Scope:local. -
-Type:required. -
-Intent: out. -
-Returned as: an integer scalar. -
-
ia
-
the row indices. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: an integer array with the ALLOCATABLE attribute. -
-
ja
-
the column indices of the elements to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: an integer array with the ALLOCATABLE attribute. -
-
val
-
the elements to be inserted. -
-Scope:local. -
-Type:required. -
-Intent: inout. -
-Specified as: a real array with the ALLOCATABLE attribute. -
-
info
-
Error code. -
-Scope: local -
-Type: required -
-Intent: out. -
-An integer value; 0 means no error has been detected. -
-
- -

-Notes - -

    -
  1. The output $nz$ is always the size of the output generated by - the current call; thus, if append=.true., the total output - size will be $nzin+nz$, with the newly extracted coefficients stored in - entries nzin+1:nzin+nz of the array arguments; -
    2. -
  2. When append=.true. the output arrays are reallocated as - necessary; -
    3. -
  3. The row and column indices are returned in the local numbering - scheme; if the global numbering is desired, the user may employ the - psb_loc_to_glob routine on the output. -
    4. -
- -

- -

- - -next - -up - -previous - -contents -
- Next: psb_sizeof Memory - Up: Data management routines - Previous: psb_get_overlap Extract -   Contents
- - - - diff --git a/docs/html/node97.html b/docs/html/node97.html deleted file mode 100644 index 9a446831..00000000 --- a/docs/html/node97.html +++ /dev/null @@ -1,125 +0,0 @@ - - - - - -psb_sizeof -- Memory occupation - - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Sorting utilities - Up: Data management routines - Previous: psb_sp_getrow Extract -   Contents -
-
- - -

-psb_sizeof -- Memory occupation -

- -

-This function computes the memory occupation of a PSBLAS object. - -

-

-isz = psb_sizeof(a)
-isz = psb_sizeof(desc_a)
-isz = psb_sizeof(prec)
-
- -

-

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
a
-
A sparse matrix -$A$. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type spdatapsb_Tspmat_type. -
-
desc_a
-
Communication descriptor. -
-Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a structured data of type descdatapsb_desc_type. -
-
prec
-
Scope: local -
-Type: required -
-Intent: in. -
-Specified as: a preconditioner data structure precdatapsb_prec_type. -
-
On Return
-
-
-
Function value
-
The memory occupation of the object specified in - the calling sequence, in bytes. -
-Scope: local -
-Returned as: an integer(psb_long_int_k_) number. -
-
- -

-

- - - diff --git a/docs/html/node98.html b/docs/html/node98.html deleted file mode 100644 index 5625baef..00000000 --- a/docs/html/node98.html +++ /dev/null @@ -1,291 +0,0 @@ - - - - - -Sorting utilities -- - - - - - - - - - - - - - - - - - -
- -next - -up - -previous - -contents -
- Next: Parallel environment routines - Up: Data management routines - Previous: psb_sizeof Memory -   Contents -
-
- - -

-Sorting utilities -- -

- -

-psb_msort -- Sorting by the Merge-sort - algorithm - -

-psb_qsort -- Sorting by the Quicksort - algorithm - -

-psb_hsort -- Sorting by the Heapsort algorithm -

-call psb_msort(x,ix,dir,flag)
-call psb_qsort(x,ix,dir,flag)
-call psb_hsort(x,ix,dir,flag)
-
- -

-These serial routines sort a sequence $X$ into ascending or -descending order. The argument meaning is identical for the three -calls; the only difference is the algorithm used to accomplish the -task (see Usage Notes below). -

-
Type:
-
Asynchronous. -
-
On Entry
-
-
-
x
-
The sequence to be sorted. -
-Type:required. -
-Specified as: an integer, real or complex array of rank 1. -
-
ix
-
A vector of indices. -
-Type:optional. -
-Specified as: an integer array of (at least) the same size as $X$. -
-
dir
-
The desired ordering. -
-Type:optional. -
-Specified as: an integer value:
-
Integer and real data:
-
psb_sort_up_, -psb_sort_down_, psb_asort_up_, psb_asort_down_; -default psb_sort_up_. -
-
Complex data:
-
psb_lsort_up_, -psb_lsort_down_, psb_asort_up_, psb_asort_down_; -default psb_lsort_up_. -
-
-
-
flag
-
Whether to keep the original values in $IX$. -
-Type:optional. -
-Specified as: an integer value psb_sort_ovw_idx_ or -psb_sort_keep_idx_; default psb_sort_ovw_idx_. - -

-

-
- -

-

-
On Return
-
-
-
x
-
The sequence of values, in the chosen ordering. -
-Type:required. -
-Specified as: an integer, real or complex array of rank 1. -
-
ix
-
A vector of indices. -
-Type: Optional -
-An integer array of rank 1, whose entries are moved to the same -position as the corresponding entries in $x$. -
-
- -

- -

-Notes - -

    -
  1. For integer or real data the sorting can be performed in the up/down direction, on the - natural or absolute values; -
    2. -
  2. For complex data the sorting can be done in a lexicographic - order (i.e.: sort on the real part with ties broken according to - the imaginary part) or on the absolute values; -
    3. -
  3. The routines return the items in the chosen ordering; the - output difference is the handling of ties (i.e. items with an - equal value) in the original input. With the merge-sort algorithm - ties are preserved in the same relative order as they had in the - original sequence, while this is not guaranteed for quicksort or - heapsort; -
    4. -
  4. If -$flag = psb\_sort\_ovw\_idx\_$ then the entries in $ix(1:n)$ - where $n$ is the size of $x$ are initialized to -$ix(i) \leftarrow -i$; thus, upon return from the subroutine, for each - index $i$ we have in $ix(i)$ the position that the item $x(i)$ - occupied in the original data sequence; -
    5. -
  5. If -$flag = psb\_sort\_keep\_idx\_$ the routine will assume that - the entries in $ix(:)$ have already been initialized by the user; -
    6. -
  6. The three sorting algorithms have a similar $O(n \log n)$ expected - running time; in the average case quicksort will be the - fastest and merge-sort the slowest. However note that: - -
      -
    1. The worst case running time for quicksort is $O(n^2)$; the algorithm - implemented here follows the well-known median-of-three heuristics, - but the worst case may still apply; -
      2. -
    2. The worst case running time for merge-sort and heap-sort is - $O(n \log n)$ as the average case; -
      3. -
    3. The merge-sort algorithm is implemented to take advantage of - subsequences that may be already in the desired ordering prior to - the subroutine call; this situation is relatively common when - dealing with groups of indices of sparse matrix entries, thus - merge-sort is the preferred choice when a sorting is needed - by other routines in the library. -
      4. -
    -
    7. -
- -

- -

- -

- - -next - -up - -previous - -contents -
- Next: Parallel environment routines - Up: Data management routines - Previous: psb_sizeof Memory -   Contents
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PSBLAS
User’s and Reference Guide
A reference guide for the Parallel Sparse BLAS library
Salvatore Filippone
Alfredo Buttari
Software version: 3.7.0
Jan 7th, 2020 + - - - -userhtml - - - - + + - - + +

+ Contents +
1 Introduction +
2 General overview +
 2.1 Basic Nomenclature +
 2.2 Library contents +
 2.3 Application structure +
 2.4 Programming model +
3 Data Structures and Classes +
 3.1 Descriptor data structure +
 3.2 Sparse Matrix class +
 3.3 Dense Vector Data Structure +
 3.4 Preconditioner data structure +
 3.5 Heap data structure +
4 Computational routines +
 4.1 psb_geaxpby — General Dense Matrix Sum +
 4.2 psb_gedot — Dot Product +
 4.3 psb_gedots — Generalized Dot Product +
 4.4 psb_normi — Infinity-Norm of Vector +
 4.5 psb_geamaxs — Generalized Infinity Norm +
 4.6 psb_norm1 — 1-Norm of Vector +
 4.7 psb_geasums — Generalized 1-Norm of Vector +
 4.8 psb_norm2 — 2-Norm of Vector +
 4.9 psb_genrm2s — Generalized 2-Norm of Vector +
 4.10 psb_norm1 — 1-Norm of Sparse Matrix +
 4.11 psb_normi — Infinity Norm of Sparse Matrix +
 4.12 psb_spmm — Sparse Matrix by Dense Matrix Product +
 4.13 psb_spsm — Triangular System Solve +
 4.14 psb_gemlt — Entrywise Product +
 4.15 psb_gediv — Entrywise Division +
 4.16 psb_geinv — Entrywise Inversion +
5 Communication routines +
 5.1 psb_halo — Halo Data Communication +
 5.2 psb_ovrl — Overlap Update +
 5.3 psb_gather — Gather Global Dense Matrix +
 5.4 psb_scatter — Scatter Global Dense Matrix +
6 Data management routines +
 6.1 psb_cdall — Allocates a communication descriptor +
 6.2 psb_cdins — Communication descriptor insert routine +
 6.3 psb_cdasb — Communication descriptor assembly routine +
 6.4 psb_cdcpy — Copies a communication descriptor +
 6.5 psb_cdfree — Frees a communication descriptor +
 6.6 psb_cdbldext — Build an extended communication descriptor +
 6.7 psb_spall — Allocates a sparse matrix +
 6.8 psb_spins — Insert a set of coefficients into a sparse matrix +
 6.9 psb_spasb — Sparse matrix assembly routine +
 6.10 psb_spfree — Frees a sparse matrix +
 6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. +
 6.12 psb_geall — Allocates a dense matrix + - + +
 6.13 psb_geins — Dense matrix insertion routine +
 6.14 psb_geasb — Assembly a dense matrix +
 6.15 psb_gefree — Frees a dense matrix +
 6.16 psb_gelp — Applies a left permutation to a dense matrix +
 6.17 psb_glob_to_loc — Global to local indices convertion +
 6.18 psb_loc_to_glob — Local to global indices conversion +
 6.19 psb_is_owned — +
 6.20 psb_owned_index — +
 6.21 psb_is_local — +
 6.22 psb_local_index — +
 6.23 psb_get_boundary — Extract list of boundary elements +
 6.24 psb_get_overlap — Extract list of overlap elements +
 6.25 psb_sp_getrow — Extract row(s) from a sparse matrix +
 6.26 psb_sizeof — Memory occupation +
 6.27 Sorting utilities — +
7 Parallel environment routines +
 7.1 psb_init — Initializes PSBLAS parallel environment +
 7.2 psb_info — Return information about PSBLAS parallel environment +
 7.3 psb_exit — Exit from PSBLAS parallel environment +
 7.4 psb_get_mpi_comm — Get the MPI communicator +
 7.5 psb_get_mpi_rank — Get the MPI rank +
 7.6 psb_wtime — Wall clock timing +
 7.7 psb_barrier — Sinchronization point parallel environment +
 7.8 psb_abort — Abort a computation +
 7.9 psb_bcast — Broadcast data +
 7.10 psb_sum — Global sum +
 7.11 psb_max — Global maximum +
 7.12 psb_min — Global minimum +
 7.13 psb_amx — Global maximum absolute value +
 7.14 psb_amn — Global minimum absolute value +
 7.15 psb_nrm2 — Global 2-norm reduction +
 7.16 psb_snd — Send data +
 7.17 psb_rcv — Receive data +
8 Error handling +
 8.1 psb_errpush — Pushes an error code onto the error stack +
 8.2 psb_error — Prints the error stack content and aborts execution +
 8.3 psb_set_errverbosity — Sets the verbosity of error messages +
 8.4 psb_set_erraction — Set the type of action to be taken upon error condition +
9 Utilities +
 9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format +
 9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format +
 9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format +
 9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format +
 9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format +
 9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format +
10 Preconditioner routines +
 10.1 init — Initialize a preconditioner +
 10.2 build — Builds a preconditioner +
 10.3 apply — Preconditioner application routine +
 10.4 descr — Prints a description of current preconditioner + - - + +
 10.5 clone — clone current preconditioner +
 10.6 free — Free a preconditioner +
11 Iterative Methods +
 11.1 psb_krylov — Krylov Methods Driver Routine +
References +
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-PSBLAS -
-
-User's and Reference - Guide -
A reference guide for the Parallel Sparse BLAS library -
-
-
-
Salvatore Filippone -
-Alfredo Buttari -
-Software version: 3.6.0 -
-Dec 1st, 2018 -

- - - - -
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+

3The subroutine style psb_precinit and psb_precbl are still supported for backward + compatibility

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+

4The string is case-insensitive

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+

5Note: the implementation is for FCG(1).

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1In our prototype implementation we provide sample scatter/gather routines.

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+

2This is the normal situation when the pattern of the sparse matrix is symmetric, which is + equivalent to say that the interaction between two variables is reciprocal. If the matrix pattern is + non-symmetric we may have one-way interactions, and these could cause a situation in which a + boundary point is not a halo point for its neighbour.

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+

Contents

+
+ 1 Introduction +
2 General overview +
 2.1 Basic Nomenclature +
 2.2 Library contents +
 2.3 Application structure +
  2.3.1 User-defined index mappings +
 2.4 Programming model +
3 Data Structures and Classes +
 3.1 Descriptor data structure +
  3.1.1 Descriptor Methods +
  3.1.2 get_local_rows — Get number of local rows +
  3.1.3 get_local_cols — Get number of local cols +
  3.1.4 get_global_rows — Get number of global rows +
  3.1.5 get_global_cols — Get number of global cols +
  3.1.6 get_global_indices — Get vector of global indices +
  3.1.7 get_context — Get communication context +
  3.1.8 Clone — clone current object +
  3.1.9 CNV — convert internal storage format +
  3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping switch +
  3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping switch +
  3.1.12 get_p_adjcncy — Get process adjacency list +
  3.1.13 set_p_adjcncy — Set process adjacency list +
  3.1.14 fnd_owner — Find the owner process of a set of indices +
  3.1.15 Named Constants +
 3.2 Sparse Matrix class +
  3.2.1 Sparse Matrix Methods +
  3.2.2 get_nrows — Get number of rows in a sparse matrix +
  3.2.3 get_ncols — Get number of columns in a sparse matrix +
  3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix +
  3.2.5 get_size — Get maximum number of nonzero elements in a sparse matrix +
  3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix +
  3.2.7 get_fmt — Short description of the dynamic type +
  3.2.8 is_bld, is_upd, is_asb — Status check +
  3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check +
  3.2.10 cscnv — Convert to a different storage format +
  3.2.11 csclip — Reduce to a submatrix +
  3.2.12 clean_zeros — Eliminate zero coefficients +
  3.2.13 get_diag — Get main diagonal +
  3.2.14 clip_diag — Cut out main diagonal + + + +
  3.2.15 tril — Return the lower triangle +
  3.2.16 triu — Return the upper triangle +
  3.2.17 psb_set_mat_default — Set default storage format +
  3.2.18 clone — Clone current object +
  3.2.19 Named Constants +
 3.3 Dense Vector Data Structure +
  3.3.1 Vector Methods +
  3.3.2 get_nrows — Get number of rows in a dense vector +
  3.3.3 sizeof — Get memory occupation in bytes of a dense vector +
  3.3.4 set — Set contents of the vector +
  3.3.5 get_vect — Get a copy of the vector contents +
  3.3.6 clone — Clone current object +
 3.4 Preconditioner data structure +
 3.5 Heap data structure +
4 Computational routines +
 4.1 psb_geaxpby — General Dense Matrix Sum +
 4.2 psb_gedot — Dot Product +
 4.3 psb_gedots — Generalized Dot Product +
 4.4 psb_normi — Infinity-Norm of Vector +
 4.5 psb_geamaxs — Generalized Infinity Norm +
 4.6 psb_norm1 — 1-Norm of Vector +
 4.7 psb_geasums — Generalized 1-Norm of Vector +
 4.8 psb_norm2 — 2-Norm of Vector +
 4.9 psb_genrm2s — Generalized 2-Norm of Vector +
 4.10 psb_norm1 — 1-Norm of Sparse Matrix +
 4.11 psb_normi — Infinity Norm of Sparse Matrix +
 4.12 psb_spmm — Sparse Matrix by Dense Matrix Product +
 4.13 psb_spsm — Triangular System Solve +
 4.14 psb_gemlt — Entrywise Product +
 4.15 psb_gediv — Entrywise Division +
 4.16 psb_geinv — Entrywise Inversion +
5 Communication routines +
 5.1 psb_halo — Halo Data Communication +
 5.2 psb_ovrl — Overlap Update +
 5.3 psb_gather — Gather Global Dense Matrix +
 5.4 psb_scatter — Scatter Global Dense Matrix +
6 Data management routines +
 6.1 psb_cdall — Allocates a communication descriptor +
 6.2 psb_cdins — Communication descriptor insert routine +
 6.3 psb_cdasb — Communication descriptor assembly routine +
 6.4 psb_cdcpy — Copies a communication descriptor +
 6.5 psb_cdfree — Frees a communication descriptor +
 6.6 psb_cdbldext — Build an extended communication descriptor +
 6.7 psb_spall — Allocates a sparse matrix +
 6.8 psb_spins — Insert a set of coefficients into a sparse matrix +
 6.9 psb_spasb — Sparse matrix assembly routine +
 6.10 psb_spfree — Frees a sparse matrix +
 6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. +
 6.12 psb_geall — Allocates a dense matrix +
 6.13 psb_geins — Dense matrix insertion routine + + + +
 6.14 psb_geasb — Assembly a dense matrix +
 6.15 psb_gefree — Frees a dense matrix +
 6.16 psb_gelp — Applies a left permutation to a dense matrix +
 6.17 psb_glob_to_loc — Global to local indices convertion +
 6.18 psb_loc_to_glob — Local to global indices conversion +
 6.19 psb_is_owned — +
 6.20 psb_owned_index — +
 6.21 psb_is_local — +
 6.22 psb_local_index — +
 6.23 psb_get_boundary — Extract list of boundary elements +
 6.24 psb_get_overlap — Extract list of overlap elements +
 6.25 psb_sp_getrow — Extract row(s) from a sparse matrix +
 6.26 psb_sizeof — Memory occupation +
 6.27 Sorting utilities — +
7 Parallel environment routines +
 7.1 psb_init — Initializes PSBLAS parallel environment +
 7.2 psb_info — Return information about PSBLAS parallel environment +
 7.3 psb_exit — Exit from PSBLAS parallel environment +
 7.4 psb_get_mpi_comm — Get the MPI communicator +
 7.5 psb_get_mpi_rank — Get the MPI rank +
 7.6 psb_wtime — Wall clock timing +
 7.7 psb_barrier — Sinchronization point parallel environment +
 7.8 psb_abort — Abort a computation +
 7.9 psb_bcast — Broadcast data +
 7.10 psb_sum — Global sum +
 7.11 psb_max — Global maximum +
 7.12 psb_min — Global minimum +
 7.13 psb_amx — Global maximum absolute value +
 7.14 psb_amn — Global minimum absolute value +
 7.15 psb_nrm2 — Global 2-norm reduction +
 7.16 psb_snd — Send data +
 7.17 psb_rcv — Receive data +
8 Error handling +
 8.1 psb_errpush — Pushes an error code onto the error stack +
 8.2 psb_error — Prints the error stack content and aborts execution +
 8.3 psb_set_errverbosity — Sets the verbosity of error messages +
 8.4 psb_set_erraction — Set the type of action to be taken upon error condition +
9 Utilities +
 9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format +
 9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format +
 9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format +
 9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format +
 9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format +
 9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format +
10 Preconditioner routines +
 10.1 init — Initialize a preconditioner +
 10.2 build — Builds a preconditioner +
 10.3 apply — Preconditioner application routine +
 10.4 descr — Prints a description of current preconditioner +
 10.5 clone — clone current preconditioner + + + +
 10.6 free — Free a preconditioner +
11 Iterative Methods +
 11.1 psb_krylov — Krylov Methods Driver Routine +
+ + + + + + + + + +

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+

References

+

+

+

+ [1]    + D. Barbieri, V. Cardellini, S. Filippone and D. Rouson Design Patterns + for Scientific Computations on Sparse Matrices, HPSS 2011, Algorithms + and Programming Tools for Next-Generation High-Performance Scientific + Software, Bordeaux, Sep. 2011 +

+

+ [2]   G. Bella, S. Filippone, A. De Maio and M. Testa, A Simulation Model + for Forest Fires, in J. Dongarra, K. Madsen, J. Wasniewski, editors, + Proceedings of PARA 04 Workshop on State of the Art in Scientific + Computing, pp. 546–553, Lecture Notes in Computer Science, Springer, + 2005. +

+

+ [3]   A. Buttari, D. di Serafino, P. D’Ambra, S. Filippone, 2LEV-D2P4: + a package of high-performance preconditioners, Applicable Algebra in + Engineering, Communications and Computing, Volume 18, Number 3, May, + 2007, pp. 223-239 +

+

+ [4]   P. D’Ambra, S. Filippone, D. Di Serafino On the Development + of PSBLAS-based Parallel Two-level Schwarz Preconditioners Applied + Numerical Mathematics, Elsevier Science, Volume 57, Issues 11-12, + November-December 2007, Pages 1181-1196. +

+

+ [5]   Dongarra, J. J., DuCroz, J., Hammarling, S. and Hanson, R., An + Extended Set of Fortran Basic Linear Algebra Subprograms, ACM Trans. + Math. Softw. vol. 14, 1–17, 1988. +

+

+ [6]   Dongarra, J., DuCroz, J., Hammarling, S. and Duff, I., A Set of level + 3 Basic Linear Algebra Subprograms, ACM Trans. Math. Softw. vol. 16, + 1–17, 1990. + + + +

+

+ [7]   J. J. Dongarra and R. C. Whaley, A User’s Guide to the BLACS + v. 1.1, Lapack Working Note 94, Tech. Rep. UT-CS-95-281, University of + Tennessee, March 1995 (updated May 1997). +

+

+ [8]   I. Duff, M. Marrone, G. Radicati and C. Vittoli, Level 3 Basic Linear + Algebra Subprograms for Sparse Matrices: a User Level Interface, ACM + Transactions on Mathematical Software, 23(3), pp. 379–401, 1997. +

+

+ [9]   I. Duff, M. Heroux and R. Pozo, An Overview of the Sparse Basic + Linear Algebra Subprograms: the New Standard from the BLAS Technical + Forum, ACM Transactions on Mathematical Software, 28(2), pp. 239–267, + 2002. +

+

+ [10]   S. Filippone and M. Colajanni, PSBLAS: A Library for Parallel + Linear Algebra Computation on Sparse Matrices, ACM Transactions on + Mathematical Software, 26(4), pp. 527–550, 2000. +

+

+ [11]   S. Filippone and A. Buttari, Object-Oriented Techniques for Sparse + Matrix Computations in Fortran 2003, ACM Transactions on Mathematical + Software, 38(4), 2012. +

+

+ [12]   S. Filippone, P. D’Ambra, M. Colajanni, Using a Parallel Library + of Sparse Linear Algebra in a Fluid Dynamics Applications Code on + Linux Clusters, in G. Joubert, A. Murli, F. Peters, M. Vanneschi, editors, + Parallel Computing - Advances & Current Issues, pp. 441–448, Imperial + College Press, 2002. +

+

+ [13]    Gamma, E., Helm, R., Johnson, R., and Vlissides, J. 1995. Design + Patterns: Elements of Reusable Object-Oriented Software. Addison-Wesley. +

+

+ [14]   Karypis, G. and Kumar, V., METIS: Unstructured Graph Partitioning + and Sparse Matrix Ordering System. Minneapolis, MN 55455: University + of Minnesota, Department of Computer Science, 1995. Internet Address: + http://www.cs.umn.edu/~karypis. + + + +

+

+ [15]   Lawson, C., Hanson, R., Kincaid, D. and Krogh, F., Basic Linear + Algebra Subprograms for Fortran usage, ACM Trans. Math. Softw. vol. 5, + 38–329, 1979. +

+

+ [16]   Machiels, L. and Deville, M. Fortran 90: An entry to object-oriented + programming for the solution of partial differential equations. ACM Trans. + Math. Softw. vol. 23, 32–49. +

+

+ [17]   Metcalf, M., Reid, J. and Cohen, M. Fortran 95/2003 explained. Oxford + University Press, 2004. +

+

+ [18]   Rouson, D.W.I., Xia, J., Xu, X.: Scientific Software Design: The + Object-Oriented Way. Cambridge University Press (2011) +

+

+ [19]   M. Snir, S. Otto, S. Huss-Lederman, D. Walker and J. Dongarra, + MPI: The Complete Reference. Volume 1 - The MPI Core, second edition, + MIT Press, 1998.

+ + + +

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+

1 Introduction

+

The PSBLAS library, developed with the aim to facilitate the parallelization of +computationally intensive scientific applications, is designed to address parallel +implementation of iterative solvers for sparse linear systems through the distributed +memory paradigm. It includes routines for multiplying sparse matrices by dense +matrices, solving block diagonal systems with triangular diagonal entries, +preprocessing sparse matrices, and contains additional routines for dense matrix +operations. The current implementation of PSBLAS addresses a distributed memory +execution model operating with message passing. +

The PSBLAS library version 3 is implemented in the Fortran 2003 [17] +programming language, with reuse and/or adaptation of existing Fortran 77 and +Fortran 95 software, plus a handful of C routines. +

The use of Fortran 2003 offers a number of advantages over Fortran 95, mostly in +the handling of requirements for evolution and adaptation of the library to new +computing architectures and integration of new algorithms. For a detailed discussion +of our design see [11]; other works discussing advanced programming in Fortran 2003 +include [1, 18]; sufficient support for Fortran 2003 is now available from many +compilers, including the GNU Fortran compiler from the Free Software Foundation +(as of version 4.8). +

Previous approaches have been based on mixing Fortran 95, with its support for +object-based design, with other languages; these have been advocated by a number of +authors, e.g. [16]. Moreover, the Fortran 95 facilities for dynamic memory +management and interface overloading greatly enhance the usability of the PSBLAS +subroutines. In this way, the library can take care of runtime memory requirements +that are quite difficult or even impossible to predict at implementation or +compilation time. +

The presentation of the PSBLAS library follows the general structure of the +proposal for serial Sparse BLAS [8, 9], which in its turn is based on the proposal for +BLAS on dense matrices [15, 5, 6]. +

The applicability of sparse iterative solvers to many different areas causes some +terminology problems because the same concept may be denoted through different +names depending on the application area. The PSBLAS features presented in this +document will be discussed referring to a finite difference discretization of a Partial +Differential Equation (PDE). However, the scope of the library is wider than that: for +example, it can be applied to finite element discretizations of PDEs, and even to +different classes of problems such as nonlinear optimization, for example in optimal +control problems. +

The design of a solver for sparse linear systems is driven by many conflicting +objectives, such as limiting occupation of storage resources, exploiting regularities in +the input data, exploiting hardware characteristics of the parallel platform. To +achieve an optimal communication to computation ratio on distributed memory +machines it is essential to keep the data locality as high as possible; this can be +done through an appropriate data allocation strategy. The choice of the + + + +preconditioner is another very important factor that affects efficiency of the +implemented application. Optimal data distribution requirements for a given +preconditioner may conflict with distribution requirements of the rest of the solver. +Finding the optimal trade-off may be very difficult because it is application +dependent. Possible solutions to these problems and other important inputs to the +development of the PSBLAS software package have come from an established +experience in applying the PSBLAS solvers to computational fluid dynamics +applications. + + + +

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+

10 Preconditioner routines

+

The base PSBLAS library contains the implementation of two simple preconditioning +techniques: +

    +
  • Diagonal Scaling +
    • +
  • Block Jacobi with ILU(0) factorization
+

The supporting data type and subroutine interfaces are defined in the module +psb_prec_mod. The old interfaces psb_precinit and psb_precbld are still +supported for backward compatibility + + + +

+  10.1 init — Initialize a preconditioner +
 10.2 build — Builds a preconditioner +
 10.3 apply — Preconditioner application routine +
 10.4 descr — Prints a description of current preconditioner +
 10.5 clone — clone current preconditioner +
 10.6 free — Free a preconditioner +
+ + + + + + + + +

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+

11 Iterative Methods

+

In this chapter we provide routines for preconditioners and iterative methods. +The interfaces for Krylov subspace methods are available in the module +psb_krylov_mod. + + + +

+  11.1 psb_krylov — Krylov Methods Driver Routine +
+ + + +

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+

2 General overview

+

The PSBLAS library is designed to handle the implementation of iterative solvers for +sparse linear systems on distributed memory parallel computers. The system +coefficient matrix A must be square; it may be real or complex, nonsymmetric, and +its sparsity pattern needs not to be symmetric. The serial computation parts are +based on the serial sparse BLAS, so that any extension made to the data structures +of the serial kernels is available to the parallel version. The overall design and +parallelization strategy have been influenced by the structure of the ScaLAPACK +parallel library. The layered structure of the PSBLAS library is shown in figure 1; +lower layers of the library indicate an encapsulation relationship with upper +layers. The ongoing discussion focuses on the Fortran 2003 layer immediately +below the application layer. The serial parts of the computation on each +process are executed through calls to the serial sparse BLAS subroutines. In a +similar way, the inter-process message exchanges are encapsulated in an +applicaiton layer that has been strongly inspired by the Basic Linear Algebra +Communication Subroutines (BLACS) library [7]. Usually there is no need to deal +directly with MPI; however, in some cases, MPI routines are used directly +to improve efficiency. For further details on our communication layer see +Sec. 7. +

+ + + + + + + +
+

+

PIC

+
Figure 1: PSBLAS library components hierarchy.
+ + + +

+

The type of linear system matrices that we address typically arise in +the numerical solution of PDEs; in such a context, it is necessary to pay +special attention to the structure of the problem from which the application +originates. The nonzero pattern of a matrix arising from the discretization of a +PDE is influenced by various factors, such as the shape of the domain, the +discretization strategy, and the equation/unknown ordering. The matrix itself can be +interpreted as the adjacency matrix of the graph associated with the discretization +mesh. +

The distribution of the coefficient matrix for the linear system is based on the +“owner computes” rule: the variable associated to each mesh point is assigned to a +process that will own the corresponding row in the coefficient matrix and will +carry out all related computations. This allocation strategy is equivalent to a +partition of the discretization mesh into sub-domains. Our library supports any +distribution that keeps together the coefficients of each matrix row; there are no +other constraints on the variable assignment. This choice is consistent with +simple data distributions such as CYCLIC(N) and BLOCK, as well as completely +arbitrary assignments of equation indices to processes. In particular it is +consistent with the usage of graph partitioning tools commonly available in +the literature, e.g. METIS [14]. Dense vectors conform to sparse matrices, +that is, the entries of a vector follow the same distribution of the matrix +rows. +

We assume that the sparse matrix is built in parallel, where each process generates +its own portion. We never require that the entire matrix be available on a single +node. However, it is possible to hold the entire matrix in one process and distribute it +explicitly1 , +even though the resulting memory bottleneck would make this option unattractive in +most cases. +

+  2.1 Basic Nomenclature +
 2.2 Library contents +
 2.3 Application structure +
  2.3.1 User-defined index mappings +
 2.4 Programming model +
+ + + + + + +

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+

3 Data Structures and Classes

+

In this chapter we illustrate the data structures used for definition of routines +interfaces. They include data structures for sparse matrices, communication +descriptors and preconditioners. +

All the data types and the basic subroutine interfaces related to descriptors and +sparse matrices are defined in the module psb_base_mod; this will have to be +included by every user subroutine that makes use of the library. The preconditioners +are defined in the module psb_prec_mod +

Integer, real and complex data types are parametrized with a kind type defined in +the library as follows: +

+psb_spk_
Kind parameter for short precision real and complex data; + corresponds to a REAL declaration and is normally 4 bytes; +
+psb_dpk_
Kind parameter for long precision real and complex data; + corresponds to a DOUBLE PRECISION declaration and is normally 8 bytes; +
+psb_mpk_
Kind parameter for 4-bytes integer data, as is always used by MPI; +
+psb_epk_
Kind parameter for 8-bytes integer data, as is always used by the + sizeof methods; +
+psb_ipk_
Kind parameter for “local” integer indices and data; with default + build options this is a 4 bytes integer; +
+psb_lpk_
Kind parameter for “global” integer indices and data; with default + build options this is an 8 bytes integer;
+

The integer kinds for local and global indices can be chosen at configure time to hold 4 +or 8 bytes, with the global indices at least as large as the local ones. Together with +the classes attributes we also discuss their methods. Most methods detailed here only +act on the local variable, i.e. their action is purely local and asynchronous unless +otherwise stated. The list of methods here is not completely exhaustive; many +methods, especially those that alter the contents of the various objects, are usually +not needed by the end-user, and therefore are described in the developer’s +documentation. + + + +

+

+  3.1 Descriptor data structure +
  3.1.1 Descriptor Methods +
  3.1.2 get_local_rows — Get number of local rows +
  3.1.3 get_local_cols — Get number of local cols +
  3.1.4 get_global_rows — Get number of global rows +
  3.1.5 get_global_cols — Get number of global cols +
  3.1.6 get_global_indices — Get vector of global indices +
  3.1.7 get_context — Get communication context +
  3.1.8 Clone — clone current object +
  3.1.9 CNV — convert internal storage format +
  3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping switch +
  3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping switch +
  3.1.12 get_p_adjcncy — Get process adjacency list +
  3.1.13 set_p_adjcncy — Set process adjacency list +
  3.1.14 fnd_owner — Find the owner process of a set of indices +
  3.1.15 Named Constants +
 3.2 Sparse Matrix class +
  3.2.1 Sparse Matrix Methods +
  3.2.2 get_nrows — Get number of rows in a sparse matrix +
  3.2.3 get_ncols — Get number of columns in a sparse matrix +
  3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix +
  3.2.5 get_size — Get maximum number of nonzero elements in a sparse matrix +
  3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix +
  3.2.7 get_fmt — Short description of the dynamic type +
  3.2.8 is_bld, is_upd, is_asb — Status check +
  3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check +
  3.2.10 cscnv — Convert to a different storage format +
  3.2.11 csclip — Reduce to a submatrix +
  3.2.12 clean_zeros — Eliminate zero coefficients +
  3.2.13 get_diag — Get main diagonal +
  3.2.14 clip_diag — Cut out main diagonal +
  3.2.15 tril — Return the lower triangle +
  3.2.16 triu — Return the upper triangle +
  3.2.17 psb_set_mat_default — Set default storage format +
  3.2.18 clone — Clone current object +
  3.2.19 Named Constants +
 3.3 Dense Vector Data Structure +
  3.3.1 Vector Methods +
  3.3.2 get_nrows — Get number of rows in a dense vector +
  3.3.3 sizeof — Get memory occupation in bytes of a dense vector +
  3.3.4 set — Set contents of the vector +
  3.3.5 get_vect — Get a copy of the vector contents +
  3.3.6 clone — Clone current object +
 3.4 Preconditioner data structure +
 3.5 Heap data structure +
+ + + + + + + +

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+

+ diff --git a/docs/html/userhtmlse4.html b/docs/html/userhtmlse4.html new file mode 100644 index 00000000..af168dc4 --- /dev/null +++ b/docs/html/userhtmlse4.html @@ -0,0 +1,84 @@ + + +Computational routines + + + + + + + +

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+

4 Computational routines

+ + + +
+  4.1 psb_geaxpby — General Dense Matrix Sum +
 4.2 psb_gedot — Dot Product +
 4.3 psb_gedots — Generalized Dot Product +
 4.4 psb_normi — Infinity-Norm of Vector +
 4.5 psb_geamaxs — Generalized Infinity Norm +
 4.6 psb_norm1 — 1-Norm of Vector +
 4.7 psb_geasums — Generalized 1-Norm of Vector +
 4.8 psb_norm2 — 2-Norm of Vector +
 4.9 psb_genrm2s — Generalized 2-Norm of Vector +
 4.10 psb_norm1 — 1-Norm of Sparse Matrix +
 4.11 psb_normi — Infinity Norm of Sparse Matrix +
 4.12 psb_spmm — Sparse Matrix by Dense Matrix Product +
 4.13 psb_spsm — Triangular System Solve +
 4.14 psb_gemlt — Entrywise Product +
 4.15 psb_gediv — Entrywise Division +
 4.16 psb_geinv — Entrywise Inversion +
+ + + + + + + + + + + + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlse5.html b/docs/html/userhtmlse5.html new file mode 100644 index 00000000..4cb38373 --- /dev/null +++ b/docs/html/userhtmlse5.html @@ -0,0 +1,52 @@ + + +Communication routines + + + + + + + +

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+

5 Communication routines

+

The routines in this chapter implement various global communication operators on +vectors associated with a discretization mesh. For auxiliary communication routines +not tied to a discretization space see 6. + + + +

+  5.1 psb_halo — Halo Data Communication +
 5.2 psb_ovrl — Overlap Update +
 5.3 psb_gather — Gather Global Dense Matrix +
 5.4 psb_scatter — Scatter Global Dense Matrix +
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlse6.html b/docs/html/userhtmlse6.html new file mode 100644 index 00000000..0eff0926 --- /dev/null +++ b/docs/html/userhtmlse6.html @@ -0,0 +1,115 @@ + + +Data management routines + + + + + + + +

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+

6 Data management routines

+

+

+  6.1 psb_cdall — Allocates a communication descriptor +
 6.2 psb_cdins — Communication descriptor insert routine +
 6.3 psb_cdasb — Communication descriptor assembly routine +
 6.4 psb_cdcpy — Copies a communication descriptor +
 6.5 psb_cdfree — Frees a communication descriptor +
 6.6 psb_cdbldext — Build an extended communication descriptor +
 6.7 psb_spall — Allocates a sparse matrix +
 6.8 psb_spins — Insert a set of coefficients into a sparse matrix +
 6.9 psb_spasb — Sparse matrix assembly routine +
 6.10 psb_spfree — Frees a sparse matrix +
 6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. +
 6.12 psb_geall — Allocates a dense matrix +
 6.13 psb_geins — Dense matrix insertion routine +
 6.14 psb_geasb — Assembly a dense matrix +
 6.15 psb_gefree — Frees a dense matrix +
 6.16 psb_gelp — Applies a left permutation to a dense matrix +
 6.17 psb_glob_to_loc — Global to local indices convertion +
 6.18 psb_loc_to_glob — Local to global indices conversion +
 6.19 psb_is_owned — +
 6.20 psb_owned_index — +
 6.21 psb_is_local — +
 6.22 psb_local_index — +
 6.23 psb_get_boundary — Extract list of boundary elements +
 6.24 psb_get_overlap — Extract list of overlap elements +
 6.25 psb_sp_getrow — Extract row(s) from a sparse matrix +
 6.26 psb_sizeof — Memory occupation +
 6.27 Sorting utilities — +
+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlse7.html b/docs/html/userhtmlse7.html new file mode 100644 index 00000000..e08cc891 --- /dev/null +++ b/docs/html/userhtmlse7.html @@ -0,0 +1,87 @@ + + +Parallel environment routines + + + + + + + +

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+

7 Parallel environment routines

+ + + +
+  7.1 psb_init — Initializes PSBLAS parallel environment +
 7.2 psb_info — Return information about PSBLAS parallel environment +
 7.3 psb_exit — Exit from PSBLAS parallel environment +
 7.4 psb_get_mpi_comm — Get the MPI communicator +
 7.5 psb_get_mpi_rank — Get the MPI rank +
 7.6 psb_wtime — Wall clock timing +
 7.7 psb_barrier — Sinchronization point parallel environment +
 7.8 psb_abort — Abort a computation +
 7.9 psb_bcast — Broadcast data +
 7.10 psb_sum — Global sum +
 7.11 psb_max — Global maximum +
 7.12 psb_min — Global minimum +
 7.13 psb_amx — Global maximum absolute value +
 7.14 psb_amn — Global minimum absolute value +
 7.15 psb_nrm2 — Global 2-norm reduction +
 7.16 psb_snd — Send data +
 7.17 psb_rcv — Receive data +
+ + + + + + + + + + + + + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlse8.html b/docs/html/userhtmlse8.html new file mode 100644 index 00000000..504703f8 --- /dev/null +++ b/docs/html/userhtmlse8.html @@ -0,0 +1,418 @@ + + +Error handling + + + + + + + +

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+

8 Error handling

+

The PSBLAS library error handling policy has been completely rewritten in version +2.0. The idea behind the design of this new error handling strategy is to keep error +messages on a stack allowing the user to trace back up to the point where the first +error message has been generated. Every routine in the PSBLAS-2.0 library has, as +last non-optional argument, an integer info variable; whenever, inside the routine, an +error is detected, this variable is set to a value corresponding to a specific +error code. Then this error code is also pushed on the error stack and then +either control is returned to the caller routine or the execution is aborted, +depending on the users choice. At the time when the execution is aborted, +an error message is printed on standard output with a level of verbosity +than can be chosen by the user. If the execution is not aborted, then, the +caller routine checks the value returned in the info variable and, if not +zero, an error condition is raised. This process continues on all the levels of +nested calls until the level where the user decides to abort the program +execution. +

Figure 9 shows the layout of a generic psb_foo routine with respect to the +PSBLAS-2.0 error handling policy. It is possible to see how, whenever an error +condition is detected, the info variable is set to the corresponding error code which +is, then, pushed on top of the stack by means of the psb_errpush. An error condition +may be directly detected inside a routine or indirectly checking the error code +returned returned by a called routine. Whenever an error is encountered, after it has +been pushed on stack, the program execution skips to a point where the error +condition is handled; the error condition is handled either by returning control to the +caller routine or by calling the psb\_error routine which prints the content of +the error stack and aborts the program execution, according to the choice +made by the user with psb_set_erraction. The default is to print the error +and terminate the program, but the user may choose to handle the error +explicitly. +

+ + + + + + + +
+

+

+
subroutine psb_foo(some args, info) 
   ... 
   if(error detected) then 
      info=errcode1 
      call psb_errpush(’psb_foo’, errcode1) 
      goto 9999 
   end if 
   ... 
   call psb_bar(some args, info) 
   if(info .ne. zero) then 
      info=errcode2 
      call psb_errpush(’psb_foo’, errcode2) 
      goto 9999 
   end if 
   ... 
9999 continue 
   if (err_act .eq. act_abort) then 
     call psb_error(icontxt) 
     return 
   else 
     return 
   end if 
 
end subroutine psb_foo +
+
+
Figure 9: The layout of a generic psb_foo routine with respect to PSBLAS-2.0 +error handling policy.
+ + + +

+

Figure 10 reports a sample error message generated by the PSBLAS-2.0 +library. This error has been generated by the fact that the user has chosen the +invalid “FOO” storage format to represent the sparse matrix. From this +error message it is possible to see that the error has been detected inside +the psb_cest subroutine called by psb_spasb ... by process 0 (i.e. the root +process). +

+ + + + + + + +
+

+

+========================================================== + 
Process: 0.  PSBLAS Error (4010) in subroutine: df_sample + 
Error from call to subroutine mat dist + 
========================================================== + 
Process: 0.  PSBLAS Error (4010) in subroutine: mat_distv + 
Error from call to subroutine psb_spasb + 
========================================================== + 
Process: 0.  PSBLAS Error (4010) in subroutine: psb_spasb + 
Error from call to subroutine psb_cest + 
========================================================== + 
Process: 0.  PSBLAS Error (136) in subroutine: psb_cest + 
Format FOO is unknown + 
========================================================== + 
Aborting... +
+

+
+
Figure 10: A sample PSBLAS-2.0 error message. Process 0 detected an error +condition inside the psb_cest subroutine
+ + + +

+ + + +
+  8.1 psb_errpush — Pushes an error code onto the error stack +
 8.2 psb_error — Prints the error stack content and aborts execution +
 8.3 psb_set_errverbosity — Sets the verbosity of error messages +
 8.4 psb_set_erraction — Set the type of action to be taken upon error condition +
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlse9.html b/docs/html/userhtmlse9.html new file mode 100644 index 00000000..466b3d20 --- /dev/null +++ b/docs/html/userhtmlse9.html @@ -0,0 +1,57 @@ + + +Utilities + + + + + + + +

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+

9 Utilities

+

We have some utilities available for input and output of sparse matrices; the +interfaces to these routines are available in the module psb_util_mod. + + + +

+  9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format +
 9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format +
 9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format +
 9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format +
 9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format +
 9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format +
+ + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu1.html b/docs/html/userhtmlsu1.html new file mode 100644 index 00000000..4e6f170e --- /dev/null +++ b/docs/html/userhtmlsu1.html @@ -0,0 +1,148 @@ + + +Basic Nomenclature + + + + + + + +

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+

2.1 Basic Nomenclature

+

Our computational model implies that the data allocation on the parallel distributed +memory machine is guided by the structure of the physical model, and specifically by +the discretization mesh of the PDE. +

Each point of the discretization mesh will have (at least) one associated +equation/variable, and therefore one index. We say that point i depends on point j if +the equation for a variable associated with i contains a term in j, or equivalently if + + + +aij≠0. After the partition of the discretization mesh into sub-domains assigned +to the parallel processes, we classify the points of a given sub-domain as +following. +

+Internal.
An internal point of a given domain depends only on points of the + same domain. If all points of a domain are assigned to one process, then + a computational step (e.g., a matrix-vector product) of the equations + associated with the internal points requires no data items from other + domains and no communications. +
+Boundary.
A point of a given domain is a boundary point if it depends on + points belonging to other domains. +
+Halo.
A halo point for a given domain is a point belonging to another domain + such that there is a boundary point which depends on it. Whenever performing + a computational step, such as a matrix-vector product, the values associated + with halo points are requested from other domains. A boundary point of a + given domain is usually a halo point for some other domain2 ; + therefore the cardinality of the boundary points set denotes the amount + of data sent to other domains. +
+Overlap.
An overlap point is a boundary point assigned to multiple domains. + Any operation that involves an overlap point has to be replicated for each + assignment.
+

Overlap points do not usually exist in the basic data distributions; however they are a +feature of Domain Decomposition Schwarz preconditioners which are the subject of +related research work [4, 3]. +

We denote the sets of internal, boundary and halo points for a given subdomain +by I, B and H. Each subdomain is assigned to one process; each process usually owns +one subdomain, although the user may choose to assign more than one subdomain to +a process. If each process i owns one subdomain, the number of rows in +the local sparse matrix is |Ii| + |Bi|, and the number of local columns (i.e. +those for which there exists at least one non-zero entry in the local rows) is +|Ii| + |Bi| + |Hi|. +

+ + + + + + + +
+

+

PIC

+
Figure 2: Point classfication.
+ + + +

+

This classification of mesh points guides the naming scheme that we adopted in +the library internals and in the data structures. We explicitly note that “Halo” points +are also often called “ghost” points in the literature. + + + +

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+

+ diff --git a/docs/html/userhtmlsu10.html b/docs/html/userhtmlsu10.html new file mode 100644 index 00000000..e1a66a1f --- /dev/null +++ b/docs/html/userhtmlsu10.html @@ -0,0 +1,233 @@ + + +psb_geaxpby — General Dense Matrix Sum + + + + + + + +

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+

4.1 psb_geaxpby — General Dense Matrix Sum

+

This subroutine is an interface to the computational kernel for dense matrix +sum: +

+y ← α x+ βy +
+

+ + + +

+call psb_geaxpby(alpha, x, beta, y, desc_a, info) +
+

+

+ + + +

+ + + +
+

+

+ + + + +
x, y, α, β Subroutine
Short Precision Real psb_geaxpby
Long Precision Real psb_geaxpby
Short Precision Complexpsb_geaxpby
Long Precision Complex psb_geaxpby
+
Table 1: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+alpha
the scalar α.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 1. +
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 1. The + rank of x must be the same of y. +
+beta
the scalar β.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 1. +
+y
the local portion of the global dense matrix y.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 1. + The rank of y must be the same of x. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+
+On Return
+ + + +
+y
the local portion of result submatrix y.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 1. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu11.html b/docs/html/userhtmlsu11.html new file mode 100644 index 00000000..926766df --- /dev/null +++ b/docs/html/userhtmlsu11.html @@ -0,0 +1,249 @@ + + +psb_gedot — Dot Product + + + + + + + +

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+

4.2 psb_gedot — Dot Product

+

This function computes dot product between two vectors x and y.
If x and y are real vectors it computes dot-product as: +

+ T +dot ← x y +
+

Else if x and y are complex vectors then it computes dot-product as: +

+dot ← xHy +
+

+ + + +

+psb_gedot(x, y, desc_a, info [,global]) +
+

+ + + +

+ + + +
+

+

+ + + + +
dot, x, y Function
Short Precision Real psb_gedot
Long Precision Real psb_gedot
Short Precision Complexpsb_gedot
Long Precision Complex psb_gedot
+
Table 2: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 2. The + rank of x must be the same of y. +
+y
the local portion of global dense matrix y.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 2. The + rank of y must be the same of x. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+global
Specifies whether the computation should include the global reduction + across all processes.
Scope: global
Type: optional.
Intent: in.
Specified as: a logical scalar. Default: global=.true.
+
+On Return
+
+Function value
is the dot product of vectors x and y.
Scope: global unless the optional variable global=.false. has been + specified
Specified as: a number of the data type indicated in Table 2. + + + +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to + compute multiple dot products at the same time; in this case, it is + possible to improve the runtime efficiency by using the following scheme: + +
        vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.) 
        vres(2) = psb_gedot(x2,y2,desc_a,info,global=.false.) 
        vres(3) = psb_gedot(x3,y3,desc_a,info,global=.false.) 
        call psb_sum(ictxt,vres(1:3)) + +
    +

    In this way the global communication, which for small sizes is a latency-bound + operation, is invoked only once.

+ + + + + + +

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+

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+

4.3 psb_gedots — Generalized Dot Product

+

This subroutine computes a series of dot products among the columns of two dense +matrices x and y: +

+ T +res(i) ← x(:,i) y(:,i) +
+

If the matrices are complex, then the usual convention applies, i.e. the conjugate +transpose of x is used. If x and y are of rank one, then res is a scalar, else it is a rank +one array. + + + +

+call psb_gedots(res, x, y, desc_a, info) +
+

+ + + +

+ + + +
+

+

+ + + + +
res, x, y Subroutine
Short Precision Real psb_gedots
Long Precision Real psb_gedots
Short Precision Complexpsb_gedots
Long Precision Complex psb_gedots
+
Table 3: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 3. The + rank of x must be the same of y. +
+y
the local portion of global dense matrix y.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 3. The + rank of y must be the same of x. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+res
is the dot product of vectors x and y.
Scope: global
Intent: out.
Specified as: a number or a rank-one array of the data type indicated in + Table 2. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu13.html b/docs/html/userhtmlsu13.html new file mode 100644 index 00000000..db09267b --- /dev/null +++ b/docs/html/userhtmlsu13.html @@ -0,0 +1,223 @@ + + +psb_normi — Infinity-Norm of Vector + + + + + + + +

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+

4.4 psb_normi — Infinity-Norm of Vector

+

This function computes the infinity-norm of a vector x.
If x is a real vector it computes infinity norm as: +

+amax ← maxi |xi| +
+

else if x is a complex vector then it computes the infinity-norm as: +

+amax ← maxi (|re(xi)|+ |im(xi)|) +
+

+ + + +

+psb_geamax(x, desc_a, info [,global]) + 
psb_normi(x, desc_a, info [,global]) +
+

+

+ + + +

+ + + +
+

+

+ + + +
amax x Function
Short Precision RealShort Precision Real psb_geamax
Long Precision Real Long Precision Real psb_geamax
Short Precision RealShort Precision Complexpsb_geamax
Long Precision Real Long Precision Complex psb_geamax
+
Table 4: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 4. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+global
Specifies whether the computation should include the global reduction + across all processes.
Scope: global
Type: optional.
Intent: in.
Specified as: a logical scalar. Default: global=.true.
+
+On Return
+
+Function value
is the infinity norm of vector x.
Scope: global unless the optional variable global=.false. has been + specified
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes + + + +

    +
  1. The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: +
        vres(1) = psb_geamax(x1,desc_a,info,global=.false.) 
        vres(2) = psb_geamax(x2,desc_a,info,global=.false.) 
        vres(3) = psb_geamax(x3,desc_a,info,global=.false.) 
        call psb_amx(ictxt,vres(1:3)) + +
    +

    In this way the global communication, which for small sizes is a latency-bound + operation, is invoked only once.

+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu14.html b/docs/html/userhtmlsu14.html new file mode 100644 index 00000000..5b9f01c1 --- /dev/null +++ b/docs/html/userhtmlsu14.html @@ -0,0 +1,177 @@ + + +psb_geamaxs — Generalized Infinity Norm + + + + + + + +

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+

4.5 psb_geamaxs — Generalized Infinity Norm

+

This subroutine computes a series of infinity norms on the columns of a dense matrix +x: +

+res(i) ← makx|x(k,i)| +
+

+ + + +

+call psb_geamaxs(res, x, desc_a, info) +
+

+

+ + + +

+ + + +
+

+

+ + + +
res x Subroutine
Short Precision RealShort Precision Real psb_geamaxs
Long Precision Real Long Precision Real psb_geamaxs
Short Precision RealShort Precision Complexpsb_geamaxs
Long Precision Real Long Precision Complex psb_geamaxs
+
Table 5: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 5. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+res
is the infinity norm of the columns of x.
Scope: global
Intent: out.
Specified as: a number or a rank-one array of long precision real numbers. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu15.html b/docs/html/userhtmlsu15.html new file mode 100644 index 00000000..61096aa2 --- /dev/null +++ b/docs/html/userhtmlsu15.html @@ -0,0 +1,224 @@ + + +psb_norm1 — 1-Norm of Vector + + + + + + + +

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+

4.6 psb_norm1 — 1-Norm of Vector

+

This function computes the 1-norm of a vector x.
If x is a real vector it computes 1-norm as: +

+asum ← ∥xi∥ +
+

else if x is a complex vector then it computes 1-norm as: +

+asum ← ∥re(x)∥ + ∥im (x)∥ + 1 1 +
+

+ + + +

+psb_geasum(x, desc_a, info [,global]) + 
psb_norm1(x, desc_a, info [,global]) +
+

+

+ + + +

+ + + +
+

+

+ + + +
asum x Function
Short Precision RealShort Precision Real psb_geasum
Long Precision Real Long Precision Real psb_geasum
Short Precision RealShort Precision Complexpsb_geasum
Long Precision Real Long Precision Complex psb_geasum
+
Table 6: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 6. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+global
Specifies whether the computation should include the global reduction + across all processes.
Scope: global
Type: optional.
Intent: in.
Specified as: a logical scalar. Default: global=.true.
+
+On Return
+
+Function value
is the 1-norm of vector x.
Scope: global unless the optional variable global=.false. has been + specified
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes + + + +

    +
  1. The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: +
        vres(1) = psb_geasum(x1,desc_a,info,global=.false.) 
        vres(2) = psb_geasum(x2,desc_a,info,global=.false.) 
        vres(3) = psb_geasum(x3,desc_a,info,global=.false.) 
        call psb_sum(ictxt,vres(1:3)) + +
    +

    In this way the global communication, which for small sizes is a latency-bound + operation, is invoked only once.

+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu16.html b/docs/html/userhtmlsu16.html new file mode 100644 index 00000000..d7792e50 --- /dev/null +++ b/docs/html/userhtmlsu16.html @@ -0,0 +1,192 @@ + + +psb_geasums — Generalized 1-Norm of Vector + + + + + + + +

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+

4.7 psb_geasums — Generalized 1-Norm of Vector

+

This subroutine computes a series of 1-norms on the columns of a dense matrix +x: +

+res(i) ← makx|x(k,i)| +
+

This function computes the 1-norm of a vector x.
If x is a real vector it computes 1-norm as: +

+res(i) ← ∥xi∥ +
+

else if x is a complex vector then it computes 1-norm as: +

+res(i) ← ∥re(x )∥1 +∥im (x )∥1 +
+

+ + + +

+call psb_geasums(res, x, desc_a, info) +
+

+

+ + + +

+ + + +
+

+

+ + + +
res x Subroutine
Short Precision RealShort Precision Real psb_geasums
Long Precision Real Long Precision Real psb_geasums
Short Precision RealShort Precision Complexpsb_geasums
Long Precision Real Long Precision Complex psb_geasums
+
Table 7: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 7. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+res
contains the 1-norm of (the columns of) x.
Scope: global
Intent: out.
Short as: a long precision real number. Specified as: a long precision real + number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu17.html b/docs/html/userhtmlsu17.html new file mode 100644 index 00000000..f040eafb --- /dev/null +++ b/docs/html/userhtmlsu17.html @@ -0,0 +1,227 @@ + + +psb_norm2 — 2-Norm of Vector + + + + + + + +

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+

4.8 psb_norm2 — 2-Norm of Vector

+

This function computes the 2-norm of a vector x.
If x is a real vector it computes 2-norm as: +

+ √ -T-- +nrm2 ← x x +
+

else if x is a complex vector then it computes 2-norm as: +

+ √---- +nrm2 ← xHx +
+

+

+ + + +

+ + + +
+

+

+ + + +
nrm2 x Function
Short Precision RealShort Precision Real psb_genrm2
Long Precision Real Long Precision Real psb_genrm2
Short Precision RealShort Precision Complexpsb_genrm2
Long Precision Real Long Precision Complex psb_genrm2
+
Table 8: Data types
+ + + +
+
+ + + +
+psb_genrm2(x, desc_a, info [,global]) + 
psb_norm2(x, desc_a, info [,global]) +
+

+

+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 8. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+global
Specifies whether the computation should include the global reduction + across all processes.
Scope: global
Type: optional.
Intent: in.
Specified as: a logical scalar. Default: global=.true.
+
+On Return
+
+Function Value
is the 2-norm of vector x.
Scope: global unless the optional variable global=.false. has been + specified
Type: required
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + +

Notes +

    +
  1. The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: +
        vres(1) = psb_genrm2(x1,desc_a,info,global=.false.) 
        vres(2) = psb_genrm2(x2,desc_a,info,global=.false.) 
        vres(3) = psb_genrm2(x3,desc_a,info,global=.false.) 
        call psb_nrm2(ictxt,vres(1:3)) + +
    +

    In this way the global communication, which for small sizes is a latency-bound + operation, is invoked only once.

+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu18.html b/docs/html/userhtmlsu18.html new file mode 100644 index 00000000..fa1be28a --- /dev/null +++ b/docs/html/userhtmlsu18.html @@ -0,0 +1,177 @@ + + +psb_genrm2s — Generalized 2-Norm of Vector + + + + + + + +

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+

4.9 psb_genrm2s — Generalized 2-Norm of Vector

+

This subroutine computes a series of 2-norms on the columns of a dense matrix +x: +

+res(i) ← ∥x(:,i)∥2 +
+

+ + + +

+call psb_genrm2s(res, x, desc_a, info) +
+

+

+ + + +

+ + + +
+

+

+ + + +
res x Subroutine
Short Precision RealShort Precision Real psb_genrm2s
Long Precision Real Long Precision Real psb_genrm2s
Short Precision RealShort Precision Complexpsb_genrm2s
Long Precision Real Long Precision Complex psb_genrm2s
+
Table 9: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 9. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+res
contains the 1-norm of (the columns of) x.
Scope: global
Intent: out.
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu19.html b/docs/html/userhtmlsu19.html new file mode 100644 index 00000000..8de063d6 --- /dev/null +++ b/docs/html/userhtmlsu19.html @@ -0,0 +1,171 @@ + + +psb_norm1 — 1-Norm of Sparse Matrix + + + + + + + +

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+

4.10 psb_norm1 — 1-Norm of Sparse Matrix

+

This function computes the 1-norm of a matrix A:
+

+nrm1 ← ∥A ∥1 +
+

where: +

+A
represents the global matrix A
+
+ + + +

+ + + +
+

+

+ + + +
A Function
Short Precision Real psb_spnrm1
Long Precision Real psb_spnrm1
Short Precision Complexpsb_spnrm1
Long Precision Complex psb_spnrm1
+
Table 10: Data types
+ + + +
+
+ + + +
+psb_spnrm1(A, desc_a, info) + 
psb_norm1(A, desc_a, info) +
+

+

+Type:
Synchronous. +
+On Entry
+
+a
the local portion of the global sparse matrix A.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_Tspmat_type. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+Function value
is the 1-norm of sparse submatrix A.
Scope: global
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu2.html b/docs/html/userhtmlsu2.html new file mode 100644 index 00000000..9c452948 --- /dev/null +++ b/docs/html/userhtmlsu2.html @@ -0,0 +1,129 @@ + + +Library contents + + + + + + + +

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+

2.2 Library contents

+

The PSBLAS library consists of various classes of subroutines: +

+Computational routines
comprising: +
    +
  • Sparse matrix by dense matrix product; +
    • +
  • Sparse triangular systems solution for block diagonal matrices; +
    • +
  • Vector and matrix norms; +
    • +
  • Dense matrix sums; +
    • +
  • Dot products.
+
+Communication routines
handling halo and overlap communications; +
+Data management and auxiliary routines
including: +
    +
  • Parallel environment management +
    • +
  • Communication descriptors allocation; +
    • +
  • Dense and sparse matrix allocation; +
    • +
  • Dense and sparse matrix build and update; +
    • +
  • Sparse matrix and data distribution preprocessing.
+
+Preconditioner routines
+
+Iterative methods
a subset of Krylov subspace iterative methods
+

The following naming scheme has been adopted for all the symbols internally defined in +the PSBLAS software package: +

    +
  • all symbols (i.e. subroutine names, data types...) are prefixed by psb_ + + + +
    • +
  • all data type names are suffixed by _type +
    • +
  • all constants are suffixed by _ +
    • +
  • all top-level subroutine names follow the rule psb_xxname where xx can be + either: +
      +
    • ge: the routine is related to dense data, +
      • +
    • sp: the routine is related to sparse data, +
      • +
    • cd: the routine is related to communication descriptor (see 3).
    +

    For example the psb_geins, psb_spins and psb_cdins perform the same + action (see 6) on dense matrices, sparse matrices and communication + descriptors respectively. Interface overloading allows the usage of the same + subroutine names for both real and complex data.

+

In the description of the subroutines, arguments or argument entries are classified +as: +

+global
For input arguments, the value must be the same on all processes + participating in the subroutine call; for output arguments the value is + guaranteed to be the same. +
+local
Each process has its own value(s) independently.
+

To finish our general description, we define a version string with the constant +

+psb_version_string_ +
+

whose current value is 3.4.0 + + + +

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+

+ diff --git a/docs/html/userhtmlsu20.html b/docs/html/userhtmlsu20.html new file mode 100644 index 00000000..6b967d32 --- /dev/null +++ b/docs/html/userhtmlsu20.html @@ -0,0 +1,171 @@ + + +psb_normi — Infinity Norm of Sparse Matrix + + + + + + + +

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+

4.11 psb_normi — Infinity Norm of Sparse Matrix

+

This function computes the infinity-norm of a matrix A:
+

+nrmi ← ∥A∥∞ +
+

where: +

+A
represents the global matrix A
+
+ + + +

+ + + +
+

+

+ + + +
A Function
Short Precision Real psb_spnrmi
Long Precision Real psb_spnrmi
Short Precision Complexpsb_spnrmi
Long Precision Complex psb_spnrmi
+
Table 11: Data types
+ + + +
+
+ + + +
+psb_spnrmi(A, desc_a, info) + 
psb_normi(A, desc_a, info) +
+

+

+Type:
Synchronous. +
+On Entry
+
+a
the local portion of the global sparse matrix A.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_Tspmat_type. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+Function value
is the infinity-norm of sparse submatrix A.
Scope: global
Specified as: a long precision real number. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu21.html b/docs/html/userhtmlsu21.html new file mode 100644 index 00000000..1473890e --- /dev/null +++ b/docs/html/userhtmlsu21.html @@ -0,0 +1,337 @@ + + +psb_spmm — Sparse Matrix by Dense Matrix Product + + + + + + + +

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+

4.12 psb_spmm — Sparse Matrix by Dense Matrix Product

+

This subroutine computes the Sparse Matrix by Dense Matrix Product: +
+
+y ← αAx + βy +
(1)
+

+
+
+y ← αAT x+ βy +
(2)
+

+
+
+ H +y ← αA x+ βy + + + +
(3)
+

+

where: +

+x
is the global dense matrix x:,: +
+y
is the global dense matrix y:,: +
+A
is the global sparse matrix A
+
+ + + +

+ + + +
+

+

+ + + + +
A, x, y, α, β Subroutine
Short Precision Real psb_spmm
Long Precision Real psb_spmm
Short Precision Complexpsb_spmm
Long Precision Complex psb_spmm
+
Table 12: Data types
+ + + +
+
+ + + +
+call psb_spmm(alpha, a, x, beta, y, desc_a, info) + 
call psb_spmm(alpha, a, x, beta, y,desc_a, info, & + 
             & trans, work) +
+

+

+Type:
Synchronous. +
+On Entry
+
+alpha
the scalar α.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 12. +
+a
the local portion of the sparse matrix A.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_Tspmat_type. +
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 12. The + rank of x must be the same of y. +
+beta
the scalar β.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 12. +
+y
the local portion of global dense matrix y.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 12. The + rank of y must be the same of x. + + + +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+trans
indicates what kind of operation to perform. +
+ trans = N
the operation is specified by equation 1 +
+ trans = T
the operation is specified by equation 2 +
+ trans = C
the operation is specified by equation 3
+

Scope: global
Type: optional
Intent: in.
Default: trans = N
Specified as: a character variable. +

+work
work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a rank one array of the same type of x and y with the TARGET + attribute. +
+On Return
+
+y
the local portion of result matrix y.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified + in Table 12. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu22.html b/docs/html/userhtmlsu22.html new file mode 100644 index 00000000..bd1ad807 --- /dev/null +++ b/docs/html/userhtmlsu22.html @@ -0,0 +1,400 @@ + + +psb_spsm — Triangular System Solve + + + + + + + +

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+

4.13 psb_spsm — Triangular System Solve

+

This subroutine computes the Triangular System Solve: +

+
+y ← αT- 1x + βy + -1 +y ← αDT x +βy +y ← αT- 1Dx +βy +y ← αT- Tx+ βy +y ← αDT -Tx + βy + - T +y ← αT Dx + βy +y ← αT- Hx +βy +y ← αDT -Hx + βy +y ← αT- HDx + βy +
+
+

where: +

+x
is the global dense matrix x:,: +
+y
is the global dense matrix y:,: +
+T
is the global sparse block triangular submatrix T +
+D
is the scaling diagonal matrix.
+ + + +
+call psb_spsm(alpha, t, x, beta, y, desc_a, info) + 
call psb_spsm(alpha, t, x, beta, y, desc_a, info,& + 
             & trans, unit, choice, diag, work) +
+

+

+ + + +

+ + + +
+

+

+ + + + +
T, x, y, D, α, β Subroutine
Short Precision Real psb_spsm
Long Precision Real psb_spsm
Short Precision Complexpsb_spsm
Long Precision Complex psb_spsm
+
Table 13: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+alpha
the scalar α.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 13. +
+t
the global portion of the sparse matrix T.
Scope: local
Type: required
Intent: in.
Specified as: an object type specified in § 3. +
+x
the local portion of global dense matrix x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 13. The + rank of x must be the same of y. +
+beta
the scalar β.
Scope: global
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 13. +
+y
the local portion of global dense matrix y.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 13. The + rank of y must be the same of x. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. + + + +
+trans
specify with unitd the operation to perform. +
+ trans = ’N’
the operation is with no transposed matrix +
+ trans = ’T’
the operation is with transposed matrix. +
+ trans = ’C’
the operation is with conjugate transposed matrix.
+

Scope: global
Type: optional
Intent: in.
Default: trans = N
Specified as: a character variable. +

+unitd
specify with trans the operation to perform. +
+ unitd = ’U’
the operation is with no scaling +
+ unitd = ’L’
the operation is with left scaling +
+ unitd = ’R’
the operation is with right scaling.
+

Scope: global
Type: optional
Intent: in.
Default: unitd = U
Specified as: a character variable. +

+choice
specifies the update of overlap elements to be performed on exit: +
+
psb_none_ +
+
psb_sum_ +
+
psb_avg_ +
+
psb_square_root_
+

Scope: global
Type: optional
Intent: in.
Default: psb_avg_
Specified as: an integer variable. + + + +

+diag
the diagonal scaling matrix.
Scope: local
Type: optional
Intent: in.
Default: diag(1) = 1(noscaling)
Specified as: a rank one array containing numbers of the type indicated in + Table 13. +
+work
a work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a rank one array of the same type of x with the TARGET + attribute. +
+On Return
+
+y
the local portion of global dense matrix y.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified + in Table 13. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu23.html b/docs/html/userhtmlsu23.html new file mode 100644 index 00000000..720f7151 --- /dev/null +++ b/docs/html/userhtmlsu23.html @@ -0,0 +1,201 @@ + + +psb_gemlt — Entrywise Product + + + + + + + +

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+

4.14 psb_gemlt — Entrywise Product

+

This function computes the entrywise product between two vectors x and +y +

+dot ← x(i)y(i). +
+

+ + + +

+psb_gemlt(x, y, desc_a, info) +
+

+ + + +

+ + + +
+

+

+ + + + +
dot, x, y Function
Short Precision Real psb_gemlt
Long Precision Real psb_gemlt
Short Precision Complexpsb_gemlt
Long Precision Complex psb_gemlt
+
Table 14: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense vector x.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +
+y
the local portion of global dense vector y.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+On Return
+
+y
the local portion of result submatrix y.
Scope: local
Type: required
Intent: inout.
Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 14. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu24.html b/docs/html/userhtmlsu24.html new file mode 100644 index 00000000..bd88f8f7 --- /dev/null +++ b/docs/html/userhtmlsu24.html @@ -0,0 +1,215 @@ + + +psb_gediv — Entrywise Division + + + + + + + +

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+

4.15 psb_gediv — Entrywise Division

+

This function computes the entrywise division between two vectors x and +y +

+∕ ← x(i)∕y(i). +
+

+ + + +

+psb_gediv(x, y, desc_a, info, [flag) +
+

+ + + +

+ + + +
+

+

+ + + + +
∕, x, y Function
Short Precision Real psb_gediv
Long Precision Real psb_gediv
Short Precision Complexpsb_gediv
Long Precision Complex psb_gediv
+
Table 15: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense vector x.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +
+y
the local portion of global dense vector y.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+flag
check if any of the y(i) = 0, and in case returns error halting the + computation.
Scope: local
Type: optional Intent: in.
Specified as: the logical value flag=.true. +
+On Return
+
+x
the local portion of result submatrix x.
Scope: local
Type: required
Intent: inout.
Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 14. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu25.html b/docs/html/userhtmlsu25.html new file mode 100644 index 00000000..2e9a6410 --- /dev/null +++ b/docs/html/userhtmlsu25.html @@ -0,0 +1,194 @@ + + +psb_geinv — Entrywise Inversion + + + + + + + +

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+

4.16 psb_geinv — Entrywise Inversion

+

This function computes the entrywise inverse of a vector x and puts it into +y +

+∕ ← 1∕x(i). +
+

+ + + +

+psb_geinv(x, y, desc_a, info, [flag) +
+

+ + + +

+ + + +
+

+

+ + + + +
∕, x, y Function
Short Precision Real psb_geinv
Long Precision Real psb_geinv
Short Precision Complexpsb_geinv
Long Precision Complex psb_geinv
+
Table 16: Data types
+ + + +
+
+
+Type:
Synchronous. +
+On Entry
+
+x
the local portion of global dense vector x.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: an object of type psb_desc_type. +
+flag
check if any of the x(i) = 0, and in case returns error halting the + computation.
Scope: local
Type: optional Intent: in.
Specified as: the logical value flag=.true. +
+On Return
+
+y
the local portion of result submatrix x.
Scope: local
Type: required
Intent: out.
Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 16. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu26.html b/docs/html/userhtmlsu26.html new file mode 100644 index 00000000..2287390e --- /dev/null +++ b/docs/html/userhtmlsu26.html @@ -0,0 +1,831 @@ + + +psb_halo — Halo Data Communication + + + + + + + +

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+

5.1 psb_halo — Halo Data Communication

+

These subroutines gathers the values of the halo elements: +

+x ← x +
+

where: +

+x
is a global dense submatrix.
+
+ + + +

+ + + +
+

+

+ + + + + +
α, x Subroutine
Integer psb_halo
Short Precision Real psb_halo
Long Precision Real psb_halo
Short Precision Complexpsb_halo
Long Precision Complex psb_halo
+
Table 17: Data types
+ + + +
+
+ +
call psb_halo(x, desc_a, info) 
call psb_halo(x, desc_a, info, work, data) + +
+
+Type:
Synchronous. +
+On Entry
+
+x
global dense matrix x.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 17. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+work
the work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a rank one array of the same type of x. +
+data
index list selector.
Scope: global
Type: optional
Specified + as: an integer. Values:psb_comm_halo_,psb_comm_mov_, psb_comm_ext_, + default: psb_comm_halo_. Chooses the index list on which to base the data + exchange. +
+On Return
+
+x
global dense result matrix x.
Scope: local
Type: required
Intent: inout.
Returned as: a rank one or two array containing numbers of type specified + in Table 17. +
+info
the local portion of result submatrix y.
Scope: local
Type: required
Intent: out.
An integer value that contains an error code.
+

+
+

+

PIC

+
Figure 7: Sample discretization mesh.
+

+

Usage Example Consider the discretization mesh depicted in fig. 7, partitioned +among two processes as shown by the dashed line; the data distribution is such that +each process will own 32 entries in the index space, with a halo made of 8 entries +placed at local indices 33 through 40. If process 0 assigns an initial value of 1 to +its entries in the x vector, and process 1 assigns a value of 2, then after +a call to psb_halo the contents of the local vectors will be the following: +

+ + + +

+ + + +
+

+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Process 0
Process 1
+
IGLOB(I)X(I) IGLOB(I)X(I)
1 1 1.0 1 33 2.0
2 2 1.0 2 34 2.0
3 3 1.0 3 35 2.0
4 4 1.0 4 36 2.0
5 5 1.0 5 37 2.0
6 6 1.0 6 38 2.0
7 7 1.0 7 39 2.0
8 8 1.0 8 40 2.0
9 9 1.0 9 41 2.0
10 10 1.010 42 2.0
11 11 1.011 43 2.0
12 12 1.012 44 2.0
13 13 1.013 45 2.0
14 14 1.014 46 2.0
15 15 1.015 47 2.0
16 16 1.016 48 2.0
17 17 1.017 49 2.0
18 18 1.018 50 2.0
19 19 1.019 51 2.0
20 20 1.020 52 2.0
21 21 1.021 53 2.0
22 22 1.022 54 2.0
23 23 1.023 55 2.0
24 24 1.024 56 2.0
25 25 1.025 57 2.0
26 26 1.026 58 2.0
27 27 1.027 59 2.0
28 28 1.028 60 2.0
29 29 1.029 61 2.0
30 30 1.030 62 2.0
31 31 1.031 63 2.0
32 32 1.032 64 2.0
33 33 2.033 25 1.0
34 34 2.034 26 1.0
35 35 2.035 27 1.0
36 36 2.036 28 1.0
37 37 2.037 29 1.0
38 38 2.038 30 1.0
39 39 2.039 31 1.0
40 40 2.040 32 1.0
+ + + +
+
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu27.html b/docs/html/userhtmlsu27.html new file mode 100644 index 00000000..2bb4e849 --- /dev/null +++ b/docs/html/userhtmlsu27.html @@ -0,0 +1,1013 @@ + + +psb_ovrl — Overlap Update + + + + + + + +

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+

5.2 psb_ovrl — Overlap Update

+

These subroutines applies an overlap operator to the input vector: +

+x ← Qx +
+

where: +

+x
is the global dense submatrix x +
+Q
is the overlap operator; it is the composition of two operators Pa and PT.
+
+ + + +

+ + + +
+

+

+ + + +
x Subroutine
Short Precision Real psb_ovrl
Long Precision Real psb_ovrl
Short Precision Complexpsb_ovrl
Long Precision Complex psb_ovrl
+
Table 18: Data types
+ + + +
+
+ +
call psb_ovrl(x, desc_a, info) 
call psb_ovrl(x, desc_a, info, update=update_type, work=work) + +
+
+Type:
Synchronous. +
+On Entry
+
+x
global dense matrix x.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 18. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+update
Update operator.
+
+ update = psb_none_
Do nothing; +
+ update = psb_add_
Sum overlap entries, i.e. apply PT; +
+ update = psb_avg_
Average overlap entries, i.e. apply PaPT;
+

Scope: global
Intent: in.
Default: update_type = psb_avg_
Scope: global
Specified as: a integer variable. +

+work
the work array.
Scope: local
Type: optional
Intent: inout.
Specified as: a one dimensional array of the same type of x. + + + +
+On Return
+
+x
global dense result matrix x.
Scope: local
Type: required
Intent: inout.
Specified as: an array of rank one or two containing numbers of type specified + in Table 18. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. If there is no overlap in the data distribution associated with the + descriptor, no operations are performed; +
    2. +
  2. The operator PT performs the reduction sum of overlap elements; it is a + “prolongation” operator PT that replicates overlap elements, accounting + for the physical replication of data; +
    3. +
  3. The operator Pa performs a scaling on the overlap elements by the + amount of replication; thus, when combined with the reduction operator, + it implements the average of replicated elements over all of their instances.
+

+ + + + + + + +
+

+

PIC

+
Figure 8: Sample discretization mesh.
+ + + +

+

Example of use Consider the discretization mesh depicted in fig. 8, partitioned +among two processes as shown by the dashed lines, with an overlap of 1 extra layer +with respect to the partition of fig. 7; the data distribution is such that +each process will own 40 entries in the index space, with an overlap of 16 +entries placed at local indices 25 through 40; the halo will run from local +index 41 through local index 48.. If process 0 assigns an initial value of 1 to +its entries in the x vector, and process 1 assigns a value of 2, then after a +call to psb_ovrl with psb_avg_ and a call to psb_halo_ the contents of +the local vectors will be the following (showing a transition among the two +subdomains) +

+ + + +

+ + + +
+

+

+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
Process 0
Process 1
+
IGLOB(I)X(I) IGLOB(I)X(I)
1 1 1.0 1 33 1.5
2 2 1.0 2 34 1.5
3 3 1.0 3 35 1.5
4 4 1.0 4 36 1.5
5 5 1.0 5 37 1.5
6 6 1.0 6 38 1.5
7 7 1.0 7 39 1.5
8 8 1.0 8 40 1.5
9 9 1.0 9 41 2.0
10 10 1.010 42 2.0
11 11 1.011 43 2.0
12 12 1.012 44 2.0
13 13 1.013 45 2.0
14 14 1.014 46 2.0
15 15 1.015 47 2.0
16 16 1.016 48 2.0
17 17 1.017 49 2.0
18 18 1.018 50 2.0
19 19 1.019 51 2.0
20 20 1.020 52 2.0
21 21 1.021 53 2.0
22 22 1.022 54 2.0
23 23 1.023 55 2.0
24 24 1.024 56 2.0
25 25 1.525 57 2.0
26 26 1.526 58 2.0
27 27 1.527 59 2.0
28 28 1.528 60 2.0
29 29 1.529 61 2.0
30 30 1.530 62 2.0
31 31 1.531 63 2.0
32 32 1.532 64 2.0
33 33 1.533 25 1.5
34 34 1.534 26 1.5
35 35 1.535 27 1.5
36 36 1.536 28 1.5
37 37 1.537 29 1.5
38 38 1.538 30 1.5
39 39 1.539 31 1.5
40 40 1.540 32 1.5
41 41 2.041 17 1.0
42 42 2.042 18 1.0
43 43 2.043 19 1.0
44 44 2.044 20 1.0
45 45 2.045 21 1.0
46 46 2.046 22 1.0
47 47 2.047 23 1.0
48 48 2.048 24 1.0
+ + + +
+
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu28.html b/docs/html/userhtmlsu28.html new file mode 100644 index 00000000..45fa580e --- /dev/null +++ b/docs/html/userhtmlsu28.html @@ -0,0 +1,225 @@ + + +psb_gather — Gather Global Dense Matrix + + + + + + + +

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+

5.3 psb_gather — Gather Global Dense Matrix

+

These subroutines collect the portions of global dense matrix distributed over all +process into one single array stored on one process. +

+glob-x ← collect(loc-xi) +
+

where: +

+glob_x
is the global submatrix glob_x1:m,1:n +
+loc_xi
is the local portion of global dense matrix on process i. +
+collect
is the collect function.
+
+ + + +

+ + + +
+

+

+ + + + + +
xi,y Subroutine
Integer psb_gather
Short Precision Real psb_gather
Long Precision Real psb_gather
Short Precision Complexpsb_gather
Long Precision Complex psb_gather
+
Table 19: Data types
+ + + +
+
+ +
call psb_gather(glob_x, loc_x, desc_a, info, root) 
call psb_gather(glob_x, loc_x, desc_a, info, root) + +
+
+Type:
Synchronous. +
+On Entry
+
+loc_x
the local portion of global dense matrix glob_x.
Scope: local
Type: required
Intent: in.
Specified as: a rank one or two array or an object of type + psb_T_vect_type indicated in Table 19. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+root
The process that holds the global copy. If root = -1 all the processes will + have a copy of the global vector.
Scope: global
Type: optional
Intent: in.
Specified as: an integer variable -1 ≤ root ≤ np - 1, default -1. +
+On Return
+
+glob_x
The array where the local parts must be gathered.
Scope: global
Type: required
Intent: out.
Specified as: a rank one or two array with the ALLOCATABLE attribute. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu29.html b/docs/html/userhtmlsu29.html new file mode 100644 index 00000000..7186e307 --- /dev/null +++ b/docs/html/userhtmlsu29.html @@ -0,0 +1,244 @@ + + +psb_scatter — Scatter Global Dense Matrix + + + + + + + +

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+

5.4 psb_scatter — Scatter Global Dense Matrix

+

These subroutines scatters the portions of global dense matrix owned by a process to +all the processes in the processes grid. +

+loc-xi ← scatter(glob-x) +
+

where: +

+glob_x
is the global matrix glob_x1:m,1:n +
+loc_xi
is the local portion of global dense matrix on process i. +
+scatter
is the scatter function.
+
+ + + +

+ + + +
+

+

+ + + + + +
xi,y Subroutine
Integer psb_scatter
Short Precision Real psb_scatter
Long Precision Real psb_scatter
Short Precision Complexpsb_scatter
Long Precision Complex psb_scatter
+
Table 20: Data types
+ + + +
+
+ +
call psb_scatter(glob_x, loc_x, desc_a, info, root, mold) + +
+
+Type:
Synchronous. +
+On Entry
+
+glob_x
The array that must be scattered into local pieces.
Scope: global
Type: required
Intent: in.
Specified as: a rank one or two array. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+root
The process that holds the global copy. If root = -1 all the processes have + a copy of the global vector.
Scope: global
Type: optional
Intent: in.
Specified as: an integer variable -1 ≤ root ≤ np - 1, default psb_root_, + i.e. process 0. +
+mold
The desired dynamic type for the internal vector storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from psb_T_base_vect_type; + this is only allowed when loc_x is of type psb_T_vect_type. +
+On Return
+
+loc_x
the local portion of global dense matrix glob_x.
Scope: local
Type: required
Intent: out.
Specified as: a rank one or two ALLOCATABLE array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 20. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu3.html b/docs/html/userhtmlsu3.html new file mode 100644 index 00000000..15721cf1 --- /dev/null +++ b/docs/html/userhtmlsu3.html @@ -0,0 +1,282 @@ + + +Application structure + + + + + + + +

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+

2.3 Application structure

+

The main underlying principle of the PSBLAS library is that the library objects are +created and exist with reference to a discretized space to which there corresponds +an index space and a matrix sparsity pattern. As an example, consider a +cell-centered finite-volume discretization of the Navier-Stokes equations on a +simulation domain; the index space 1…n is isomorphic to the set of cell centers, +whereas the pattern of the associated linear system matrix is isomorphic to the +adjacency graph imposed on the discretization mesh by the discretization +stencil. +

Thus the first order of business is to establish an index space, and this is done +with a call to psb_cdall in which we specify the size of the index space n and the +allocation of the elements of the index space to the various processes making up the +MPI (virtual) parallel machine. +

The index space is partitioned among processes, and this creates a mapping from +the “global” numbering 1…n to a numbering “local” to each process; each process i +will own a certain subset 1…nrowi, each element of which corresponds to a certain +element of 1…n. The user does not set explicitly this mapping; when the application +needs to indicate to which element of the index space a certain item is related, +such as the row and column index of a matrix coefficient, it does so in the +“global” numbering, and the library will translate into the appropriate “local” +numbering. +

For a given index space 1…n there are many possible associated topologies, i.e. +many different discretization stencils; thus the description of the index space is not +completed until the user has defined a sparsity pattern, either explicitly through +psb_cdins or implicitly through psb_spins. The descriptor is finalized with a call to +psb_cdasb and a sparse matrix with a call to psb_spasb. After psb_cdasb each +process i will have defined a set of “halo” (or “ghost”) indices nrowi + 1…ncol +i, +denoting elements of the index space that are not assigned to process i; however the +variables associated with them are needed to complete computations associated with +the sparse matrix A, and thus they have to be fetched from (neighbouring) +processes. The descriptor of the index space is built exactly for the purpose +of properly sequencing the communication steps required to achieve this +objective. +

A simple application structure will walk through the index space allocation, +matrix/vector creation and linear system solution as follows: +

    +
  1. Initialize parallel environment with psb_init +
    2. +
  2. Initialize index space with psb_cdall +
    3. +
  3. Allocate sparse matrix and dense vectors with psb_spall and psb_geall + + + +
    4. +
  4. Loop over all local rows, generate matrix and vector entries, and insert + them with psb_spins and psb_geins +
    5. +
  5. Assemble the various entities: +
      +
    1. psb_cdasb +
      2. +
    2. psb_spasb +
      3. +
    3. psb_geasb
    +
    6. +
  6. Choose the preconditioner to be used with prec%init and build it with + prec%build3 . +
    7. +
  7. Call the iterative method of choice, e.g. psb_bicgstab
+

This is the structure of the sample programs in the directory test/pargen/. +

For a simulation in which the same discretization mesh is used over multiple time +steps, the following structure may be more appropriate: +

    +
  1. Initialize parallel environment with psb_init +
    2. +
  2. Initialize index space with psb_cdall +
    3. +
  3. Loop over the topology of the discretization mesh and build the descriptor + with psb_cdins +
    4. +
  4. Assemble the descriptor with psb_cdasb +
    5. +
  5. Allocate the sparse matrices and dense vectors with psb_spall and + psb_geall +
    6. +
  6. Loop over the time steps: +
      +
    1. If after first time step, reinitialize the sparse matrix with psb_sprn; + also zero out the dense vectors; +
      2. +
    2. Loop over the mesh, generate the coefficients and insert/update them + with psb_spins and psb_geins + + + +
      3. +
    3. Assemble with psb_spasb and psb_geasb +
      4. +
    4. Choose and build preconditioner with prec%init and prec%build +
      5. +
    5. Call the iterative method of choice, e.g. psb_bicgstab
    +
+

The insertion routines will be called as many times as needed; they only need to be +called on the data that is actually allocated to the current process, i.e. each process +generates its own data. +

In principle there is no specific order in the calls to psb_spins, nor is there a +requirement to build a matrix row in its entirety before calling the routine; this +allows the application programmer to walk through the discretization mesh element +by element, generating the main part of a given matrix row but also contributions to +the rows corresponding to neighbouring elements. +

From a functional point of view it is even possible to execute one call for each +nonzero coefficient; however this would have a substantial computational +overhead. It is therefore advisable to pack a certain amount of data into each +call to the insertion routine, say touching on a few tens of rows; the best +performng value would depend on both the architecture of the computer being +used and on the problem structure. At the opposite extreme, it would be +possible to generate the entire part of a coefficient matrix residing on a +process and pass it in a single call to psb_spins; this, however, would entail a +doubling of memory occupation, and thus would be almost always far from +optimal. +

+

2.3.1 User-defined index mappings
+

PSBLAS supports user-defined global to local index mappings, subject to the +constraints outlined in sec. 2.3: +

    +
  1. The set of indices owned locally must be mapped to the set 1…nrowi; +
    2. +
  2. The set of halo points must be mapped to the set nrowi + 1…ncol +i;
+

but otherwise the mapping is arbitrary. The user application is responsible to ensure +consistency of this mapping; some errors may be caught by the library, but +this is not guaranteed. The application structure to support this usage is as +follows: +

    +
  1. Initialize index + space with psb_cdall(ictx,desc,info,vl=vl,lidx=lidx) passing the + vectors vl(:) containing the set of global indices owned by the current + process and lidx(:) containing the corresponding local indices; + + + +
    2. +
  2. Add the halo points ja(:) and their associated local indices lidx(:) with + a(some) call(s) to psb_cdins(nz,ja,desc,info,lidx=lidx); +
    3. +
  3. Assemble the descriptor with psb_cdasb; +
    4. +
  4. Build the sparse matrices and vectors, optionally making use in psb_spins + and psb_geins of the local argument specifying that the indices in ia, + ja and irw, respectively, are already local indices.
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu30.html b/docs/html/userhtmlsu30.html new file mode 100644 index 00000000..10ee1c9c --- /dev/null +++ b/docs/html/userhtmlsu30.html @@ -0,0 +1,419 @@ + + +psb_cdall — Allocates a communication descriptor + + + + + + + +

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+

6.1 psb_cdall — Allocates a communication descriptor

+ + + +
+call psb_cdall(icontxt, desc_a, info,mg=mg,parts=parts) + 
call psb_cdall(icontxt, desc_a, info,vg=vg,[mg=mg,flag=flag]) + 
call psb_cdall(icontxt, desc_a, info,vl=vl,[nl=nl,globalcheck=.false.,lidx=lidx]) + 
call psb_cdall(icontxt, desc_a, info,nl=nl) + 
call psb_cdall(icontxt, desc_a, info,mg=mg,repl=.true.) +
+

+

This subroutine initializes the communication descriptor associated with an index +space. One of the optional arguments parts, vg, vl, nl or repl must be specified, +thereby choosing the specific initialization strategy. +

+On Entry
+
+Type:
Synchronous. +
+icontxt
the communication context.
Scope:global.
Type:required.
Intent: in.
Specified as: an integer value. +
+vg
Data allocation: each index i ∈{1…mg} is allocated to process vg(i).
Scope:global.
Type:optional.
Intent: in.
Specified as: an integer array. +
+flag
Specifies whether entries in vg are zero- or one-based.
Scope:global.
Type:optional.
Intent: in.
Specified as: an integer value 0,1, default 0. +
+mg
the (global) number of rows of the problem.
Scope:global.
Type:optional.
Intent: in.
Specified as: an integer value. It is required if parts or repl is specified, + it is optional if vg is specified. +
+parts
the subroutine that defines the partitioning scheme.
Scope:global.
Type:required.
Specified as: a subroutine. + + + +
+vl
Data allocation: the set of global indices vl(1 : nl) belonging to the calling + process.
Scope:local.
Type:optional.
Intent: in.
Specified as: an integer array. +
+nl
Data allocation: in a generalized block-row distribution the number of indices + belonging to the current process.
Scope:local.
Type:optional.
Intent: in.
Specified as: an integer value. May be specified together with vl. +
+repl
Data allocation: build a replicated index space (i.e. all processes own all + indices).
Scope:global.
Type:optional.
Intent: in.
Specified as: the logical value .true. +
+globalcheck
Data allocation: do global checks on the local index lists vl
Scope:global.
Type:optional.
Intent: in.
Specified as: a logical value, default: .false. +
+lidx
Data allocation: the set of local indices lidx(1 : nl) to be assigned to the + global indices vl.
Scope:local.
Type:optional.
Intent: in.
Specified as: an integer array.
+

+

+On Return
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: out.
Specified as: a structured data of type psb_desc_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. One of the optional arguments parts, vg, vl, nl or repl must be specified, + thereby choosing the initialization strategy as follows: +
    + parts
    In this case we have a subroutine specifying the mapping between global + indices and process/local index pairs. If this optional argument is + specified, then it is mandatory to specify the argument mg as well. The + subroutine must conform to the following interface: + + + +
    +   interface +  
         subroutine psb_parts(glob_index,mg,np,pv,nv) +  
           integer, intent (in)  :: glob_index,np,mg +  
           integer, intent (out) :: nv, pv(*) +  
         end subroutine psb_parts +  
      end interface +
    +

    The input arguments are: +

    + glob_index
    The global index to be mapped; +
    + np
    The number of processes in the mapping; +
    + mg
    The total number of global rows in the mapping;
    +

    The output arguments are: +

    + nv
    The number of entries in pv; +
    + pv
    A vector containing the indices of the processes to which the + global index should be assigend; each entry must satisfy 0 ≤ + pv(i) < np; if nv > 1 we have an index assigned to multiple + processes, i.e. we have an overlap among the subdomains.
    +
    + vg
    In this case the association between an index and a process is specified via + an integer vector vg(1:mg); each index i ∈{1…mg} is assigned to process + vg(i). The vector vg must be identical on all calling processes; its + entries may have the ranges (0…np - 1) or (1…np) according to the + value of flag. The size mg may be specified via the optional + argument mg; the default is to use the entire vector vg, thus having + mg=size(vg). +
    + vl
    In this case we are specifying the list of indices vl(1:nl) assigned to the + current process; thus, the global problem size mg is given by the range of + the aggregate of the individual vectors vl specified in the calling + processes. The size may be specified via the optional argument nl; the + default is to use the entire vector vl, thus having nl=size(vl). If + globalcheck=.true. the subroutine will check how many times each + entry in the global index space (1…mg) is specified in the input lists vl, + thus allowing for the presence of overlap in the input, and checking for + “orphan” indices. If globalcheck=.false., the subroutine will not + check for overlap, and may be significantly faster, but the user is + implicitly guaranteeing that there are neither orphan nor overlap + indices. + + + +
    + lidx
    The optional argument lidx is available for those cases in which the user + has already established a global-to-local mapping; if it is specified, each + index in vl(i) will be mapped to the corresponding local index lidx(i). + When specifying the argument lidx the user would also likely employ + lidx in calls to psb_cdins and local in calls to psb_spins and + psb_geins; see also sec. 2.3.1. +
    + nl
    If this argument is specified alone (i.e. without vl) the result is a + generalized row-block distribution in which each process I gets assigned a + consecutive chunk of NI = nl global indices. +
    + repl
    This arguments specifies to replicate all indices on all processes. This is a + special purpose data allocation that is useful in the construction of some + multilevel preconditioners.
    +
    2. +
  2. On exit from this routine the descriptor is in the build state. +
    3. +
  3. Calling the routine with vg or parts implies that every process will scan the + entire index space to figure out the local indices. +
    4. +
  4. Overlapped indices are possible with both parts and vl invocations. +
    5. +
  5. When the subroutine is invoked with vl in conjunction with globalcheck=.true., + it will perform a scan of the index space to search for overlap or orphan + indices. +
    6. +
  6. When the subroutine is invoked with vl in conjunction with globalcheck=.false., + no index space scan will take place. Thus it is the responsibility of the user to + make sure that the indices specified in vl have neither orphans nor overlaps; if + this assumption fails, results will be unpredictable. +
    7. +
  7. Orphan and overlap indices are impossible by construction when the subroutine + is invoked with nl (alone), or vg.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu31.html b/docs/html/userhtmlsu31.html new file mode 100644 index 00000000..d666e2d5 --- /dev/null +++ b/docs/html/userhtmlsu31.html @@ -0,0 +1,206 @@ + + +psb_cdins — Communication descriptor insert routine + + + + + + + +

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+

6.2 psb_cdins — Communication descriptor insert routine

+ + + +
+call psb_cdins(nz, ia, ja, desc_a, info [,ila,jla]) + 
call psb_cdins(nz,ja,desc,info[,jla,mask,lidx]) +
+

+

This subroutine examines the edges of the graph associated with the +discretization mesh (and isomorphic to the sparsity pattern of a linear system +coefficient matrix), storing them as necessary into the communication descriptor. In +the first form the edges are specified as pairs of indices ia(i),ja(i); the starting index +ia(i) should belong to the current process. In the second form only the remote indices +ja(i) are specified. +

+

+Type:
Asynchronous. +
+On Entry
+
+nz
the number of points being inserted.
Scope: local.
Type: required.
Intent: in.
Specified as: an integer value. +
+ia
the indices of the starting vertex of the edges being inserted.
Scope: local.
Type: required.
Intent: in.
Specified as: an integer array of length nz. +
+ja
the indices of the end vertex of the edges being inserted.
Scope: local.
Type: required.
Intent: in.
Specified as: an integer array of length nz. +
+mask
Mask entries in ja, they are inserted only when the corresponding mask + entries are .true.
Scope: local.
Type: optional.
Intent: in.
Specified as: a logical array of length nz, default .true.. + + + +
+lidx
User defined local indices for ja.
Scope: local.
Type: optional.
Intent: in.
Specified as: an integer array of length nz.
+

+

+On Return
+
+desc_a
the updated communication descriptor.
Scope:local.
Type:required.
Intent: inout.
Specified as: a structured data of type psb_desc_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected. +
+ila
the local indices of the starting vertex of the edges being inserted.
Scope: local.
Type: optional.
Intent: out.
Specified as: an integer array of length nz. +
+jla
the local indices of the end vertex of the edges being inserted.
Scope: local.
Type: optional.
Intent: out.
Specified as: an integer array of length nz. +
+

Notes +

    +
  1. This routine may only be called if the descriptor is in the build state; +
    2. +
  2. This routine automatically ignores edges that do not insist on the current + process, i.e. edges for which neither the starting nor the end vertex belong + to the current process. +
    3. +
  3. The second form of this routine will be useful when dealing with + user-specified index mappings; see also 2.3.1.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu32.html b/docs/html/userhtmlsu32.html new file mode 100644 index 00000000..78ac9388 --- /dev/null +++ b/docs/html/userhtmlsu32.html @@ -0,0 +1,136 @@ + + +psb_cdasb — Communication descriptor assembly routine + + + + + + + +

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+

6.3 psb_cdasb — Communication descriptor assembly routine

+ + + +
+call psb_cdasb(desc_a, info [, mold]) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: inout.
Specified as: a structured data of type psb_desc_type. +
+mold
The desired dynamic type for the internal index storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: a object of type derived from (integer) + psb_T_base_vect_type.
+

+

+On Return
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: inout.
Specified as: a structured data of type psb_desc_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. On exit from this routine the descriptor is in the assembled state.
+ + + +

This call will set up all the necessary information for the halo data exchanges. In doing +so, the library will need to identify the set of processes owning the halo indices +through the use of the desc%fnd_owner() method; the owning processes +are the topological neighbours of the calling process. If the user has some +background information on the processes that are neighbours of the current one, +it is possible to specify explicitly the list of adjacent processes with a call +to desc%set_p_adjcncy(list); this will speed up the subsequent call to +psb_cdasb. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu33.html b/docs/html/userhtmlsu33.html new file mode 100644 index 00000000..ca2898fe --- /dev/null +++ b/docs/html/userhtmlsu33.html @@ -0,0 +1,100 @@ + + +psb_cdcpy — Copies a communication descriptor + + + + + + + +

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+

6.4 psb_cdcpy — Copies a communication descriptor

+ + + +
+call psb_cdcpy(desc_in, desc_out, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc_in
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+

+

+On Return
+
+desc_out
the communication descriptor copy.
Scope:local.
Type:required.
Intent: out.
Specified as: a structured data of type psb_desc_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu34.html b/docs/html/userhtmlsu34.html new file mode 100644 index 00000000..ed9d8573 --- /dev/null +++ b/docs/html/userhtmlsu34.html @@ -0,0 +1,83 @@ + + +psb_cdfree — Frees a communication descriptor + + + + + + + +

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+

6.5 psb_cdfree — Frees a communication descriptor

+ + + +
+call psb_cdfree(desc_a, info) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
the communication descriptor to be freed.
Scope:local.
Type:required.
Intent: inout.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu35.html b/docs/html/userhtmlsu35.html new file mode 100644 index 00000000..414a315a --- /dev/null +++ b/docs/html/userhtmlsu35.html @@ -0,0 +1,163 @@ + + +psb_cdbldext — Build an extended communication descriptor + + + + + + + +

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+

6.6 psb_cdbldext — Build an extended communication descriptor

+ + + +
+call psb_cdbldext(a,desc_a,nl,desc_out, info, extype) +
+

+

This subroutine builds an extended communication descriptor, based on the input +descriptor desc_a and on the stencil specified through the input sparse matrix +a. +

+Type:
Synchronous. +
+On Entry
+
+a
A sparse matrix Scope:local.
Type:required.
Intent: in.
Specified as: a structured data type. +
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_Tspmat_type. +
+nl
the number of additional layers desired.
Scope:global.
Type:required.
Intent: in.
Specified as: an integer value nl ≥ 0. +
+extype
the kind of estension required.
Scope:global.
Type:optional .
Intent: in.
Specified as: an integer value psb_ovt_xhal_, psb_ovt_asov_, default: + psb_ovt_xhal_ +
+

+

+On Return
+ + + +
+desc_out
the extended communication descriptor.
Scope:local.
Type:required.
Intent: inout.
Specified as: a structured data of type psb_desc_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. Specifying psb_ovt_xhal_ for the extype argument the user will obtain a + descriptor for a domain partition in which the additional layers are fetched + as part of an (extended) halo; however the index-to-process mapping is + identical to that of the base descriptor; +
    2. +
  2. Specifying psb_ovt_asov_ for the extype argument the user will obtain + a descriptor with an overlapped decomposition: the additional layer is + aggregated to the local subdomain (and thus is an overlap), and a new + halo extending beyond the last additional layer is formed.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu36.html b/docs/html/userhtmlsu36.html new file mode 100644 index 00000000..2d09e07a --- /dev/null +++ b/docs/html/userhtmlsu36.html @@ -0,0 +1,128 @@ + + +psb_spall — Allocates a sparse matrix + + + + + + + +

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+

6.7 psb_spall — Allocates a sparse matrix

+ + + +
+call psb_spall(a, desc_a, info, nnz) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+nnz
An estimate of the number of nonzeroes in the local part of the assembled + matrix.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value.
+

+

+On Return
+
+a
the matrix to be allocated.
Scope:local
Type:required
Intent: out.
Specified as: a structured data of type psb_Tspmat_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. On exit from this routine the sparse matrix is in the build state. + + + +
    2. +
  2. The descriptor may be in either the build or assembled state. +
    3. +
  3. Providing a good estimate for the number of nonzeroes nnz in the + assembled matrix may substantially improve performance in the matrix + build phase, as it will reduce or eliminate the need for (potentially + multiple) data reallocations.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu37.html b/docs/html/userhtmlsu37.html new file mode 100644 index 00000000..85e282e3 --- /dev/null +++ b/docs/html/userhtmlsu37.html @@ -0,0 +1,311 @@ + + +psb_spins — Insert a set of coefficients into a sparse matrix + + + + + + + +

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+

6.8 psb_spins — Insert a set of coefficients into a sparse matrix

+ + + +
+call psb_spins(nz, ia, ja, val, a, desc_a, info [,local]) + 
call psb_spins(nr, irw, irp, ja, val, a, desc_a, info [,local]) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+nz
the number of coefficients to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer scalar. +
+nr
the number of rows to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer scalar. +
+irw
the first row to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer scalar. +
+ia
the row indices of the coefficients to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer array of size nz. +
+irp
the row pointers of the coefficients to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer array of size nr + 1. + + + +
+ja
the column indices of the coefficients to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer array of size nz. +
+val
the coefficients to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an array of size nz. Must be of the same type and kind of + the coefficients of the sparse matrix a. +
+desc_a
The communication descriptor.
Scope: local.
Type: required.
Intent: inout.
Specified as: a variable of type psb_desc_type.
+
+local
Whether the entries in the indices vectors ia, ja are already in local + numbering.
Scope:local.
Type:optional.
Specified as: a logical value; default: .false.. +
+

+

+On Return
+
+a
the matrix into which coefficients will be inserted.
Scope:local
Type:required
Intent: inout.
Specified as: a structured data of type psb_Tspmat_type. +
+desc_a
The communication descriptor.
Scope: local.
Type: required.
Intent: inout.
Specified as: a variable of type psb_desc_type.
+ + + +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. On entry to this routine the descriptor may be in either the build or + assembled state. +
    2. +
  2. On entry to this routine the sparse matrix may be in either the build or + update state. +
    3. +
  3. If the descriptor is in the build state, then the sparse matrix must also be + in the build state; the action of the routine is to (implicitly) call psb_cdins + to add entries to the sparsity pattern; each sparse matrix entry implicitly + defines a graph edge, that is passed to the descriptor routine for the + appropriate processing; +
    4. +
  4. The input data can be passed in either COO or CSR formats; +
    5. +
  5. In COO format the coefficients to be inserted are represented by the + ordered triples ia(i),ja(i),val(i), for i = 1,…,nz; these triples should + belong to the current process, i.e. ia(i) should be one of the local indices, + but are otherwise arbitrary; +
    6. +
  6. In CSR format the coefficients to be inserted for each input row i = 1,nr + are represented by the ordered triples (i + irw - 1),ja(j),val(j), for + j = irp(i),…,irp(i + 1) - 1; these triples should belong to the current + process, i.e. i+irw-1 should be one of the local indices, but are otherwise + arbitrary; +
    7. +
  7. There is no requirement that a given row must be passed in its entirety + to a single call to this routine: the buildup of a row may be split into as + many calls as desired (even in the CSR format); +
    8. +
  8. Coefficients from different rows may also be mixed up freely in a single + call, according to the application needs; +
    9. +
  9. Any coefficients from matrix rows not owned by the calling process are + silently ignored; + + + +
    10. +
  10. If the descriptor is in the assembled state, then any entries in the sparse + matrix that would generate additional communication requirements are + ignored; +
    11. +
  11. If the matrix is in the update state, any entries in positions that were not + present in the original matrix are ignored.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu38.html b/docs/html/userhtmlsu38.html new file mode 100644 index 00000000..d3f70743 --- /dev/null +++ b/docs/html/userhtmlsu38.html @@ -0,0 +1,186 @@ + + +psb_spasb — Sparse matrix assembly routine + + + + + + + +

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+

6.9 psb_spasb — Sparse matrix assembly routine

+ + + +
+call psb_spasb(a, desc_a, info, afmt, upd, dupl, mold) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+afmt
the storage format for the sparse matrix.
Scope: local.
Type: optional.
Intent: in.
Specified as: an array of characters. Defalt: ’CSR’. +
+upd
Provide for updates to the matrix coefficients.
Scope: global.
Type: optional.
Intent: in.
Specified as: integer, possible values: psb_upd_srch_, psb_upd_perm_ +
+dupl
How to handle duplicate coefficients.
Scope: global.
Type: optional.
Intent: in.
Specified as: integer, possible values: psb_dupl_ovwrt_, psb_dupl_add_, + psb_dupl_err_. +
+mold
The desired dynamic type for the internal matrix storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from psb_T_base_sparse_mat.
+

+ + + +

+On Return
+
+a
the matrix to be assembled.
Scope:local
Type:required
Intent: inout.
Specified as: a structured data of type psb_Tspmat_type. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. On entry to this routine the descriptor must be in the assembled state, + i.e. psb_cdasb must already have been called. +
    2. +
  2. The sparse matrix may be in either the build or update state; +
    3. +
  3. Duplicate entries are detected and handled in both build and update state, + with the exception of the error action that is only taken in the build state, + i.e. on the first assembly; +
    4. +
  4. If the update choice is psb_upd_perm_, then subsequent calls to psb_spins + to update the matrix must be arranged in such a way as to produce exactly + the same sequence of coefficient values as encountered at the first assembly; +
    5. +
  5. The output storage format need not be the same on all processes; +
    6. +
  6. On exit from this routine the matrix is in the assembled state, and thus + is suitable for the computational routines.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu39.html b/docs/html/userhtmlsu39.html new file mode 100644 index 00000000..e767aef9 --- /dev/null +++ b/docs/html/userhtmlsu39.html @@ -0,0 +1,98 @@ + + +psb_spfree — Frees a sparse matrix + + + + + + + +

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+

6.10 psb_spfree — Frees a sparse matrix

+ + + +
+call psb_spfree(a, desc_a, info) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+a
the matrix to be freed.
Scope:local
Type:required
Intent: inout.
Specified as: a structured data of type psb_Tspmat_type. +
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu4.html b/docs/html/userhtmlsu4.html new file mode 100644 index 00000000..ffc95516 --- /dev/null +++ b/docs/html/userhtmlsu4.html @@ -0,0 +1,61 @@ + + +Programming model + + + + + + + +

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+

2.4 Programming model

+

The PSBLAS librarary is based on the Single Program Multiple Data (SPMD) +programming model: each process participating in the computation performs the +same actions on a chunk of data. Parallelism is thus data-driven. +

Because of this structure, many subroutines coordinate their action across the +various processes, thus providing an implicit synchronization point, and therefore +must be called simultaneously by all processes participating in the computation. This +is certainly true for the data allocation and assembly routines, for all the +computational routines and for some of the tools routines. +

However there are many cases where no synchronization, and indeed no +communication among processes, is implied; for instance, all the routines in sec. 3 +are only acting on the local data structures, and thus may be called independently. +The most important case is that of the coefficient insertion routines: since the +number of coefficients in the sparse and dense matrices varies among the processors, +and since the user is free to choose an arbitrary order in builiding the matrix entries, +these routines cannot imply a synchronization. +

Throughout this user’s guide each subroutine will be clearly indicated +as: +

+Synchronous:
must be called simultaneously by all the processes in the + relevant communication context; +
+Asynchronous:
may be called in a totally independent manner.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu40.html b/docs/html/userhtmlsu40.html new file mode 100644 index 00000000..2e95eec1 --- /dev/null +++ b/docs/html/userhtmlsu40.html @@ -0,0 +1,114 @@ + + +psb_sprn — Reinit sparse matrix structure for psblas routines. + + + + + + + +

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+

6.11 psb_sprn — Reinit sparse matrix structure for psblas routines.

+ + + +
+call psb_sprn(a, decsc_a, info, clear) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+a
the matrix to be reinitialized.
Scope:local
Type:required
Intent: inout.
Specified as: a structured data of type psb_Tspmat_type. +
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+clear
Choose whether to zero out matrix coefficients
Scope:local.
Type:optional.
Intent: in.
Default: true.
+

+

+On Return
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. On exit from this routine the sparse matrix is in the update state.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu41.html b/docs/html/userhtmlsu41.html new file mode 100644 index 00000000..46b2ba28 --- /dev/null +++ b/docs/html/userhtmlsu41.html @@ -0,0 +1,132 @@ + + +psb_geall — Allocates a dense matrix + + + + + + + +

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+

6.12 psb_geall — Allocates a dense matrix

+ + + +
+call psb_geall(x, desc_a, info, n, lb) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
The communication descriptor.
Scope: local
Type: required
Intent: in.
Specified as: a variable of type psb_desc_type.
+
+n
The number of columns of the dense matrix to be allocated.
Scope: local
Type: optional
Intent: in.
Specified as: Integer scalar, default 1. It is not a valid argument if x is a + rank-1 array. +
+lb
The lower bound for the column index range of the dense matrix to be + allocated.
Scope: local
Type: optional
Intent: in.
Specified as: Integer scalar, default 1. It is not a valid argument if x is a + rank-1 array.
+

+

+On Return
+
+x
The dense matrix to be allocated.
Scope: local
Type: required
Intent: out.
Specified as: a rank one or two array with the ALLOCATABLE attribute + or an object of type psb_T_vect_type, of type real, complex or integer.
+ + + +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu42.html b/docs/html/userhtmlsu42.html new file mode 100644 index 00000000..7f215524 --- /dev/null +++ b/docs/html/userhtmlsu42.html @@ -0,0 +1,178 @@ + + +psb_geins — Dense matrix insertion routine + + + + + + + +

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+

6.13 psb_geins — Dense matrix insertion routine

+ + + +
+call psb_geins(m, irw, val, x, desc_a, info [,dupl,local]) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+m
Number of rows in val to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: an integer value. +
+irw
Indices of the rows to be inserted. Specifically, row i of val will be + inserted into the local row corresponding to the global row index irw(i). + Scope:local.
Type:required.
Intent: in.
Specified as: an integer array. +
+val
the dense submatrix to be inserted.
Scope:local.
Type:required.
Intent: in.
Specified as: a rank 1 or 2 array. Specified as: an integer value. +
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+dupl
How to handle duplicate coefficients.
Scope: global.
Type: optional.
Intent: in.
Specified as: integer, possible values: psb_dupl_ovwrt_, psb_dupl_add_. + + + +
+local
Whether the entries in the index vector irw, are already in local + numbering.
Scope:local.
Type:optional.
Specified as: a logical value; default: .false.. +
+

+

+On Return
+
+x
the output dense matrix.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array or an object of type + psb_T_vect_type, of type real, complex or integer.
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. Dense vectors/matrices do not have an associated state; +
    2. +
  2. Duplicate entries are either overwritten or added, there is no provision for + raising an error condition.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu43.html b/docs/html/userhtmlsu43.html new file mode 100644 index 00000000..3befcce9 --- /dev/null +++ b/docs/html/userhtmlsu43.html @@ -0,0 +1,123 @@ + + +psb_geasb — Assembly a dense matrix + + + + + + + +

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+

6.14 psb_geasb — Assembly a dense matrix

+ + + +
+call psb_geasb(x, desc_a, info, mold) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+desc_a
The communication descriptor.
Scope: local
Type: required
Intent: in.
Specified as: a variable of type psb_desc_type.
+
+mold
The desired dynamic type for the internal vector storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from psb_T_base_vect_type; + this is only allowed when x is of type psb_T_vect_type.
+

+

+On Return
+
+x
The dense matrix to be assembled.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array with the ALLOCATABLE or an + object of type psb_T_vect_type, of type real, complex or integer.
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu44.html b/docs/html/userhtmlsu44.html new file mode 100644 index 00000000..90a8c1c7 --- /dev/null +++ b/docs/html/userhtmlsu44.html @@ -0,0 +1,102 @@ + + +psb_gefree — Frees a dense matrix + + + + + + + +

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+

6.15 psb_gefree — Frees a dense matrix

+ + + +
+call psb_gefree(x, desc_a, info) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+x
The dense matrix to be freed.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one or two array with the ALLOCATABLE or an + object of type psb_T_vect_type, of type real, complex or integer.
+
+desc_a
The communication descriptor.
Scope: local
Type: required
Intent: in.
Specified as: a variable of type psb_desc_type.
+

+

+On Return
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu45.html b/docs/html/userhtmlsu45.html new file mode 100644 index 00000000..559a173a --- /dev/null +++ b/docs/html/userhtmlsu45.html @@ -0,0 +1,109 @@ + + +psb_gelp — Applies a left permutation to a dense matrix + + + + + + + +

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+

6.16 psb_gelp — Applies a left permutation to a dense matrix

+ + + +
+call psb_gelp(trans, iperm, x, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+trans
A character that specifies whether to permute A or AT.
Scope: local
Type: required
Intent: in.
Specified as: a single character with value ’N’ for A or ’T’ for AT.
+
+iperm
An integer array containing permutation information.
Scope: local
Type: required
Intent: in.
Specified as: an integer one-dimensional array.
+
+x
The dense matrix to be permuted.
Scope: local
Type: required
Intent: inout.
Specified as: a one or two dimensional array.
+

+

+On Return
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu46.html b/docs/html/userhtmlsu46.html new file mode 100644 index 00000000..3d5b5a42 --- /dev/null +++ b/docs/html/userhtmlsu46.html @@ -0,0 +1,162 @@ + + +psb_glob_to_loc — Global to local indices convertion + + + + + + + +

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+

6.17 psb_glob_to_loc — Global to local indices convertion

+ + + +
+call psb_glob_to_loc(x, y, desc_a, info, iact,owned) + 
call psb_glob_to_loc(x, desc_a, info, iact,owned) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
An integer vector of indices to be converted.
Scope: local
Type: required
Intent: in, inout.
Specified as: a rank one integer array.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+iact
specifies action to be taken in case of range errors. Scope: global
Type: optional
Intent: in.
Specified as: a character variable Ignore, Warning or Abort, default Ignore. +
+owned
Specfies valid range of input Scope: global
Type: optional
Intent: in.
If true, then only indices strictly owned by the current process are + considered valid, if false then halo indices are also accepted. Default: false.
+

+

+On Return
+
+x
If y is not present, then x is overwritten with the translated integer indices. + Scope: global
Type: required
Intent: inout.
Specified as: a rank one integer array. + + + +
+y
If y is present, then y is overwritten with the translated integer indices, and + x is left unchanged. Scope: global
Type: optional
Intent: out.
Specified as: a rank one integer array. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. If an input index is out of range, then the corresponding output index is + set to a negative number; +
    2. +
  2. The default Ignore means that the negative output is the only action + taken on an out-of-range input.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu47.html b/docs/html/userhtmlsu47.html new file mode 100644 index 00000000..166f1bad --- /dev/null +++ b/docs/html/userhtmlsu47.html @@ -0,0 +1,140 @@ + + +psb_loc_to_glob — Local to global indices conversion + + + + + + + +

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+

6.18 psb_loc_to_glob — Local to global indices conversion

+ + + +
+call psb_loc_to_glob(x, y, desc_a, info, iact) + 
call psb_loc_to_glob(x, desc_a, info, iact) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
An integer vector of indices to be converted.
Scope: local
Type: required
Intent: in, inout.
Specified as: a rank one integer array.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+iact
specifies action to be taken in case of range errors. Scope: global
Type: optional
Intent: in.
Specified as: a character variable Ignore, Warning or Abort, default Ignore.
+

+

+On Return
+
+x
If y is not present, then x is overwritten with the translated integer indices. + Scope: global
Type: required
Intent: inout.
Specified as: a rank one integer array. +
+y
If y is not present, then y is overwritten with the translated integer indices, + and x is left unchanged. Scope: global
Type: optional
Intent: out.
Specified as: a rank one integer array. + + + +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu48.html b/docs/html/userhtmlsu48.html new file mode 100644 index 00000000..9ed049f8 --- /dev/null +++ b/docs/html/userhtmlsu48.html @@ -0,0 +1,103 @@ + + +psb_is_owned — + + + + + + + +

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+

6.19 psb_is_owned —

+ + + +
+call psb_is_owned(x, desc_a) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
Integer index.
Scope: local
Type: required
Intent: in.
Specified as: a scalar integer.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+Function value
A logical mask which is true if x is owned by the current + process Scope: local
Type: required
Intent: out.
+

Notes +

    +
  1. This routine returns a .true. value for an index that is strictly owned by + the current process, excluding the halo indices
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu49.html b/docs/html/userhtmlsu49.html new file mode 100644 index 00000000..03b88635 --- /dev/null +++ b/docs/html/userhtmlsu49.html @@ -0,0 +1,131 @@ + + +psb_owned_index — + + + + + + + +

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+

6.20 psb_owned_index —

+ + + +
+call psb_owned_index(y, x, desc_a, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
Integer indices.
Scope: local
Type: required
Intent: in, inout.
Specified as: a scalar or a rank one integer array.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+iact
specifies action to be taken in case of range errors. Scope: global
Type: optional
Intent: in.
Specified as: a character variable Ignore, Warning or Abort, default Ignore.
+

+

+On Return
+
+y
A logical mask which is true for all corresponding entries of x that are owned + by the current process Scope: local
Type: required
Intent: out.
Specified as: a scalar or rank one logical array. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + +

Notes +

    +
  1. This routine returns a .true. value for those indices that are strictly + owned by the current process, excluding the halo indices
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu5.html b/docs/html/userhtmlsu5.html new file mode 100644 index 00000000..a3b5df1a --- /dev/null +++ b/docs/html/userhtmlsu5.html @@ -0,0 +1,814 @@ + + +Descriptor data structure + + + + + + + + + + +

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+

3.1 Descriptor data structure

+

All the general matrix informations and elements to be exchanged among processes +are stored within a data structure of the type psb_desc_type. Every structure of this +type is associated with a discretization pattern and enables data communications and +other operations that are necessary for implementing the various algorithms of +interest to us. +

The data structure itself psb_desc_type can be treated as an opaque object +handled via the tools routines of Sec. 6 or the query routines detailed below; +nevertheless we include here a description for the curious reader. +

First we describe the psb_indx_map type. This is a data structure that keeps +track of a certain number of basic issues such as: +

    +
  • The value of the communication/MPI context; +
    • +
  • The number of indices in the index space, i.e. global number of rows and + columns of a sparse matrix; +
    • +
  • The local set of indices, including: +
      +
    • The number of local indices (and local rows); +
      • +
    • The number of halo indices (and therefore local columns); +
      • +
    • The global indices corresponding to the local ones.
    +
+

There are many different schemes for storing these data; therefore there are a number of +types extending the base one, and the descriptor structure holds a polymorphic +object whose dynamic type can be any of the extended types. The methods +associated with this data type answer the following queries: +

    +
  • For a given set of local indices, find the corresponding indices in the global + numbering; +
    • +
  • For a given set of global indices, find the corresponding indices in the local + numbering, if any, or return an invalid +
    • +
  • Add a global index to the set of halo indices; +
    • +
  • Find the process owner of each member of a set of global indices.
+ + + +

All methods but the last are purely local; the last method potentially requires +communication among processes, and thus is a synchronous method. The +choice of a specific dynamic type for the index map is made at the time the +descriptor is initially allocated, according to the mode of initialization (see +also 6). +

The descriptor contents are as follows: +

+indxmap
A polymorphic variable of a type that is any extension of the + indx_map type described above.
+
+halo_index
A list of the halo and boundary elements for the current process to be + exchanged with other processes; for each processes with which it is necessary to + communicate: +
    +
  1. Process identifier; +
    2. +
  2. Number of points to be received; +
    3. +
  3. Indices of points to be received; +
    4. +
  4. Number of points to be sent; +
    5. +
  5. Indices of points to be sent;
+

Specified as: a vector of integer type, see 3.3. +

+ext_index
A list of element indices to be exchanged to implement the mapping + between a base descriptor and a descriptor with overlap.
Specified as: a vector of integer type, see 3.3. +
+ovrlap_index
A list of the overlap elements for the current process, organized in + groups like the previous vector: +
    +
  1. Process identifier; +
    2. +
  2. Number of points to be received; +
    3. +
  3. Indices of points to be received; +
    4. +
  4. Number of points to be sent; +
    5. +
  5. Indices of points to be sent;
+ + + +

Specified as: a vector of integer type, see 3.3. +

+ovr_mst_idx
A list to retrieve the value of each overlap element from the respective + master process.
Specified as: a vector of integer type, see 3.3. +
+ovrlap_elem
For all overlap points belonging to th ecurrent process: +
    +
  1. Overlap point index; +
    2. +
  2. Number of processes sharing that overlap points; +
    3. +
  3. Index of a “master” process:
+

Specified as: an allocatable integer array of rank two. +

+bnd_elem
A list of all boundary points, i.e. points that have a connection with + other processes.
+

The Fortran 2003 declaration for psb_desc_type structures is as follows:

+
+

+

+type psb_desc_type + 
    class(psb_indx_map), allocatable :: indxmap + 
    type(psb_i_vect_type) :: v_halo_index + 
    type(psb_i_vect_type) :: v_ext_index + 
    type(psb_i_vect_type) :: v_ovrlap_index + 
    type(psb_i_vect_type) :: v_ovr_mst_idx + 
    integer, allocatable  :: ovrlap_elem(:,:) + 
    integer, allocatable  :: bnd_elem(:) + 
end type psb_desc_type +
+

+
Figure 3: The PSBLAS defined data type that contains the communication +descriptor.
+

+

A communication descriptor associated with a sparse matrix has a state, which +can take the following values: +

+Build:
State entered after the first allocation, and before the first assembly; in + this state it is possible to add communication requirements among different + processes. + + + +
+Assembled:
State entered after the assembly; computations using the + associated sparse matrix, such as matrix-vector products, are only possible + in this state.
+

+

3.1.1 Descriptor Methods
+

+

3.1.2 get_local_rows — Get number of local rows
+ + + +
+nr = desc%get_local_rows() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+Function value
The number of local rows, i.e. the number of rows owned by + the current process; as explained in 1, it is equal to |Ii|+|Bi|. The returned + value is specific to the calling process.
+

+

3.1.3 get_local_cols — Get number of local cols
+ + + +
+nc = desc%get_local_cols() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+Function value
The number of local cols, i.e. the number of indices used by + the current process, including both local and halo indices; as explained + in 1, it is equal to |Ii| + |Bi| + |Hi|. The returned value is specific to the + calling process.
+

+

3.1.4 get_global_rows — Get number of global rows
+ + + +
+nr = desc%get_global_rows() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+Function value
The number of global rows, i.e. the size of the global index + space.
+

+

3.1.5 get_global_cols — Get number of global cols
+ + + +
+nr = desc%get_global_cols() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+Function value
The number of global cols; usually this is equal to the number + of global rows.
+

+

3.1.6 get_global_indices — Get vector of global indices
+ + + +
+myidx = desc%get_global_indices([owned]) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
Type: required.
+
+owned
Choose if you only want owned indices (owned=.true.) or also halo + indices (owned=.false.). Scope: local.
Type: optional; default: .true..
+

+

+On Return
+
+Function value
The global indices, returned as an allocatable integer array of + kind psb_lpk_ and rank 1.
+

+

3.1.7 get_context — Get communication context
+ + + +
+ictxt = desc%get_context() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+Function value
The communication context.
+

+

3.1.8 Clone — clone current object
+ + + +
+call  desc%clone(descout,info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+

+

+On Return
+
+descout
A copy of the input object. +
+info
Return code.
+

+

3.1.9 CNV — convert internal storage format
+ + + +
+call  desc%cnv(mold) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope: local.
+
+mold
the desired integer storage format.
Scope: local.
Specified as: a object of type derived from (integer) + psb_T_base_vect_type.
+

The mold arguments may be employed to interface with special devices, such as GPUs +and other accelerators. +

+

3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping +switch
+ + + +
+ith = psb_cd_get_large_threshold() +
+

+

+

+Type:
Asynchronous. +
+On Return
+
+Function value
The current value for the size threshold. +
+

+

3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping +switch
+ + + +
+call psb_cd_set_large_threshold(ith) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+ith
the new threshold for communication descriptors.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer value greater than zero.
+

Note: the threshold value is only queried by the library at the time a call to psb_cdall +is executed, therefore changing the threshold has no effect on communication +descriptors that have already been initialized. Moreover the threshold must have the +same value on all processes. +

+

3.1.12 get_p_adjcncy — Get process adjacency list
+ + + +
+list =  desc%get_p_adjcncy() +
+

+

+

+Type:
Asynchronous. +
+On Return
+
+Function value
The current list of adjacent processes, i.e. processes with + which the current one has to exchange halo data. +
+

+

3.1.13 set_p_adjcncy — Set process adjacency list
+ + + +
+call desc%set_p_adjcncy(list) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+list
the list of adjacent processes.
Scope: local.
Type: required.
Intent: in.
Specified as: a one-dimensional array of integers of kind psb_ipk_.
+

Note: this method can be called after a call to psb_cdall and before a call to +psb_cdasb. The user is specifying here some knowledge about which processes are +topological neighbours of the current process. The availability of this information +may speed up the execution of the assembly call psb_cdasb. +

+

3.1.14 fnd_owner — Find the owner process of a set of indices
+ + + +
+call desc%fnd_owner(idx,iprc,info) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+idx
the list of global indices for which we need the owning processes.
Scope: local.
Type: required.
Intent: in.
Specified as: a one-dimensional array of integers of kind psb_lpk_. +
+On Return
+
+iprc
the list of processes owning the indices in idx.
Scope: local.
Type: required.
Intent: in.
Specified as: an allocatable one-dimensional array of integers of kind + psb_ipk_.
+

Note: this method may or may not actually require communications, depending on the +exact internal data storage; given that the choice of storage may be altered by +runtime parameters, it is necessary for safety that this method is called by all +processes. +

+

3.1.15 Named Constants
+

+

+psb_none_
Generic no-op; +
+psb_root_
Default root process for broadcast and scatter operations; +
+psb_nohalo_
Do not fetch halo elements; +
+psb_halo_
Fetch halo elements from neighbouring processes; + + + +
+psb_sum_
Sum overlapped elements +
+psb_avg_
Average overlapped elements +
+psb_comm_halo_
Exchange data based on the halo_index list; +
+psb_comm_ext_
Exchange data based on the ext_index list; +
+psb_comm_ovr_
Exchange data based on the ovrlap_index list; +
+psb_comm_mov_
Exchange data based on the ovr_mst_idx list; +
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu50.html b/docs/html/userhtmlsu50.html new file mode 100644 index 00000000..abeeb70d --- /dev/null +++ b/docs/html/userhtmlsu50.html @@ -0,0 +1,103 @@ + + +psb_is_local — + + + + + + + +

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+

6.21 psb_is_local —

+ + + +
+call psb_is_local(x, desc_a) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
Integer index.
Scope: local
Type: required
Intent: in.
Specified as: a scalar integer.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+Function value
A logical mask which is true if x is local to the current process + Scope: local
Type: required
Intent: out.
+

Notes +

    +
  1. This routine returns a .true. value for an index that is local to the current + process, including the halo indices
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu51.html b/docs/html/userhtmlsu51.html new file mode 100644 index 00000000..98b2f4aa --- /dev/null +++ b/docs/html/userhtmlsu51.html @@ -0,0 +1,131 @@ + + +psb_local_index — + + + + + + + +

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+

6.22 psb_local_index —

+ + + +
+call psb_local_index(y, x, desc_a, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
Integer indices.
Scope: local
Type: required
Intent: in, inout.
Specified as: a scalar or a rank one integer array.
+
+desc_a
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+iact
specifies action to be taken in case of range errors. Scope: global
Type: optional
Intent: in.
Specified as: a character variable Ignore, Warning or Abort, default Ignore.
+

+

+On Return
+
+y
A logical mask which is true for all corresponding entries of x that are local + to the current process Scope: local
Type: required
Intent: out.
Specified as: a scalar or rank one logical array. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + +

Notes +

    +
  1. This routine returns a .true. value for those indices that are local to the + current process, including the halo indices.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu52.html b/docs/html/userhtmlsu52.html new file mode 100644 index 00000000..d970c404 --- /dev/null +++ b/docs/html/userhtmlsu52.html @@ -0,0 +1,107 @@ + + +psb_get_boundary — Extract list of boundary elements + + + + + + + +

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+

6.23 psb_get_boundary — Extract list of boundary elements

+ + + +
+call psb_get_boundary(bndel, desc, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+bndel
The list of boundary elements on the calling process, in local numbering.
Scope: local
Type: required
Intent: out.
Specified as: a rank one array with the ALLOCATABLE attribute, of type + integer.
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. If there are no boundary elements (i.e., if the local part of the connectivity + graph is self-contained) the output vector is set to the “not allocated” + state. +
    2. +
  2. Otherwise the size of bndel will be exactly equal to the number of + boundary elements.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu53.html b/docs/html/userhtmlsu53.html new file mode 100644 index 00000000..4d5f699c --- /dev/null +++ b/docs/html/userhtmlsu53.html @@ -0,0 +1,106 @@ + + +psb_get_overlap — Extract list of overlap elements + + + + + + + +

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+

6.24 psb_get_overlap — Extract list of overlap elements

+ + + +
+call psb_get_overlap(ovrel, desc, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+desc
the communication descriptor.
Scope:local.
Type:required.
Intent: in.
Specified as: a structured data of type psb_desc_type.
+

+

+On Return
+
+ovrel
The list of overlap elements on the calling process, in local numbering.
Scope: local
Type: required
Intent: out.
Specified as: a rank one array with the ALLOCATABLE attribute, of type + integer.
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. If there are no overlap elements the output vector is set to the “not + allocated” state. +
    2. +
  2. Otherwise the size of ovrel will be exactly equal to the number of overlap + elements.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu54.html b/docs/html/userhtmlsu54.html new file mode 100644 index 00000000..e37335c6 --- /dev/null +++ b/docs/html/userhtmlsu54.html @@ -0,0 +1,209 @@ + + +psb_sp_getrow — Extract row(s) from a sparse matrix + + + + + + + +

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+

6.25 psb_sp_getrow — Extract row(s) from a sparse matrix

+ + + +
+call psb_sp_getrow(row, a, nz, ia, ja, val, info, & + 
              & append, nzin, lrw) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+row
The (first) row to be extracted.
Scope:local
Type:required
Intent: in.
Specified as: an integer > 0. +
+a
the matrix from which to get rows.
Scope:local
Type:required
Intent: in.
Specified as: a structured data of type psb_Tspmat_type. +
+append
Whether to append or overwrite existing output.
Scope:local
Type:optional
Intent: in.
Specified as: a logical value default: false (overwrite). +
+nzin
Input size to be appended to.
Scope:local
Type:optional
Intent: in.
Specified as: an integer > 0. When append is true, specifies how many + entries in the output vectors are already filled. +
+lrw
The last row to be extracted.
Scope:local
Type:optional
Intent: in.
Specified as: an integer > 0, default: row. +
+ + + +

+

+On Return
+
+nz
the number of elements returned by this call.
Scope:local.
Type:required.
Intent: out.
Returned as: an integer scalar. +
+ia
the row indices.
Scope:local.
Type:required.
Intent: inout.
Specified as: an integer array with the ALLOCATABLE attribute. +
+ja
the column indices of the elements to be inserted.
Scope:local.
Type:required.
Intent: inout.
Specified as: an integer array with the ALLOCATABLE attribute. +
+val
the elements to be inserted.
Scope:local.
Type:required.
Intent: inout.
Specified as: a real array with the ALLOCATABLE attribute. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

Notes +

    +
  1. The output nz is always the size of the output generated by the current + call; thus, if append=.true., the total output size will be nzin + nz, with + the newly extracted coefficients stored in entries nzin+1:nzin+nz of the + array arguments; +
    2. +
  2. When append=.true. the output arrays are reallocated as necessary; +
    3. +
  3. The row and column indices are returned in the local numbering + scheme; if the global numbering is desired, the user may employ the + psb_loc_to_glob routine on the output.
+ + + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu55.html b/docs/html/userhtmlsu55.html new file mode 100644 index 00000000..35b7c749 --- /dev/null +++ b/docs/html/userhtmlsu55.html @@ -0,0 +1,113 @@ + + +psb_sizeof — Memory occupation + + + + + + + +

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+

6.26 psb_sizeof — Memory occupation

+

This function computes the memory occupation of a PSBLAS object. + + + +

+isz = psb_sizeof(a) + 
isz = psb_sizeof(desc_a) + 
isz = psb_sizeof(prec) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
A sparse matrix A.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_Tspmat_type. +
+desc_a
Communication descriptor.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+prec
Scope: local
Type: required
Intent: in.
Specified as: a preconditioner data structure psb_prec_type. +
+On Return
+
+Function value
The memory occupation of the object specified in the calling + sequence, in bytes.
Scope: local
Returned as: an integer(psb_long_int_k_) number.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu56.html b/docs/html/userhtmlsu56.html new file mode 100644 index 00000000..047a538f --- /dev/null +++ b/docs/html/userhtmlsu56.html @@ -0,0 +1,229 @@ + + +Sorting utilities — + + + + + + + +

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+

6.27 Sorting utilities —

+

psb_msort — Sorting by the Merge-sort algorithm +

psb_qsort — Sorting by the Quicksort algorithm +

psb_hsort — Sorting by the Heapsort algorithm + + + +

+call psb_msort(x,ix,dir,flag) + 
call psb_qsort(x,ix,dir,flag) + 
call psb_hsort(x,ix,dir,flag) +
+

+

These serial routines sort a sequence X into ascending or descending order. The +argument meaning is identical for the three calls; the only difference is the algorithm +used to accomplish the task (see Usage Notes below). +

+Type:
Asynchronous. +
+On Entry
+
+x
The sequence to be sorted.
Type:required.
Specified as: an integer, real or complex array of rank 1. +
+ix
A vector of indices.
Type:optional.
Specified as: an integer array of (at least) the same size as X. +
+dir
The desired ordering.
Type:optional.
Specified as: an integer value: +
+ Integer and real data:
psb_sort_up_, psb_sort_down_, + psb_asort_up_, psb_asort_down_; default psb_sort_up_. +
+ Complex data:
psb_lsort_up_, psb_lsort_down_, psb_asort_up_, + psb_asort_down_; default psb_lsort_up_.
+
+flag
Whether to keep the original values in IX.
Type:optional.
Specified as: an integer value psb_sort_ovw_idx_ or psb_sort_keep_idx_; + default psb_sort_ovw_idx_. +
+

+

+On Return
+ + + +
+x
The sequence of values, in the chosen ordering.
Type:required.
Specified as: an integer, real or complex array of rank 1. +
+ix
A vector of indices.
Type: Optional
An integer array of rank 1, whose entries are moved to the same position + as the corresponding entries in x.
+

Notes +

    +
  1. For integer or real data the sorting can be performed in the up/down + direction, on the natural or absolute values; +
    2. +
  2. For complex data the sorting can be done in a lexicographic order (i.e.: + sort on the real part with ties broken according to the imaginary part) or + on the absolute values; +
    3. +
  3. The routines return the items in the chosen ordering; the output difference + is the handling of ties (i.e. items with an equal value) in the original input. + With the merge-sort algorithm ties are preserved in the same relative + order as they had in the original sequence, while this is not guaranteed for + quicksort or heapsort; +
    4. +
  4. If flag = psb_sort_ovw_idx_ then the entries in ix(1 : n) where n is the size + of x are initialized to ix(i) ← i; thus, upon return from the subroutine, + for each index i we have in ix(i) the position that the item x(i) occupied + in the original data sequence; +
    5. +
  5. If flag = psb_sort_keep_idx_ the routine will assume that the entries in + ix(:) have already been initialized by the user; +
    6. +
  6. The three sorting algorithms have a similar O(nlog n) expected running time; + in the average case quicksort will be the fastest and merge-sort the slowest. + However note that: +
      +
    1. The worst case running time for quicksort is O(n2); the algorithm + implemented here follows the well-known median-of-three heuristics, + but the worst case may still apply; +
      2. +
    2. The worst case running time for merge-sort and heap-sort is + O(nlog n) as the average case; + + + +
      3. +
    3. The merge-sort algorithm is implemented to take advantage of + subsequences that may be already in the desired ordering prior to + the subroutine call; this situation is relatively common when dealing + with groups of indices of sparse matrix entries, thus merge-sort is the + preferred choice when a sorting is needed by other routines in the + library.
    +
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu57.html b/docs/html/userhtmlsu57.html new file mode 100644 index 00000000..9b44edbc --- /dev/null +++ b/docs/html/userhtmlsu57.html @@ -0,0 +1,121 @@ + + +psb_init — Initializes PSBLAS parallel environment + + + + + + + +

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+

7.1 psb_init — Initializes PSBLAS parallel environment

+ + + +
+call psb_init(icontxt, np, basectxt, ids) +
+

+

This subroutine initializes the PSBLAS parallel environment, defining a virtual +parallel machine. +

+Type:
Synchronous. +
+On Entry
+
+np
Number of processes in the PSBLAS virtual parallel machine.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value.  Default: use all available processes. +
+basectxt
the initial communication context. The new context will be defined + from the processes participating in the initial one.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value.  Default: use MPI_COMM_WORLD. +
+ids
Identities of the processes to use for the new context; the argument is + ignored when np is not specified. This allows the processes in the new + environment to be in an order different from the original one.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer array.  Default: use the indices (0…np - 1).
+

+

+On Return
+
+icontxt
the communication context identifying the virtual parallel machine. + Note that this is always a duplicate of basectxt, so that library + communications are completely separated from other communication + operations.
Scope: global.
Type: required.
Intent: out.
Specified as: an integer variable.
+ + + +

Notes +

    +
  1. A call to this routine must precede any other PSBLAS call. +
    2. +
  2. It is an error to specify a value for np greater than the number of processes + available in the underlying base parallel environment.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu58.html b/docs/html/userhtmlsu58.html new file mode 100644 index 00000000..2d6a8e06 --- /dev/null +++ b/docs/html/userhtmlsu58.html @@ -0,0 +1,118 @@ + + +psb_info — Return information about PSBLAS parallel environment + + + + + + + +

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+

7.2 psb_info — Return information about PSBLAS parallel environment

+ + + +
+call psb_info(icontxt, iam, np) +
+

+

This subroutine returns information about the PSBLAS parallel environment, +defining a virtual parallel machine. +

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable.
+

+

+On Return
+
+iam
Identifier of current process in the PSBLAS virtual parallel machine.
Scope: local.
Type: required.
Intent: out.
Specified as: an integer value. -1 ≤ iam ≤ np - 1  +
+np
Number of processes in the PSBLAS virtual parallel machine.
Scope: global.
Type: required.
Intent: out.
Specified as: an integer variable.  
+

Notes +

    +
  1. For processes in the virtual parallel machine the identifier will satisfy + 0 ≤ iam ≤ np - 1; +
    2. +
  2. If the user has requested on psb_init a number of processes less than + the total available in the parallel execution environment, the remaining + processes will have on return iam = -1; the only call involving icontxt + that any such process may execute is to psb_exit.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu59.html b/docs/html/userhtmlsu59.html new file mode 100644 index 00000000..6634744c --- /dev/null +++ b/docs/html/userhtmlsu59.html @@ -0,0 +1,101 @@ + + +psb_exit — Exit from PSBLAS parallel environment + + + + + + + +

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+

7.3 psb_exit — Exit from PSBLAS parallel environment

+ + + +
+call psb_exit(icontxt) + 
call psb_exit(icontxt,close) +
+

+

This subroutine exits from the PSBLAS parallel virtual machine. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+close
Whether to close all data structures related to the virtual parallel + machine, besides those associated with icontxt.
Scope: global.
Type: optional.
Intent: in.
Specified as: a logical variable, default value: true.
+

Notes +

    +
  1. This routine may be called even if a previous call to psb_info has returned + with iam = -1; indeed, it it is the only routine that may be called with + argument icontxt in this situation. +
    2. +
  2. A call to this routine with close=.true. implies a call to MPI_Finalize, + after which no parallel routine may be called. +
    3. +
  3. If the user whishes to use multiple communication contexts in the + same program, or to enter and exit multiple times into the parallel + environment, this routine may be called to selectively close the contexts + with close=.false., while on the last call it should be called with + close=.true. to shutdown in a clean way the entire parallel environment.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu6.html b/docs/html/userhtmlsu6.html new file mode 100644 index 00000000..18b94c13 --- /dev/null +++ b/docs/html/userhtmlsu6.html @@ -0,0 +1,963 @@ + + +Sparse Matrix class + + + + + + + +

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+

3.2 Sparse Matrix class

+

The psb_Tspmat_type class contains all information about the local portion of the +sparse matrix and its storage mode. Its design is based on the STATE design +pattern [13] as detailed in [11]; the type declaration is shown in figure 4 where T is a +placeholder for the data type and precision variants +

+S
Single precision real; +
+D
Double precision real; +
+C
Single precision complex; +
+Z
Double precision complex.
+

The actual data is contained in the polymorphic component a%a of type +psb_T_base_sparse_mat; its specific layout can be chosen dynamically among the +predefined types, or an entirely new storage layout can be implemented and passed to +the library at runtime via the psb_spasb routine.

+
+

+

+  type :: psb_Tspmat_type + 
    class(psb_T_base_sparse_mat), allocatable  :: a + 
  end type  psb_Tspmat_type +
+

+
Figure 4: The PSBLAS defined data type that contains a sparse matrix.
+

+

The following very common formats are precompiled in PSBLAS and thus are +always available: +

+psb_T_coo_sparse_mat
Coordinate storage; +
+psb_T_csr_sparse_mat
Compressed storage by rows; +
+psb_T_csc_sparse_mat
Compressed storage by columns;
+ + + +

The inner sparse matrix has an associated state, which can take the following +values: +

+Build:
State entered after the first allocation, and before the first assembly; in + this state it is possible to add nonzero entries. +
+Assembled:
State entered after the assembly; computations using the sparse + matrix, such as matrix-vector products, are only possible in this state; +
+Update:
State entered after a reinitalization; this is used to handle applications + in which the same sparsity pattern is used multiple times with different + coefficients. In this state it is only possible to enter coefficients for already + existing nonzero entries.
+

The only storage variant supporting the build state is COO; all other variants are +obtained by conversion to/from it. +

+

3.2.1 Sparse Matrix Methods
+

+

3.2.2 get_nrows — Get number of rows in a sparse matrix
+ + + +
+nr = a%get_nrows() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
The number of rows of sparse matrix a.
+

+

3.2.3 get_ncols — Get number of columns in a sparse matrix
+ + + +
+nc = a%get_ncols() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
The number of columns of sparse matrix a.
+

+

3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix
+ + + +
+nz = a%get_nnzeros() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
The number of nonzero elements stored in sparse matrix a.
+

Notes +

    +
  1. The function value is specific to the storage format of matrix a; some + storage formats employ padding, thus the returned value for the same + matrix may be different for different storage choices.
+

+

3.2.5 get_size — Get maximum number of nonzero elements in a sparse +matrix
+ + + +
+maxnz = a%get_size() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
The maximum number of nonzero elements that can be stored + in sparse matrix a using its current memory allocation.
+

+

3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix
+ + + +
+memory_size = a%sizeof() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
The memory occupation in bytes.
+

+

3.2.7 get_fmt — Short description of the dynamic type
+ + + +
+write(*,*) a%get_fmt() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
A short string describing the dynamic type of the matrix. + Predefined values include NULL, COO, CSR and CSC.
+

+

3.2.8 is_bld, is_upd, is_asb — Status check
+ + + +
+if (a%is_bld()) then + 
if (a%is_upd()) then + 
if (a%is_asb()) then +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
A logical value indicating whether the matrix is in the Build, + Update or Assembled state, respectively.
+

+

3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check
+ + + +
+if (a%is_triangle()) then + 
if (a%is_upper()) then + 
if (a%is_lower()) then + 
if (a%is_unit()) then +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix
Scope: local
+

+

+On Return
+
+Function value
A logical value indicating whether the matrix is triangular; + if is_triangle() returns .true. check also if it is lower, upper and with + a unit (i.e. assumed) diagonal.
+

+

3.2.10 cscnv — Convert to a different storage format
+ + + +
+call  a%cscnv(b,info [, type, mold, dupl]) + 
call  a%cscnv(info [, type, mold, dupl]) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+
+type
a string requesting a new format.
Type: optional. +
+mold
a variable of class(psb_T_base_sparse_mat) requesting a new format.
Type: optional. +
+dupl
an integer value specifing how to handle duplicates (see Named Constants + below)
+

+

+On Return
+
+b,a
A copy of a with a new storage format.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

The mold arguments may be employed to interface with special devices, such as GPUs +and other accelerators. +

+

3.2.11 csclip — Reduce to a submatrix
+ + + +
+    call a%csclip(b,info[,& + 
       & imin,imax,jmin,jmax,rscale,cscale]) +
+

+

Returns the submatrix A(imin:imax,jmin:jmax), optionally rescaling row/col +indices to the range 1:imax-imin+1,1:jmax-jmin+1. +

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+
+imin,imax,jmin,jmax
Minimum and maximum row and column indices.
Type: optional. +
+rscale,cscale
Whether to rescale row/column indices. Type: optional.
+

+

+On Return
+
+b
A copy of a submatrix of a.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

+

3.2.12 clean_zeros — Eliminate zero coefficients
+ + + +
+    call a%clean_zeros(info) +
+

+

Eliminates zero coefficients in the input matrix. Note that depending on the +internal storage format, there may still be some amount of zero padding in the +output. +

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+

+

+On Return
+
+a
The matrix a without zero coefficients.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

+

3.2.13 get_diag — Get main diagonal
+ + + +
+    call a%get_diag(d,info) +
+

+

Returns a copy of the main diagonal. +

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+

+

+On Return
+
+d
A copy of the main diagonal.
A one-dimensional array of the appropriate type. +
+info
Return code.
+

+

3.2.14 clip_diag — Cut out main diagonal
+ + + +
+    call a%clip_diag(b,info) +
+

+

Returns a copy of a without the main diagonal. +

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+

+

+On Return
+
+b
A copy of a without the main diagonal.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

+

3.2.15 tril — Return the lower triangle
+ + + +
+    call a%tril(l,info[,& + 
       & diag,imin,imax,jmin,jmax,rscale,cscale,u]) +
+

+

Returns the lower triangular part of submatrix A(imin:imax,jmin:jmax), +optionally rescaling row/col indices to the range 1:imax-imin+1,1:jmax-jmin+1 and +returing the complementary upper triangle. +

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+
+diag
Include diagonals up to this one; diag=1 means the first superdiagonal, + diag=-1 means the first subdiagonal. Default 0. +
+imin,imax,jmin,jmax
Minimum and maximum row and column indices.
Type: optional. +
+rscale,cscale
Whether to rescale row/column indices. Type: optional.
+

+

+On Return
+
+l
A copy of the lower triangle of a.
A variable of type psb_Tspmat_type. +
+u
(optional) A copy of the upper triangle of a.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

+

3.2.16 triu — Return the upper triangle
+ + + +
+    call a%triu(u,info[,& + 
       & diag,imin,imax,jmin,jmax,rscale,cscale,l]) +
+

+

Returns the upper triangular part of submatrix A(imin:imax,jmin:jmax), +optionally rescaling row/col indices to the range 1:imax-imin+1,1:jmax-jmin+1, +and returing the complementary lower triangle. +

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
A variable of type psb_Tspmat_type.
Scope: local.
+
+diag
Include diagonals up to this one; diag=1 means the first superdiagonal, + diag=-1 means the first subdiagonal. Default 0. +
+imin,imax,jmin,jmax
Minimum and maximum row and column indices.
Type: optional. +
+rscale,cscale
Whether to rescale row/column indices. Type: optional.
+

+

+On Return
+
+u
A copy of the upper triangle of a.
A variable of type psb_Tspmat_type. +
+l
(optional) A copy of the lower triangle of a.
A variable of type psb_Tspmat_type. +
+info
Return code.
+

+

3.2.17 psb_set_mat_default — Set default storage format
+ + + +
+call  psb_set_mat_default(a) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
a variable of class(psb_T_base_sparse_mat) requesting a new default + storage format.
Type: required.
+

+

3.2.18 clone — Clone current object
+ + + +
+call  a%clone(b,info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix.
Scope: local.
+

+

+On Return
+
+b
A copy of the input object. +
+info
Return code.
+

+

3.2.19 Named Constants
+

+

+psb_dupl_ovwrt_
Duplicate coefficients should be overwritten (i.e. ignore + duplications) +
+psb_dupl_add_
Duplicate coefficients should be added; +
+psb_dupl_err_
Duplicate coefficients should trigger an error conditino +
+psb_upd_dflt_
Default update strategy for matrix coefficients; +
+psb_upd_srch_
Update strategy based on search into the data structure; +
+psb_upd_perm_
Update strategy based on additional permutation data (see + tools routine description).
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu60.html b/docs/html/userhtmlsu60.html new file mode 100644 index 00000000..fb131e3f --- /dev/null +++ b/docs/html/userhtmlsu60.html @@ -0,0 +1,84 @@ + + +psb_get_mpi_comm — Get the MPI communicator + + + + + + + +

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+

7.4 psb_get_mpi_comm — Get the MPI communicator

+ + + +
+icomm = psb_get_mpi_comm(icontxt) +
+

+

This function returns the MPI communicator associated with a PSBLAS +context +

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable.
+

+

+On Return
+
+Function value
The MPI communicator associated with the PSBLAS virtual + parallel machine.
Scope: global.
Type: required.
Intent: out.
+

Notes The subroutine version psb_get_mpicomm is still available but is +deprecated. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu61.html b/docs/html/userhtmlsu61.html new file mode 100644 index 00000000..cad2fd88 --- /dev/null +++ b/docs/html/userhtmlsu61.html @@ -0,0 +1,99 @@ + + +psb_get_mpi_rank — Get the MPI rank + + + + + + + +

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+

7.5 psb_get_mpi_rank — Get the MPI rank

+ + + +
+rank = psb_get_mpi_rank(icontxt, id) +
+

+

This function returns the MPI rank of the PSBLAS process id +

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+id
Identifier of a process in the PSBLAS virtual parallel machine.
Scope: local.
Type: required.
Intent: in.
Specified as: an integer value. 0 ≤ id ≤ np - 1 
+

+

+On Return
+
+Funciton value
The MPI rank associated with the PSBLAS process id.
Scope: local.
Type: required.
Intent: out.
+

Notes The subroutine version psb_get_rank is still available but is deprecated. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu62.html b/docs/html/userhtmlsu62.html new file mode 100644 index 00000000..2786fa5e --- /dev/null +++ b/docs/html/userhtmlsu62.html @@ -0,0 +1,58 @@ + + +psb_wtime — Wall clock timing + + + + + + + +

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+

7.6 psb_wtime — Wall clock timing

+ + + +
+time = psb_wtime() +
+

+

This function returns a wall clock timer. The resolution of the timer is dependent +on the underlying parallel environment implementation. +

+Type:
Asynchronous. +
+On Exit
+
+Function value
the elapsed time in seconds.
Returned as: a real(psb_dpk_) variable.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu63.html b/docs/html/userhtmlsu63.html new file mode 100644 index 00000000..dd7f5c80 --- /dev/null +++ b/docs/html/userhtmlsu63.html @@ -0,0 +1,63 @@ + + +psb_barrier — Sinchronization point parallel environment + + + + + + + +

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+

7.7 psb_barrier — Sinchronization point parallel environment

+ + + +
+call psb_barrier(icontxt) +
+

+

This subroutine acts as an explicit synchronization point for the PSBLAS parallel +virtual machine. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu64.html b/docs/html/userhtmlsu64.html new file mode 100644 index 00000000..a1df06cb --- /dev/null +++ b/docs/html/userhtmlsu64.html @@ -0,0 +1,62 @@ + + +psb_abort — Abort a computation + + + + + + + +

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+

7.8 psb_abort — Abort a computation

+ + + +
+call psb_abort(icontxt) +
+

+

This subroutine aborts computation on the parallel virtual machine. +

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu65.html b/docs/html/userhtmlsu65.html new file mode 100644 index 00000000..8c6cf1df --- /dev/null +++ b/docs/html/userhtmlsu65.html @@ -0,0 +1,110 @@ + + +psb_bcast — Broadcast data + + + + + + + +

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+

7.9 psb_bcast — Broadcast data

+ + + +
+call psb_bcast(icontxt, dat, root) +
+

+

This subroutine implements a broadcast operation based on the underlying +communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
On the root process, the data to be broadcast.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array, or a character or logical variable, which may be + a scalar or rank 1 array.  Type, kind, rank and size must agree on all + processes. +
+root
Root process holding data to be broadcast.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value 0 <= root <= np - 1, default 0  
+

+

+On Return
+
+dat
On processes other than root, the data to be broadcast.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array, or a character or logical scalar.  Type, kind, rank + and size must agree on all processes.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu66.html b/docs/html/userhtmlsu66.html new file mode 100644 index 00000000..8a22d312 --- /dev/null +++ b/docs/html/userhtmlsu66.html @@ -0,0 +1,124 @@ + + +psb_sum — Global sum + + + + + + + +

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+

7.10 psb_sum — Global sum

+ + + +
+call psb_sum(icontxt, dat, root) +
+

+

This subroutine implements a sum reduction operation based on the underlying +communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global sum.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +
+root
Process to hold the final sum, or -1 to make it available on all processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.  
+

+

+On Return
+
+dat
On destination process(es), the result of the sum operation.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array.
Type, kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +
    2. +
  2. The dat argument may also be a long integer scalar.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu67.html b/docs/html/userhtmlsu67.html new file mode 100644 index 00000000..d9951c08 --- /dev/null +++ b/docs/html/userhtmlsu67.html @@ -0,0 +1,125 @@ + + +psb_max — Global maximum + + + + + + + +

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+

7.11 psb_max — Global maximum

+ + + +
+call psb_max(icontxt, dat, root) +
+

+

This subroutine implements a maximum valuereduction operation based on the +underlying communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global maximum.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.  Type, kind, rank and size must agree on all processes. +
+root
Process to hold the final maximum, or -1 to make it available on all + processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.
+

+

+On Return
+
+dat
On destination process(es), the result of the maximum operation.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.  Type, kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +
    2. +
  2. The dat argument may also be a long integer scalar.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu68.html b/docs/html/userhtmlsu68.html new file mode 100644 index 00000000..d05498b6 --- /dev/null +++ b/docs/html/userhtmlsu68.html @@ -0,0 +1,125 @@ + + +psb_min — Global minimum + + + + + + + +

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+

7.12 psb_min — Global minimum

+ + + +
+call psb_min(icontxt, dat, root) +
+

+

This subroutine implements a minimum value reduction operation based on the +underlying communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global minimum.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.  Type, kind, rank and size must agree on all processes. +
+root
Process to hold the final value, or -1 to make it available on all processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.
+

+

+On Return
+
+dat
On destination process(es), the result of the minimum operation.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.
Type, kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +
    2. +
  2. The dat argument may also be a long integer scalar.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu69.html b/docs/html/userhtmlsu69.html new file mode 100644 index 00000000..5c330ac6 --- /dev/null +++ b/docs/html/userhtmlsu69.html @@ -0,0 +1,124 @@ + + +psb_amx — Global maximum absolute value + + + + + + + +

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+

7.13 psb_amx — Global maximum absolute value

+ + + +
+call psb_amx(icontxt, dat, root) +
+

+

This subroutine implements a maximum absolute value reduction operation based +on the underlying communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global maximum.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +
+root
Process to hold the final value, or -1 to make it available on all processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.
+

+

+On Return
+
+dat
On destination process(es), the result of the maximum operation.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +
    2. +
  2. The dat argument may also be a long integer scalar.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu7.html b/docs/html/userhtmlsu7.html new file mode 100644 index 00000000..87e649d8 --- /dev/null +++ b/docs/html/userhtmlsu7.html @@ -0,0 +1,352 @@ + + +Dense Vector Data Structure + + + + + + + +

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+

3.3 Dense Vector Data Structure

+

The psb_T_vect_type data structure encapsulates the dense vectors in a way similar +to sparse matrices, i.e. including a base type psb_T_base_vect_type. The user will +not, in general, access the vector components directly, but rather via the routines of +sec. 6. Among other simple things, we define here an extraction method that +can be used to get a full copy of the part of the vector stored on the local +process. +

The type declaration is shown in figure 5 where T is a placeholder for the data +type and precision variants +

+I
Integer; +
+S
Single precision real; +
+D
Double precision real; +
+C
Single precision complex; +
+Z
Double precision complex.
+

The actual data is contained in the polymorphic component v%v; the separation between +the application and the actual data is essential for cases where it is necessary to link +to data storage made available elsewhere outside the direct control of the +compiler/application, e.g. data stored in a graphics accelerator’s private memory. +

+
+

+

+  type psb_T_base_vect_type + 
    TYPE(KIND_), allocatable :: v(:) + 
  end type psb_T_base_vect_type + 
+ 
  type psb_T_vect_type + 
    class(psb_T_base_vect_type), allocatable :: v + 
  end type  psb_T_vect_type + 
+
+

+ + + +
Figure 5: The PSBLAS defined data type that contains a dense vector.
+

+

+

3.3.1 Vector Methods
+

+

3.3.2 get_nrows — Get number of rows in a dense vector
+ + + +
+nr = v%get_nrows() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+v
the dense vector
Scope: local
+

+

+On Return
+
+Function value
The number of rows of dense vector v.
+

+

3.3.3 sizeof — Get memory occupation in bytes of a dense vector
+ + + +
+memory_size = v%sizeof() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+v
the dense vector
Scope: local
+

+

+On Return
+
+Function value
The memory occupation in bytes.
+

+

3.3.4 set — Set contents of the vector
+ + + +
+ call  v%set(alpha[,first,last]) + 
 call  v%set(vect[,first,last]) + 
 call  v%zero() +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+v
the dense vector
Scope: local
+
+alpha
A scalar value.
Scope: local
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 1. +
+first,last
Boundaries for setting in the vector.
Scope: local
Type: optional
Intent: in.
Specified as: integers. +
+vect
An array
Scope: local
Type: required
Intent: in.
Specified as: a number of the data type indicated in Table 1.
+

Note that a call to v%zero() is provided as a shorthand, but is equivalent to a call +to v%set(zero) with the zero constant having the appropriate type and +kind. +

+

+On Return
+
+v
the dense vector, with updated entries
Scope: local
+ + + +

+

3.3.5 get_vect — Get a copy of the vector contents
+ + + +
+extv = v%get_vect([n]) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+v
the dense vector
Scope: local
+
+n
Size to be returned
Scope: local.
Type: optional; default: entire vector.
+
+

+

+On Return
+
+Function value
An allocatable array holding a copy of the dense vector + contents. If the argument n is specified, the size of the returned array + equals the minimum between n and the internal size of the vector, or 0 if + n is negative; otherwise, the size of the array is the same as the internal + size of the vector.
+

+

3.3.6 clone — Clone current object
+ + + +
+call  x%clone(y,info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+x
the dense vector.
Scope: local.
+

+

+On Return
+
+y
A copy of the input object. +
+info
Return code.
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu70.html b/docs/html/userhtmlsu70.html new file mode 100644 index 00000000..4a8fda93 --- /dev/null +++ b/docs/html/userhtmlsu70.html @@ -0,0 +1,125 @@ + + +psb_amn — Global minimum absolute value + + + + + + + +

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+

7.14 psb_amn — Global minimum absolute value

+ + + +
+call psb_amn(icontxt, dat, root) +
+

+

This subroutine implements a minimum absolute value reduction operation based +on the underlying communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global minimum.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +
+root
Process to hold the final value, or -1 to make it available on all processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.
+

+

+On Return
+
+dat
On destination process(es), the result of the minimum operation.
Scope: global.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array.
Type, kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +
    2. +
  2. The dat argument may also be a long integer scalar.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu71.html b/docs/html/userhtmlsu71.html new file mode 100644 index 00000000..11cd03ac --- /dev/null +++ b/docs/html/userhtmlsu71.html @@ -0,0 +1,141 @@ + + +psb_nrm2 — Global 2-norm reduction + + + + + + + +

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+

7.15 psb_nrm2 — Global 2-norm reduction

+ + + +
+call psb_nrm2(icontxt, dat, root) +
+

+

This subroutine implements a 2-norm value reduction operation based on the +underlying communication library. +

+Type:
Synchronous. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The local contribution to the global minimum.
Scope: local.
Type: required.
Intent: inout.
Specified as: a real variable, which may be a scalar, or a rank 1 array. +  Kind, rank and size must agree on all processes. +
+root
Process to hold the final value, or -1 to make it available on all processes.
Scope: global.
Type: optional.
Intent: in.
Specified as: an integer value -1 <= root <= np - 1, default -1.
+

+

+On Return
+
+dat
On destination process(es), the result of the 2-norm reduction.
Scope: global.
Type: required.
Intent: inout.
Specified as: a real variable, which may be a scalar, or a rank 1 array.
Kind, rank and size must agree on all processes.
+

Notes + + + +

    +
  1. This reduction is appropriate to compute the results of multiple (local) + NRM2 operations at the same time. +
    2. +
  2. Denoting by dati the value of the variable dat on process i, the output res + is equivalent to the computation of +
    + ∘ ------- + ∑ 2 +res = dati, + i +
    +

    with care taken to avoid unnecessary overflow. +

    3. +
  3. The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu72.html b/docs/html/userhtmlsu72.html new file mode 100644 index 00000000..c4e31009 --- /dev/null +++ b/docs/html/userhtmlsu72.html @@ -0,0 +1,129 @@ + + +psb_snd — Send data + + + + + + + +

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+

7.16 psb_snd — Send data

+ + + +
+call psb_snd(icontxt, dat, dst, m) +
+

+

This subroutine sends a packet of data to a destination. +

+Type:
Synchronous: see usage notes. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+dat
The data to be sent.
Scope: local.
Type: required.
Intent: in.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array, or a character or logical scalar.  Type, kind and + rank must agree on sender and receiver process; if m is not specified, size + must agree as well. +
+dst
Destination process.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer value 0 <= dst <= np - 1.
+
+m
Number of rows.
Scope: global.
Type: Optional.
Intent: in.
Specified as: an integer value 0 <= m <= size(dat,1).
When dat is a rank 2 array, specifies the number of rows to be sent + independently of the leading dimension size(dat,1); must have the same + value on sending and receiving processes.
+

+

+On Return
+ + + +

Notes +

    +
  1. This subroutine implies a synchronization, but only between the calling + process and the destination process dst.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu73.html b/docs/html/userhtmlsu73.html new file mode 100644 index 00000000..58de2fb4 --- /dev/null +++ b/docs/html/userhtmlsu73.html @@ -0,0 +1,124 @@ + + +psb_rcv — Receive data + + + + + + + +

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+

7.17 psb_rcv — Receive data

+ + + +
+call psb_rcv(icontxt, dat, src, m) +
+

+

This subroutine receives a packet of data to a destination. +

+Type:
Synchronous: see usage notes. +
+On Entry
+
+icontxt
the communication context identifying the virtual parallel machine.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer variable. +
+src
Source process.
Scope: global.
Type: required.
Intent: in.
Specified as: an integer value 0 <= src <= np - 1.
+
+m
Number of rows.
Scope: global.
Type: Optional.
Intent: in.
Specified as: an integer value 0 <= m <= size(dat,1).
When dat is a rank 2 array, specifies the number of rows to be sent + independently of the leading dimension size(dat,1); must have the same + value on sending and receiving processes.
+

+

+On Return
+
+dat
The data to be received.
Scope: local.
Type: required.
Intent: inout.
Specified as: an integer, real or complex variable, which may be a scalar, + or a rank 1 or 2 array, or a character or logical scalar.  Type, kind and + rank must agree on sender and receiver process; if m is not specified, size + must agree as well.
+ + + +

Notes +

    +
  1. This subroutine implies a synchronization, but only between the calling + process and the source process src.
+ + + +

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+

+ diff --git a/docs/html/userhtmlsu74.html b/docs/html/userhtmlsu74.html new file mode 100644 index 00000000..e9a4bf75 --- /dev/null +++ b/docs/html/userhtmlsu74.html @@ -0,0 +1,93 @@ + + +psb_errpush — Pushes an error code onto the error stack + + + + + + + +

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+

8.1 psb_errpush — Pushes an error code onto the error stack

+ +
call psb_errpush(err_c, r_name, i_err, a_err) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+err_c
the error code
Scope: local
Type: required
Intent: in.
Specified as: an integer. +
+r_name
the soutine where the error has been caught.
Scope: local
Type: required
Intent: in.
Specified as: a string.
+
+i_err
addional info for error code
Scope: local
Type: optional
Specified as: an integer array
+
+a_err
addional info for error code
Scope: local
Type: optional
Specified as: a string.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu75.html b/docs/html/userhtmlsu75.html new file mode 100644 index 00000000..b4726464 --- /dev/null +++ b/docs/html/userhtmlsu75.html @@ -0,0 +1,61 @@ + + +psb_error — Prints the error stack content and aborts execution + + + + + + + +

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+

8.2 psb_error — Prints the error stack content and aborts execution

+ +
call psb_error(icontxt) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context.
Scope: global
Type: optional
Intent: in.
Specified as: an integer.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu76.html b/docs/html/userhtmlsu76.html new file mode 100644 index 00000000..218404fa --- /dev/null +++ b/docs/html/userhtmlsu76.html @@ -0,0 +1,61 @@ + + +psb_set_errverbosity — Sets the verbosity of error messages + + + + + + + +

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+

8.3 psb_set_errverbosity — Sets the verbosity of error messages

+ +
call psb_set_errverbosity(v) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+v
the verbosity level
Scope: global
Type: required
Intent: in.
Specified as: an integer.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu77.html b/docs/html/userhtmlsu77.html new file mode 100644 index 00000000..e1e62e1b --- /dev/null +++ b/docs/html/userhtmlsu77.html @@ -0,0 +1,63 @@ + + +psb_set_erraction — Set the type of action to be taken upon error condition + + + + + + + +

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+

8.4 psb_set_erraction — Set the type of action to be taken upon error +condition

+ +
call psb_set_erraction(err_act) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+err_act
the type of action.
Scope: global
Type: required
Intent: in.
Specified as: an integer. Possible values: psb_act_ret, psb_act_abort.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu78.html b/docs/html/userhtmlsu78.html new file mode 100644 index 00000000..d7e6fd9f --- /dev/null +++ b/docs/html/userhtmlsu78.html @@ -0,0 +1,110 @@ + + + hb_read — Read a sparse matrix from a file in the Harwell–Boeing +format + + + + + + + +

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+

9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing +format

+ +
call hb_read(a, iret, iunit, filename, b, mtitle) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+filename
The name of the file to be read.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -.
+

+

+On Return
+
+a
the sparse matrix read from file.
Type:required.
Specified as: a structured data of type psb_Tspmat_type. + + + +
+b
Rigth hand side(s).
Type: Optional
An array of type real or complex, rank 2 and having the ALLOCATABLE + attribute; will be allocated and filled in if the input file contains a right + hand side, otherwise will be left in the UNALLOCATED state. +
+mtitle
Matrix title.
Type: Optional
A charachter variable of length 72 holding a copy of the matrix title as + specified by the Harwell-Boeing format and contained in the input file. +
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu79.html b/docs/html/userhtmlsu79.html new file mode 100644 index 00000000..47418d21 --- /dev/null +++ b/docs/html/userhtmlsu79.html @@ -0,0 +1,121 @@ + + +hb_write — Write a sparse matrix to a file in the Harwell–Boeing format + + + + + + + +

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+

9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing +format

+ +
call hb_write(a, iret, iunit, filename, key, rhs, mtitle) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix to be written.
Type:required.
Specified as: a structured data of type psb_Tspmat_type. +
+b
Rigth hand side.
Type: Optional
An array of type real or complex, rank 1 and having the ALLOCATABLE + attribute; will be allocated and filled in if the input file contains a right + hand side. +
+filename
The name of the file to be written to.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default output unit 6 (i.e. standard output in Unix jargon) + is used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -. +
+key
Matrix key.
Type: Optional
A charachter variable of length 8 holding the matrix key as specified by + the Harwell-Boeing format and to be written to file. + + + +
+mtitle
Matrix title.
Type: Optional
A charachter variable of length 72 holding the matrix title as specified by + the Harwell-Boeing format and to be written to file.
+

+

+On Return
+
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu8.html b/docs/html/userhtmlsu8.html new file mode 100644 index 00000000..5c0ff71c --- /dev/null +++ b/docs/html/userhtmlsu8.html @@ -0,0 +1,71 @@ + + +Preconditioner data structure + + + + + + + +

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+

3.4 Preconditioner data structure

+

Our base library offers support for simple well known preconditioners like Diagonal +Scaling or Block Jacobi with incomplete factorization ILU(0). +

A preconditioner is held in the psb_prec_type data structure reported in +figure 6. The psb_prec_type data type may contain a simple preconditioning matrix +with the associated communication descriptor.The internal preconditioner is +allocated appropriately with the dynamic type corresponding to the desired +preconditioner.

+ + + + + + + +
+

+

+ 
  type psb_Tprec_type + 
    class(psb_T_base_prec_type), allocatable :: prec + 
  end type psb_Tprec_type + 
+
+

+
Figure 6: The PSBLAS defined data type that contains a preconditioner.
+ + + +

+ + + +

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+

+ diff --git a/docs/html/userhtmlsu80.html b/docs/html/userhtmlsu80.html new file mode 100644 index 00000000..ee9c2c16 --- /dev/null +++ b/docs/html/userhtmlsu80.html @@ -0,0 +1,94 @@ + + +mm_mat_read — Read a sparse matrix from a file in the MatrixMarket +format + + + + + + + +

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+

9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket +format

+ +
call mm_mat_read(a, iret, iunit, filename) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+filename
The name of the file to be read.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -.
+

+

+On Return
+
+a
the sparse matrix read from file.
Type:required.
Specified as: a structured data of type psb_Tspmat_type. +
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu81.html b/docs/html/userhtmlsu81.html new file mode 100644 index 00000000..7bcaa337 --- /dev/null +++ b/docs/html/userhtmlsu81.html @@ -0,0 +1,93 @@ + + +mm_array_read — Read a dense array from a file in the MatrixMarket +format + + + + + + + +

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+

9.4 mm_array_read — Read a dense array from a file in the MatrixMarket +format

+ +
call mm_array_read(b, iret, iunit, filename) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+filename
The name of the file to be read.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -.
+

+

+On Return
+
+b
Rigth hand side(s).
Type: required
An array of type real or complex, rank 1 or 2 and having the + ALLOCATABLE attribute; will be allocated and filled in if the input file + contains a right hand side, otherwise will be left in the UNALLOCATED + state. +
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu82.html b/docs/html/userhtmlsu82.html new file mode 100644 index 00000000..eb9a66d0 --- /dev/null +++ b/docs/html/userhtmlsu82.html @@ -0,0 +1,105 @@ + + +mm_mat_write — Write a sparse matrix to a file in the MatrixMarket +format + + + + + + + +

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+

9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket +format

+ +
call mm_mat_write(a, mtitle, iret, iunit, filename) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+a
the sparse matrix to be written.
Type:required.
Specified as: a structured data of type psb_Tspmat_type. +
+mtitle
Matrix title.
Type: required
A charachter variable holding a descriptive title for the matrix to be + written to file. +
+filename
The name of the file to be written to.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default output unit 6 (i.e. standard output in Unix jargon) + is used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -.
+

+

+On Return
+
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu83.html b/docs/html/userhtmlsu83.html new file mode 100644 index 00000000..68d93ce9 --- /dev/null +++ b/docs/html/userhtmlsu83.html @@ -0,0 +1,88 @@ + + +mm_array_write — Write a dense array from a file in the MatrixMarket +format + + + + + + + +

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+

9.6 mm_array_write — Write a dense array from a file in the MatrixMarket +format

+ +
call mm_array_write(b, iret, iunit, filename) + +
+

+

+Type:
Asynchronous. +
+On Entry
+
+b
Rigth hand side(s).
Type: required
An array of type real or complex, rank 1 or 2; will be written..  +
+filename
The name of the file to be written.
Type:optional.
Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +
+iunit
The Fortran file unit number.
Type:optional.
Specified as: an integer value. Only meaningful if filename is not -.
+

+

+On Return
+
+iret
Error code.
Type: required
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu84.html b/docs/html/userhtmlsu84.html new file mode 100644 index 00000000..627c4fd6 --- /dev/null +++ b/docs/html/userhtmlsu84.html @@ -0,0 +1,125 @@ + + +init — Initialize a preconditioner + + + + + + + +

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+

10.1 init — Initialize a preconditioner

+ + + +
+call prec%init(icontxt,ptype, info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+icontxt
the communication context.
Scope:global.
Type:required.
Intent: in.
Specified as: an integer value. +
+ptype
the type of preconditioner. Scope: global
Type: required
Intent: in.
Specified as: a character string, see usage notes. +
+On Exit
+
+prec
Scope: local
Type: required
Intent: inout.
Specified as: a preconditioner data structure psb_prec_type. +
+info
Scope: global
Type: required
Intent: out.
Error code: if no error, 0 is returned.
+

Notes Legal inputs to this subroutine are interpreted depending on the ptype string as +follows4 : +

+NONE
No preconditioning, i.e. the preconditioner is just a copy operator. +
+DIAG
Diagonal scaling; each entry of the input vector is multiplied by the + reciprocal of the sum of the absolute values of the coefficients in the + corresponding row of matrix A; + + + +
+BJAC
Precondition by a factorization of the block-diagonal of matrix A, + where block boundaries are determined by the data allocation boundaries + for each process; requires no communication. Only the incomplete + factorization ILU(0) is currently implemented.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu85.html b/docs/html/userhtmlsu85.html new file mode 100644 index 00000000..a8b076fd --- /dev/null +++ b/docs/html/userhtmlsu85.html @@ -0,0 +1,186 @@ + + +build — Builds a preconditioner + + + + + + + +

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+

10.2 build — Builds a preconditioner

+ + + +
+call prec%build(a, desc_a, info[,amold,vmold,imold]) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+a
the system sparse matrix. Scope: local
Type: required
Intent: in, target.
Specified as: a sparse matrix data structure psb_Tspmat_type. +
+prec
the preconditioner.
Scope: local
Type: required
Intent: inout.
Specified as: an already initialized precondtioner data structure + psb_prec_type
+
+desc_a
the problem communication descriptor. Scope: local
Type: required
Intent: in, target.
Specified as: a communication descriptor data structure psb_desc_type. +
+amold
The desired dynamic type for the internal matrix storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from psb_T_base_sparse_mat. +
+vmold
The desired dynamic type for the internal vector storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from psb_T_base_vect_type. +
+imold
The desired dynamic type for the internal integer vector storage.
Scope: local.
Type: optional.
Intent: in.
Specified as: an object of a class derived from (integer) + psb_T_base_vect_type.
+

+

+On Return
+
+prec
the preconditioner.
Scope: local
Type: required
Intent: inout.
Specified as: a precondtioner data structure psb_prec_type
+
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+

The amold, vmold and imold arguments may be employed to interface with special +devices, such as GPUs and other accelerators. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu86.html b/docs/html/userhtmlsu86.html new file mode 100644 index 00000000..49e92286 --- /dev/null +++ b/docs/html/userhtmlsu86.html @@ -0,0 +1,149 @@ + + +apply — Preconditioner application routine + + + + + + + +

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+

10.3 apply — Preconditioner application routine

+ + + +
+call prec%apply(x,y,desc_a,info,trans,work) + 
call prec%apply(x,desc_a,info,trans) +
+

+

+

+Type:
Synchronous. +
+On Entry
+
+prec
the preconditioner. Scope: local
Type: required
Intent: in.
Specified as: a preconditioner data structure psb_prec_type. +
+x
the source vector. Scope: local
Type: required
Intent: inout.
Specified as: a rank one array or an object of type psb_T_vect_type. +
+desc_a
the problem communication descriptor. Scope: local
Type: required
Intent: in.
Specified as: a communication data structure psb_desc_type. +
+trans
Scope:
Type: optional
Intent: in.
Specified as: a character. +
+work
an optional work space Scope: local
Type: optional
Intent: inout.
Specified as: a double precision array.
+

+

+On Return
+
+y
the destination vector. Scope: local
Type: required
Intent: inout.
Specified as: a rank one array or an object of type psb_T_vect_type. + + + +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu87.html b/docs/html/userhtmlsu87.html new file mode 100644 index 00000000..25207037 --- /dev/null +++ b/docs/html/userhtmlsu87.html @@ -0,0 +1,91 @@ + + +descr — Prints a description of current preconditioner + + + + + + + +

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+

10.4 descr — Prints a description of current preconditioner

+ + + +
+call prec%descr() + 
call prec%descr(iout, root) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+prec
the preconditioner. Scope: local
Type: required
Intent: in.
Specified as: a preconditioner data structure psb_prec_type. +
+iout
output unit. Scope: local
Type: optional
Intent: in.
Specified as: an integer number. Default: default output unit. +
+root
Process from which to print Scope: local
Type: optional
Intent: in.
Specified as: an integer number between 0 and np - 1, in which case + the specified process will print the description, or -1, in which case all + processes will print. Default: 0.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu88.html b/docs/html/userhtmlsu88.html new file mode 100644 index 00000000..1478c831 --- /dev/null +++ b/docs/html/userhtmlsu88.html @@ -0,0 +1,69 @@ + + +clone — clone current preconditioner + + + + + + + +

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+

10.5 clone — clone current preconditioner

+ + + +
+call  prec%clone(precout,info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+prec
the preconditioner.
Scope: local.
+

+

+On Return
+
+precout
A copy of the input object. +
+info
Return code.
+ + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu89.html b/docs/html/userhtmlsu89.html new file mode 100644 index 00000000..7d0b20b2 --- /dev/null +++ b/docs/html/userhtmlsu89.html @@ -0,0 +1,94 @@ + + +free — Free a preconditioner + + + + + + + +

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+

10.6 free — Free a preconditioner

+ + + +
+call prec%free(info) +
+

+

+

+Type:
Asynchronous. +
+On Entry
+
+prec
the preconditioner.
Scope: local.
Type: required
Intent: inout.
Specified as: a preconditioner data structure psb_prec_type. +
+On Exit
+
+prec
Scope: local
Type: required
Intent: inout.
Specified as: a preconditioner data structure psb_prec_type. +
+info
Scope: global
Type: required
Intent: out.
Error code: if no error, 0 is returned.
+

Notes Releases all internal storage. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu9.html b/docs/html/userhtmlsu9.html new file mode 100644 index 00000000..e78edec3 --- /dev/null +++ b/docs/html/userhtmlsu9.html @@ -0,0 +1,79 @@ + + +Heap data structure + + + + + + + +

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+

3.5 Heap data structure

+

Among the tools routines of sec. 6, we have a number of sorting utilities; the heap +sort is implemented in terms of heaps having the following signatures: +

+psb_T_heap
: a heap containing elements of type T, where T can be i,s,c,d,z + for integer, real and complex data; +
+psb_T_idx_heap
: a heap containing elements of type T, as above, together + with an integer index.
+

Given a heap object, the following methods are defined on it: +

+init
Initialize memory; also choose ascending or descending order; +
+howmany
Current heap occupancy; +
+insert
Add an item (or an item and its index); +
+get_first
Remove and return the first element; +
+dump
Print on file; +
+free
Release memory.
+

These objects are used in MLD2P4 to implement the factorization algorithms. + + + + + + +

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+

+ diff --git a/docs/html/userhtmlsu90.html b/docs/html/userhtmlsu90.html new file mode 100644 index 00000000..137cfae2 --- /dev/null +++ b/docs/html/userhtmlsu90.html @@ -0,0 +1,361 @@ + + +psb_krylov — Krylov Methods Driver Routine + + + + + + + +

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+

11.1 psb_krylov — Krylov Methods Driver Routine

+

This subroutine is a driver that provides a general interface for all the Krylov-Subspace +family methods implemented in PSBLAS version 2. +

The stopping criterion can take the following values: +

+1
normwise backward error in the infinity norm; the iteration is stopped when +
+ err = -----∥ri∥------< eps + (∥A ∥∥xi∥ + ∥b∥) +
+

+

+2
Relative residual in the 2-norm; the iteration is stopped when +
+ err = ∥ri∥-< eps + ∥b∥2 +
+

+

+3
Relative residual reduction in the 2-norm; the iteration is stopped when +
+ err = -∥ri∥-< eps + ∥r0∥2 +
+

+

The behaviour is controlled by the istop argument (see later). In the above formulae, xi +is the tentative solution and ri = b - Axi the corresponding residual at the i-th +iteration. + +

call psb_krylov(method,a,prec,b,x,eps,desc_a,info,& 
     & itmax,iter,err,itrace,irst,istop,cond) + +
+

+ + + +

+Type:
Synchronous. +
+On Entry
+
+method
a string that defines the iterative method to be used. Supported values + are: +
+ CG:
the Conjugate Gradient method; +
+ CGS:
the Conjugate Gradient Stabilized method; +
+ GCR:
the Generalized Conjugate Residual method; +
+ FCG:
the Flexible Conjugate Gradient method5 ; +
+ BICG:
the Bi-Conjugate Gradient method; +
+ BICGSTAB:
the Bi-Conjugate Gradient Stabilized method; +
+ BICGSTABL:
the Bi-Conjugate Gradient Stabilized method with + restarting; +
+ RGMRES:
the Generalized Minimal Residual method with restarting.
+
+a
the local portion of global sparse matrix A.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_Tspmat_type. +
+prec
The data structure containing the preconditioner.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_prec_type. +
+b
The RHS vector.
Scope: local
Type: required
Intent: in.
Specified as: a rank one array or an object of type psb_T_vect_type. + + + +
+x
The initial guess.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one array or an object of type psb_T_vect_type. +
+eps
The stopping tolerance.
Scope: global
Type: required
Intent: in.
Specified as: a real number. +
+desc_a
contains data structures for communications.
Scope: local
Type: required
Intent: in.
Specified as: a structured data of type psb_desc_type. +
+itmax
The maximum number of iterations to perform.
Scope: global
Type: optional
Intent: in.
Default: itmax = 1000.
Specified as: an integer variable itmax ≥ 1. +
+itrace
If > 0 print out an informational message about convergence every itrace + iterations. If = 0 print a message in case of convergence failure.
Scope: global
Type: optional
Intent: in.
Default: itrace = -1.
+
+irst
An integer specifying the restart parameter.
Scope: global
Type: optional.
Intent: in.
Values: irst > 0. This is employed for the BiCGSTABL or RGMRES methods, + otherwise it is ignored. +
+istop
An integer specifying the stopping criterion.
Scope: global
Type: optional.
Intent: in.
Values: 1: use the normwise backward error, 2: use the scaled 2-norm + + + + of the residual, 3: use the residual reduction in the 2-norm. Default: + 2. +
+On Return
+
+x
The computed solution.
Scope: local
Type: required
Intent: inout.
Specified as: a rank one array or an object of type psb_T_vect_type. +
+iter
The number of iterations performed.
Scope: global
Type: optional
Intent: out.
Returned as: an integer variable. +
+err
The convergence estimate on exit.
Scope: global
Type: optional
Intent: out.
Returned as: a real number. +
+cond
An estimate of the condition number of matrix A; only available with the CG + method on real data.
Scope: global
Type: optional
Intent: out.
Returned as: a real number. A correct result will be greater than or + equal to one; if specified for non-real data, or an error occurred, zero is + returned. +
+info
Error code.
Scope: local
Type: required
Intent: out.
An integer value; 0 means no error has been detected.
+ + + + + + +

+ + + +

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+

+ diff --git a/docs/psblas-3.6.pdf b/docs/psblas-3.7.pdf similarity index 74% rename from docs/psblas-3.6.pdf rename to docs/psblas-3.7.pdf index 03e4ad20..4da4c8d6 100644 --- a/docs/psblas-3.6.pdf +++ b/docs/psblas-3.7.pdf @@ -4,24 +4,24 @@ << /Type /ObjStm /N 100 -/First 818 -/Length 4691 +/First 819 +/Length 6377 >> stream 1 0 5 38 6 77 9 117 10 144 13 185 14 217 17 263 18 299 21 345 22 379 25 425 26 464 29 515 30 562 33 608 34 643 37 684 38 727 41 773 -42 816 45 867 46 905 49 947 50 981 53 1023 54 1057 57 1099 58 1134 61 1176 -62 1211 65 1253 66 1291 69 1333 70 1361 73 1403 74 1422 77 1464 78 1481 81 1524 -82 1576 85 1619 86 1671 89 1722 90 1757 93 1803 94 1840 97 1891 98 1932 101 1975 -102 2002 105 2046 106 2073 109 2117 110 2146 113 2190 114 2217 117 2261 118 2283 121 2327 -122 2353 125 2397 126 2444 129 2488 130 2555 133 2599 134 2619 137 2663 138 2684 141 2728 -142 2757 145 2801 146 2827 149 2871 150 2898 153 2942 154 2961 157 3005 158 3024 161 3068 -162 3111 165 3155 166 3175 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207.304 543.314 cm +1 0 0 1 207.304 543.167 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 210.293 543.115 Td [(ro)28(ws)]TJ +/F8 9.9626 Tf 210.293 542.968 Td [(ro)28(ws)-334(|)-333(Get)-333(n)28(um)27(b)-27(er)-334(of)-333(lo)-28(cal)-333(ro)28(ws)]TJ 0 g 0 G - [-411(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-893(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-1084(12)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -40.659 -12.08 Td [(get)]TJ + -72.54 -12.091 Td [(3.1.3)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 531.235 cm +1 0 0 1 183.515 531.076 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 531.035 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 186.504 530.877 Td [(lo)-28(cal)]TJ ET q -1 0 0 1 207.304 531.235 cm +1 0 0 1 207.304 531.076 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 210.293 531.035 Td [(cols)]TJ +/F8 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446.478 Td [(get)]TJ +/F8 9.9626 Tf 201.769 422.194 Td [(set)]TJ ET q -1 0 0 1 215.65 446.677 cm +1 0 0 1 214.599 422.393 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 218.639 446.478 Td [(large)]TJ +/F8 9.9626 Tf 217.588 422.194 Td [(large)]TJ ET q -1 0 0 1 240.297 446.677 cm +1 0 0 1 239.245 422.393 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 243.286 446.478 Td [(threshold)]TJ +/F8 9.9626 Tf 242.234 422.194 Td [(threshold)-228(|)-227(Set)-228(threshold)-227(for)-228(index)-227(map-)]TJ -72.6 -11.956 Td [(ping)-333(switc)27(h)]TJ 0 g 0 G - [-460(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-716(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-1084(14)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -73.652 -12.08 Td [(psb)]TJ + -31.881 -12.091 Td [(3.1.12)-644(ge)-1(t)]TJ ET q -1 0 0 1 185.231 434.597 cm +1 0 0 1 183.515 398.347 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 188.22 434.398 Td [(cd)]TJ +/F8 9.9626 Tf 186.504 398.147 Td [(p)]TJ ET q -1 0 0 1 198.78 434.597 cm +1 0 0 1 192.637 398.347 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 201.769 434.398 Td [(set)]TJ +/F8 9.9626 Tf 195.625 398.147 Td [(adjcncy)-333(|)-334(Get)-333(pro)-28(cess)-333(adjacency)-334(list)]TJ +0 g 0 G + [-697(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-1084(15)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -57.872 -12.091 Td [(3.1.13)-644(s)-1(et)]TJ ET q -1 0 0 1 214.599 434.597 cm +1 0 0 1 182.464 386.256 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 217.588 434.398 Td [(large)]TJ +/F8 9.9626 Tf 185.452 386.056 Td [(p)]TJ ET q -1 0 0 1 239.245 434.597 cm +1 0 0 1 191.585 386.256 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 242.234 434.398 Td [(threshold)]TJ +/F8 9.9626 Tf 194.574 386.056 Td [(adjcncy)-333(|)-334(Set)-333(pro)-28(cess)-333(adjacency)-333(list)]TJ 0 g 0 G - [-565(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-255(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(14)]TJ + [-1084(15)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -56.821 -12.091 Td [(3.1.14)-644(fnd)]TJ +ET +q +1 0 0 1 184.345 374.165 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 187.334 373.965 Td [(o)28(wner)-334(|)-333(Find)-333(the)-333(o)27(wner)-333(pro)-28(cess)-333(of)-334(a)-333(set)-333(of)-334(ind)1(ic)-1(es)]TJ +0 g 0 G + [-984(.)]TJ +0 g 0 G + [-1083(15)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -104.481 -12.08 Td [(3.1.2)-1144(Nam)-1(ed)-333(Constan)28(ts)]TJ + -49.581 -12.091 Td [(3.1.15)-644(Nam)-1(ed)-333(Constan)28(ts)]TJ 0 g 0 G [-1017(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(15)]TJ + [-1084(16)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -22.914 -12.08 Td [(3.2)-1022(Sparse)-334(Matri)1(x)-334(class)]TJ + -22.914 -12.091 Td [(3.2)-1022(Sparse)-334(Matri)1(x)-334(class)]TJ 0 g 0 G [-372(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(15)]TJ + [-1084(16)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 22.914 -12.079 Td [(3.2.1)-1144(Sparse)-334(Matrix)-333(Metho)-28(ds)]TJ + 22.914 -12.091 Td [(3.2.1)-1144(Sparse)-334(Matrix)-333(Metho)-28(ds)]TJ 0 g 0 G [-844(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(16)]TJ + [-1084(17)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 31.881 -12.08 Td [(get)]TJ + 0 -12.091 Td [(3.2.2)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 386.278 cm +1 0 0 1 183.515 325.801 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 386.079 Td [(nro)28(ws)]TJ +/F8 9.9626 Tf 186.504 325.601 Td [(nro)28(ws)-334(|)-333(Get)-333(n)28(um)27(b)-27(er)-334(of)-333(ro)28(ws)-334(in)-333(a)-333(sparse)-334(matrix)]TJ 0 g 0 G - [-687(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ + [-707(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(16)]TJ + [-1084(17)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.08 Td [(get)]TJ + -48.751 -12.091 Td [(3.2.3)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 374.199 cm +1 0 0 1 183.515 313.71 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 373.999 Td [(ncols)]TJ +/F8 9.9626 Tf 186.504 313.51 Td [(ncols)-333(|)-334(Get)-333(n)28(um)27(b)-27(er)-334(of)-333(columns)-333(in)-334(a)-333(sparse)-333(matrix)]TJ 0 g 0 G - [-273(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-269(.)-500(.)]TJ 0 g 0 G - [-1084(16)]TJ + [-1084(17)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.079 Td [(get)]TJ + -48.751 -12.091 Td [(3.2.4)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 362.119 cm +1 0 0 1 183.515 301.619 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 361.92 Td [(nnzeros)]TJ +/F8 9.9626 Tf 186.504 301.419 Td [(nnzeros)-231(|)-231(Get)-231(n)28(um)28(b)-28(er)-231(of)-230(nonzero)-231(elemen)27(t)1(s)-231(in)-231(a)-231(sparse)]TJ -16.87 -11.955 Td [(matrix)]TJ 0 g 0 G - [-715(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-441(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(17)]TJ + [-1083(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.08 Td [(get)]TJ + -31.881 -12.091 Td [(3.2.5)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 350.039 cm +1 0 0 1 183.515 277.572 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 349.84 Td [(size)]TJ +/F8 9.9626 Tf 186.504 277.373 Td [(size)-331(|)-332(Get)-331(maxim)28(um)-331(n)28(um)27(b)-27(er)-332(of)-331(nonzero)-331(elemen)28(ts)-332(in)]TJ -16.87 -11.955 Td [(a)-333(sparse)-334(matrix)]TJ 0 g 0 G - [-884(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-483(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(17)]TJ + [-1084(18)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.08 Td [(sizeof)]TJ + -31.881 -12.091 Td [(3.2.6)-1144(s)-1(i)1(z)-1(eof)-266(|)-266(Get)-266(memory)-267(o)-27(cc)-1(u)1(pation)-267(in)-266(b)28(ytes)-266(of)-267(a)-266(sparse)-266(matrix)]TJ 0 g 0 G - [-994(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ 0 g 0 G - [-1084(18)]TJ + [-550(19)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 0 -12.079 Td [(get)]TJ + 0 -12.091 Td [(3.2.7)-1144(ge)-1(t)]TJ ET q -1 0 0 1 183.515 325.88 cm +1 0 0 1 183.515 241.435 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 325.681 Td [(fm)28(t)]TJ +/F8 9.9626 Tf 186.504 241.236 Td [(fm)28(t)-334(|)-333(Short)-333(description)-333(of)-334(the)-333(dynamic)-333(t)27(yp)-27(e)]TJ 0 g 0 G - [-946(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-518(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G - [-1084(18)]TJ + [-1084(19)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.08 Td [(is)]TJ + -48.751 -12.091 Td [(3.2.8)-1144(is)]TJ ET q -1 0 0 1 176.929 313.8 cm +1 0 0 1 176.929 229.344 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 179.918 313.601 Td [(bld,)-333(is)]TJ +/F8 9.9626 Tf 179.918 229.145 Td [(bld,)-333(is)]TJ ET q -1 0 0 1 207.138 313.8 cm +1 0 0 1 207.138 229.344 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 210.127 313.601 Td [(up)-28(d,)-333(is)]TJ +/F8 9.9626 Tf 210.127 229.145 Td [(up)-28(d,)-333(is)]TJ ET q -1 0 0 1 240.391 313.8 cm +1 0 0 1 240.391 229.344 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 243.38 313.601 Td [(asb)]TJ +/F8 9.9626 Tf 243.38 229.145 Td [(asb)-333(|)-334(Status)-333(c)28(hec)28(k)]TJ 0 g 0 G - [-731(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-587(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(18)]TJ + [-1084(19)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -73.746 -12.08 Td [(is)]TJ + -105.626 -12.091 Td [(3.2.9)-1144(is)]TJ ET q -1 0 0 1 176.929 301.72 cm +1 0 0 1 176.929 217.253 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 179.918 301.521 Td [(lo)28(w)28(er,)-334(is)]TJ +/F8 9.9626 Tf 179.918 217.054 Td [(lo)28(w)28(er,)-334(is)]TJ ET q -1 0 0 1 216.021 301.72 cm +1 0 0 1 216.021 217.253 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 219.01 301.521 Td [(upp)-28(er,)-333(is)]TJ +/F8 9.9626 Tf 219.01 217.054 Td [(upp)-28(er,)-333(is)]TJ ET q -1 0 0 1 257.604 301.72 cm +1 0 0 1 257.604 217.253 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 260.593 301.521 Td [(triangle,)-333(is)]TJ +/F8 9.9626 Tf 260.593 217.054 Td [(triangle,)-333(is)]TJ ET q -1 0 0 1 307.213 301.72 cm +1 0 0 1 307.213 217.253 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 310.202 301.521 Td [(unit)]TJ +/F8 9.9626 Tf 310.201 217.054 Td [(unit)-333(|)-334(F)84(ormat)-334(c)28(hec)28(k)]TJ 0 g 0 G - [-696(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-929(.)-500(.)]TJ 0 g 0 G - [-1084(19)]TJ + [-1084(20)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -140.568 -12.08 Td [(cscn)28(v)]TJ + -172.448 -12.091 Td [(3.2.10)-644(c)-1(scn)28(v)-333(|)-333(Con)27(v)28(ert)-333(to)-334(a)-333(di\013eren)28(t)-333(storage)-334(format)]TJ 0 g 0 G - [-1022(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ + [-283(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G - [-1084(19)]TJ + [-1084(20)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 0 -12.079 Td [(csclip)]TJ + 0 -12.091 Td [(3.2.11)-644(c)-1(sclip)-333(|)-333(Reduce)-334(to)-333(a)-333(submatrix)]TJ 0 g 0 G - [-967(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-972(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(20)]TJ + [-1083(21)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 0 -12.08 Td [(clean)]TJ + 0 -12.091 Td [(3.2.12)-644(c)-1(l)1(e)-1(an)]TJ ET q -1 0 0 1 192.371 265.481 cm +1 0 0 1 192.371 180.98 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 195.36 265.282 Td [(zeros)]TJ +/F8 9.9626 Tf 195.36 180.781 Td [(zeros)-333(|)-334(Eliminate)-333(zero)-333(co)-28(e\016cien)27(ts)]TJ 0 g 0 G - [-937(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-303(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(20)]TJ + [-1084(21)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -25.726 -12.08 Td [(get)]TJ + -57.607 -12.091 Td [(3.2.13)-644(ge)-1(t)]TJ ET q -1 0 0 1 183.515 253.402 cm +1 0 0 1 183.515 168.889 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 186.504 253.202 Td [(diag)]TJ +/F8 9.9626 Tf 186.504 168.69 Td [(diag)-333(|)-334(Get)-333(main)-333(diagonal)]TJ 0 g 0 G - [-612(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-938(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(21)]TJ + [-1084(22)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -16.87 -12.079 Td [(clip)]TJ + -48.751 -12.091 Td [(3.2.14)-644(c)-1(l)1(ip)]TJ ET q -1 0 0 1 185.729 241.322 cm +1 0 0 1 185.729 156.798 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 188.718 241.123 Td [(diag)]TJ +/F8 9.9626 Tf 188.718 156.599 Td [(diag)-333(|)-334(Cut)-333(out)-333(main)-334(d)1(iagonal)]TJ 0 g 0 G - [-390(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-446(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(21)]TJ + [-1084(22)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -19.084 -12.08 Td [(tril)]TJ + -50.965 -12.091 Td [(3.2.15)-644(tril)-334(|)-333(Return)-333(the)-334(lo)28(w)28(er)-333(triangle)]TJ 0 g 0 G - [-469(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-947(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(21)]TJ + [-1084(22)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - 0 -12.08 Td [(triu)]TJ + 0 -12.091 Td [(3.2.16)-644(triu)-334(|)-333(Return)-333(the)-334(upp)-27(er)-334(triangle)]TJ 0 g 0 G - 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[-584(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(47)]TJ + [-1084(48)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(4.13)-522(psb)]TJ ET q -1 0 0 1 181.246 490.928 cm +1 0 0 1 204.16 406.37 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 490.728 Td [(spsm)]TJ +/F8 9.9626 Tf 207.149 406.17 Td [(spsm)-333(|)-334(T)84(riangular)-334(System)-333(Solv)28(e)]TJ 0 g 0 G - [-929(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-284(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(49)]TJ + [-1084(50)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -33.53 -22.125 Td [(5)-925(Comm)32(unication)-383(r)-1(ou)1(t)-1(ines)]TJ -0 g 0 G - [-19454(52)]TJ -0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -12.08 Td [(psb)]TJ + -41.5 -12.079 Td [(4.14)-522(psb)]TJ ET q -1 0 0 1 181.246 456.722 cm +1 0 0 1 204.16 394.29 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 456.523 Td [(halo)]TJ +/F8 9.9626 Tf 207.149 394.091 Td [(gemlt)-333(|)-334(En)28(trywise)-333(Pro)-28(duct)]TJ 0 g 0 G - [-495(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-906(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-1084(53)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.08 Td [(4.15)-522(psb)]TJ ET q -1 0 0 1 181.246 444.643 cm +1 0 0 1 204.16 382.21 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 444.444 Td [(o)28(vrl)]TJ +/F8 9.9626 Tf 207.149 382.011 Td [(gediv)-333(|)-334(En)28(trywise)-333(Division)]TJ 0 g 0 G - [-659(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ + [-1015(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(56)]TJ + [-1084(55)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(4.16)-522(psb)]TJ ET q -1 0 0 1 181.246 432.563 cm +1 0 0 1 204.16 370.131 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 432.364 Td [(gather)]TJ +/F8 9.9626 Tf 207.149 369.931 Td [(gein)28(v)-334(|)-333(En)28(trywise)-333(In)27(v)28(ersion)]TJ 0 g 0 G - [-326(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-664(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(60)]TJ + [-1084(57)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG +/F27 9.9626 Tf -56.444 -22.125 Td [(5)-925(Comm)32(unication)-383(r)-1(ou)1(t)-1(ines)]TJ 0 g 0 G + [-19454(58)]TJ 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ +/F8 9.9626 Tf 14.944 -12.08 Td [(5.1)-1022(psb)]TJ ET q -1 0 0 1 181.246 420.483 cm +1 0 0 1 204.16 335.925 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 420.284 Td [(scatter)]TJ +/F8 9.9626 Tf 207.149 335.726 Td [(halo)-333(|)-334(Halo)-333(Data)-333(Comm)27(un)1(ic)-1(ati)1(o)-1(n)]TJ 0 g 0 G - [-932(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-320(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(62)]TJ + [-1084(59)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -33.53 -22.125 Td [(6)-925(Data)-383(managem)-1(e)1(n)31(t)-383(routines)]TJ -0 g 0 G - [-18205(64)]TJ -0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(5.2)-1022(psb)]TJ ET q -1 0 0 1 181.246 386.278 cm +1 0 0 1 204.16 323.846 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 386.079 Td [(cdall)]TJ +/F8 9.9626 Tf 207.149 323.647 Td [(o)28(vrl)-333(|)-334(Ov)28(erlap)-333(Up)-28(date)]TJ 0 g 0 G - [-273(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-579(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(64)]TJ + [-1084(62)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(5.3)-1022(psb)]TJ ET q -1 0 0 1 181.246 374.199 cm +1 0 0 1 204.16 311.766 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 373.999 Td [(cdins)]TJ +/F8 9.9626 Tf 207.149 311.567 Td [(gather)-333(|)-334(Gather)-333(Global)-333(Dense)-334(Matrix)]TJ 0 g 0 G - [-879(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-903(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(68)]TJ + [-1084(66)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.08 Td [(5.4)-1022(psb)]TJ ET q -1 0 0 1 181.246 362.119 cm +1 0 0 1 204.16 299.686 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 361.92 Td [(cdasb)]TJ +/F8 9.9626 Tf 207.149 299.487 Td [(scatter)-333(|)-334(Scatter)-333(Global)-333(Dense)-334(Matrix)]TJ +0 g 0 G + [-682(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-657(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1084(68)]TJ 0 g 0 G - [-1083(70)]TJ +0 0 1 rg 0 0 1 RG +/F27 9.9626 Tf -56.444 -22.125 Td [(6)-925(Data)-383(managem)-1(e)1(n)31(t)-383(routines)]TJ 0 g 0 G + [-18205(70)]TJ 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ +/F8 9.9626 Tf 14.944 -12.08 Td [(6.1)-1022(psb)]TJ ET q -1 0 0 1 181.246 350.039 cm +1 0 0 1 204.16 265.481 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 349.84 Td [(cdcp)28(y)]TJ +/F8 9.9626 Tf 207.149 265.282 Td [(cdall)-333(|)-334(Allo)-27(cates)-334(a)-333(comm)27(u)1(nication)-334(descriptor)]TJ 0 g 0 G - [-607(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-817(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(71)]TJ + [-1084(70)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.2)-1022(psb)]TJ ET q -1 0 0 1 181.246 337.96 cm +1 0 0 1 204.16 253.402 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 337.76 Td [(cdfree)]TJ +/F8 9.9626 Tf 207.149 253.202 Td [(cdins)-333(|)-334(Comm)28(unication)-333(descriptor)-333(inse)-1(r)1(t)-334(routine)]TJ 0 g 0 G - [-520(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ + [-861(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(72)]TJ + [-1084(74)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.079 Td [(6.3)-1022(psb)]TJ ET q -1 0 0 1 181.246 325.88 cm +1 0 0 1 204.16 241.322 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 325.681 Td [(cdbldext)]TJ +/F8 9.9626 Tf 207.149 241.123 Td [(cdasb)-333(|)-334(Comm)28(unication)-333(descriptor)-334(assem)28(bly)-333(routine)]TJ 0 g 0 G - [-912(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-748(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(73)]TJ + [-1084(76)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.4)-1022(psb)]TJ ET q -1 0 0 1 181.246 313.8 cm +1 0 0 1 204.16 229.242 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 313.601 Td [(spall)]TJ +/F8 9.9626 Tf 207.149 229.043 Td [(cdcp)28(y)-334(|)-333(Copies)-333(a)-334(comm)28(unication)-333(descriptor)]TJ 0 g 0 G - [-323(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-706(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(75)]TJ + [-1084(77)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.5)-1022(psb)]TJ ET q -1 0 0 1 181.246 301.72 cm +1 0 0 1 204.16 217.162 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 301.521 Td [(spins)]TJ +/F8 9.9626 Tf 207.149 216.963 Td [(cdfree)-333(|)-334(F)84(rees)-334(a)-333(comm)28(unication)-334(descriptor)]TJ 0 g 0 G - [-929(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-492(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(76)]TJ + [-1084(78)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.079 Td [(6.6)-1022(psb)]TJ ET q -1 0 0 1 181.246 289.641 cm +1 0 0 1 204.16 205.083 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 289.441 Td [(spasb)]TJ +/F8 9.9626 Tf 207.149 204.884 Td [(cdbldext)-333(|)-334(Build)-333(an)-333(extended)-333(co)-1(mm)28(unication)-333(descriptor)]TJ 0 g 0 G - [-707(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-614(.)-500(.)]TJ 0 g 0 G - [-1083(79)]TJ + [-1084(79)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.08 Td [(6.7)-1022(psb)]TJ ET q -1 0 0 1 181.246 277.561 cm +1 0 0 1 204.16 193.003 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 277.362 Td [(spfree)]TJ +/F8 9.9626 Tf 207.149 192.804 Td [(spall)-333(|)-334(Allo)-27(cates)-334(a)-333(sparse)-334(matrix)]TJ 0 g 0 G - [-570(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ + [-806(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)]TJ 0 g 0 G [-1084(81)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.8)-1022(psb)]TJ ET q -1 0 0 1 181.246 265.481 cm +1 0 0 1 204.16 180.923 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 265.282 Td [(sprn)]TJ +/F8 9.9626 Tf 207.149 180.724 Td [(spins)-333(|)-334(Insert)-333(a)-333(set)-334(of)-333(co)-28(e\016cien)28(ts)-334(in)28(to)-333(a)-333(sparse)-334(matrix)]TJ 0 g 0 G - [-431(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ + [-814(.)-500(.)-500(.)]TJ 0 g 0 G [-1084(82)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.9)-1022(psb)]TJ ET q -1 0 0 1 181.246 253.402 cm +1 0 0 1 204.16 168.844 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 253.202 Td [(geall)]TJ +/F8 9.9626 Tf 207.149 168.644 Td [(spasb)-333(|)-334(Sparse)-333(matrix)-333(assem)27(bly)-333(routine)]TJ 0 g 0 G - [-329(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-853(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(83)]TJ + [-1084(85)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.079 Td [(6.10)-522(psb)]TJ ET q -1 0 0 1 181.246 241.322 cm +1 0 0 1 204.16 156.764 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 241.123 Td [(geins)]TJ +/F8 9.9626 Tf 207.149 156.565 Td [(spfree)-333(|)-334(F)84(rees)-334(a)-333(sparse)-334(matri)1(x)]TJ 0 g 0 G - [-934(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-482(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(84)]TJ + [-1084(87)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.11)-522(psb)]TJ ET q -1 0 0 1 181.246 229.242 cm +1 0 0 1 204.16 144.684 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 229.043 Td [(geasb)]TJ +/F8 9.9626 Tf 207.149 144.485 Td [(sprn)-333(|)-334(Reinit)-333(sparse)-333(matrix)-334(structure)-333(for)-333(psblas)-333(routines.)]TJ 0 g 0 G - [-712(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1012(.)]TJ 0 g 0 G - [-1084(86)]TJ + [-1084(88)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ + -41.5 -12.08 Td [(6.12)-522(psb)]TJ ET q -1 0 0 1 181.246 217.162 cm +1 0 0 1 204.16 132.605 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 216.963 Td [(gefree)]TJ +/F8 9.9626 Tf 207.149 132.405 Td [(geall)-333(|)-334(Allo)-27(cates)-334(a)-333(dense)-334(matrix)]TJ 0 g 0 G - [-576(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-320(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(87)]TJ + [-1084(89)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.079 Td [(psb)]TJ + -41.5 -12.079 Td [(6.13)-522(psb)]TJ ET q -1 0 0 1 181.246 205.083 cm +1 0 0 1 204.16 120.525 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 204.884 Td [(gelp)]TJ +/F8 9.9626 Tf 207.149 120.326 Td [(geins)-333(|)-334(Dense)-333(matrix)-333(insertion)-334(routine)]TJ 0 g 0 G - [-551(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-656(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-1083(90)]TJ +0 g 0 G +0 g 0 G + 112.644 -29.888 Td [(ii)]TJ +0 g 0 G +ET + +endstream +endobj +738 0 obj +<< +/Length 17894 +>> +stream 0 g 0 G - [-1084(88)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -12.08 Td [(psb)]TJ +BT +/F8 9.9626 Tf 114.839 706.129 Td [(6.14)-522(psb)]TJ ET q -1 0 0 1 181.246 193.003 cm +1 0 0 1 153.351 706.328 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 192.804 Td [(glob)]TJ +/F8 9.9626 Tf 156.339 706.129 Td [(geasb)-333(|)-334(Assem)28(bly)-333(a)-334(dense)-333(matrix)]TJ +0 g 0 G + [-559(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-1084(92)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -41.5 -12.382 Td [(6.15)-522(psb)]TJ ET q -1 0 0 1 203.097 193.003 cm +1 0 0 1 153.351 693.946 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 206.086 192.804 Td [(to)]TJ +/F8 9.9626 Tf 156.339 693.747 Td [(gefree)-333(|)-334(F)84(rees)-334(a)-333(dense)-334(matrix)]TJ +0 g 0 G + [-773(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-1084(93)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -41.5 -12.382 Td [(6.16)-522(psb)]TJ ET q -1 0 0 1 215.54 193.003 cm +1 0 0 1 153.351 681.564 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 218.528 192.804 Td [(lo)-28(c)]TJ +/F8 9.9626 Tf 156.339 681.365 Td [(gelp)-333(|)-334(Applies)-333(a)-333(left)-334(p)-27(erm)27(utation)-333(to)-333(a)-334(dense)-333(matrix)]TJ 0 g 0 G - [-747(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-317(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(89)]TJ + [-1084(94)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -52.879 -12.08 Td [(psb)]TJ + -41.5 -12.383 Td [(6.17)-522(psb)]TJ ET q -1 0 0 1 181.246 180.923 cm +1 0 0 1 153.351 669.182 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 180.724 Td [(lo)-28(c)]TJ +/F8 9.9626 Tf 156.339 668.982 Td [(glob)]TJ ET q -1 0 0 1 197.286 180.923 cm +1 0 0 1 175.202 669.182 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 200.275 180.724 Td [(to)]TJ +/F8 9.9626 Tf 178.191 668.982 Td [(to)]TJ ET q -1 0 0 1 209.728 180.923 cm +1 0 0 1 187.644 669.182 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 212.717 180.724 Td [(glob)]TJ +/F8 9.9626 Tf 190.633 668.982 Td [(lo)-28(c)-333(|)-333(G)-1(l)1(obal)-334(to)-333(lo)-28(cal)-333(indices)-334(con)28(v)28(ertion)]TJ 0 g 0 G - [-748(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-821(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(91)]TJ + [-1083(95)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -47.068 -12.08 Td [(psb)]TJ + -75.794 -12.382 Td [(6.18)-522(psb)]TJ +ET +q +1 0 0 1 153.351 656.8 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 156.339 656.6 Td [(lo)-28(c)]TJ ET q -1 0 0 1 181.246 168.844 cm +1 0 0 1 169.39 656.8 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 168.644 Td [(is)]TJ +/F8 9.9626 Tf 172.379 656.6 Td [(to)]TJ ET q -1 0 0 1 191.53 168.844 cm +1 0 0 1 181.833 656.8 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 194.518 168.644 Td [(o)28(wned)]TJ +/F8 9.9626 Tf 184.822 656.6 Td [(glob)-333(|)-334(Lo)-27(cal)-334(to)-333(global)-333(indices)-334(con)28(v)28(ersion)]TJ 0 g 0 G - [-880(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-753(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(92)]TJ + [-1084(97)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -28.869 -12.079 Td [(psb)]TJ + -69.983 -12.382 Td [(6.19)-522(psb)]TJ ET q -1 0 0 1 181.246 156.764 cm +1 0 0 1 153.351 644.417 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 156.565 Td [(o)28(wned)]TJ +/F8 9.9626 Tf 156.339 644.218 Td [(is)]TJ ET q -1 0 0 1 212.23 156.764 cm +1 0 0 1 163.634 644.417 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 215.219 156.565 Td [(index)]TJ +/F8 9.9626 Tf 166.623 644.218 Td [(o)28(wned)-334(|)]TJ 0 g 0 G - [-746(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1135(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1083(93)]TJ + [-1084(98)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -49.57 -12.08 Td [(psb)]TJ + -51.784 -12.382 Td [(6.20)-522(psb)]TJ ET q -1 0 0 1 181.246 144.684 cm +1 0 0 1 153.351 632.035 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 144.485 Td [(is)]TJ +/F8 9.9626 Tf 156.339 631.836 Td [(o)28(wned)]TJ ET q -1 0 0 1 191.53 144.684 cm +1 0 0 1 184.334 632.035 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 194.518 144.485 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 187.323 631.836 Td [(index)-333(|)]TJ 0 g 0 G - [-824(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1002(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(94)]TJ + [-1083(99)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -28.869 -12.08 Td [(psb)]TJ + -72.484 -12.382 Td [(6.21)-522(psb)]TJ ET q -1 0 0 1 181.246 132.605 cm +1 0 0 1 153.351 619.653 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 132.405 Td [(lo)-28(cal)]TJ +/F8 9.9626 Tf 156.339 619.454 Td [(is)]TJ ET q -1 0 0 1 205.035 132.605 cm +1 0 0 1 163.634 619.653 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 208.023 132.405 Td [(index)]TJ +/F8 9.9626 Tf 166.623 619.454 Td [(lo)-28(cal)-333(|)]TJ 0 g 0 G - [-691(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1080(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(95)]TJ + [-584(100)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -42.374 -12.079 Td [(psb)]TJ + -51.784 -12.382 Td [(6.22)-522(psb)]TJ ET q -1 0 0 1 181.246 120.525 cm +1 0 0 1 153.351 607.271 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 184.235 120.326 Td [(get)]TJ +/F8 9.9626 Tf 156.339 607.072 Td [(lo)-28(cal)]TJ ET q -1 0 0 1 198.116 120.525 cm +1 0 0 1 177.139 607.271 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 201.105 120.326 Td [(b)-28(oundary)]TJ -0 g 0 G - [-354(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-1083(96)]TJ -0 g 0 G -0 g 0 G - 118.688 -29.888 Td [(ii)]TJ +/F8 9.9626 Tf 180.128 607.072 Td [(index)-333(|)]TJ 0 g 0 G -ET - -endstream -endobj -715 0 obj -<< -/Length 18018 ->> -stream + [-947(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G + [-584(101)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -BT -/F8 9.9626 Tf 114.839 706.129 Td [(psb)]TJ + -65.289 -12.382 Td [(6.23)-522(psb)]TJ ET q -1 0 0 1 130.436 706.328 cm +1 0 0 1 153.351 594.889 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 706.129 Td [(get)]TJ +/F8 9.9626 Tf 156.339 594.69 Td [(get)]TJ ET q -1 0 0 1 147.307 706.328 cm +1 0 0 1 170.221 594.889 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 150.295 706.129 Td [(o)28(v)28(e)-1(r)1(lap)]TJ +/F8 9.9626 Tf 173.209 594.69 Td [(b)-28(oundary)-333(|)-333(Extract)-334(list)-333(of)-333(b)-28(oundary)-333(elemen)28(ts)]TJ 0 g 0 G - [-605(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-330(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1084(97)]TJ + [-584(102)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -35.456 -11.955 Td [(psb)]TJ + -58.37 -12.382 Td [(6.24)-522(psb)]TJ ET q -1 0 0 1 130.436 694.373 cm +1 0 0 1 153.351 582.507 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 694.174 Td [(sp)]TJ +/F8 9.9626 Tf 156.339 582.307 Td [(get)]TJ ET q -1 0 0 1 143.488 694.373 cm +1 0 0 1 170.221 582.507 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 146.476 694.174 Td [(getro)28(w)]TJ +/F8 9.9626 Tf 173.209 582.307 Td [(o)28(v)28(e)-1(r)1(lap)-334(|)-333(Extract)-333(list)-334(of)-333(o)28(v)28(erlap)-334(elemen)28(ts)]TJ 0 g 0 G - [-433(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-830(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ 0 g 0 G - [-1084(98)]TJ + [-584(103)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -31.637 -11.955 Td [(psb)]TJ + -58.37 -12.382 Td [(6.25)-522(psb)]TJ ET q -1 0 0 1 130.436 682.418 cm +1 0 0 1 153.351 570.125 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 682.219 Td [(sizeof)]TJ -0 g 0 G - [-740(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-584(100)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -18.586 -11.956 Td [(Sorting)-333(utilities)]TJ -0 g 0 G - [-519(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-583(101)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -14.944 -21.917 Td [(7)-925(P)32(arallel)-384(en)32(vironmen)32(t)-383(routines)]TJ -0 g 0 G - [-16316(103)]TJ -0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -11.956 Td [(psb)]TJ +/F8 9.9626 Tf 156.339 569.925 Td [(sp)]TJ ET q -1 0 0 1 130.436 636.59 cm +1 0 0 1 166.402 570.125 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 636.39 Td [(init)]TJ +/F8 9.9626 Tf 169.39 569.925 Td [(getro)28(w)-334(|)-333(Extract)-333(ro)28(w\050s)-1(\051)-333(from)-333(a)-333(s)-1(p)1(arse)-334(matrix)]TJ 0 g 0 G - [-829(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-810(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-583(104)]TJ + [-584(104)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -54.551 -12.382 Td [(6.26)-522(psb)]TJ ET q -1 0 0 1 130.436 624.634 cm +1 0 0 1 153.351 557.742 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 624.435 Td [(info)]TJ +/F8 9.9626 Tf 156.339 557.543 Td [(sizeof)-333(|)-334(Memory)-333(o)-28(ccupation)]TJ +0 g 0 G + [-520(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-583(106)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -41.5 -12.382 Td [(6.27)-522(Sorting)-333(utilities)-334(|)]TJ +0 g 0 G + [-775(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-584(107)]TJ 0 g 0 G - [-584(105)]TJ +0 0 1 rg 0 0 1 RG +/F27 9.9626 Tf -14.944 -22.629 Td [(7)-925(P)32(arallel)-384(en)32(vironmen)32(t)-383(routines)]TJ 0 g 0 G + [-16316(109)]TJ 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ +/F8 9.9626 Tf 14.944 -12.382 Td [(7.1)-1022(psb)]TJ ET q -1 0 0 1 130.436 612.679 cm +1 0 0 1 153.351 510.349 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 612.48 Td [(exit)]TJ +/F8 9.9626 Tf 156.339 510.15 Td [(init)-333(|)-334(Initializes)-333(PSBLAS)-333(parallel)-333(e)-1(n)28(vironmen)28(t)]TJ 0 g 0 G - [-690(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-920(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(106)]TJ + [-584(110)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.383 Td [(7.2)-1022(psb)]TJ ET q -1 0 0 1 130.436 600.724 cm +1 0 0 1 153.351 497.967 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 600.525 Td [(get)]TJ +/F8 9.9626 Tf 156.339 497.767 Td [(info)-329(|)-328(Return)-329(information)-329(ab)-27(out)-329(PSBLAS)-329(parallel)-328(en)27(vir)1(on-)]TJ -18.586 -11.955 Td [(men)28(t)]TJ +0 g 0 G + [-478(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-584(111)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -22.914 -12.382 Td [(7.3)-1022(psb)]TJ ET q -1 0 0 1 147.307 600.724 cm +1 0 0 1 153.351 473.629 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 150.295 600.525 Td [(mpicomm)]TJ +/F8 9.9626 Tf 156.339 473.43 Td [(exit)-333(|)-334(Exit)-333(from)-333(PSBLAS)-334(p)1(arallel)-334(en)28(vironmen)28(t)]TJ 0 g 0 G - [-1024(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-742(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-583(107)]TJ + [-584(112)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -35.456 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.4)-1022(psb)]TJ ET q -1 0 0 1 130.436 588.769 cm +1 0 0 1 153.351 461.247 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 588.57 Td [(get)]TJ +/F8 9.9626 Tf 156.339 461.048 Td [(get)]TJ ET q -1 0 0 1 147.307 588.769 cm +1 0 0 1 170.221 461.247 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 150.295 588.57 Td [(rank)]TJ -0 g 0 G - [-994(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-584(108)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -35.456 -11.955 Td [(psb)]TJ +/F8 9.9626 Tf 173.209 461.048 Td [(mpi)]TJ ET q -1 0 0 1 130.436 576.814 cm +1 0 0 1 190.412 461.247 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 576.615 Td [(wtime)]TJ +/F8 9.9626 Tf 193.4 461.048 Td [(comm)-334(|)-333(Get)-333(the)-334(MPI)-333(comm)28(unicator)]TJ 0 g 0 G - [-440(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-868(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(109)]TJ + [-584(113)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.956 Td [(psb)]TJ + -78.561 -12.382 Td [(7.5)-1022(psb)]TJ ET q -1 0 0 1 130.436 564.859 cm +1 0 0 1 153.351 448.865 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 564.659 Td [(barrier)]TJ -0 g 0 G - [-931(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ -0 g 0 G - [-584(110)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ +/F8 9.9626 Tf 156.339 448.666 Td [(get)]TJ ET q -1 0 0 1 130.436 552.903 cm +1 0 0 1 170.221 448.865 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 552.704 Td [(ab)-28(ort)]TJ -0 g 0 G - [-742(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ -0 g 0 G - [-584(111)]TJ -0 g 0 G -0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ +/F8 9.9626 Tf 173.209 448.666 Td [(mpi)]TJ ET q -1 0 0 1 130.436 540.948 cm +1 0 0 1 190.412 448.865 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 540.749 Td [(b)-28(cast)]TJ +/F8 9.9626 Tf 193.4 448.666 Td [(rank)-333(|)-334(Get)-333(the)-333(MPI)-334(rank)]TJ 0 g 0 G - [-795(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-282(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(112)]TJ + [-584(114)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -78.561 -12.382 Td [(7.6)-1022(psb)]TJ ET q -1 0 0 1 130.436 528.993 cm +1 0 0 1 153.351 436.483 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 528.794 Td [(sum)]TJ +/F8 9.9626 Tf 156.339 436.284 Td [(wtime)-333(|)-334(W)84(all)-334(clo)-28(c)28(k)-333(timing)]TJ 0 g 0 G - [-546(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ + [-445(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(113)]TJ + [-584(115)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.7)-1022(psb)]TJ ET q -1 0 0 1 130.436 517.038 cm +1 0 0 1 153.351 424.101 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 516.839 Td [(max)]TJ +/F8 9.9626 Tf 156.339 423.902 Td [(barrier)-333(|)-334(Sinc)28(hronization)-333(p)-28(oin)28(t)-333(parallel)-333(en)27(vironmen)28(t)]TJ 0 g 0 G - [-468(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-845(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-583(114)]TJ + [-584(116)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.383 Td [(7.8)-1022(psb)]TJ ET q -1 0 0 1 130.436 505.083 cm +1 0 0 1 153.351 411.719 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 504.884 Td [(min)]TJ +/F8 9.9626 Tf 156.339 411.519 Td [(ab)-28(ort)-333(|)-333(Ab)-28(ort)-333(a)-334(computation)]TJ 0 g 0 G - [-662(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-717(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(115)]TJ + [-583(117)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.956 Td [(psb)]TJ + -41.5 -12.382 Td [(7.9)-1022(psb)]TJ ET q -1 0 0 1 130.436 493.128 cm +1 0 0 1 153.351 399.337 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 492.928 Td [(amx)]TJ +/F8 9.9626 Tf 156.339 399.137 Td [(b)-28(cast)-333(|)-334(Broadcast)-333(data)]TJ 0 g 0 G - [-468(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-278(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-583(116)]TJ + [-584(118)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.10)-522(psb)]TJ ET q -1 0 0 1 130.436 481.172 cm +1 0 0 1 153.351 386.954 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 480.973 Td [(amn)]TJ +/F8 9.9626 Tf 156.339 386.755 Td [(sum)-333(|)-334(Global)-333(sum)]TJ 0 g 0 G - [-440(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-900(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(117)]TJ + [-584(119)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.11)-522(psb)]TJ ET q -1 0 0 1 130.436 469.217 cm +1 0 0 1 153.351 374.572 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 469.018 Td [(nrm2)]TJ +/F8 9.9626 Tf 156.339 374.373 Td [(max)-333(|)-334(Global)-333(maxim)28(um)]TJ 0 g 0 G - [-826(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-605(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(118)]TJ + [-583(120)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.12)-522(psb)]TJ ET q -1 0 0 1 130.436 457.262 cm +1 0 0 1 153.351 362.19 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 457.063 Td [(snd)]TJ +/F8 9.9626 Tf 156.339 361.991 Td [(min)-333(|)-334(Global)-333(minim)28(um)]TJ 0 g 0 G - [-823(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-994(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)]TJ 0 g 0 G - [-584(119)]TJ + [-584(121)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.13)-522(psb)]TJ ET q -1 0 0 1 130.436 445.307 cm +1 0 0 1 153.351 349.808 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 445.108 Td [(rcv)]TJ -0 g 0 G - [-965(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +/F8 9.9626 Tf 156.339 349.609 Td [(amx)-333(|)-334(Global)-333(maxim)28(um)-334(absolute)-333(v)56(alue)]TJ 0 g 0 G - [-584(120)]TJ + [-294(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G -0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -33.53 -21.918 Td [(8)-925(Error)-383(handling)]TJ + [-584(122)]TJ 0 g 0 G - [-23812(121)]TJ 0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.14)-522(psb)]TJ ET q -1 0 0 1 130.436 411.434 cm +1 0 0 1 153.351 337.426 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 411.235 Td [(errpush)]TJ +/F8 9.9626 Tf 156.339 337.227 Td [(amn)-333(|)-334(Global)-333(minim)28(um)-334(absolu)1(te)-334(v)56(alue)]TJ 0 g 0 G - [-595(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ + [-461(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-584(123)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.955 Td [(psb)]TJ + -41.5 -12.383 Td [(7.15)-522(psb)]TJ ET q -1 0 0 1 130.436 399.479 cm +1 0 0 1 153.351 325.044 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 399.28 Td [(error)]TJ +/F8 9.9626 Tf 156.339 324.844 Td [(nrm2)-333(|)-334(Global)-333(2-norm)-333(reduction)]TJ 0 g 0 G - [-987(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-847(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-584(124)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -18.586 -11.956 Td [(psb)]TJ -ET -q -1 0 0 1 130.436 387.524 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 133.425 387.324 Td [(set)]TJ + -41.5 -12.382 Td [(7.16)-522(psb)]TJ ET q -1 0 0 1 146.255 387.524 cm +1 0 0 1 153.351 312.662 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 149.244 387.324 Td [(errv)28(erb)-28(osit)28(y)]TJ +/F8 9.9626 Tf 156.339 312.462 Td [(snd)-333(|)-334(Send)-333(data)]TJ 0 g 0 G - [-977(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1023(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G [-584(125)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -34.405 -11.955 Td [(psb)]TJ + -41.5 -12.382 Td [(7.17)-522(psb)]TJ ET q -1 0 0 1 130.436 375.568 cm +1 0 0 1 153.351 300.279 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 133.425 375.369 Td [(set)]TJ -ET -q -1 0 0 1 146.255 375.568 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 149.244 375.369 Td [(erraction)]TJ +/F8 9.9626 Tf 156.339 300.08 Td [(rcv)-333(|)-334(Receiv)28(e)-333(data)]TJ 0 g 0 G - [-735(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)]TJ + [-762(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(126)]TJ + [-583(126)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -/F27 9.9626 Tf -49.349 -21.918 Td [(9)-925(Utilities)]TJ +/F27 9.9626 Tf -56.444 -22.629 Td [(8)-925(Error)-383(handling)]TJ 0 g 0 G - [-27238(127)]TJ + [-23812(127)]TJ 0 0 1 rg 0 0 1 RG -/F8 9.9626 Tf 14.944 -11.955 Td [(h)28(b)]TJ +/F8 9.9626 Tf 14.944 -12.382 Td [(8.1)-1022(psb)]TJ ET q -1 0 0 1 126.23 341.695 cm +1 0 0 1 153.351 265.268 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 129.219 341.496 Td [(read)]TJ +/F8 9.9626 Tf 156.339 265.069 Td [(errpush)-333(|)-334(Pushes)-333(an)-333(error)-334(co)-27(de)-334(on)28(to)-333(the)-334(error)-333(stac)28(k)]TJ 0 g 0 G - [-859(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-1026(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(128)]TJ + [-583(129)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -14.38 -11.955 Td [(h)28(b)]TJ + -41.5 -12.383 Td [(8.2)-1022(psb)]TJ ET q -1 0 0 1 126.23 329.74 cm +1 0 0 1 153.351 252.886 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 129.219 329.541 Td [(write)]TJ +/F8 9.9626 Tf 156.339 252.686 Td [(error)-333(|)-334(Prin)28(ts)-333(the)-333(e)-1(r)1(ror)-334(stac)28(k)-333(con)27(ten)28(t)-333(and)-333(ab)-28(orts)-333(e)-1(xecution)]TJ 0 g 0 G - [-526(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(129)]TJ + [-1087(130)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -14.38 -11.955 Td [(mm)]TJ + -41.5 -12.382 Td [(8.3)-1022(psb)]TJ ET q -1 0 0 1 132.042 317.785 cm +1 0 0 1 153.351 240.504 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 135.03 317.586 Td [(mat)]TJ +/F8 9.9626 Tf 156.339 240.304 Td [(set)]TJ ET q -1 0 0 1 152.786 317.785 cm +1 0 0 1 169.169 240.504 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 155.775 317.586 Td [(read)]TJ +/F8 9.9626 Tf 172.158 240.304 Td [(errv)28(erb)-28(osit)28(y)-333(|)-334(Sets)-333(the)-334(v)28(erb)-27(os)-1(it)28(y)-333(of)-333(error)-334(messages)]TJ 0 g 0 G - [-527(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-804(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(130)]TJ + [-584(131)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG - -40.936 -11.955 Td [(mm)]TJ + -57.319 -12.382 Td [(8.4)-1022(psb)]TJ ET q -1 0 0 1 132.042 305.83 cm +1 0 0 1 153.351 228.121 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 135.03 305.631 Td [(arra)28(y)]TJ +/F8 9.9626 Tf 156.339 227.922 Td [(set)]TJ ET q -1 0 0 1 158.376 305.83 cm +1 0 0 1 169.169 228.121 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 161.365 305.631 Td [(read)]TJ +/F8 9.9626 Tf 172.158 227.922 Td [(erraction)-274(|)-274(Set)-275(th)1(e)-275(t)28(yp)-28(e)-274(of)-274(action)-274(to)-274(b)-28(e)-274(tak)27(en)-274(up)-27(on)-275(error)]TJ -34.405 -11.955 Td [(condition)]TJ 0 g 0 G - [-744(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ + [-950(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-499(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-584(131)]TJ + [-584(132)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG +/F27 9.9626 Tf -37.858 -22.629 Td [(9)-925(Utilities)]TJ 0 g 0 G + [-27238(133)]TJ 0 0 1 rg 0 0 1 RG - -46.526 -11.955 Td [(mm)]TJ +/F8 9.9626 Tf 14.944 -12.383 Td [(9.1)-1490(h)28(b)]TJ ET q -1 0 0 1 132.042 293.875 cm +1 0 0 1 153.803 181.155 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 135.03 293.676 Td [(mat)]TJ +/F8 9.9626 Tf 156.792 180.955 Td [(read)-468(|)-467(Read)-468(a)-468(sparse)-468(matri)1(x)-468(from)-468(a)-467(\014le)-468(in)-468(the)-467(Harw)27(ell{)]TJ -19.039 -11.955 Td [(Bo)-28(eing)-333(format)]TJ +0 g 0 G + [-294(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ +0 g 0 G + [-583(134)]TJ +0 g 0 G +0 0 1 rg 0 0 1 RG + -22.914 -12.382 Td [(9.2)-1022(h)28(b)]TJ ET q -1 0 0 1 152.786 293.875 cm +1 0 0 1 149.144 156.817 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 155.775 293.676 Td [(write)]TJ +/F8 9.9626 Tf 152.133 156.618 Td [(write)-291(|)-290(W)83(rite)-290(a)-291(sparse)-290(matrix)-291(to)-290(a)-291(\014le)-290(in)-291(the)-290(Harw)28(ell{Bo)-28(eing)]TJ -14.38 -11.955 Td [(format)]TJ 0 g 0 G - 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9.9626 Tf 121.269 479.848 Td [(epk)]TJ -ET -q -1 0 0 1 139.619 480.048 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F30 9.9626 Tf 10.71 0 Td [(sp)]TJ/F8 9.9626 Tf 10.461 0 Td [(:)-444(the)-334(routine)-333(is)-333(related)-334(to)-333(sparse)-333(data,)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 148.038 479.848 Td [(Kind)-426(parameter)-426(for)-427(8-b)28(ytes)-426(in)28(teger)-427(data,)-449(as)-426(is)-427(alw)28(a)28(ys)-426(used)-427(b)28(y)-426(the)]TJ/F30 9.9626 Tf -23.236 -11.955 Td [(sizeof)]TJ/F8 9.9626 Tf 34.703 0 Td [(metho)-28(ds;)]TJ +/F27 9.9626 Tf -21.171 -18.081 Td [({)]TJ 0 g 0 G -/F27 9.9626 Tf -59.61 -21.029 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 447.063 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 446.864 Td [(ipk)]TJ -ET -q -1 0 0 1 137.551 447.063 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F30 9.9626 Tf 10.71 0 Td [(cd)]TJ/F8 9.9626 Tf 10.461 0 Td [(:)-444(the)-334(routine)-333(is)-333(related)-334(to)-333(comm)28(unication)-334(d)1(e)-1(scriptor)-333(\050see)]TJ +0 0 1 rg 0 0 1 RG + [-333(3)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 145.969 446.864 Td [(Kind)-470(parameter)-471(for)-470(\134lo)-28(cal")-471(in)28(teger)-470(indices)-471(and)-470(data;)-539(with)-471(default)]TJ -21.167 -11.956 Td [(build)-333(options)-333(this)-334(is)-333(a)-333(4)-334(b)28(ytes)-333(in)27(teger;)]TJ + [(\051.)]TJ -32.379 -24.208 Td [(F)83(or)-275(example)-276(the)]TJ/F30 9.9626 Tf 72.33 0 Td [(psb_geins)]TJ/F8 9.9626 Tf 47.073 0 Td [(,)]TJ/F30 9.9626 Tf 5.628 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 49.818 0 Td [(and)]TJ/F30 9.9626 Tf 18.797 0 Td [(psb_cdins)]TJ/F8 9.9626 Tf 49.818 0 Td [(p)-28(erform)-275(the)-276(same)]TJ -243.464 -11.955 Td [(action)-343(\050see)]TJ +0 0 1 rg 0 0 1 RG + [-343(6)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -21.029 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 414.078 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 413.879 Td [(lpk)]TJ -ET -q -1 0 0 1 137.551 414.078 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q + [(\051)-343(on)-342(dense)-343(matrices,)-345(s)-1(p)1(ars)-1(e)-342(matrices)-343(and)-343(comm)28(unication)-343(de-)]TJ 0 -11.956 Td [(scriptors)-357(resp)-28(ectiv)28(ely)83(.)-514(In)27(terface)-356(o)27(v)28(erloading)-357(allo)28(ws)-357(the)-357(u)1(s)-1(age)-356(of)-357(the)-357(same)]TJ 0 -11.955 Td [(subroutine)-333(names)-334(for)-333(b)-28(oth)-333(real)-333(and)-334(complex)-333(data.)]TJ -24.907 -23.137 Td [(In)-320(the)-320(desc)-1(r)1(iption)-321(of)-320(the)-320(subroutines,)-323(argumen)28(ts)-320(or)-320(argumen)27(t)-320(en)28(tries)-320(are)-320(clas)-1(si-)]TJ 0 -11.955 Td [(\014ed)-333(as:)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 145.969 413.879 Td [(Kind)-409(parameter)-409(for)-409(\134global")-409(in)28(teger)-409(indices)-410(and)-409(data;)-447(with)-409(defaul)1(t)]TJ -21.167 -11.955 Td 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70.797 0 Td [(can)-281(b)-28(e)-281(treate)-1(d)-281(as)-281(an)-281(opaque)-282(ob)-55(ject)]TJ -193.7 -11.955 Td [(handled)-406(via)-406(the)-406(to)-28(ols)-406(routi)1(nes)-407(of)-405(Sec)-1(.)]TJ -0 0 1 rg 0 0 1 RG - [-405(6)]TJ +/F27 9.9626 Tf 0 -23.137 Td [(global)]TJ 0 g 0 G - [-406(or)-406(the)-406(query)-406(routines)-406(detailed)-406(b)-28(elo)28(w;)]TJ 0 -11.956 Td [(nev)28(ertheless)-334(w)28(e)-333(include)-334(here)-333(a)-333(description)-334(for)-333(the)-333(curious)-333(reader.)]TJ 14.944 -12.231 Td [(First)-248(w)28(e)-248(describ)-28(e)-248(t)1(he)]TJ/F30 9.9626 Tf 91.264 0 Td [(psb_indx_map)]TJ/F8 9.9626 Tf 65.233 0 Td [(t)28(yp)-28(e.)-416(This)-248(is)-248(a)-247(data)-248(structure)-248(that)-248(k)28(eeps)]TJ -171.441 -11.955 Td [(trac)28(k)-334(of)-333(a)-333(certain)-334(n)28(um)28(b)-28(er)-333(of)-333(basic)-334(issues)-333(suc)28(h)-334(as:)]TJ +/F8 9.9626 Tf 34.738 0 Td [(F)83(or)-228(input)-228(argumen)28(ts,)-250(the)-228(v)56(alue)-229(m)28(ust)-228(b)-28(e)-228(the)-228(same)-229(on)-228(all)-228(pro)-28(cesses)-229(part)1(ic)-1(i)1(-)]TJ -9.831 -11.955 Td [(pating)-253(i)1(n)-253(the)-253(subroutin)1(e)-253(call;)-280(for)-252(output)-253(argumen)28(ts)-252(the)-253(v)56(alue)-253(is)-253(guaran)28(teed)]TJ 0 -11.955 Td [(to)-333(b)-28(e)-333(the)-334(same.)]TJ 0 g 0 G -/F14 9.9626 Tf 14.944 -20.753 Td [(\017)]TJ +/F27 9.9626 Tf -24.907 -24.208 Td [(lo)-32(cal)]TJ 0 g 0 G -/F8 9.9626 Tf 9.963 0 Td [(The)-333(v)55(alue)-333(of)-333(the)-334(comm)28(unication/MPI)-333(con)28(te)-1(x)1(t;)]TJ +/F8 9.9626 Tf 28.055 0 Td [(Eac)28(h)-334(p)1(ro)-28(cess)-334(has)-333(its)-333(o)27(wn)-333(v)56(alue\050s\051)-334(indep)-27(enden)27(tly)84(.)]TJ -28.055 -23.137 Td [(T)83(o)-333(\014nish)-333(our)-334(general)-333(description,)-333(w)28(e)-334(de\014ne)-333(a)-333(v)27(ersion)-333(string)-333(with)-334(th)1(e)-334(constan)28(t)]TJ/F30 9.9626 Tf 122.168 -24.059 Td [(psb_version_string_)]TJ/F8 9.9626 Tf -122.168 -24.059 Td [(whose)-333(curren)27(t)-333(v)56(alue)-334(is)]TJ/F30 9.9626 Tf 99.793 0 Td [(3.4.0)]TJ 0 g 0 G - 144.458 -29.888 Td [(9)]TJ +/F8 9.9626 Tf 69.572 -29.888 Td [(5)]TJ 0 g 0 G ET endstream endobj -855 0 obj +843 0 obj << -/Length 6827 +/Length 8659 >> stream 0 g 0 G 0 g 0 G -0 g 0 G BT -/F14 9.9626 Tf 165.649 706.129 Td [(\017)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(2.3)-1125(Application)-375(structure)]TJ/F8 9.9626 Tf 0 -18.928 Td [(The)-274(main)-275(und)1(e)-1(r)1(lying)-275(principle)-274(of)-274(the)-274(PSBLAS)-275(librar)1(y)-275(is)-274(that)-274(the)-275(library)-274(ob)-55(jects)]TJ 0 -11.955 Td [(are)-311(created)-311(and)-311(exist)-311(with)-312(r)1(e)-1(f)1(e)-1(rence)-311(to)-311(a)-311(discretized)-311(space)-311(to)-311(whic)27(h)-311(there)-311(corre-)]TJ 0 -11.955 Td 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-16.182 Td [({)]TJ + [-500(Allo)-28(cate)-301(sparse)-302(matrix)-301(and)-302(dense)-302(v)28(ectors)-301(with)]TJ/F30 9.9626 Tf 215.329 0 Td [(psb_spall)]TJ/F8 9.9626 Tf 50.077 0 Td [(and)]TJ/F30 9.9626 Tf 19.055 0 Td [(psb_geall)]TJ 0 g 0 G -/F8 9.9626 Tf 10.71 0 Td [(The)-333(n)27(um)28(b)-28(er)-333(of)-333(halo)-333(indices)-334(\050and)-333(therefore)-333(lo)-28(cal)-333(c)-1(olu)1(m)-1(n)1(s)-1(\051;)]TJ +/F8 9.9626 Tf -284.461 -21.082 Td [(4.)]TJ 0 g 0 G -/F27 9.9626 Tf -10.71 -16.181 Td [({)]TJ + [-500(Lo)-28(op)-411(o)28(v)28(er)-411(all)-411(lo)-28(cal)-411(ro)27(ws,)-430(generate)-411(matrix)-411(and)-411(v)27(ector)-411(en)28(tries,)-431(an)1(d)-412(in)1(s)-1(ert)]TJ 12.73 -11.955 Td [(them)-333(with)]TJ/F30 9.9626 Tf 48.153 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 50.393 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(psb_geins)]TJ 0 g 0 G -/F8 9.9626 Tf 10.71 0 Td [(The)-333(global)-334(indices)-333(corresp)-28(onding)-333(to)-333(the)-334(lo)-27(cal)-334(ones.)]TJ -46.824 -20.409 Td [(There)-376(are)-376(m)-1(an)28(y)-376(di\013eren)28(t)-376(sc)27(hemes)-376(for)-376(storing)-376(these)-377(data;)-397(therefore)-376(there)-377(are)-376(a)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)-389(of)-389(t)28(yp)-28(es)-389(extending)-389(the)-388(base)-389(one,)-403(and)-389(the)-389(descriptor)-389(structure)-389(hold)1(s)-389(a)]TJ 0 -11.955 Td [(p)-28(olymorphic)-290(ob)-56(ject)-290(whose)-291(dyn)1(am)-1(ic)-290(t)28(yp)-28(e)-290(can)-291(b)-28(e)-290(an)28(y)-291(of)-290(the)-291(extend)1(e)-1(d)-290(t)28(yp)-28(es.)-430(The)]TJ 0 -11.955 Td [(metho)-28(ds)-333(asso)-28(ciated)-333(with)-334(this)-333(data)-333(t)28(yp)-28(e)-334(answ)28(er)-333(the)-334(f)1(ollo)27(wing)-333(queries:)]TJ +/F8 9.9626 Tf -130.648 -21.083 Td [(5.)]TJ 0 g 0 G -/F14 9.9626 Tf 14.944 -20.288 Td [(\017)]TJ + [-500(Assem)28(ble)-334(the)-333(v)56(arious)-334(en)28(tities:)]TJ 0 g 0 G -/F8 9.9626 Tf 9.962 0 Td [(F)83(or)-271(a)-271(giv)28(en)-272(set)-271(of)-271(lo)-28(cal)-271(indices,)-284(\014nd)-271(the)-271(corresp)-28(onding)-271(indices)-272(in)-271(the)-271(global)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(ering;)]TJ + 16.936 -21.082 Td [(\050a\051)]TJ 0 g 0 G -/F14 9.9626 Tf -9.962 -20.408 Td [(\017)]TJ +/F30 9.9626 Tf 17.711 0 Td [(psb_cdasb)]TJ 0 g 0 G -/F8 9.9626 Tf 9.962 0 Td [(F)83(or)-271(a)-271(giv)28(en)-272(set)-271(of)-271(global)-271(indices,)-284(\014nd)-271(the)-271(c)-1(or)1(re)-1(sp)-27(onding)-271(indices)-272(in)-271(the)-271(lo)-28(cal)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(ering,)-333(if)-334(an)28(y)83(,)-333(or)-333(return)-333(an)-334(in)28(v)56(alid)]TJ +/F8 9.9626 Tf -18.264 -16.519 Td [(\050b\051)]TJ 0 g 0 G -/F14 9.9626 Tf -9.962 -20.409 Td [(\017)]TJ -0 g 0 G -/F8 9.9626 Tf 9.962 0 Td [(Add)-333(a)-334(global)-333(index)-333(to)-333(the)-334(set)-333(of)-334(h)1(alo)-334(indices;)]TJ -0 g 0 G -/F14 9.9626 Tf -9.962 -20.408 Td [(\017)]TJ -0 g 0 G -/F8 9.9626 Tf 9.962 0 Td [(Find)-333(the)-334(pro)-27(cess)-334(o)28(wner)-333(of)-334(eac)28(h)-333(mem)27(b)-27(er)-334(of)-333(a)-333(set)-334(of)-333(global)-333(indices.)]TJ -24.906 -20.288 Td [(All)-355(metho)-28(ds)-355(but)-355(the)-355(last)-355(are)-355(purely)-355(lo)-28(cal;)-366(the)-355(last)-355(metho)-28(d)-355(p)-28(oten)28(tially)-355(requires)]TJ 0 -11.955 Td [(comm)28(unication)-259(among)-258(pro)-28(cesses,)-274(and)-258(th)28(us)-259(is)-258(a)-259(sync)28(hronous)-259(metho)-27(d.)-420(The)-258(c)27(hoice)]TJ 0 -11.955 Td [(of)-309(a)-310(sp)-28(eci\014c)-309(dynamic)-310(t)28(yp)-27(e)-310(for)-309(the)-310(index)-309(map)-310(is)-309(made)-310(at)-309(the)-309(time)-310(the)-309(descriptor)]TJ 0 -11.955 Td [(is)-333(initially)-334(al)1(lo)-28(cated,)-334(according)-333(to)-333(the)-334(mo)-27(de)-334(of)-333(initialization)-333(\050see)-334(also)]TJ -0 0 1 rg 0 0 1 RG - [-333(6)]TJ +/F30 9.9626 Tf 18.264 0 Td [(psb_spasb)]TJ 0 g 0 G - [(\051.)]TJ 14.944 -12.076 Td [(The)-333(descriptor)-334(con)28(ten)28(ts)-333(are)-334(as)-333(follo)28(ws:)]TJ +/F8 9.9626 Tf -17.157 -16.519 Td [(\050c\051)]TJ 0 g 0 G -/F27 9.9626 Tf -14.944 -20.288 Td [(indxmap)]TJ +/F30 9.9626 Tf 17.157 0 Td [(psb_geasb)]TJ 0 g 0 G -/F8 9.9626 Tf 48.422 0 Td [(A)-222(p)-28(olymorphic)-222(v)56(ariable)-223(of)-222(a)-222(t)28(yp)-28(e)-222(that)-222(is)-223(an)28(y)-222(extension)-222(of)-222(the)-223(indx)]TJ -ET -q -1 0 0 1 476.354 370.98 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 479.343 370.78 Td [(map)]TJ -303.732 -11.955 Td [(t)28(yp)-28(e)-333(describ)-28(ed)-333(ab)-28(o)28(v)27(e.)]TJ +/F8 9.9626 Tf 122.541 -29.888 Td [(6)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -32.363 Td [(halo)]TJ ET -q -1 0 0 1 172.238 326.661 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 175.675 326.462 Td [(index)]TJ -0 g 0 G -/F8 9.9626 Tf 32.191 0 Td [(A)-384(list)-384(of)-385(the)-384(halo)-384(and)-384(b)-28(oundary)-384(elemen)28(ts)-384(for)-385(the)-384(curren)28(t)-384(pro)-28(cess)]TJ -32.255 -11.955 Td [(to)-347(b)-28(e)-347(exc)28(hanged)-347(with)-347(other)-348(p)1(ro)-28(cesses;)-354(for)-348(eac)28(h)-347(pro)-28(cesses)-347(with)-347(whic)28(h)-347(it)-347(is)]TJ 0 -11.956 Td [(necessary)-334(to)-333(comm)28(unicate:)]TJ -0 g 0 G - 9.188 -20.408 Td [(1.)]TJ -0 g 0 G - [-500(Pro)-28(cess)-333(iden)28(ti\014er;)]TJ + +endstream +endobj +857 0 obj +<< +/Length 7719 +>> +stream 0 g 0 G - 0 -16.182 Td [(2.)]TJ 0 g 0 G - [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ 0 g 0 G - 0 -16.181 Td [(3.)]TJ +BT +/F8 9.9626 Tf 112.072 706.129 Td [(6.)]TJ 0 g 0 G - [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(rece)-1(i)1(v)27(ed;)]TJ + [-500(Cho)-28(ose)-382(the)-382(preconditioner)-382(to)-382(b)-28(e)-382(used)-382(with)]TJ/F30 9.9626 Tf 205.032 0 Td [(prec%init)]TJ/F8 9.9626 Tf 50.879 0 Td [(and)-382(build)-382(it)-382(with)]TJ/F30 9.9626 Tf -243.181 -11.955 Td [(prec%build)]TJ +0 0 1 rg 0 0 1 RG +/F7 6.9738 Tf 52.303 3.615 Td [(3)]TJ 0 g 0 G - 0 -16.182 Td [(4.)]TJ +/F8 9.9626 Tf 4.47 -3.615 Td [(.)]TJ 0 g 0 G - [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ + -69.503 -22.397 Td [(7.)]TJ 0 g 0 G - 0 -16.182 Td [(5.)]TJ + [-500(Call)-333(the)-334(iterativ)28(e)-333(metho)-28(d)-333(of)-334(c)28(hoice,)-333(e.g.)]TJ/F30 9.9626 Tf 189.595 0 Td [(psb_bicgstab)]TJ/F8 9.9626 Tf -201.772 -21.778 Td [(This)-333(is)-334(the)-333(structure)-333(of)-334(the)-333(sample)-333(programs)-334(in)-333(the)-333(directory)]TJ/F30 9.9626 Tf 269.435 0 Td [(test/pargen/)]TJ/F8 9.9626 Tf 62.764 0 Td [(.)]TJ -317.255 -12.573 Td [(F)83(or)-291(a)-292(sim)28(ulation)-292(in)-291(whic)27(h)-291(the)-292(same)-292(discretization)-291(mes)-1(h)-291(is)-292(used)-291(o)27(v)28(er)-292(m)28(ultiple)]TJ -14.944 -11.955 Td [(time)-333(ste)-1(p)1(s)-1(,)-333(the)-333(follo)28(wing)-334(structure)-333(ma)28(y)-333(b)-28(e)-334(more)-333(appropriate:)]TJ 0 g 0 G - [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ -9.188 -20.408 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-334(of)-333(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ -0 0 1 rg 0 0 1 RG - [-333(3.3)]TJ + 12.177 -21.779 Td [(1.)]TJ 0 g 0 G - [(.)]TJ + [-500(Initialize)-333(parallel)-334(en)28(vironmen)28(t)-333(with)]TJ/F30 9.9626 Tf 169.421 0 Td [(psb_init)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -20.409 Td [(ext)]TJ -ET -q -1 0 0 1 167.146 176.799 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 170.583 176.599 Td [(index)]TJ +/F8 9.9626 Tf -169.421 -22.397 Td [(2.)]TJ 0 g 0 G -/F8 9.9626 Tf 32.191 0 Td [(A)-274(list)-274(of)-274(elemen)28(t)-274(indices)-274(to)-273(b)-28(e)-274(exc)28(hanged)-274(to)-274(implemen)28(t)-274(the)-274(mapping)]TJ -27.163 -11.955 Td [(b)-28(et)28(w)28(een)-334(a)-333(base)-333(descriptor)-334(and)-333(a)-333(descriptor)-334(with)-333(o)28(v)28(erlap.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-334(of)-333(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ -0 0 1 rg 0 0 1 RG - [-333(3.3)]TJ + [-500(Initialize)-333(index)-334(space)-333(with)]TJ/F30 9.9626 Tf 130.123 0 Td [(psb_cdall)]TJ 0 g 0 G - [(.)]TJ +/F8 9.9626 Tf -130.123 -22.396 Td [(3.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -20.408 Td [(o)32(vrlap)]TJ -ET -q -1 0 0 1 182.684 132.48 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 186.122 132.281 Td [(index)]TJ + [-500(Lo)-28(op)-271(o)28(v)27(er)-271(the)-272(top)-27(ology)-272(of)-271(the)-272(discretization)-271(mesh)-272(and)-271(build)-271(the)-272(descriptor)]TJ 12.73 -11.955 Td [(with)]TJ/F30 9.9626 Tf 22.693 0 Td [(psb_cdins)]TJ 0 g 0 G -/F8 9.9626 Tf 32.191 0 Td [(A)-320(list)-320(of)-320(the)-320(o)28(v)28(erlap)-320(eleme)-1(n)28(ts)-320(for)-320(the)-320(curren)28(t)-320(pro)-28(cess,)-322(organized)]TJ -42.702 -11.955 Td [(in)-333(groups)-334(lik)28(e)-333(the)-333(previous)-334(v)28(ector:)]TJ +/F8 9.9626 Tf -35.423 -22.397 Td [(4.)]TJ 0 g 0 G - 141.968 -29.888 Td [(10)]TJ + [-500(Assem)28(ble)-334(the)-333(descriptor)-333(with)]TJ/F30 9.9626 Tf 143.019 0 Td [(psb_cdasb)]TJ 0 g 0 G -ET - -endstream -endobj -866 0 obj -<< -/Length 5178 ->> -stream +/F8 9.9626 Tf -143.019 -22.396 Td [(5.)]TJ 0 g 0 G + [-500(Allo)-28(cate)-222(the)-222(sparse)-223(matrices)-222(and)-222(dense)-222(v)27(ectors)-222(with)]TJ/F30 9.9626 Tf 233.375 0 Td [(psb_spall)]TJ/F8 9.9626 Tf 49.287 0 Td [(and)]TJ/F30 9.9626 Tf 18.265 0 Td [(psb_geall)]TJ 0 g 0 G +/F8 9.9626 Tf -300.927 -22.396 Td [(6.)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 133.99 706.129 Td [(1.)]TJ + [-500(Lo)-28(op)-333(o)28(v)28(e)-1(r)-333(the)-333(time)-334(steps:)]TJ 0 g 0 G - [-500(Pro)-28(cess)-333(iden)28(ti\014er;)]TJ + 16.936 -22.397 Td [(\050a\051)]TJ 0 g 0 G - 0 -17.286 Td [(2.)]TJ + [-500(If)-340(after)-339(\014rst)-340(time)-339(step,)-341(reinitialize)-340(the)-339(s)-1(p)1(a)-1(r)1(s)-1(e)-339(matrix)-340(with)]TJ/F30 9.9626 Tf 269.988 0 Td [(psb_sprn)]TJ/F8 9.9626 Tf 41.843 0 Td [(;)]TJ -294.119 -11.955 Td [(also)-333(zero)-334(out)-333(the)-333(dense)-334(v)28(ectors;)]TJ 0 g 0 G - [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)28(ts)-334(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ + -18.265 -17.176 Td [(\050b\051)]TJ 0 g 0 G - 0 -17.287 Td [(3.)]TJ + [-500(Lo)-28(op)-252(o)28(v)27(er)-252(the)-253(mesh,)-268(generate)-253(the)-253(co)-27(e\016cie)-1(n)28(ts)-252(and)-253(insert/up)-27(date)-253(them)]TJ 18.265 -11.955 Td [(with)]TJ/F30 9.9626 Tf 22.693 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 50.394 0 Td [(and)]TJ/F30 9.9626 Tf 19.371 0 Td [(psb_geins)]TJ 0 g 0 G - [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ +/F8 9.9626 Tf -109.616 -17.176 Td [(\050c\051)]TJ 0 g 0 G - 0 -17.286 Td [(4.)]TJ + [-500(Assem)28(ble)-334(with)]TJ/F30 9.9626 Tf 83.686 0 Td [(psb_spasb)]TJ/F8 9.9626 Tf 50.394 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(psb_geasb)]TJ 0 g 0 G - [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)28(ts)-334(to)-333(b)-28(e)-333(sen)27(t;)]TJ +/F8 9.9626 Tf -154.559 -17.176 Td [(\050d\051)]TJ 0 g 0 G - 0 -17.286 Td [(5.)]TJ + [-500(Cho)-28(ose)-333(and)-333(build)-334(pr)1(e)-1(condi)1(tioner)-334(with)]TJ/F30 9.9626 Tf 186.357 0 Td [(prec%init)]TJ/F8 9.9626 Tf 50.394 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(prec%build)]TJ 0 g 0 G - [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ -9.188 -22.618 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-333(of)-334(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ -0 0 1 rg 0 0 1 RG - [-333(3.3)]TJ +/F8 9.9626 Tf -255.016 -17.175 Td [(\050e\051)]TJ 0 g 0 G - [(.)]TJ + [-500(Call)-333(the)-334(iterativ)28(e)-333(metho)-28(d)-333(of)-334(c)28(hoice,)-333(e.g.)]TJ/F30 9.9626 Tf 194.023 0 Td [(psb_bicgstab)]TJ/F8 9.9626 Tf -223.69 -22.397 Td [(The)-370(insertion)-370(routines)-370(will)-370(b)-27(e)-370(c)-1(all)1(e)-1(d)-369(as)-370(man)27(y)-370(times)-370(as)-370(needed;)-388(they)-370(only)-370(need)]TJ 0 -11.955 Td [(to)-404(b)-27(e)-404(called)-404(on)-404(the)-403(data)-404(that)-404(is)-403(actually)-404(allo)-28(cated)-403(to)-404(the)-404(curren)28(t)-404(pro)-27(ce)-1(ss,)-421(i.e.)]TJ 0 -11.955 Td [(eac)28(h)-334(pro)-27(cess)-334(generates)-333(its)-334(o)28(wn)-333(data.)]TJ 14.944 -12.573 Td [(In)-326(principle)-326(there)-327(is)-326(no)-326(sp)-28(eci\014c)-326(order)-327(in)-326(the)-326(calls)-327(to)]TJ/F30 9.9626 Tf 225.879 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td [(,)-328(nor)-326(is)-326(there)]TJ -287.896 -11.955 Td [(a)-393(requiremen)27(t)-393(to)-393(build)-394(a)-393(matrix)-393(ro)28(w)-394(in)-393(its)-394(en)28(tiret)28(y)-393(b)-28(efore)-393(c)-1(alli)1(ng)-394(the)-393(routine;)]TJ 0 -11.955 Td [(this)-288(allo)28(ws)-288(the)-288(application)-288(programmer)-288(to)-288(w)27(alk)-288(through)-288(the)-288(discretization)-288(mesh)]TJ 0 -11.956 Td [(elemen)28(t)-402(b)28(y)-401(elemen)28(t,)-419(generating)-401(the)-401(main)-401(part)-401(of)-402(a)-401(giv)28(en)-401(matrix)-402(ro)28(w)-401(but)-401(also)]TJ 0 -11.955 Td [(con)28(tributions)-333(to)-334(the)-333(ro)28(ws)-334(corresp)-28(on)1(ding)-334(to)-333(neigh)28(b)-28(ouring)-333(elemen)28(ts)-1(.)]TJ 14.944 -12.573 Td [(F)83(rom)-410(a)-410(functional)-410(p)-28(oin)28(t)-410(of)-410(view)-410(it)-410(is)-410(ev)27(en)-410(p)-27(os)-1(sibl)1(e)-411(to)-410(execute)-410(one)-410(call)-410(for)]TJ -14.944 -11.955 Td [(eac)28(h)-372(nonzero)-372(co)-28(e\016cien)28(t;)-391(ho)27(w)28(ev)28(er)-372(this)-372(w)28(ould)-372(ha)28(v)28(e)-372(a)-372(substan)27(tial)-371(com)-1(p)1(utational)]TJ 0 -11.955 Td [(o)28(v)28(e)-1(r)1(head.)-412(It)-236(is)-236(therefore)-236(advisable)-236(to)-235(pac)27(k)-236(a)-235(certain)-236(amoun)28(t)-236(of)-236(data)-236(in)28(to)-236(eac)28(h)-236(call)]TJ 0 -11.955 Td [(to)-308(the)-307(insertion)-308(routin)1(e)-1(,)-312(sa)28(y)-308(touc)28(hing)-308(on)-307(a)-308(few)-307(tens)-308(of)-307(ro)27(ws;)-316(the)-307(b)-28(est)-308(p)-27(erformng)]TJ 0 -11.955 Td [(v)56(alue)-386(w)28(ould)-385(dep)-28(end)-386(on)-385(b)-28(oth)-385(the)-385(arc)27(hitecture)-385(of)-385(the)-386(computer)-385(b)-28(eing)-385(used)-386(and)]TJ 0 -11.956 Td [(on)-450(the)-450(problem)-450(structure.)-794(A)28(t)-450(the)-450(opp)-27(os)-1(i)1(te)-450(extrem)-1(e,)-479(it)-449(w)27(ould)-449(b)-28(e)-450(p)-28(ossible)-450(to)]TJ 0 -11.955 Td [(generate)-310(the)-311(en)28(tire)-310(part)-310(of)-311(a)-310(co)-28(e\016cien)28(t)-311(matrix)-310(residing)-310(on)-310(a)-311(pro)-27(ces)-1(s)-310(and)-310(pass)-310(it)]TJ 0 -11.955 Td [(in)-309(a)-309(single)-309(call)-309(to)]TJ/F30 9.9626 Tf 76.89 0 Td [(psb_spins)]TJ/F8 9.9626 Tf 47.073 0 Td [(;)-317(this,)-314(ho)28(w)28(ev)27(er,)-314(w)28(ould)-309(en)28(tail)-309(a)-309(doubling)-309(of)-309(memory)]TJ -123.963 -11.955 Td [(o)-28(ccupation,)-333(and)-333(th)27(u)1(s)-334(w)28(ould)-333(b)-28(e)-333(almos)-1(t)-333(alw)28(a)28(ys)-334(far)-333(from)-333(optimal.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -22.617 Td [(o)32(vr)]TJ ET q -1 0 0 1 116.758 591.948 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 99.895 139.245 cm +[]0 d 0 J 0.398 w 0 0 m 137.482 0 l S Q BT -/F27 9.9626 Tf 120.195 591.749 Td [(mst)]TJ +/F32 5.9776 Tf 110.987 132.603 Td [(3)]TJ/F31 7.9701 Tf 4.151 -2.813 Td [(The)-323(subroutine)-324(st)30(yle)]TJ/F45 7.9701 Tf 78.401 0 Td [(psb)]TJ ET q -1 0 0 1 139.405 591.948 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 206.75 129.989 cm +[]0 d 0 J 0.398 w 0 0 m 2.541 0 l S Q BT -/F27 9.9626 Tf 142.842 591.749 Td [(idx)]TJ -0 g 0 G -/F8 9.9626 Tf 20.575 0 Td [(A)-368(l)1(is)-1(t)-367(to)-368(r)1(e)-1(tri)1(e)-1(v)28(e)-367(the)-368(v)56(alue)-368(of)-367(eac)28(h)-368(o)28(v)28(erlap)-368(elemen)28(t)-368(from)-367(the)-368(re-)]TJ -38.615 -11.955 Td [(sp)-28(ectiv)28(e)-333(mas)-1(ter)-333(pro)-28(cess.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-333(of)-334(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ -0 0 1 rg 0 0 1 RG - [-333(3.3)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.907 -22.618 Td [(o)32(vrlap)]TJ +/F45 7.9701 Tf 209.29 129.79 Td [(precinit)]TJ/F31 7.9701 Tf 36.45 0 Td [(and)]TJ/F45 7.9701 Tf 16.22 0 Td [(psb)]TJ ET q -1 0 0 1 131.875 545.42 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 275.171 129.989 cm +[]0 d 0 J 0.398 w 0 0 m 2.541 0 l S Q BT -/F27 9.9626 Tf 135.312 545.221 Td [(elem)]TJ +/F45 7.9701 Tf 277.711 129.79 Td [(precbl)]TJ/F31 7.9701 Tf 27.982 0 Td [(are)-323(still)-324(supp)-29(orted)-323(for)-324(ba)1(c)29(kw)30(ard)-324(com-)]TJ -205.798 -9.464 Td [(patibilit)29(y)]TJ 0 g 0 G -/F8 9.9626 Tf 28.214 0 Td [(F)83(or)-333(all)-333(o)28(v)27(erlap)-333(p)-28(oin)28(ts)-333(b)-28(elonging)-333(to)-334(th)-333(ecurren)28(t)-333(pro)-28(cess:)]TJ 0 g 0 G - -29.536 -22.617 Td [(1.)]TJ +/F8 9.9626 Tf 169.365 -29.888 Td [(7)]TJ 0 g 0 G - [-500(Ov)28(erlap)-333(p)-28(oin)28(t)-334(index;)]TJ +ET + +endstream +endobj +878 0 obj +<< +/Length 7473 +>> +stream 0 g 0 G - 0 -17.287 Td [(2.)]TJ 0 g 0 G - [-500(Num)28(b)-28(er)-333(of)-334(pr)1(o)-28(cesses)-334(sharing)-333(that)-333(o)27(v)28(erlap)-333(p)-28(oin)28(ts;)]TJ +BT +/F27 9.9626 Tf 150.705 706.129 Td [(2.3.1)-1150(User-de\014ned)-383(index)-384(mappings)]TJ/F8 9.9626 Tf 0 -18.389 Td [(PSBLAS)-385(s)-1(u)1(pp)-28(orts)-386(user-de\014ned)-385(global)-386(to)-386(lo)-27(cal)-386(index)-386(mappings,)-398(sub)-56(ject)-385(to)-386(the)]TJ 0 -11.956 Td [(constrain)28(ts)-334(ou)1(tlined)-334(in)-333(sec.)]TJ +0 0 1 rg 0 0 1 RG + [-333(2.3)]TJ 0 g 0 G - 0 -17.286 Td [(3.)]TJ + [(:)]TJ 0 g 0 G - [-500(Index)-333(of)-334(a)-333(\134master")-333(pro)-28(cess:)]TJ -9.188 -22.617 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(allo)-28(catable)-333(in)28(teger)-333(arra)27(y)-333(of)-333(rank)-334(t)28(w)28(o.)]TJ + 12.176 -19.925 Td [(1.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -22.618 Td [(bnd)]TJ -ET -q -1 0 0 1 119.678 442.996 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 123.115 442.796 Td [(elem)]TJ + [-500(The)-333(set)-334(of)-333(indices)-333(o)27(wned)-333(lo)-28(cally)-333(m)28(ust)-334(b)-27(e)-334(mapp)-28(ed)-333(to)-333(the)-334(set)-333(1)]TJ/F11 9.9626 Tf 282.774 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 19.263 -1.494 Td [(ro)28(w)]TJ/F9 4.9813 Tf 15.802 -0.997 Td [(i)]TJ/F8 9.9626 Tf 3.654 2.491 Td [(;)]TJ 0 g 0 G -/F8 9.9626 Tf 28.213 0 Td [(A)-270(list)-269(of)-270(all)-269(b)-28(oundary)-269(p)-28(oin)28(ts,)-283(i.e.)-423(p)-28(oin)28(ts)-269(that)-270(ha)28(v)28(e)-270(a)-269(connection)-270(with)]TJ -26.526 -11.955 Td [(other)-333(pro)-28(cesses.)]TJ -24.907 -21.944 Td [(The)-450(F)83(ortran)-450(2003)-450(declaration)-450(for)]TJ/F30 9.9626 Tf 152.457 0 Td [(psb_desc_type)]TJ/F8 9.9626 Tf 72.477 0 Td [(structures)-450(is)-450(as)-450(follo)28(ws:)-678(A)]TJ + -321.493 -19.925 Td [(2.)]TJ +0 g 0 G + [-500(The)-333(set)-334(of)-333(halo)-333(p)-28(oin)28(ts)-334(m)28(ust)-333(b)-28(e)-333(mapp)-28(ed)-333(to)-334(the)-333(set)]TJ/F11 9.9626 Tf 232.684 0 Td [(n)]TJ/F8 9.9626 Tf 5.98 -1.495 Td [(ro)28(w)]TJ/F9 4.9813 Tf 15.802 -0.996 Td [(i)]TJ/F8 9.9626 Tf 5.868 2.491 Td [(+)-222(1)]TJ/F11 9.9626 Tf 16.604 0 Td [(:)-167(:)-166(:)-167(n)]TJ/F8 9.9626 Tf 19.263 -3.487 Td [(col)]TJ/F9 4.9813 Tf 12.177 -0.996 Td [(i)]TJ/F8 9.9626 Tf 3.654 4.483 Td [(;)]TJ -324.208 -19.926 Td [(but)-366(otherwise)-366(the)-365(mapping)-366(is)-366(arbitrary)84(.)-542(The)-366(user)-366(application)-366(is)-365(resp)-28(onsible)-366(to)]TJ 0 -11.955 Td [(ensure)-356(consistency)-356(of)-356(this)-356(mapping;)-367(some)-356(errors)-356(ma)27(y)-356(b)-27(e)-356(caugh)27(t)-356(b)28(y)-356(the)-356(library)84(,)]TJ 0 -11.955 Td [(but)-377(this)-378(is)-377(not)-377(guaran)28(te)-1(ed.)-576(The)-377(application)-378(structure)-377(to)-377(s)-1(u)1(pp)-28(ort)-378(t)1(his)-378(usage)-377(is)]TJ 0 -11.955 Td [(as)-333(follo)27(ws:)]TJ +0 g 0 G + 12.176 -19.925 Td [(1.)]TJ 0 g 0 G + [-500(Initialize)-222(index)-222(space)-223(with)]TJ/F30 9.9626 Tf 125.696 0 Td [(psb_cdall\050ictx,desc,info,vl=vl,lidx=lidx\051)]TJ/F8 9.9626 Tf -112.966 -11.955 Td [(passing)-253(the)-254(v)28(ectors)]TJ/F30 9.9626 Tf 83.59 0 Td [(vl\050:\051)]TJ/F8 9.9626 Tf 28.674 0 Td [(con)28(taining)-253(the)-254(set)-253(of)-253(global)-253(indices)-254(o)28(wned)-253(b)28(y)-253(the)]TJ -112.264 -11.956 Td [(curren)28(t)-334(pr)1(o)-28(cess)-334(and)]TJ/F30 9.9626 Tf 88.751 0 Td [(lidx\050:\051)]TJ/F8 9.9626 Tf 39.933 0 Td [(con)28(taining)-333(the)-334(corresp)-28(ondin)1(g)-334(lo)-28(cal)-333(indices;)]TJ 0 g 0 G + -141.414 -19.925 Td [(2.)]TJ 0 g 0 G + [-500(Add)-266(the)-266(halo)-266(p)-27(oin)27(ts)]TJ/F30 9.9626 Tf 100.593 0 Td [(ja\050:\051)]TJ/F8 9.9626 Tf 28.801 0 Td [(and)-266(their)-266(asso)-28(ciated)-265(lo)-28(cal)-266(indices)]TJ/F30 9.9626 Tf 143.508 0 Td [(lidx\050:\051)]TJ/F8 9.9626 Tf 39.261 0 Td [(with)]TJ -299.433 -11.955 Td [(a\050some\051)-333(c)-1(all\050)1(s)-1(\051)-333(to)]TJ/F30 9.9626 Tf 79.812 0 Td [(psb_cdins\050nz,ja,desc,info,lidx=lidx\051)]TJ/F8 9.9626 Tf 188.293 0 Td [(;)]TJ 0 g 0 G + -280.835 -19.925 Td [(3.)]TJ 0 g 0 G -/F30 9.9626 Tf -207.747 -21.604 Td [(type)-525(psb_desc_type)]TJ 20.921 -11.955 Td [(class\050psb_indx_map\051,)-525(allocatable)-525(::)-525(indxmap)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_halo_index)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ext_index)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ovrlap_index)]TJ 0 -11.956 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ovr_mst_idx)]TJ 0 -11.955 Td [(integer,)-525(allocatable)-1050(::)-525(ovrlap_elem\050:,:\051)]TJ 0 -11.955 Td [(integer,)-525(allocatable)-1050(::)-525(bnd_elem\050:\051)]TJ -20.921 -11.955 Td [(end)-525(type)-525(psb_desc_type)]TJ/F8 9.9626 Tf -17.187 -30.054 Td [(Figure)-464(3:)-705(The)-464(PSBLAS)-464(de\014ned)-464(data)-464(t)28(yp)-28(e)-464(that)-463(con)27(tains)-464(th)1(e)-464(com)-1(m)28(unication)]TJ 0 -11.955 Td [(descriptor.)]TJ + [-500(Assem)28(ble)-334(the)-333(descriptor)-333(with)]TJ/F30 9.9626 Tf 143.02 0 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 47.073 0 Td [(;)]TJ 0 g 0 G - 0 -24.98 Td [(comm)28(unication)-415(desc)-1(ri)1(ptor)-416(asso)-27(ciate)-1(d)-415(with)-415(a)-415(sparse)-415(matrix)-415(has)-416(a)-415(state,)-435(whic)27(h)]TJ 0 -11.955 Td [(can)-333(tak)27(e)-333(the)-333(follo)28(wing)-334(v)56(alues:)]TJ + -190.093 -19.926 Td [(4.)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -21.944 Td [(Build:)]TJ + [-500(Build)-240(the)-240(sparse)-240(matrices)-240(and)-240(v)27(ectors,)-258(optionally)-240(making)-240(use)-241(in)]TJ/F30 9.9626 Tf 284.462 0 Td [(psb_spins)]TJ/F8 9.9626 Tf -271.732 -11.955 Td [(and)]TJ/F30 9.9626 Tf 19.727 0 Td [(psb_geins)]TJ/F8 9.9626 Tf 50.749 0 Td [(of)-369(the)]TJ/F30 9.9626 Tf 29.214 0 Td [(local)]TJ/F8 9.9626 Tf 29.827 0 Td [(argumen)28(t)-369(sp)-28(ecifying)-369(that)-369(the)-369(indices)-369(in)]TJ/F30 9.9626 Tf 176.06 0 Td [(ia)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)]TJ/F30 9.9626 Tf -316.038 -11.955 Td [(ja)]TJ/F8 9.9626 Tf 13.782 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(irw)]TJ/F8 9.9626 Tf 15.691 0 Td [(,)-333(resp)-28(ectiv)28(ely)83(,)-333(are)-334(already)-333(lo)-28(cal)-333(indices.)]TJ/F16 11.9552 Tf -73.751 -27.888 Td [(2.4)-1125(Programming)-375(mo)-31(del)]TJ/F8 9.9626 Tf 0 -18.39 Td [(The)-325(PSBLAS)-324(librarary)-325(is)-325(based)-324(o)-1(n)-324(the)-325(Single)-325(Program)-324(Multiple)-325(Data)-325(\050SPMD\051)]TJ 0 -11.955 Td [(programming)-413(mo)-28(del:)-603(eac)27(h)-413(pro)-27(cess)-413(participating)-413(in)-413(the)-413(computation)-413(p)-28(erforms)]TJ 0 -11.955 Td [(the)-333(same)-334(actions)-333(on)-333(a)-334(c)28(h)28(unk)-333(of)-334(data.)-444(P)28(arallelism)-334(is)-333(th)28(us)-334(data-d)1(riv)27(en.)]TJ 14.944 -11.955 Td [(Because)-389(of)-389(this)-389(structure,)-402(m)-1(an)28(y)-389(subrou)1(tines)-389(co)-28(ordinate)-389(their)-389(action)-389(across)]TJ -14.944 -11.956 Td [(the)-478(v)56(arious)-478(pro)-28(cesses,)-514(th)28(us)-478(pro)28(viding)-477(a)-1(n)-477(implicit)-478(sync)28(hronization)-478(p)-28(oin)28(t,)-514(and)]TJ 0 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71.504 0 Td [(m)28(ust)-359(b)-28(e)-359(called)-359(sim)28(ultaneously)-359(b)28(y)-359(all)-359(the)-359(pro)-28(cesses)-359(in)-359(the)-359(rele-)]TJ -46.597 -11.955 Td [(v)56(an)27(t)-333(comm)28(unication)-333(c)-1(on)28(text;)]TJ 0 g 0 G - 141.968 -29.888 Td [(11)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(Async)32(hronous:)]TJ +0 g 0 G +/F8 9.9626 Tf 78.32 0 Td [(ma)28(y)-334(b)-27(e)-334(called)-333(in)-333(a)-334(totally)-333(indep)-28(enden)28(t)-333(manner.)]TJ +0 g 0 G + 91.045 -72.817 Td [(8)]TJ 0 g 0 G ET endstream endobj -881 0 obj +889 0 obj << -/Length 5199 +/Length 8464 >> stream 0 g 0 G 0 g 0 G BT -/F27 9.9626 Tf 150.705 706.129 Td [(3.1.1)-1150(Descriptor)-384(M)1(etho)-32(ds)]TJ 0 -18.549 Td [(get)]TJ +/F16 14.3462 Tf 99.895 706.129 Td [(3)-1125(Data)-375(Structures)-375(and)-375(Classes)]TJ/F8 9.9626 Tf 0 -22.335 Td [(In)-369(th)1(is)-369(c)28(hapter)-369(w)28(e)-369(il)1(lustrate)-369(the)-369(d)1(ata)-369(structures)-369(u)1(s)-1(ed)-368(for)-368(de\014nition)-369(of)-368(routines)]TJ 0 -11.955 Td [(in)28(terfaces.)-796(They)-450(include)-451(data)-450(structures)-450(for)-451(sparse)-450(matrices,)-480(comm)28(unication)]TJ 0 -11.955 Td [(descriptors)-333(and)-334(precondition)1(e)-1(rs.)]TJ 14.944 -12.231 Td [(All)-319(the)-319(data)-319(t)28(yp)-28(es)-319(and)-319(the)-319(b)1(as)-1(i)1(c)-319(s)-1(u)1(broutine)-319(in)28(terface)-1(s)-318(relate)-1(d)-318(to)-319(descriptors)]TJ -14.944 -11.956 Td [(and)-445(sparse)-444(matrices)-445(are)-445(de\014ned)-445(in)-444(the)-445(mo)-28(dule)]TJ/F30 9.9626 Tf 213.082 0 Td [(psb_base_mod)]TJ/F8 9.9626 Tf 62.764 0 Td [(;)-500(this)-445(will)-445(ha)28(v)28(e)]TJ -275.846 -11.955 Td [(to)-451(b)-28(e)-451(included)-452(b)28(y)-451(ev)28(ery)-452(user)-451(subroutine)-451(that)-451(mak)27(es)-451(use)-451(of)-452(th)1(e)-452(library)84(.)-799(The)]TJ 0 -11.955 Td [(preconditioners)-333(are)-334(de\014ned)-333(in)-333(the)-334(mo)-27(dule)]TJ/F30 9.9626 Tf 184.725 0 Td [(psb_prec_mod)]TJ/F8 9.9626 Tf -169.781 -12.231 Td [(In)28(teger,)-510(real)-475(and)-475(complex)-475(data)-475(t)28(yp)-28(es)-474(are)-475(parametrized)-475(with)-475(a)-475(kind)-474(t)27(yp)-27(e)]TJ -14.944 -11.955 Td [(de\014ned)-333(in)-334(the)-333(library)-333(as)-333(follo)27(ws:)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -20.754 Td [(psb)]TJ ET q -1 0 0 1 166.827 687.78 cm +1 0 0 1 117.832 567.046 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 170.264 687.58 Td [(lo)-32(cal)]TJ +/F27 9.9626 Tf 121.269 566.847 Td [(spk)]TJ ET q -1 0 0 1 194.025 687.78 cm +1 0 0 1 138.887 567.046 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -BT -/F27 9.9626 Tf 197.462 687.58 Td [(ro)32(ws)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(lo)-32(cal)-383(ro)32(ws)]TJ 0 g 0 G +BT +/F8 9.9626 Tf 147.306 566.847 Td [(Kind)-472(parameter)-472(for)-472(short)-472(precision)-473(real)-472(and)-472(complex)-472(data;)-542(corre-)]TJ -22.504 -11.955 Td [(sp)-28(onds)-333(to)-333(a)]TJ/F30 9.9626 Tf 53.522 0 Td [(REAL)]TJ/F8 9.9626 Tf 24.242 0 Td [(declaration)-333(and)-334(i)1(s)-334(normally)-333(4)-333(b)27(ytes;)]TJ 0 g 0 G -/F30 9.9626 Tf -46.757 -18.548 Td [(nr)-525(=)-525(desc%get_local_rows\050\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -20.267 Td [(desc)]TJ -0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -80.358 -34.13 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -20.267 Td [(F)96(unction)-384(v)64(alue)]TJ -0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(The)-460(n)28(um)27(b)-27(er)-461(of)-460(lo)-28(cal)-460(ro)28(ws,)-492(i.e.)-825(the)-460(n)28(um)27(b)-27(er)-461(of)-460(ro)28(ws)-460(o)28(wned)]TJ -53.48 -11.955 Td [(b)28(y)-401(the)-401(curren)27(t)-401(pro)-27(ces)-1(s;)-435(as)-401(explained)-401(in)]TJ -0 0 1 rg 0 0 1 RG - [-401(1)]TJ -0 g 0 G - [(,)-418(it)-401(is)-401(equal)-401(to)]TJ/F14 9.9626 Tf 249.678 0 Td [(jI)]TJ/F10 6.9738 Tf 8.192 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.431 0 Td [(+)]TJ/F14 9.9626 Tf 10.413 0 Td [(jB)]TJ/F10 6.9738 Tf 9.311 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)-648(The)]TJ -292.426 -11.955 Td [(returned)-333(v)55(alue)-333(is)-333(sp)-28(eci\014c)-334(to)-333(the)-333(calling)-334(p)1(ro)-28(cess.)]TJ/F27 9.9626 Tf -24.906 -26.35 Td [(get)]TJ +/F27 9.9626 Tf -102.671 -21.03 Td [(psb)]TJ ET q -1 0 0 1 166.827 489.912 cm +1 0 0 1 117.832 534.062 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 170.264 489.712 Td [(lo)-32(cal)]TJ +/F27 9.9626 Tf 121.269 533.863 Td [(dpk)]TJ ET q -1 0 0 1 194.025 489.912 cm +1 0 0 1 140.733 534.062 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -BT -/F27 9.9626 Tf 197.462 489.712 Td [(cols)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(lo)-32(cal)-383(cols)]TJ 0 g 0 G +BT +/F8 9.9626 Tf 149.152 533.863 Td [(Kind)-494(parameter)-495(for)-494(long)-495(precision)-494(real)-495(and)-494(complex)-495(d)1(ata;)-576(corr)1(e)-1(-)]TJ -24.35 -11.956 Td [(sp)-28(onds)-333(to)-333(a)]TJ/F30 9.9626 Tf 53.522 0 Td [(DOUBLE)-525(PRECISION)]TJ/F8 9.9626 Tf 87.006 0 Td [(declaration)-333(and)-334(is)-333(normally)-333(8)-333(b)27(ytes;)]TJ 0 g 0 G -/F30 9.9626 Tf -46.757 -18.548 Td [(nc)-525(=)-525(desc%get_local_cols\050\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -20.267 Td [(desc)]TJ +/F27 9.9626 Tf -165.435 -21.029 Td [(psb)]TJ +ET +q +1 0 0 1 117.832 501.077 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 121.269 500.878 Td [(mpk)]TJ +ET +q +1 0 0 1 143.916 501.077 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q 0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +BT +/F8 9.9626 Tf 152.334 500.878 Td [(Kind)-312(parameter)-311(for)-312(4-b)28(ytes)-312(in)28(teger)-312(data,)-316(as)-312(is)-312(alw)28(a)28(ys)-312(used)-312(b)28(y)-312(MPI;)]TJ 0 g 0 G -/F27 9.9626 Tf -80.358 -34.129 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -52.439 -21.03 Td [(psb)]TJ +ET +q +1 0 0 1 117.832 480.048 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 121.269 479.848 Td [(epk)]TJ +ET +q +1 0 0 1 139.619 480.048 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q 0 g 0 G +BT +/F8 9.9626 Tf 148.038 479.848 Td 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[(Kind)-470(parameter)-471(for)-470(\134lo)-28(cal")-471(in)28(teger)-470(indices)-471(and)-470(data;)-539(with)-471(default)]TJ -21.167 -11.956 Td [(build)-333(options)-333(this)-334(is)-333(a)-333(4)-334(b)28(ytes)-333(in)27(teger;)]TJ 0 g 0 G - [(,)-346(it)-343(is)-344(equal)-343(to)]TJ/F14 9.9626 Tf 81.777 0 Td [(jI)]TJ/F10 6.9738 Tf 8.192 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.049 0 Td [(+)]TJ/F14 9.9626 Tf 10.031 0 Td [(jB)]TJ/F10 6.9738 Tf 9.311 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.049 0 Td [(+)]TJ/F14 9.9626 Tf 10.03 0 Td [(jH)]TJ/F10 6.9738 Tf 11.181 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 2.768 0 Td [(.)-475(The)-344(returned)-343(v)55(al)1(ue)-344(is)-344(sp)-27(ec)-1(i)1(\014c)-344(to)-344(the)]TJ -153.339 -11.956 Td [(calling)-333(pro)-28(cess.)]TJ/F27 9.9626 Tf -24.906 -26.349 Td [(get)]TJ +/F27 9.9626 Tf -24.907 -21.029 Td [(psb)]TJ ET q -1 0 0 1 166.827 280.088 cm +1 0 0 1 117.832 414.078 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 170.264 279.889 Td [(global)]TJ +/F27 9.9626 Tf 121.269 413.879 Td [(lpk)]TJ ET q -1 0 0 1 200.708 280.088 cm +1 0 0 1 137.551 414.078 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q +0 g 0 G +BT +/F8 9.9626 Tf 145.969 413.879 Td [(Kind)-409(parameter)-409(for)-409(\134global")-409(in)28(teger)-409(indices)-410(and)-409(data;)-447(with)-409(defaul)1(t)]TJ -21.167 -11.955 Td [(build)-333(options)-333(this)-334(is)-333(an)-333(8)-334(b)28(ytes)-333(in)28(te)-1(ger;)]TJ -24.907 -20.754 Td [(The)-378(in)27(teger)-378(kinds)-378(for)-379(lo)-28(cal)-378(and)-378(global)-379(indices)-378(can)-379(b)-27(e)-379(c)28(hosen)-378(at)-379(con\014gure)-378(time)]TJ 0 -11.955 Td [(to)-352(hold)-352(4)-352(or)-352(8)-352(b)28(ytes,)-357(with)-352(the)-352(global)-352(indices)-352(at)-352(least)-352(as)-352(large)-352(as)-352(the)-352(lo)-28(cal)-352(ones.)]TJ 0 -11.955 Td [(T)83(ogether)-311(with)-311(the)-311(classes)-311(attributes)-311(w)28(e)-311(also)-311(discuss)-311(their)-311(metho)-28(ds.)-437(Most)-311(meth-)]TJ 0 -11.955 Td [(o)-28(ds)-342(detailed)-342(here)-342(only)-343(act)-342(on)-342(the)-342(lo)-28(cal)-342(v)55(ariable,)-344(i.e.)-471(their)-342(action)-343(i)1(s)-343(purely)-342(lo)-28(cal)]TJ 0 -11.956 Td [(and)-299(async)28(hronous)-299(unless)-298(otherwise)-299(stated.)-433(The)-299(list)-299(of)-299(metho)-27(ds)-299(here)-299(is)-299(not)-298(com)-1(-)]TJ 0 -11.955 Td [(pletely)-418(exhaustiv)27(e;)-460(man)27(y)-418(metho)-28(ds,)-439(esp)-28(ecially)-419(th)1(os)-1(e)-418(that)-418(alter)-419(th)1(e)-419(con)28(ten)28(ts)-419(of)]TJ 0 -11.955 Td [(the)-379(v)55(ariou)1(s)-380(ob)-55(jects,)-391(are)-379(usually)-379(not)-379(needed)-379(b)28(y)-379(the)-379(e)-1(n)1(d-use)-1(r)1(,)-391(and)-379(therefore)-379(are)]TJ 0 -11.955 Td [(describ)-28(ed)-333(in)-333(the)-334(dev)28(elop)-28(er's)-333(do)-28(cumen)28(tation.)]TJ/F16 11.9552 Tf 0 -29.353 Td [(3.1)-1125(Descriptor)-375(data)-375(structure)]TJ/F8 9.9626 Tf 0 -18.903 Td [(All)-349(the)-349(general)-349(matrix)-349(informations)-349(and)-349(elemen)28(ts)-349(to)-349(b)-28(e)-349(exc)28(hanged)-349(among)-349(pro-)]TJ 0 -11.955 Td [(cesses)-453(are)-453(stored)-453(within)-452(a)-453(data)-453(structure)-452(of)-453(the)-453(t)28(yp)-28(e)]TJ/F30 9.9626 Tf 242.532 0 Td [(psb)]TJ +ET +q +1 0 0 1 358.746 237.472 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 361.884 237.273 Td [(desc)]TJ +ET +q +1 0 0 1 383.433 237.472 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q BT -/F27 9.9626 Tf 204.145 279.889 Td [(ro)32(ws)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(global)-383(ro)32(ws)]TJ +/F30 9.9626 Tf 386.571 237.273 Td [(type)]TJ/F8 9.9626 Tf 20.922 0 Td [(.)-803(Ev)28(ery)]TJ -307.598 -11.956 Td [(structure)-437(of)-438(this)-437(t)28(yp)-28(e)-437(is)-438(asso)-28(ciated)-437(with)-437(a)-438(discretization)-437(pattern)-437(and)-438(enables)]TJ 0 -11.955 Td [(data)-302(comm)28(unications)-301(and)-302(other)-301(op)-28(erations)-302(that)-301(are)-302(necessary)-301(for)-302(implemen)28(ting)]TJ 0 -11.955 Td [(the)-333(v)55(arious)-333(algorithms)-333(of)-334(in)28(terest)-333(to)-334(us.)]TJ 14.944 -12.231 Td [(The)-281(data)-282(structure)-281(itself)]TJ/F30 9.9626 Tf 107.959 0 Td [(psb_desc_type)]TJ/F8 9.9626 Tf 70.797 0 Td [(can)-281(b)-28(e)-281(treate)-1(d)-281(as)-281(an)-281(opaque)-282(ob)-55(ject)]TJ -193.7 -11.955 Td [(handled)-406(via)-406(the)-406(to)-28(ols)-406(routi)1(nes)-407(of)-405(Sec)-1(.)]TJ +0 0 1 rg 0 0 1 RG + [-405(6)]TJ 0 g 0 G + [-406(or)-406(the)-406(query)-406(routines)-406(detailed)-406(b)-28(elo)28(w;)]TJ 0 -11.956 Td [(nev)28(ertheless)-334(w)28(e)-333(include)-334(here)-333(a)-333(description)-334(for)-333(the)-333(curious)-333(reader.)]TJ 14.944 -12.231 Td [(First)-248(w)28(e)-248(describ)-28(e)-248(t)1(he)]TJ/F30 9.9626 Tf 91.264 0 Td [(psb_indx_map)]TJ/F8 9.9626 Tf 65.233 0 Td [(t)28(yp)-28(e.)-416(This)-248(is)-248(a)-247(data)-248(structure)-248(that)-248(k)28(eeps)]TJ -171.441 -11.955 Td [(trac)28(k)-334(of)-333(a)-333(certain)-334(n)28(um)28(b)-28(er)-333(of)-333(basic)-334(issues)-333(suc)28(h)-334(as:)]TJ 0 g 0 G -/F30 9.9626 Tf -53.44 -18.548 Td [(nr)-525(=)-525(desc%get_global_rows\050\051)]TJ +/F14 9.9626 Tf 14.944 -20.753 Td [(\017)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ +/F8 9.9626 Tf 9.963 0 Td [(The)-333(v)55(alue)-333(of)-333(the)-334(comm)28(unication/MPI)-333(con)28(te)-1(x)1(t;)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ + 144.458 -29.888 Td [(9)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ +ET + +endstream +endobj +897 0 obj +<< +/Length 6827 +>> +stream 0 g 0 G 0 g 0 G - 0 -20.268 Td [(desc)]TJ 0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +BT +/F14 9.9626 Tf 165.649 706.129 Td [(\017)]TJ 0 g 0 G -/F27 9.9626 Tf -80.358 -34.129 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 9.962 0 Td [(The)-331(n)27(u)1(m)27(b)-27(e)-1(r)-331(of)-331(indices)-331(in)-331(the)-332(index)-331(space,)-332(i.e.)-443(global)-332(n)28(um)28(b)-28(er)-331(of)-331(ro)27(ws)-331(and)]TJ 0 -11.955 Td [(columns)-333(of)-334(a)-333(sparse)-333(matrix;)]TJ 0 g 0 G +/F14 9.9626 Tf -9.962 -20.409 Td [(\017)]TJ 0 g 0 G - 0 -20.267 Td [(F)96(unction)-384(v)64(alue)]TJ +/F8 9.9626 Tf 9.962 0 Td [(The)-333(lo)-28(cal)-334(set)-333(of)-333(indices,)-334(inclu)1(ding:)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(The)-390(n)28(um)27(b)-27(er)-391(of)-390(global)-390(ro)28(ws,)-405(i.e.)-615(the)-390(size)-391(of)-390(the)-390(global)-390(index)]TJ -53.48 -11.955 Td [(space.)]TJ +/F27 9.9626 Tf 11.208 -20.408 Td [({)]TJ 0 g 0 G - 141.968 -29.888 Td [(12)]TJ +/F8 9.9626 Tf 10.71 0 Td [(The)-333(n)27(um)28(b)-28(er)-333(of)-333(lo)-28(cal)-333(indices)-334(\050and)-333(lo)-28(cal)-333(ro)28(ws\051;)]TJ 0 g 0 G -ET - -endstream -endobj -885 0 obj -<< -/Length 4312 ->> -stream +/F27 9.9626 Tf -10.71 -16.182 Td [({)]TJ 0 g 0 G +/F8 9.9626 Tf 10.71 0 Td [(The)-333(n)27(um)28(b)-28(er)-333(of)-333(halo)-333(indices)-334(\050and)-333(therefore)-333(lo)-28(cal)-333(c)-1(olu)1(m)-1(n)1(s)-1(\051;)]TJ 0 g 0 G -BT -/F27 9.9626 Tf 99.895 706.129 Td [(get)]TJ -ET -q -1 0 0 1 116.018 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 119.455 706.129 Td [(global)]TJ -ET -q -1 0 0 1 149.899 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 153.336 706.129 Td [(cols)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(global)-383(cols)]TJ +/F27 9.9626 Tf -10.71 -16.181 Td [({)]TJ 0 g 0 G +/F8 9.9626 Tf 10.71 0 Td [(The)-333(global)-334(indices)-333(corresp)-28(onding)-333(to)-333(the)-334(lo)-27(cal)-334(ones.)]TJ -46.824 -20.409 Td [(There)-376(are)-376(m)-1(an)28(y)-376(di\013eren)28(t)-376(sc)27(hemes)-376(for)-376(storing)-376(these)-377(data;)-397(therefore)-376(there)-377(are)-376(a)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(er)-389(of)-389(t)28(yp)-28(es)-389(extending)-389(the)-388(base)-389(one,)-403(and)-389(the)-389(descriptor)-389(structure)-389(hold)1(s)-389(a)]TJ 0 -11.955 Td [(p)-28(olymorphic)-290(ob)-56(ject)-290(whose)-291(dyn)1(am)-1(ic)-290(t)28(yp)-28(e)-290(can)-291(b)-28(e)-290(an)28(y)-291(of)-290(the)-291(extend)1(e)-1(d)-290(t)28(yp)-28(es.)-430(The)]TJ 0 -11.955 Td [(metho)-28(ds)-333(asso)-28(ciated)-333(with)-334(this)-333(data)-333(t)28(yp)-28(e)-334(answ)28(er)-333(the)-334(f)1(ollo)27(wing)-333(queries:)]TJ 0 g 0 G -/F30 9.9626 Tf -53.441 -18.505 Td [(nr)-525(=)-525(desc%get_global_cols\050\051)]TJ +/F14 9.9626 Tf 14.944 -20.288 Td [(\017)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.105 Td [(T)32(yp)-32(e:)]TJ +/F8 9.9626 Tf 9.962 0 Td [(F)83(or)-271(a)-271(giv)28(en)-272(set)-271(of)-271(lo)-28(cal)-271(indices,)-284(\014nd)-271(the)-271(corresp)-28(onding)-271(indices)-272(in)-271(the)-271(global)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(ering;)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F14 9.9626 Tf -9.962 -20.408 Td [(\017)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.175 Td [(On)-383(En)32(try)]TJ +/F8 9.9626 Tf 9.962 0 Td [(F)83(or)-271(a)-271(giv)28(en)-272(set)-271(of)-271(global)-271(indices,)-284(\014nd)-271(the)-271(c)-1(or)1(re)-1(sp)-27(onding)-271(indices)-272(in)-271(the)-271(lo)-28(cal)]TJ 0 -11.955 Td [(n)28(um)28(b)-28(ering,)-333(if)-334(an)28(y)83(,)-333(or)-333(return)-333(an)-334(in)28(v)56(alid)]TJ 0 g 0 G +/F14 9.9626 Tf -9.962 -20.409 Td [(\017)]TJ 0 g 0 G - 0 -20.174 Td [(desc)]TJ +/F8 9.9626 Tf 9.962 0 Td [(Add)-333(a)-334(global)-333(index)-333(to)-333(the)-334(set)-333(of)-334(h)1(alo)-334(indices;)]TJ 0 g 0 G -/F8 9.9626 Tf 26.209 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +/F14 9.9626 Tf -9.962 -20.408 Td [(\017)]TJ 0 g 0 G -/F27 9.9626 Tf -80.359 -34.06 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 9.962 0 Td [(Find)-333(the)-334(pro)-27(cess)-334(o)28(wner)-333(of)-334(eac)28(h)-333(mem)27(b)-27(er)-334(of)-333(a)-333(set)-334(of)-333(global)-333(indices.)]TJ -24.906 -20.288 Td [(All)-355(metho)-28(ds)-355(but)-355(the)-355(last)-355(are)-355(purely)-355(lo)-28(cal;)-366(the)-355(last)-355(metho)-28(d)-355(p)-28(oten)28(tially)-355(requires)]TJ 0 -11.955 Td [(comm)28(unication)-259(among)-258(pro)-28(cesses,)-274(and)-258(th)28(us)-259(is)-258(a)-259(sync)28(hronous)-259(metho)-27(d.)-420(The)-258(c)27(hoice)]TJ 0 -11.955 Td [(of)-309(a)-310(sp)-28(eci\014c)-309(dynamic)-310(t)28(yp)-27(e)-310(for)-309(the)-310(index)-309(map)-310(is)-309(made)-310(at)-309(the)-309(time)-310(the)-309(descriptor)]TJ 0 -11.955 Td [(is)-333(initially)-334(al)1(lo)-28(cated,)-334(according)-333(to)-333(the)-334(mo)-27(de)-334(of)-333(initialization)-333(\050see)-334(also)]TJ +0 0 1 rg 0 0 1 RG + [-333(6)]TJ 0 g 0 G + [(\051.)]TJ 14.944 -12.076 Td [(The)-333(descriptor)-334(con)28(ten)28(ts)-333(are)-334(as)-333(follo)28(ws:)]TJ 0 g 0 G - 0 -20.174 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -14.944 -20.288 Td [(indxmap)]TJ 0 g 0 G -/F8 9.9626 Tf 78.387 0 Td [(The)-273(n)28(um)28(b)-28(er)-273(of)-272(global)-273(cols;)-293(usually)-273(this)-273(is)-272(e)-1(q)1(ual)-273(to)-273(the)-273(n)28(um)28(b)-28(er)]TJ -53.48 -11.956 Td [(of)-333(global)-334(ro)28(ws.)]TJ/F27 9.9626 Tf -24.907 -26.226 Td [(get)]TJ +/F8 9.9626 Tf 48.422 0 Td [(A)-222(p)-28(olymorphic)-222(v)56(ariable)-223(of)-222(a)-222(t)28(yp)-28(e)-222(that)-222(is)-223(an)28(y)-222(extension)-222(of)-222(the)-223(indx)]TJ ET q -1 0 0 1 116.018 520.998 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 476.354 370.98 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F27 9.9626 Tf 119.455 520.799 Td [(global)]TJ +/F8 9.9626 Tf 479.343 370.78 Td [(map)]TJ -303.732 -11.955 Td [(t)28(yp)-28(e)-333(describ)-28(ed)-333(ab)-28(o)28(v)27(e.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -32.363 Td [(halo)]TJ ET q -1 0 0 1 149.899 520.998 cm +1 0 0 1 172.238 326.661 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 153.336 520.799 Td [(indices)-383(|)-384(Get)-383(v)32(ector)-383(of)-384(global)-383(indices)]TJ -0 g 0 G +/F27 9.9626 Tf 175.675 326.462 Td [(index)]TJ 0 g 0 G -/F30 9.9626 Tf -53.441 -18.505 Td [(myidx)-525(=)-525(desc%get_global_indices\050[owned]\051)]TJ +/F8 9.9626 Tf 32.191 0 Td [(A)-384(list)-384(of)-385(the)-384(halo)-384(and)-384(b)-28(oundary)-384(elemen)28(ts)-384(for)-385(the)-384(curren)28(t)-384(pro)-28(cess)]TJ -32.255 -11.955 Td [(to)-347(b)-28(e)-347(exc)28(hanged)-347(with)-347(other)-348(p)1(ro)-28(cesses;)-354(for)-348(eac)28(h)-347(pro)-28(cesses)-347(with)-347(whic)28(h)-347(it)-347(is)]TJ 0 -11.956 Td [(necessary)-334(to)-333(comm)28(unicate:)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.105 Td [(T)32(yp)-32(e:)]TJ + 9.188 -20.408 Td [(1.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ + [-500(Pro)-28(cess)-333(iden)28(ti\014er;)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.174 Td [(On)-383(En)32(try)]TJ + 0 -16.182 Td [(2.)]TJ 0 g 0 G + [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ 0 g 0 G - 0 -20.175 Td [(desc)]TJ + 0 -16.181 Td [(3.)]TJ 0 g 0 G -/F8 9.9626 Tf 26.209 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ + [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(rece)-1(i)1(v)27(ed;)]TJ 0 g 0 G -/F27 9.9626 Tf -96.416 -32.13 Td [(o)32(wned)]TJ + 0 -16.182 Td [(4.)]TJ 0 g 0 G -/F8 9.9626 Tf 36.647 0 Td [(Cho)-28(ose)-439(if)-439(y)28(ou)-439(only)-439(w)27(an)28(t)-439(o)28(wned)-439(indices)-439(\050)]TJ/F30 9.9626 Tf 183.494 0 Td [(owned=.true.)]TJ/F8 9.9626 Tf 62.764 0 Td [(\051)-439(or)-439(also)-439(halo)]TJ -257.998 -11.955 Td [(indices)-333(\050)]TJ/F30 9.9626 Tf 36.585 0 Td [(owned=.false.)]TJ/F8 9.9626 Tf 67.994 0 Td [(\051.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 43.449 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -171.101 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(;)-333(default:)]TJ/F30 9.9626 Tf 43.448 0 Td [(.true.)]TJ/F8 9.9626 Tf 31.382 0 Td [(.)]TJ + [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ 0 g 0 G -/F27 9.9626 Tf -169.925 -34.06 Td [(On)-383(Return)]TJ + 0 -16.182 Td [(5.)]TJ 0 g 0 G + [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ -9.188 -20.408 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-334(of)-333(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ +0 0 1 rg 0 0 1 RG + [-333(3.3)]TJ 0 g 0 G - 0 -20.174 Td [(F)96(unction)-384(v)64(alue)]TJ + [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 78.387 0 Td [(The)-292(global)-292(ind)1(ice)-1(s,)-300(returned)-291(as)-292(an)-292(allo)-28(catable)-292(in)28(teger)-292(arra)28(y)-292(of)]TJ -53.48 -11.956 Td [(rank)-333(1.)]TJ/F27 9.9626 Tf -24.907 -26.226 Td [(get)]TJ +/F27 9.9626 Tf -24.906 -20.409 Td [(ext)]TJ ET q -1 0 0 1 116.018 267.673 cm +1 0 0 1 167.146 176.799 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 119.455 267.474 Td [(con)32(text)-383(|)-384(Get)-383(comm)32(unication)-384(con)32(text)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -19.56 -18.505 Td [(ictxt)-525(=)-525(desc%get_context\050\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -22.105 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -20.174 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -20.175 Td [(desc)]TJ -0 g 0 G -/F8 9.9626 Tf 26.209 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +/F27 9.9626 Tf 170.583 176.599 Td [(index)]TJ 0 g 0 G -/F27 9.9626 Tf -80.359 -34.06 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 32.191 0 Td [(A)-274(list)-274(of)-274(elemen)28(t)-274(indices)-274(to)-273(b)-28(e)-274(exc)28(hanged)-274(to)-274(implemen)28(t)-274(the)-274(mapping)]TJ -27.163 -11.955 Td [(b)-28(et)28(w)28(een)-334(a)-333(base)-333(descriptor)-334(and)-333(a)-333(descriptor)-334(with)-333(o)28(v)28(erlap.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-334(of)-333(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ +0 0 1 rg 0 0 1 RG + [-333(3.3)]TJ 0 g 0 G + [(.)]TJ 0 g 0 G - 0 -20.174 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -24.906 -20.408 Td [(o)32(vrlap)]TJ +ET +q +1 0 0 1 182.684 132.48 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 186.122 132.281 Td [(index)]TJ 0 g 0 G -/F8 9.9626 Tf 78.387 0 Td [(The)-333(comm)27(unication)-333(con)28(text.)]TJ +/F8 9.9626 Tf 32.191 0 Td [(A)-320(list)-320(of)-320(the)-320(o)28(v)28(erlap)-320(eleme)-1(n)28(ts)-320(for)-320(the)-320(curren)28(t)-320(pro)-28(cess,)-322(organized)]TJ -42.702 -11.955 Td [(in)-333(groups)-334(lik)28(e)-333(the)-333(previous)-334(v)28(ector:)]TJ 0 g 0 G - 88.488 -29.888 Td [(13)]TJ + 141.968 -29.888 Td [(10)]TJ 0 g 0 G ET endstream endobj -890 0 obj +908 0 obj << -/Length 4851 +/Length 5178 >> stream 0 g 0 G 0 g 0 G -BT -/F27 9.9626 Tf 150.705 706.129 Td [(Clone)-383(|)-384(clone)-383(curren)32(t)-383(ob)-64(ject)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf 0 -18.844 Td [(call)-1050(desc%clone\050descout,info\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -22.65 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -20.902 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -20.902 Td [(desc)]TJ -0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -80.358 -34.605 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -20.902 Td [(descout)]TJ -0 g 0 G -/F8 9.9626 Tf 42.757 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-334(in)1(put)-334(ob)-55(ject.)]TJ 0 g 0 G -/F27 9.9626 Tf -42.757 -20.902 Td [(info)]TJ +BT +/F8 9.9626 Tf 133.99 706.129 Td [(1.)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -27.192 Td [(CNV)-383(|)-384(con)32(v)32(ert)-383(in)32(ternal)-384(storage)-383(format)]TJ + [-500(Pro)-28(cess)-333(iden)28(ti\014er;)]TJ 0 g 0 G + 0 -17.286 Td [(2.)]TJ 0 g 0 G -/F30 9.9626 Tf 0 -18.844 Td [(call)-1050(desc%cnv\050mold\051)]TJ + [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)28(ts)-334(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.65 Td [(T)32(yp)-32(e:)]TJ + 0 -17.287 Td [(3.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ + [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(receiv)27(ed;)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.902 Td [(On)-383(En)32(try)]TJ + 0 -17.286 Td [(4.)]TJ 0 g 0 G + [-500(Num)28(b)-28(er)-333(of)-334(p)-27(oin)28(ts)-334(to)-333(b)-28(e)-333(sen)27(t;)]TJ 0 g 0 G - 0 -20.902 Td [(desc)]TJ + 0 -17.286 Td [(5.)]TJ 0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ + [-500(Indices)-333(of)-334(p)-27(oin)27(ts)-333(to)-333(b)-28(e)-333(sen)27(t;)]TJ -9.188 -22.618 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-333(of)-334(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ +0 0 1 rg 0 0 1 RG + [-333(3.3)]TJ 0 g 0 G -/F27 9.9626 Tf -80.358 -32.858 Td [(mold)]TJ + [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 29.805 0 Td [(the)-333(desred)-334(in)28(teger)-333(storage)-334(format.)]TJ -4.899 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(Sp)-28(eci\014ed)-222(as:)-389(a)-222(ob)-56(ject)-222(of)-222(t)28(yp)-28(e)-222(deriv)28(e)-1(d)-222(from)-222(\050in)28(teger\051)]TJ/F30 9.9626 Tf 219.871 0 Td [(psb)]TJ +/F27 9.9626 Tf -24.907 -22.617 Td [(o)32(vr)]TJ ET q -1 0 0 1 411.8 355.452 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 116.758 591.948 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 414.939 355.253 Td [(T)]TJ +/F27 9.9626 Tf 120.195 591.749 Td [(mst)]TJ ET q -1 0 0 1 420.797 355.452 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 423.935 355.253 Td [(base)]TJ -ET -q -1 0 0 1 445.484 355.452 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 448.622 355.253 Td [(vect)]TJ -ET -q -1 0 0 1 470.171 355.452 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 473.309 355.253 Td [(type)]TJ/F8 9.9626 Tf 20.922 0 Td [(.)]TJ -343.526 -22.895 Td [(The)]TJ/F30 9.9626 Tf 20.085 0 Td [(mold)]TJ/F8 9.9626 Tf 23.848 0 Td [(argumen)28(ts)-294(ma)28(y)-294(b)-28(e)-294(emplo)28(y)28(ed)-294(to)-294(in)28(terface)-294(with)-293(sp)-28(ecial)-294(devices,)-302(suc)28(h)-294(as)]TJ -43.933 -11.955 Td [(GPUs)-333(and)-334(other)-333(accelerators.)]TJ/F27 9.9626 Tf 0 -27.191 Td [(psb)]TJ -ET -q -1 0 0 1 168.641 293.411 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 172.078 293.212 Td [(cd)]TJ -ET -q -1 0 0 1 184.223 293.411 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 187.66 293.212 Td [(get)]TJ -ET -q -1 0 0 1 203.782 293.411 cm +1 0 0 1 139.405 591.948 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 207.22 293.212 Td [(large)]TJ +/F27 9.9626 Tf 142.842 591.749 Td [(idx)]TJ +0 g 0 G +/F8 9.9626 Tf 20.575 0 Td [(A)-368(l)1(is)-1(t)-367(to)-368(r)1(e)-1(tri)1(e)-1(v)28(e)-367(the)-368(v)56(alue)-368(of)-367(eac)28(h)-368(o)28(v)28(erlap)-368(elemen)28(t)-368(from)-367(the)-368(re-)]TJ -38.615 -11.955 Td [(sp)-28(ectiv)28(e)-333(mas)-1(ter)-333(pro)-28(cess.)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)28(ector)-333(of)-334(in)28(teger)-333(t)27(yp)-27(e,)-334(see)]TJ +0 0 1 rg 0 0 1 RG + [-333(3.3)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -22.618 Td [(o)32(vrlap)]TJ ET q -1 0 0 1 232.357 293.411 cm +1 0 0 1 131.875 545.42 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 235.794 293.212 Td [(threshold)-268(|)-268(Get)-268(threshold)-269(for)-268(index)-268(mapping)-268(switc)32(h)]TJ +/F27 9.9626 Tf 135.312 545.221 Td [(elem)]TJ 0 g 0 G +/F8 9.9626 Tf 28.214 0 Td [(F)83(or)-333(all)-333(o)28(v)27(erlap)-333(p)-28(oin)28(ts)-333(b)-28(elonging)-333(to)-334(th)-333(ecurren)28(t)-333(pro)-28(cess:)]TJ 0 g 0 G -/F30 9.9626 Tf -85.089 -18.844 Td [(ith)-525(=)-525(psb_cd_get_large_threshold\050\051)]TJ + -29.536 -22.617 Td [(1.)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.65 Td [(T)32(yp)-32(e:)]TJ + [-500(Ov)28(erlap)-333(p)-28(oin)28(t)-334(index;)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ + 0 -17.287 Td [(2.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.902 Td [(On)-383(Return)]TJ + [-500(Num)28(b)-28(er)-333(of)-334(pr)1(o)-28(cesses)-334(sharing)-333(that)-333(o)27(v)28(erlap)-333(p)-28(oin)28(ts;)]TJ 0 g 0 G + 0 -17.286 Td [(3.)]TJ 0 g 0 G - 0 -20.903 Td [(F)96(unction)-384(v)64(alue)]TJ + [-500(Index)-333(of)-334(a)-333(\134master")-333(pro)-28(cess:)]TJ -9.188 -22.617 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(allo)-28(catable)-333(in)28(teger)-333(arra)27(y)-333(of)-333(rank)-334(t)28(w)28(o.)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(The)-333(curren)27(t)-333(v)56(alue)-334(for)-333(the)-333(size)-334(threshold.)]TJ/F27 9.9626 Tf -78.386 -27.191 Td [(psb)]TJ -ET -q -1 0 0 1 168.641 182.921 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 172.078 182.722 Td [(cd)]TJ -ET -q -1 0 0 1 184.223 182.921 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 187.66 182.722 Td [(set)]TJ -ET -q -1 0 0 1 202.573 182.921 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 206.01 182.722 Td [(large)]TJ +/F27 9.9626 Tf -24.907 -22.618 Td [(bnd)]TJ ET q -1 0 0 1 231.147 182.921 cm +1 0 0 1 119.678 442.996 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 234.585 182.722 Td [(threshold)-323(|)-324(Set)-323(threshold)-323(for)-324(index)-323(mapping)-324(switc)32(h)]TJ +/F27 9.9626 Tf 123.115 442.796 Td [(elem)]TJ +0 g 0 G +/F8 9.9626 Tf 28.213 0 Td [(A)-270(list)-269(of)-270(all)-269(b)-28(oundary)-269(p)-28(oin)28(ts,)-283(i.e.)-423(p)-28(oin)28(ts)-269(that)-270(ha)28(v)28(e)-270(a)-269(connection)-270(with)]TJ -26.526 -11.955 Td [(other)-333(pro)-28(cesses.)]TJ -24.907 -21.944 Td [(The)-450(F)83(ortran)-450(2003)-450(declaration)-450(for)]TJ/F30 9.9626 Tf 152.457 0 Td [(psb_desc_type)]TJ/F8 9.9626 Tf 72.477 0 Td [(structures)-450(is)-450(as)-450(follo)28(ws:)-678(A)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -83.88 -18.844 Td [(call)-525(psb_cd_set_large_threshold\050ith\051)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.65 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.902 Td [(On)-383(En)32(try)]TJ +/F30 9.9626 Tf -207.747 -21.604 Td [(type)-525(psb_desc_type)]TJ 20.921 -11.955 Td [(class\050psb_indx_map\051,)-525(allocatable)-525(::)-525(indxmap)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_halo_index)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ext_index)]TJ 0 -11.955 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ovrlap_index)]TJ 0 -11.956 Td [(type\050psb_i_vect_type\051)-525(::)-525(v_ovr_mst_idx)]TJ 0 -11.955 Td [(integer,)-525(allocatable)-1050(::)-525(ovrlap_elem\050:,:\051)]TJ 0 -11.955 Td [(integer,)-525(allocatable)-1050(::)-525(bnd_elem\050:\051)]TJ -20.921 -11.955 Td [(end)-525(type)-525(psb_desc_type)]TJ/F8 9.9626 Tf -17.187 -30.054 Td [(Figure)-464(3:)-705(The)-464(PSBLAS)-464(de\014ned)-464(data)-464(t)28(yp)-28(e)-464(that)-463(con)27(tains)-464(th)1(e)-464(com)-1(m)28(unication)]TJ 0 -11.955 Td [(descriptor.)]TJ 0 g 0 G + 0 -24.98 Td [(comm)28(unication)-415(desc)-1(ri)1(ptor)-416(asso)-27(ciate)-1(d)-415(with)-415(a)-415(sparse)-415(matrix)-415(has)-416(a)-415(state,)-435(whic)27(h)]TJ 0 -11.955 Td [(can)-333(tak)27(e)-333(the)-333(follo)28(wing)-334(v)56(alues:)]TJ 0 g 0 G -/F8 9.9626 Tf 166.874 -29.888 Td [(14)]TJ +/F27 9.9626 Tf 0 -21.944 Td [(Build:)]TJ +0 g 0 G +/F8 9.9626 Tf 35.409 0 Td [(State)-306(en)28(tered)-306(after)-307(the)-306(\014rst)-306(allo)-28(cation,)-311(and)-306(b)-28(efore)-306(the)-306(\014rst)-306(assem)27(bly;)-315(in)]TJ -10.502 -11.956 Td [(this)-224(state)-223(it)-224(is)-223(p)-28(ossible)-224(to)-223(add)-224(comm)28(unication)-224(requiremen)28(ts)-224(among)-223(di\013eren)27(t)]TJ 0 -11.955 Td [(pro)-28(cesses.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -22.617 Td [(Assem)32(bled:)]TJ +0 g 0 G +/F8 9.9626 Tf 61.508 0 Td [(State)-351(en)28(tered)-351(after)-351(the)-350(assem)27(bly;)-359(computations)-351(using)-351(the)-350(ass)-1(o)-27(ci-)]TJ -36.601 -11.955 Td [(ated)-392(sparse)-391(matrix,)-406(suc)28(h)-392(as)-391(m)-1(atr)1(ix-v)27(ector)-391(pro)-28(ducts,)-406(are)-392(only)-391(p)-28(ossible)-391(in)]TJ 0 -11.955 Td [(this)-333(state.)]TJ +0 g 0 G + 141.968 -29.888 Td [(11)]TJ 0 g 0 G ET endstream endobj -898 0 obj +923 0 obj << -/Length 9583 +/Length 5236 >> stream 0 g 0 G 0 g 0 G -0 g 0 G BT -/F27 9.9626 Tf 99.895 706.129 Td [(ith)]TJ -0 g 0 G -/F8 9.9626 Tf 18.985 0 Td [(the)-333(new)-334(threshold)-333(for)-333(comm)27(u)1(nication)-334(descriptors.)]TJ 5.922 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)-333(greater)-333(than)-334(zero.)]TJ -24.907 -22.293 Td [(Note:)-756(the)-490(threshold)-489(v)56(alue)-489(is)-490(only)-489(queried)-489(b)28(y)-490(th)1(e)-490(library)-489(at)-489(the)-489(time)-490(a)-489(call)]TJ 0 -11.955 Td [(to)]TJ/F30 9.9626 Tf 13.432 0 Td [(psb_cdall)]TJ/F8 9.9626 Tf 51.648 0 Td [(is)-459(executed,)-491(therefore)-459(c)27(hangi)1(ng)-460(the)-459(threshold)-459(has)-459(no)-460(e\013ect)-459(on)]TJ -65.08 -11.955 Td [(comm)28(unication)-464(desc)-1(r)1(iptors)-465(that)-464(ha)28(v)28(e)-464(already)-464(b)-28(een)-464(initialized.)-837(Moreo)28(v)27(er)-464(the)]TJ 0 -11.956 Td [(threshold)-333(m)27(ust)-333(ha)28(v)28(e)-334(the)-333(same)-333(v)55(alue)-333(on)-333(all)-334(pro)-27(c)-1(esses.)]TJ/F27 9.9626 Tf 0 -26.393 Td [(3.1.2)-1150(Named)-383(Constan)31(ts)]TJ -0 g 0 G - 0 -18.564 Td [(psb)]TJ +/F27 9.9626 Tf 150.705 706.129 Td [(3.1.1)-1150(Descriptor)-384(M)1(etho)-32(ds)]TJ 0 -18.549 Td [(3.1.2)-1150(get)]TJ ET q -1 0 0 1 117.832 555.391 cm +1 0 0 1 201.835 687.78 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 121.269 555.192 Td [(none)]TJ +/F27 9.9626 Tf 205.272 687.58 Td [(lo)-32(cal)]TJ ET q -1 0 0 1 145.666 555.391 cm +1 0 0 1 229.032 687.78 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 154.084 555.192 Td [(Generic)-333(no-op;)]TJ +/F27 9.9626 Tf 232.469 687.58 Td [(ro)32(ws)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(lo)-32(cal)-383(ro)32(ws)]TJ 0 g 0 G -/F27 9.9626 Tf -54.189 -20.301 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 535.09 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 534.891 Td [(ro)-32(ot)]TJ -ET -q -1 0 0 1 142.905 535.09 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q 0 g 0 G -BT -/F8 9.9626 Tf 151.324 534.891 Td [(Default)-333(ro)-28(ot)-333(pro)-28(cess)-334(for)-333(broadcast)-333(and)-333(scatte)-1(r)-333(op)-28(erations;)]TJ +/F30 9.9626 Tf -81.764 -18.548 Td [(nr)-525(=)-525(desc%get_local_rows\050\051)]TJ 0 g 0 G -/F27 9.9626 Tf -51.429 -20.301 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 514.789 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 514.59 Td [(nohalo)]TJ -ET -q -1 0 0 1 154.895 514.789 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 163.314 514.59 Td [(Do)-333(not)-334(fetc)28(h)-333(halo)-333(elem)-1(en)28(ts;)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -63.419 -20.301 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 494.489 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 494.289 Td [(halo)]TJ -ET -q -1 0 0 1 142.802 494.489 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 151.22 494.289 Td [(F)83(etc)28(h)-333(halo)-334(elemen)28(ts)-333(from)-334(neigh)28(b)-27(ouring)-334(pro)-27(ces)-1(ses;)]TJ 0 g 0 G -/F27 9.9626 Tf -51.325 -20.3 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 474.188 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 473.989 Td [(sum)]TJ -ET -q -1 0 0 1 142.388 474.188 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q + 0 -20.267 Td [(desc)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 150.806 473.989 Td [(Sum)-333(o)27(v)28(erlapp)-27(e)-1(d)-333(elemen)28(ts)]TJ +/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -50.911 -20.301 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 453.887 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 453.688 Td [(a)32(vg)]TJ -ET -q -1 0 0 1 138.983 453.887 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F27 9.9626 Tf -80.358 -34.13 Td [(On)-383(Return)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 147.401 453.688 Td [(Av)28(erage)-334(o)28(v)28(erlapp)-28(ed)-333(elemen)28(ts)]TJ 0 g 0 G -/F27 9.9626 Tf -47.506 -20.301 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 433.586 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 433.387 Td [(comm)]TJ -ET -q -1 0 0 1 151.872 433.586 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 155.309 433.387 Td [(halo)]TJ -ET -q -1 0 0 1 176.842 433.586 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q + 0 -20.267 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 185.26 433.387 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(halo_index)]TJ/F8 9.9626 Tf 55.625 0 Td [(list;)]TJ +/F8 9.9626 Tf 78.386 0 Td [(The)-460(n)28(um)27(b)-27(er)-461(of)-460(lo)-28(cal)-460(ro)28(ws,)-492(i.e.)-825(the)-460(n)28(um)27(b)-27(er)-461(of)-460(ro)28(ws)-460(o)28(wned)]TJ -53.48 -11.955 Td [(b)28(y)-401(the)-401(curren)27(t)-401(pro)-27(ces)-1(s;)-435(as)-401(explained)-401(in)]TJ +0 0 1 rg 0 0 1 RG + [-401(1)]TJ 0 g 0 G -/F27 9.9626 Tf -267.377 -20.301 Td [(psb)]TJ + [(,)-418(it)-401(is)-401(equal)-401(to)]TJ/F14 9.9626 Tf 249.678 0 Td [(jI)]TJ/F10 6.9738 Tf 8.192 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.431 0 Td [(+)]TJ/F14 9.9626 Tf 10.413 0 Td [(jB)]TJ/F10 6.9738 Tf 9.311 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(.)-648(The)]TJ -292.426 -11.955 Td [(returned)-333(v)55(alue)-333(is)-333(sp)-28(eci\014c)-334(to)-333(the)-333(calling)-334(p)1(ro)-28(cess.)]TJ/F27 9.9626 Tf -24.906 -26.35 Td [(3.1.3)-1150(get)]TJ ET q -1 0 0 1 117.832 413.286 cm +1 0 0 1 201.835 489.912 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 121.269 413.086 Td [(comm)]TJ +/F27 9.9626 Tf 205.272 489.712 Td [(lo)-32(cal)]TJ ET q -1 0 0 1 151.872 413.286 cm +1 0 0 1 229.032 489.912 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 155.309 413.086 Td [(ext)]TJ -ET -q -1 0 0 1 171.75 413.286 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F27 9.9626 Tf 232.469 489.712 Td [(cols)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(lo)-32(cal)-383(cols)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -81.764 -18.548 Td [(nc)-525(=)-525(desc%get_local_cols\050\051)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -20.267 Td [(desc)]TJ +0 g 0 G +/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -34.129 Td [(On)-383(Return)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 180.168 413.086 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(ext_index)]TJ/F8 9.9626 Tf 50.394 0 Td [(list;)]TJ 0 g 0 G -/F27 9.9626 Tf -257.054 -20.3 Td [(psb)]TJ + 0 -20.267 Td [(F)96(unction)-384(v)64(alue)]TJ +0 g 0 G +/F8 9.9626 Tf 78.386 0 Td [(The)-361(n)28(um)28(b)-28(er)-360(of)-361(lo)-27(cal)-361(cols,)-367(i.e.)-526(the)-361(n)28(um)28(b)-28(er)-360(of)-361(indices)-360(used)-361(b)28(y)]TJ -53.48 -11.955 Td [(the)-421(curren)28(t)-421(pro)-28(cess,)-443(including)-421(b)-27(oth)-421(lo)-28(cal)-421(and)-421(halo)-421(ind)1(ice)-1(s;)-464(as)-421(explained)]TJ 0 -11.955 Td [(in)]TJ +0 0 1 rg 0 0 1 RG + [-344(1)]TJ +0 g 0 G + [(,)-346(it)-343(is)-344(equal)-343(to)]TJ/F14 9.9626 Tf 81.777 0 Td [(jI)]TJ/F10 6.9738 Tf 8.192 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.049 0 Td [(+)]TJ/F14 9.9626 Tf 10.031 0 Td [(jB)]TJ/F10 6.9738 Tf 9.311 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 5.049 0 Td [(+)]TJ/F14 9.9626 Tf 10.03 0 Td [(jH)]TJ/F10 6.9738 Tf 11.181 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(j)]TJ/F8 9.9626 Tf 2.768 0 Td [(.)-475(The)-344(returned)-343(v)55(al)1(ue)-344(is)-344(sp)-27(ec)-1(i)1(\014c)-344(to)-344(the)]TJ -153.339 -11.956 Td [(calling)-333(pro)-28(cess.)]TJ/F27 9.9626 Tf -24.906 -26.349 Td [(3.1.4)-1150(get)]TJ ET q -1 0 0 1 117.832 392.985 cm +1 0 0 1 201.835 280.088 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 121.269 392.786 Td [(comm)]TJ +/F27 9.9626 Tf 205.272 279.889 Td [(global)]TJ ET q -1 0 0 1 151.872 392.985 cm +1 0 0 1 235.716 280.088 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 155.309 392.786 Td [(o)32(vr)]TJ -ET -q -1 0 0 1 172.172 392.985 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F27 9.9626 Tf 239.153 279.889 Td [(ro)32(ws)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(global)-383(ro)32(ws)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 180.59 392.786 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.387 0 Td [(ovrlap_index)]TJ/F8 9.9626 Tf 66.085 0 Td [(list;)]TJ 0 g 0 G -/F27 9.9626 Tf -273.167 -20.301 Td [(psb)]TJ +/F30 9.9626 Tf -88.448 -18.548 Td [(nr)-525(=)-525(desc%get_global_rows\050\051)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -22.174 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -20.267 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -20.268 Td [(desc)]TJ +0 g 0 G +/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -34.129 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -20.267 Td [(F)96(unction)-384(v)64(alue)]TJ +0 g 0 G +/F8 9.9626 Tf 78.386 0 Td [(The)-390(n)28(um)27(b)-27(er)-391(of)-390(global)-390(ro)28(ws,)-405(i.e.)-615(the)-390(size)-391(of)-390(the)-390(global)-390(index)]TJ -53.48 -11.955 Td [(space.)]TJ +0 g 0 G + 141.968 -29.888 Td [(12)]TJ +0 g 0 G ET -q -1 0 0 1 117.832 372.684 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q + +endstream +endobj +927 0 obj +<< +/Length 4435 +>> +stream +0 g 0 G +0 g 0 G BT -/F27 9.9626 Tf 121.269 372.485 Td [(comm)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(3.1.5)-1150(get)]TJ ET q -1 0 0 1 151.872 372.684 cm +1 0 0 1 151.025 706.328 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 155.309 372.485 Td [(mo)32(v)]TJ +/F27 9.9626 Tf 154.462 706.129 Td [(global)]TJ ET q -1 0 0 1 177.001 372.684 cm +1 0 0 1 184.906 706.328 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -0 g 0 G -BT -/F8 9.9626 Tf 185.419 372.485 Td [(Exc)28(hange)-334(d)1(ata)-334(based)-333(on)-333(the)]TJ/F30 9.9626 Tf 126.388 0 Td [(ovr_mst_idx)]TJ/F8 9.9626 Tf 60.854 0 Td [(list;)]TJ/F16 11.9552 Tf -272.766 -28.386 Td [(3.2)-1125(Sparse)-375(Matrix)-375(class)]TJ/F8 9.9626 Tf 0 -18.564 Td [(The)]TJ/F30 9.9626 Tf 20.653 0 Td [(psb)]TJ -ET -q -1 0 0 1 136.867 325.734 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 140.005 325.535 Td [(Tspmat)]TJ -ET -q -1 0 0 1 172.015 325.734 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q BT -/F30 9.9626 Tf 175.153 325.535 Td [(type)]TJ/F8 9.9626 Tf 24.416 0 Td [(class)-351(con)28(tains)-351(all)-351(information)-350(ab)-28(out)-351(the)-351(lo)-27(cal)-351(p)-28(ortion)-351(of)]TJ -99.674 -11.956 Td [(the)-249(sparse)-249(matrix)-248(and)-249(its)-249(storage)-249(mo)-27(de.)-417(Its)-248(design)-249(is)-249(based)-249(on)-248(the)-249(ST)83(A)83(TE)-248(design)]TJ 0 -11.955 Td [(pattern)-347([)]TJ -1 0 0 rg 1 0 0 RG - [(13)]TJ +/F27 9.9626 Tf 188.343 706.129 Td [(cols)-383(|)-384(Get)-383(n)32(um)32(b)-32(er)-383(of)-384(global)-383(cols)]TJ 0 g 0 G - [(])-346(as)-347(detailed)-347(in)-347([)]TJ -1 0 0 rg 1 0 0 RG - [(11)]TJ 0 g 0 G - [(];)-353(the)-347(t)28(yp)-28(e)-346(declaration)-347(is)-347(sho)28(wn)-347(in)-347(\014)1(gure)]TJ -0 0 1 rg 0 0 1 RG - [-347(4)]TJ +/F30 9.9626 Tf -88.448 -18.505 Td [(nr)-525(=)-525(desc%get_global_cols\050\051)]TJ 0 g 0 G - [-347(where)]TJ/F30 9.9626 Tf 0 -11.955 Td [(T)]TJ/F8 9.9626 Tf 8.552 0 Td [(is)-333(a)-334(placeholder)-333(for)-333(the)-334(d)1(ata)-334(t)28(yp)-28(e)-333(and)-333(precision)-334(v)56(arian)28(ts)]TJ +/F27 9.9626 Tf 0 -22.105 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F27 9.9626 Tf -8.552 -20.207 Td [(S)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 11.347 0 Td [(Single)-333(precision)-334(real;)]TJ +/F27 9.9626 Tf -33.797 -20.175 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F27 9.9626 Tf -11.347 -20.301 Td [(D)]TJ 0 g 0 G -/F8 9.9626 Tf 13.768 0 Td [(Double)-333(precision)-334(real;)]TJ + 0 -20.174 Td [(desc)]TJ +0 g 0 G +/F8 9.9626 Tf 26.209 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -13.768 -20.3 Td [(C)]TJ +/F27 9.9626 Tf -80.359 -34.06 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 13.256 0 Td [(Single)-333(precision)-334(complex;)]TJ 0 g 0 G -/F27 9.9626 Tf -13.256 -20.301 Td [(Z)]TJ + 0 -20.174 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F8 9.9626 Tf 11.983 0 Td [(Double)-333(precision)-334(complex.)]TJ -11.983 -20.207 Td [(The)-222(actual)-222(data)-223(is)-222(con)28(tained)-222(in)-222(the)-223(p)-27(olymorphic)-223(comp)-27(onen)27(t)]TJ/F30 9.9626 Tf 255.515 0 Td [(a%a)]TJ/F8 9.9626 Tf 17.905 0 Td [(of)-222(t)28(yp)-28(e)]TJ/F30 9.9626 Tf 31.548 0 Td [(psb)]TJ +/F8 9.9626 Tf 78.387 0 Td [(The)-273(n)28(um)28(b)-28(er)-273(of)-272(global)-273(cols;)-293(usually)-273(this)-273(is)-272(e)-1(q)1(ual)-273(to)-273(the)-273(n)28(um)28(b)-28(er)]TJ -53.48 -11.956 Td [(of)-333(global)-334(ro)28(ws.)]TJ/F27 9.9626 Tf -24.907 -26.226 Td [(3.1.6)-1150(get)]TJ ET q -1 0 0 1 421.182 188.552 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 151.025 520.998 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 424.32 188.353 Td [(T)]TJ +/F27 9.9626 Tf 154.462 520.799 Td [(global)]TJ ET q -1 0 0 1 430.178 188.552 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 184.906 520.998 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 433.316 188.353 Td [(base)]TJ -ET -q -1 0 0 1 454.865 188.552 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 458.003 188.353 Td [(sparse)]TJ -ET -q -1 0 0 1 490.013 188.552 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 493.151 188.353 Td [(mat)]TJ/F8 9.9626 Tf 15.691 0 Td [(;)]TJ -408.947 -11.955 Td [(its)-300(sp)-28(eci\014c)-301(la)28(y)28(out)-300(can)-301(b)-28(e)-300(c)28(hosen)-301(dyn)1(am)-1(ically)-300(among)-300(the)-301(prede\014ned)-300(t)28(yp)-28(es,)-307(or)-300(an)]TJ 0 -11.955 Td [(en)28(tirely)-419(new)-419(storage)-419(la)28(y)27(out)-419(can)-419(b)-27(e)-419(implemen)27(ted)-419(and)-418(pass)-1(ed)-418(to)-419(the)-419(library)-419(at)]TJ 0 -11.955 Td [(run)28(time)-420(via)-419(the)]TJ/F30 9.9626 Tf 73.447 0 Td [(psb_spasb)]TJ/F8 9.9626 Tf 51.252 0 Td [(routine.)-703(The)-419(follo)28(wing)-420(v)28(ery)-419(common)-420(formats)-419(are)]TJ -124.699 -11.956 Td [(precompiled)-333(in)-334(PSBLAS)-333(and)-333(th)28(us)-334(are)-333(alw)28(a)28(ys)-334(a)28(v)56(ailable:)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -20.206 Td [(psb)]TJ -ET -q -1 0 0 1 117.832 120.525 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 121.269 120.326 Td [(T)]TJ -ET -q -1 0 0 1 129.926 120.525 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 133.364 120.326 Td 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Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -80.358 -35.518 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -22.119 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(The)-333(matrix)]TJ/F30 9.9626 Tf 52.886 0 Td [(a)]TJ/F8 9.9626 Tf 8.551 0 Td [(without)-333(zero)-334(co)-27(e\016)-1(cien)28(ts.)]TJ -47.081 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +/F27 9.9626 Tf -33.797 -19.757 Td [(On)-383(Return)]TJ 0 g 0 G -/F27 9.9626 Tf -185.304 -22.118 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ -0 g 0 G - 143.116 -29.888 Td [(20)]TJ + 0 -19.756 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G +/F8 9.9626 Tf 78.387 0 Td [(The)-498(c)-1(u)1(rren)27(t)-498(list)-499(of)-498(adjacen)28(t)-499(pro)-28(cesses,)-540(i.e.)-940(pro)-27(cesse)-1(s)-498(with)]TJ -53.48 -11.955 Td 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-/F27 9.9626 Tf -14.944 -19.829 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf 0 -21.496 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.878 Td [(On)-383(En)32(try)]TJ -0 g 0 G +/F27 9.9626 Tf -33.797 -19.756 Td [(On)-383(En)32(try)]TJ 0 g 0 G - 0 -19.877 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.956 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -80.359 -33.753 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -19.878 Td [(d)]TJ -0 g 0 G -/F8 9.9626 Tf 11.347 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-333(m)-1(ai)1(n)-334(diagonal.)]TJ 13.56 -11.955 Td [(A)-333(one-dimensional)-334(arra)28(y)-333(of)-333(the)-334(appropriate)-333(t)28(yp)-28(e.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.877 Td [(info)]TJ + 0 -19.757 Td [(list)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -25.876 Td [(clip)]TJ +/F8 9.9626 Tf 20.321 0 Td [(the)-333(list)-334(of)-333(adjacen)28(t)-334(p)1(ro)-28(cesses.)]TJ 4.586 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(one-dimensional)-333(arra)28(y)-334(of)-333(in)28(tegers)-334(of)-333(kind)]TJ/F30 9.9626 Tf 247.378 0 Td [(psb_ipk_)]TJ/F8 9.9626 Tf 41.843 0 Td [(.)]TJ -314.128 -21.496 Td [(Note:)-643(this)-432(metho)-28(d)-432(can)-433(b)-27(e)-433(called)-432(after)-433(a)-432(call)-432(to)]TJ/F30 9.9626 Tf 216.836 0 Td [(psb_cdall)]TJ/F8 9.9626 Tf 51.381 0 Td [(and)-432(b)-28(efore)-432(a)-433(call)]TJ -268.217 -11.955 Td [(to)]TJ/F30 9.9626 Tf 12.939 0 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 47.073 0 Td [(.)-674(The)-410(user)-410(is)-409(s)-1(p)-27(ecifying)-410(here)-410(some)-410(kno)28(wledge)-410(ab)-28(out)-409(whic)27(h)-409(pro-)]TJ -60.012 -11.955 Td [(cesses)-304(are)-304(top)-28(ological)-304(neigh)28(b)-28(ours)-304(of)-304(the)-304(curren)28(t)-304(pro)-28(cess.)-435(The)-304(a)28(v)56(ailabilit)27(y)-304(of)-304(this)]TJ 0 -11.956 Td [(information)-333(ma)28(y)-334(sp)-28(eed)-333(up)-333(the)-334(execution)-333(of)-333(the)-334(assem)28(bly)-333(call)]TJ/F30 9.9626 Tf 268.079 0 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 47.073 0 Td [(.)]TJ/F27 9.9626 Tf -315.152 -25.823 Td [(3.1.14)-1150(fnd)]TJ ET q -1 0 0 1 118.405 471.307 cm +1 0 0 1 157.549 247.744 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 121.842 471.107 Td [(diag)-383(|)-384(Cut)-383(out)-383(main)-384(diagonal)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -1.025 -18.389 Td [(call)-525(a%clip_diag\050b,info\051)]TJ/F8 9.9626 Tf -5.978 -21.798 Td [(Returns)-333(a)-334(cop)28(y)-333(of)]TJ/F30 9.9626 Tf 80.753 0 Td [(a)]TJ/F8 9.9626 Tf 8.551 0 Td [(without)-333(the)-334(main)-333(diagonal.)]TJ -0 g 0 G -/F27 9.9626 Tf -104.248 -19.83 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.877 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf 160.987 247.544 Td [(o)32(wner)-383(|)-384(Find)-383(the)-383(o)32(wner)-384(pro)-32(cess)-383(of)-383(a)-384(set)-383(of)-383(indices)]TJ 0 g 0 G 0 g 0 G - 0 -19.878 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -80.359 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Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(;)-333(default:)-445(en)28(tire)-333(v)28(ec)-1(tor)1(.)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ 0 g 0 G -/F27 9.9626 Tf -95.094 -35.174 Td [(On)-383(Return)]TJ + -57.286 -35.944 Td [(On)-383(Return)]TJ 0 g 0 G 0 g 0 G - 0 -21.66 Td [(F)96(unction)-384(v)64(alue)]TJ + 0 -22.687 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(An)-353(allo)-28(catable)-354(arra)28(y)-353(holding)-354(a)-353(cop)28(y)-354(of)-353(the)-354(dense)-353(v)28(ec)-1(t)1(o)-1(r)-353(con-)]TJ -53.48 -11.956 Td [(ten)28(ts.)-440(If)-319(the)-320(argumen)28(t)]TJ/F11 9.9626 Tf 99.799 0 Td [(n)]TJ/F8 9.9626 Tf 9.161 0 Td [(is)-319(sp)-28(eci\014ed,)-322(the)-320(size)-319(of)-319(the)-320(returned)-319(arra)28(y)-320(equals)]TJ 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Tf 11.028 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-333(input)-334(ob)-55(ject.)]TJ 0 g 0 G -/F27 9.9626 Tf -11.028 -21.66 Td [(info)]TJ + 0 -22.686 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F16 11.9552 Tf -23.758 -30.189 Td [(3.4)-1125(Preconditioner)-375(data)-375(structure)]TJ/F8 9.9626 Tf 0 -19.197 Td [(Our)-383(base)-383(library)-383(o\013ers)-383(supp)-28(ort)-383(for)-383(simple)-383(w)28(ell)-383(kno)27(wn)-383(precondition)1(e)-1(r)1(s)-384(lik)28(e)-383(Di-)]TJ 0 -11.955 Td [(agonal)-333(Scaling)-334(or)-333(Blo)-28(c)28(k)-333(Jacobi)-334(with)-333(incomplete)-333(factorization)-333(ILU\0500\051.)]TJ 14.944 -12.389 Td [(A)-427(preconditioner)-428(is)-427(held)-428(in)-427(the)]TJ/F30 9.9626 Tf 142.723 0 Td [(psb)]TJ +/F8 9.9626 Tf 78.387 0 Td [(A)-484(short)-483(string)-484(describing)-484(the)-484(dynamic)-484(t)28(yp)-27(e)-484(of)-484(the)-484(matrix.)]TJ -53.48 -11.956 Td [(Prede\014ned)-333(v)55(alues)-333(include)]TJ/F30 9.9626 Tf 113.408 0 Td [(NULL)]TJ/F8 9.9626 Tf 20.922 0 Td [(,)]TJ/F30 9.9626 Tf 6.088 0 Td [(COO)]TJ/F8 9.9626 Tf 15.691 0 Td [(,)]TJ/F30 9.9626 Tf 6.088 0 Td [(CSR)]TJ/F8 9.9626 Tf 19.012 0 Td [(and)]TJ/F30 9.9626 Tf 19.372 0 Td [(CSC)]TJ/F8 9.9626 Tf 15.691 0 Td [(.)]TJ/F27 9.9626 Tf -241.179 -29.558 Td [(3.2.8)-1150(is)]TJ ET q -1 0 0 1 324.691 168.346 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 143.292 316.012 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 327.829 168.146 Td [(prec)]TJ +/F27 9.9626 Tf 146.729 315.813 Td [(bld,)-383(is)]TJ ET q -1 0 0 1 349.378 168.346 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 178.032 316.012 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 352.516 168.146 Td [(type)]TJ/F8 9.9626 Tf 25.18 0 Td [(data)-427(structure)-428(rep)-28(orted)-427(in)]TJ -226.991 -11.955 Td [(\014gure)]TJ -0 0 1 rg 0 0 1 RG - [-361(6)]TJ +/F27 9.9626 Tf 181.469 315.813 Td [(up)-32(d,)-383(is)]TJ +ET +q +1 0 0 1 216.273 316.012 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 219.71 315.813 Td [(asb)-383(|)-384(Status)-383(c)32(hec)32(k)]TJ 0 g 0 G - [(.)-527(The)]TJ/F30 9.9626 Tf 61.729 0 Td [(psb_prec_type)]TJ/F8 9.9626 Tf 71.59 0 Td [(data)-361(t)28(yp)-28(e)-361(ma)28(y)-361(con)28(tain)-361(a)-361(simple)-361(preconditionin)1(g)]TJ -133.319 -11.955 Td [(matrix)-488(with)-487(the)-488(asso)-28(ciated)-488(comm)28(unication)-487(des)-1(crip)1(tor.The)-488(in)28(ternal)-488(precondi-)]TJ 0 -11.955 Td [(tioner)-417(is)-417(allo)-28(cated)-417(app)1(ropriately)-417(with)-417(the)-417(dynamic)-417(t)28(yp)-28(e)-417(corresp)-28(onding)-417(to)-417(th)1(e)]TJ 0 -11.955 Td [(desired)-333(preconditioner.)]TJ 0 g 0 G - 166.874 -29.888 Td [(26)]TJ +/F30 9.9626 Tf -119.815 -19.674 Td [(if)-525(\050a%is_bld\050\051\051)-525(then)]TJ 0 -11.955 Td [(if)-525(\050a%is_upd\050\051\051)-525(then)]TJ 0 -11.955 Td [(if)-525(\050a%is_asb\050\051\051)-525(then)]TJ 0 g 0 G -ET - -endstream -endobj -965 0 obj -<< -/Length 3656 ->> -stream +/F27 9.9626 Tf 0 -23.989 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G +/F27 9.9626 Tf -33.797 -22.687 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G + 0 -22.686 Td [(a)]TJ 0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)]TJ 14.356 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ 0 g 0 G + -57.286 -35.944 Td [(On)-383(Return)]TJ 0 g 0 G -BT -/F47 8.9664 Tf 126.497 705.133 Td [(type)-525(psb_Tprec_type)]TJ 9.414 -10.959 Td [(class\050psb_T_base_prec_type\051,)-525(allocatable)-525(::)-525(prec)]TJ -9.414 -10.959 Td [(end)-525(type)-525(psb_Tprec_type)]TJ 0 g 0 G -/F8 9.9626 Tf -14.633 -38.799 Td [(Figure)-333(6:)-445(The)-333(PSBLAS)-333(de\014ned)-334(data)-333(t)28(yp)-28(e)-333(that)-333(c)-1(on)28(tains)-333(a)-333(preconditioner.)]TJ + 0 -22.686 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G +/F8 9.9626 Tf 78.387 0 Td [(A)]TJ/F30 9.9626 Tf 9.727 0 Td [(logical)]TJ/F8 9.9626 Tf 38.87 0 Td [(v)56(alue)-227(indicating)-226(whether)-227(the)-226(matrix)-227(is)-226(in)-227(the)-227(Bui)1(ld,)]TJ -102.077 -11.955 Td [(Up)-28(date)-333(or)-333(Asse)-1(m)28(bled)-333(state,)-333(res)-1(p)-27(ectiv)27(ely)84(.)]TJ 0 g 0 G -/F16 11.9552 Tf -11.969 -31.825 Td [(3.5)-1125(Heap)-375(data)-375(structure)]TJ/F8 9.9626 Tf 0 -18.39 Td [(Among)-393(the)-393(to)-28(ols)-393(routines)-393(of)-393(sec.)]TJ -0 0 1 rg 0 0 1 RG - [-393(6)]TJ + 141.968 -29.888 Td [(19)]TJ 0 g 0 G - [(,)-408(w)28(e)-393(ha)28(v)27(e)-393(a)-393(n)28(um)28(b)-28(er)-393(of)-393(sorting)-393(utilities;)-423(the)]TJ 0 -11.955 Td [(heap)-333(sort)-334(is)-333(implemen)28(ted)-334(in)-333(terms)-333(of)-334(heaps)-333(ha)28(ving)-333(the)-334(follo)28(wing)-333(signatures:)]TJ -0 g 0 G -/F30 9.9626 Tf 0 -19.925 Td [(psb)]TJ ET -q -1 0 0 1 116.214 562.52 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q + +endstream +endobj +967 0 obj +<< +/Length 4632 +>> +stream +0 g 0 G +0 g 0 G BT -/F30 9.9626 Tf 119.352 562.321 Td [(T)]TJ +/F27 9.9626 Tf 150.705 706.129 Td [(3.2.9)-1150(is)]TJ ET q -1 0 0 1 125.21 562.52 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 194.101 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 128.348 562.321 Td [(heap)]TJ -0 g 0 G -/F8 9.9626 Tf 25.903 0 Td [(:)-425(a)-295(heap)-296(con)28(taining)-295(elemen)28(ts)-295(of)-295(t)27(yp)-27(e)-296(T,)-295(where)-295(T)-295(can)-295(b)-28(e)]TJ/F30 9.9626 Tf 242.282 0 Td [(i,s,c,d,z)]TJ/F8 9.9626 Tf -271.731 -11.955 Td [(for)-333(in)28(tege)-1(r)1(,)-334(real)-333(and)-333(complex)-334(data;)]TJ -0 g 0 G -/F30 9.9626 Tf -24.907 -19.925 Td [(psb)]TJ +/F27 9.9626 Tf 197.538 706.129 Td [(lo)32(w)32(er,)-384(is)]TJ ET q -1 0 0 1 116.214 530.64 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 239.447 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 119.352 530.441 Td [(T)]TJ +/F27 9.9626 Tf 242.884 706.129 Td [(upp)-32(er,)-383(is)]TJ ET q -1 0 0 1 125.21 530.64 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 287.658 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 128.348 530.441 Td [(idx)]TJ +/F27 9.9626 Tf 291.095 706.129 Td [(triangle,)-383(i)-1(s)]TJ ET q -1 0 0 1 144.667 530.64 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 344.938 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 147.805 530.441 Td [(heap)]TJ +/F27 9.9626 Tf 348.375 706.129 Td [(unit)-383(|)-384(F)96(ormat)-383(c)32(hec)32(k)]TJ 0 g 0 G -/F8 9.9626 Tf 25.903 0 Td [(:)-408(a)-260(heap)-260(con)28(taining)-260(elemen)28(ts)-260(of)-260(t)28(yp)-28(e)-260(T,)-260(as)-259(ab)-28(o)28(v)27(e,)-274(together)-260(with)]TJ -48.906 -11.956 Td [(an)-333(in)28(tege)-1(r)-333(index.)]TJ -24.907 -19.925 Td [(Giv)28(en)-334(a)-333(heap)-333(ob)-56(ject,)-333(the)-333(follo)27(wing)-333(metho)-28(ds)-333(are)-333(de\014ned)-334(on)-333(it:)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -19.925 Td [(init)]TJ +/F30 9.9626 Tf -197.67 -19.048 Td [(if)-525(\050a%is_triangle\050\051\051)-525(then)]TJ 0 -11.955 Td [(if)-525(\050a%is_upper\050\051\051)-525(then)]TJ 0 -11.955 Td [(if)-525(\050a%is_lower\050\051\051)-525(then)]TJ 0 -11.955 Td [(if)-525(\050a%is_unit\050\051\051)-525(then)]TJ 0 g 0 G -/F8 9.9626 Tf 22.167 0 Td [(Initialize)-333(memory;)-334(also)-333(c)28(ho)-28(ose)-334(ascending)-333(or)-333(descending)-333(order;)]TJ +/F27 9.9626 Tf 0 -22.979 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F27 9.9626 Tf -22.167 -19.926 Td [(ho)32(wman)32(y)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 52.242 0 Td [(Curren)28(t)-333(heap)-334(o)-28(ccupan)1(c)-1(y;)]TJ +/F27 9.9626 Tf -33.797 -21.341 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F27 9.9626 Tf -52.242 -19.925 Td [(insert)]TJ 0 g 0 G -/F8 9.9626 Tf 33.473 0 Td [(Add)-333(an)-334(item)-333(\050or)-333(an)-334(item)-333(and)-333(its)-334(ind)1(e)-1(x)1(\051;)]TJ + 0 -21.34 Td [(a)]TJ 0 g 0 G -/F27 9.9626 Tf -33.473 -19.925 Td [(get)]TJ -ET -q -1 0 0 1 116.018 419.058 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 119.455 418.859 Td [(\014rst)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)]TJ 14.355 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ 0 g 0 G -/F8 9.9626 Tf 25.039 0 Td [(Remo)28(v)27(e)-333(and)-333(return)-333(the)-334(\014rst)-333(elemen)28(t;)]TJ + -57.285 -34.934 Td [(On)-383(Return)]TJ 0 g 0 G -/F27 9.9626 Tf -44.599 -19.925 Td [(dump)]TJ 0 g 0 G -/F8 9.9626 Tf 33.624 0 Td [(Prin)28(t)-333(on)-334(\014le;)]TJ + 0 -21.341 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F27 9.9626 Tf -33.624 -19.926 Td [(free)]TJ +/F8 9.9626 Tf 78.386 0 Td [(A)]TJ/F30 9.9626 Tf 10.615 0 Td [(logical)]TJ/F8 9.9626 Tf 39.755 0 Td [(v)56(alue)-316(indicating)-315(whether)-316(the)-315(matrix)-316(i)1(s)-316(triangular;)]TJ -103.85 -11.955 Td [(if)]TJ/F30 9.9626 Tf 8.896 0 Td [(is_triangle\050\051)]TJ/F8 9.9626 Tf 71.079 0 Td [(returns)]TJ/F30 9.9626 Tf 34.189 0 Td [(.true.)]TJ/F8 9.9626 Tf 34.466 0 Td [(c)28(hec)27(k)-309(also)-310(if)-309(it)-310(is)-309(lo)27(w)28(er,)-314(upp)-28(er)-309(and)-310(with)]TJ -148.63 -11.955 Td [(a)-333(unit)-334(\050i.e.)-444(assumed\051)-333(diagonal.)]TJ/F27 9.9626 Tf -24.906 -27.773 Td [(3.2.10)-1150(cscn)32(v)-384(|)-383(Con)32(v)32(ert)-383(to)-384(a)-383(di\013eren)32(t)-383(storage)-384(format)]TJ 0 g 0 G -/F8 9.9626 Tf 23.703 0 Td [(Release)-334(memory)84(.)]TJ -23.703 -19.925 Td [(These)-333(ob)-56(jects)-333(are)-334(used)-333(in)-333(MLD2P4)-334(to)-333(implemen)28(t)-334(the)-333(factorization)-333(algorithms.)]TJ 0 g 0 G - 166.875 -268.645 Td [(27)]TJ +/F30 9.9626 Tf 0 -19.048 Td [(call)-1050(a%cscnv\050b,info)-525([,)-525(type,)-525(mold,)-525(dupl]\051)]TJ 0 -11.955 Td [(call)-1050(a%cscnv\050info)-525([,)-525(type,)-525(mold,)-525(dupl]\051)]TJ 0 g 0 G -ET - -endstream -endobj -970 0 obj -<< -/Length 158 ->> -stream +/F27 9.9626 Tf 0 -22.979 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -BT -/F16 14.3462 Tf 150.705 706.129 Td [(4)-1125(Computational)-375(routines)]TJ +/F27 9.9626 Tf -33.797 -21.34 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -21.341 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.355 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -33.295 Td [(t)32(yp)-32(e)]TJ +0 g 0 G +/F8 9.9626 Tf 27.099 0 Td [(a)-333(string)-334(requesting)-333(a)-333(new)-334(format.)]TJ -2.193 -11.956 Td [(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -21.34 Td [(mold)]TJ +0 g 0 G +/F8 9.9626 Tf 29.805 0 Td [(a)-312(v)56(ariable)-312(of)]TJ/F30 9.9626 Tf 56.396 0 Td [(class\050psb_T_base_sparse_mat\051)]TJ/F8 9.9626 Tf 149.557 0 Td [(requesting)-312(a)-312(new)-312(format.)]TJ -210.852 -11.955 Td [(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -21.34 Td [(dupl)]TJ +0 g 0 G +/F8 9.9626 Tf 27.259 0 Td [(an)-268(in)28(teger)-268(v)56(alue)-268(sp)-28(eci\014ng)-267(ho)27(w)-267(to)-268(handle)-268(duplicates)-268(\050see)-268(Named)-267(Constan)27(ts)]TJ -2.353 -11.956 Td [(b)-28(elo)28(w\051)]TJ 0 g 0 G -/F8 9.9626 Tf 166.874 -615.691 Td [(28)]TJ +/F27 9.9626 Tf -24.906 -22.979 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -21.34 Td [(b,a)]TJ +0 g 0 G +/F8 9.9626 Tf 20.098 0 Td [(A)-333(cop)27(y)-333(of)]TJ/F30 9.9626 Tf 45.385 0 Td [(a)]TJ/F8 9.9626 Tf 8.552 0 Td [(with)-333(a)-334(new)-333(storage)-333(format.)]TJ -49.129 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.304 -21.34 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ -23.758 -23.333 Td [(The)]TJ/F30 9.9626 Tf 20.085 0 Td [(mold)]TJ/F8 9.9626 Tf 23.848 0 Td [(argumen)28(ts)-294(ma)28(y)-294(b)-28(e)-294(emplo)28(y)28(ed)-294(to)-294(in)28(terface)-294(with)-293(sp)-28(ecial)-294(devices,)-302(suc)28(h)-294(as)]TJ -43.933 -11.955 Td [(GPUs)-333(and)-334(other)-333(accelerators.)]TJ +0 g 0 G + 166.874 -29.888 Td [(20)]TJ 0 g 0 G ET endstream endobj -981 0 obj +971 0 obj << -/Length 7361 +/Length 4114 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(geaxpb)31(y)-375(|)-375(General)-375(Dense)-375(Matrix)-375(Sum)]TJ/F8 9.9626 Tf -25.091 -18.578 Td [(This)-436(subroutine)-436(is)-436(an)-436(in)28(te)-1(r)1(fac)-1(e)-436(to)-436(the)-436(computational)-436(k)28(ernel)-436(for)-436(dense)-436(matrix)]TJ 0 -11.955 Td [(sum:)]TJ/F11 9.9626 Tf 142.538 -12.258 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-226(x)]TJ/F8 9.9626 Tf 16.532 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(3.2.11)-1150(csclip)-384(|)-383(Reduce)-383(to)-384(a)-383(submatrix)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -189.771 -22.424 Td [(call)-525(psb_geaxpby\050alpha,)-525(x,)-525(beta,)-525(y,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf 20.922 -19.41 Td [(call)-525(a%csclip\050b,info[,&)]TJ 15.691 -11.955 Td [(&)-525(imin,imax,jmin,jmax,rscale,cscale]\051)]TJ/F8 9.9626 Tf -21.669 -24.111 Td [(Returns)-222(the)-222(s)-1(u)1(bmatrix)]TJ/F30 9.9626 Tf 99.101 0 Td [(A\050imin:imax,jmin:jmax\051)]TJ/F8 9.9626 Tf 115.068 0 Td [(,)-244(optionally)-222(res)-1(calin)1(g)-223(ro)28(w/-)]TJ 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[(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ -ET -q -1 0 0 1 319.972 583.4 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 322.961 583.201 Td [(geaxpb)28(y)]TJ -138.995 -11.956 Td [(Short)-333(Precision)-333(C)-1(omplex)-1200(p)1(s)-1(b)]TJ -ET -q -1 0 0 1 319.972 571.445 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 322.961 571.245 Td [(geaxpb)28(y)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ -ET -q -1 0 0 1 319.972 559.49 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 322.961 559.29 Td [(geaxpb)28(y)]TJ -ET -q -1 0 0 1 177.988 555.504 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S -Q +/F27 9.9626 Tf -33.797 -22.119 Td [(On)-383(En)32(try)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 228.067 527.465 Td [(T)83(able)-333(1:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G + 0 -22.118 Td [(a)]TJ 0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.956 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -128.172 -34.102 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -80.359 -34.073 Td [(imin,imax,jmin,jma)-1(x)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +/F8 9.9626 Tf 108.413 0 Td [(Minim)28(um)-333(and)-334(maxim)28(um)-333(ro)27(w)-333(and)-333(column)-333(indices.)]TJ -83.506 -11.956 Td [(T)28(yp)-28(e:)-444(optional.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -20.33 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -24.907 -22.118 Td [(rscale,cscale)]TJ 0 g 0 G +/F8 9.9626 Tf 65.203 0 Td [(Whether)-333(to)-334(rescale)-333(ro)28(w/column)-334(ind)1(ic)-1(es.)-444(T)28(yp)-28(e:)-444(optional.)]TJ 0 g 0 G - 0 -20.329 Td [(alpha)]TJ +/F27 9.9626 Tf -65.203 -24.111 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 32.033 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.468 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(.)]TJ -59.004 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(1)]TJ 0 g 0 G - [(.)]TJ + 0 -22.118 Td [(b)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -20.33 Td [(x)]TJ +/F8 9.9626 Tf 11.347 0 Td [(A)-333(cop)27(y)-333(of)-333(a)-333(s)-1(u)1(bmatrix)-334(of)]TJ/F30 9.9626 Tf 112.439 0 Td [(a)]TJ/F8 9.9626 Tf 5.231 0 Td [(.)]TJ -104.11 -11.956 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ -ET -q -1 0 0 1 385.864 336.932 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 389.002 336.732 Td [(T)]TJ -ET -q -1 0 0 1 394.86 336.932 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 397.998 336.732 Td [(vect)]TJ +/F27 9.9626 Tf -185.305 -22.118 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -28.805 Td [(3.2.12)-1150(clean)]TJ ET q -1 0 0 1 419.547 336.932 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 166.779 371.924 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 422.685 336.732 Td [(type)]TJ +/F27 9.9626 Tf 170.216 371.725 Td [(zeros)-383(|)-384(Eliminate)-383(zero)-383(co)-32(e\016cien)32(t)-1(s)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-375(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-376(of)-375(t)28(yp)-28(e)-375(sp)-28(eci\014ed)-375(in)-375(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-375(1)]TJ 0 g 0 G - [(.)-570(The)-376(rank)-375(of)]TJ/F11 9.9626 Tf 274.03 0 Td [(x)]TJ/F8 9.9626 Tf 9.432 0 Td [(m)28(ust)-376(b)-27(e)]TJ -283.462 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ +/F30 9.9626 Tf -49.399 -19.41 Td [(call)-525(a%clean_zeros\050info\051)]TJ/F8 9.9626 Tf -5.978 -24.111 Td [(Eliminates)-285(zero)-284(co)-28(e\016cien)27(ts)-284(in)-285(the)-285(inp)1(ut)-285(matrix.)-428(Note)-285(that)-285(dep)-27(ending)-285(on)-285(the)]TJ -14.944 -11.955 Td [(in)28(ternal)-333(storage)-333(format,)-334(th)1(e)-1(r)1(e)-334(ma)28(y)-333(still)-333(b)-28(e)-333(some)-333(amoun)28(t)-334(of)-333(zero)-333(padding)-333(in)-333(the)]TJ 0 -11.955 Td [(output.)]TJ 0 g 0 G -/F27 9.9626 Tf -83.615 -20.33 Td [(b)-32(eta)]TJ +/F27 9.9626 Tf 0 -24.111 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 26.941 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.468 0 Td [(\014)]TJ/F8 9.9626 Tf 6.161 0 Td [(.)]TJ -53.663 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(1)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G - [(.)]TJ +/F27 9.9626 Tf -33.797 -22.119 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -20.329 Td [(y)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(the)-333(global)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 193.276 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -184.639 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ -ET -q -1 0 0 1 385.864 176.72 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 389.002 176.521 Td [(T)]TJ -ET -q -1 0 0 1 394.86 176.72 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 397.998 176.521 Td [(vect)]TJ -ET -q -1 0 0 1 419.547 176.72 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 422.685 176.521 Td [(type)]TJ + 0 -22.118 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-334(n)28(um)27(b)-27(ers)-335(of)-334(the)-334(t)28(yp)-28(e)-334(indicated)-334(in)-334(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-334(1)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ 0 g 0 G - [(.)-447(The)-334(rank)-334(of)]TJ/F11 9.9626 Tf 288.869 0 Td [(y)]TJ/F8 9.9626 Tf 8.571 0 Td [(m)28(ust)]TJ -297.44 -11.955 Td [(b)-28(e)-333(the)-333(sam)-1(e)-333(of)]TJ/F11 9.9626 Tf 67.027 0 Td [(x)]TJ/F8 9.9626 Tf 5.693 0 Td [(.)]TJ +/F27 9.9626 Tf -80.359 -35.518 Td [(On)-383(Return)]TJ 0 g 0 G -/F27 9.9626 Tf -97.627 -20.33 Td [(desc)]TJ -ET -q -1 0 0 1 121.81 132.48 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 125.247 132.281 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ + 0 -22.119 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(The)-333(matrix)]TJ/F30 9.9626 Tf 52.885 0 Td [(a)]TJ/F8 9.9626 Tf 8.551 0 Td [(without)-333(zero)-334(co)-28(e\016cien)28(ts.)]TJ -47.08 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -22.118 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ 0 g 0 G -/F8 9.9626 Tf 109.589 -29.888 Td [(29)]TJ + 143.117 -29.888 Td [(21)]TJ 0 g 0 G ET endstream endobj -987 0 obj +975 0 obj << -/Length 2655 +/Length 4061 >> stream 0 g 0 G 0 g 0 G BT -/F8 9.9626 Tf 175.611 706.129 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ -ET -q -1 0 0 1 327.588 682.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 330.727 682.219 Td [(desc)]TJ +/F27 9.9626 Tf 150.705 706.129 Td [(3.2.13)-1150(get)]TJ ET q -1 0 0 1 352.275 682.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 207.563 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 355.414 682.219 Td [(type)]TJ +/F27 9.9626 Tf 211 706.129 Td [(diag)-383(|)-384(Get)-383(main)-383(dia)-1(gonal)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -225.63 -21.918 Td [(On)-383(Return)]TJ +/F30 9.9626 Tf -39.374 -18.389 Td [(call)-525(a%get_diag\050d,info\051)]TJ/F8 9.9626 Tf -5.977 -21.799 Td [(Returns)-333(a)-334(cop)28(y)-333(of)-333(the)-334(main)-333(diagonal.)]TJ 0 g 0 G +/F27 9.9626 Tf -14.944 -19.829 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G - 0 -19.926 Td [(y)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(submatrix)]TJ/F11 9.9626 Tf 162.364 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -153.727 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ -ET -q -1 0 0 1 436.673 592.754 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 439.811 592.555 Td [(T)]TJ -ET -q -1 0 0 1 445.669 592.754 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 448.807 592.555 Td [(vect)]TJ +/F27 9.9626 Tf -33.797 -19.878 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.877 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.355 -11.956 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -33.753 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.878 Td [(d)]TJ +0 g 0 G +/F8 9.9626 Tf 11.346 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-334(main)-333(diagonal.)]TJ 13.56 -11.955 Td [(A)-333(one-dimensional)-334(arra)28(y)-333(of)-333(the)-334(appropriate)-333(t)28(yp)-28(e.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.877 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -25.876 Td [(3.2.14)-1150(clip)]TJ ET q -1 0 0 1 470.356 592.754 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 209.95 471.307 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 473.495 592.555 Td [(type)]TJ +/F27 9.9626 Tf 213.387 471.107 Td [(diag)-383(|)-384(Cut)-383(out)-383(main)-384(diagonal)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(the)-334(t)28(yp)-28(e)-333(indicated)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-334(1)]TJ 0 g 0 G - [(.)]TJ +/F30 9.9626 Tf -41.761 -18.389 Td [(call)-525(a%clip_diag\050b,info\051)]TJ/F8 9.9626 Tf -5.977 -21.798 Td [(Returns)-333(a)-334(cop)28(y)-333(of)]TJ/F30 9.9626 Tf 80.753 0 Td [(a)]TJ/F8 9.9626 Tf 8.551 0 Td [(without)-333(the)-334(main)-333(diagonal.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.926 Td [(info)]TJ +/F27 9.9626 Tf -104.248 -19.83 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.877 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.878 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)28(yp)-28(e)]TJ/F30 9.9626 Tf 81.942 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.456 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -33.754 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.877 Td [(b)]TJ +0 g 0 G +/F8 9.9626 Tf 11.346 0 Td [(A)-333(cop)27(y)-333(of)]TJ/F30 9.9626 Tf 45.386 0 Td [(a)]TJ/F8 9.9626 Tf 8.551 0 Td [(without)-333(the)-334(main)-333(diagonal.)]TJ -40.376 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(y)1(p)-28(e)]TJ/F30 9.9626 Tf 81.942 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.456 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -19.878 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -25.875 Td [(3.2.15)-1150(tril)-384(|)-383(Return)-383(the)-384(lo)32(w)32(er)-383(triangle)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf 20.921 -18.389 Td [(call)-525(a%tril\050l,info[,&)]TJ 15.691 -11.956 Td [(&)-525(diag,imin,imax,jmin,jmax,rscale,cscale,u]\051)]TJ/F8 9.9626 Tf -21.668 -21.798 Td [(Returns)-376(the)-376(lo)28(w)28(er)-376(triangular)-375(part)-376(of)-376(submatrix)]TJ/F30 9.9626 Tf 210.932 0 Td [(A\050imin:imax,jmin:jmax\051)]TJ/F8 9.9626 Tf 115.068 0 Td [(,)]TJ -340.944 -11.955 Td [(optionally)-222(rescaling)-222(ro)27(w/col)-222(indices)-222(to)-222(the)-222(range)]TJ/F30 9.9626 Tf 205.535 0 Td [(1:imax-imin+1,1:jmax-jmin+1)]TJ/F8 9.9626 Tf -205.535 -11.955 Td [(and)-333(returing)-333(the)-334(complemen)28(tary)-333(upp)-28(er)-333(triangle.)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -19.83 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.877 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ 0 g 0 G - 141.968 -422.416 Td [(30)]TJ +/F8 9.9626 Tf 166.874 -29.888 Td [(22)]TJ 0 g 0 G ET endstream endobj -996 0 obj +979 0 obj << -/Length 7700 +/Length 5497 +>> +stream +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F27 9.9626 Tf 99.895 706.129 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.359 -30.78 Td [(diag)]TJ +0 g 0 G +/F8 9.9626 Tf 25.827 0 Td [(Include)-392(diagonals)-391(up)-392(to)-392(this)-391(one;)]TJ/F30 9.9626 Tf 149.735 0 Td [(diag=1)]TJ/F8 9.9626 Tf 35.284 0 Td [(means)-392(the)-392(\014rst)-391(sup)-28(erdiagonal,)]TJ/F30 9.9626 Tf -185.939 -11.955 Td [(diag=-1)]TJ/F8 9.9626 Tf 39.933 0 Td [(means)-333(the)-334(\014rst)-333(sub)-28(diagonal.)-444(Default)-333(0.)]TJ +0 g 0 G +/F27 9.9626 Tf -64.84 -18.824 Td [(imin,imax,jmin,jmax)]TJ +0 g 0 G +/F8 9.9626 Tf 108.413 0 Td [(Minim)28(um)-333(and)-334(maxim)28(um)-333(ro)28(w)-334(and)-333(column)-333(indices.)]TJ -83.506 -11.955 Td [(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.824 Td [(rscale,cscale)]TJ +0 g 0 G +/F8 9.9626 Tf 65.203 0 Td [(Whether)-333(to)-334(rescale)-333(ro)28(w/column)-334(ind)1(ic)-1(es.)-444(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -65.203 -19.165 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -18.824 Td [(l)]TJ +0 g 0 G +/F8 9.9626 Tf 8.164 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-334(lo)28(w)28(er)-333(triangle)-334(of)]TJ/F30 9.9626 Tf 136.489 0 Td [(a)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ -124.976 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -18.824 Td [(u)]TJ +0 g 0 G +/F8 9.9626 Tf 11.347 0 Td [(\050optional\051)-333(A)-334(cop)28(y)-333(of)-333(the)-334(upp)-27(er)-334(triangle)-333(of)]TJ/F30 9.9626 Tf 185.471 0 Td [(a)]TJ/F8 9.9626 Tf 5.231 0 Td [(.)]TJ -177.142 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -18.825 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -25.421 Td [(3.2.16)-1150(triu)-384(|)-383(Return)-383(the)-383(upp)-32(er)-384(triangle)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf 20.922 -18.39 Td [(call)-525(a%triu\050u,info[,&)]TJ 15.691 -11.955 Td [(&)-525(diag,imin,imax,jmin,jmax,rscale,cscale,l]\051)]TJ/F8 9.9626 Tf -21.669 -19.165 Td [(Returns)-340(the)-340(upp)-28(er)-340(triangular)-340(part)-340(of)-340(submatrix)]TJ/F30 9.9626 Tf 210.933 0 Td [(A\050imin:imax,jmin:jmax\051)]TJ/F8 9.9626 Tf 115.067 0 Td [(,)]TJ -340.944 -11.955 Td [(optionally)-222(rescaling)-222(ro)27(w/col)-222(indices)-222(to)-222(the)-222(range)]TJ/F30 9.9626 Tf 205.536 0 Td [(1:imax-imin+1,1:jmax-jmin+1)]TJ/F8 9.9626 Tf 141.219 0 Td [(,)]TJ -346.755 -11.955 Td [(and)-333(returing)-334(th)1(e)-334(complemen)28(tary)-333(lo)27(w)28(er)-333(triangle.)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -17.723 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -18.824 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -18.824 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.356 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ -160.398 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.359 -30.78 Td [(diag)]TJ +0 g 0 G +/F8 9.9626 Tf 25.827 0 Td [(Include)-392(diagonals)-391(up)-392(to)-392(this)-391(one;)]TJ/F30 9.9626 Tf 149.735 0 Td [(diag=1)]TJ/F8 9.9626 Tf 35.284 0 Td [(means)-392(the)-392(\014rst)-391(sup)-28(erdiagonal,)]TJ/F30 9.9626 Tf -185.939 -11.955 Td [(diag=-1)]TJ/F8 9.9626 Tf 39.933 0 Td [(means)-333(the)-334(\014rst)-333(sub)-28(diagonal.)-444(Default)-333(0.)]TJ +0 g 0 G +/F27 9.9626 Tf -64.84 -18.824 Td [(imin,imax,jmin,jma)-1(x)]TJ +0 g 0 G +/F8 9.9626 Tf 108.413 0 Td [(Minim)28(um)-333(and)-334(maxim)28(um)-333(ro)27(w)-333(and)-333(column)-333(indices.)]TJ -83.506 -11.955 Td [(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.824 Td [(rscale,cscale)]TJ +0 g 0 G +/F8 9.9626 Tf 65.203 0 Td [(Whether)-333(to)-334(rescale)-333(ro)28(w/column)-334(ind)1(ic)-1(es.)-444(T)28(yp)-28(e:)-444(optional.)]TJ +0 g 0 G +/F27 9.9626 Tf -65.203 -19.165 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -18.824 Td [(u)]TJ +0 g 0 G +/F8 9.9626 Tf 11.347 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-333(upp)-28(er)-333(triangle)-334(of)]TJ/F30 9.9626 Tf 138.979 0 Td [(a)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ -130.649 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -18.824 Td [(l)]TJ +0 g 0 G +/F8 9.9626 Tf 8.164 0 Td [(\050optional\051)-333(A)-334(cop)28(y)-333(of)-333(the)-334(lo)28(w)28(er)-334(tr)1(iangle)-334(of)]TJ/F30 9.9626 Tf 182.981 0 Td [(a)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ -171.468 -11.955 Td [(A)-333(v)55(ariable)-333(of)-333(t)27(yp)-27(e)]TJ/F30 9.9626 Tf 81.943 0 Td [(psb_Tspmat_type)]TJ/F8 9.9626 Tf 78.455 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -185.305 -18.824 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ +0 g 0 G + 143.117 -29.888 Td [(23)]TJ +0 g 0 G +ET + +endstream +endobj +985 0 obj +<< +/Length 7723 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F27 9.9626 Tf 150.705 706.129 Td [(3.2.17)-1150(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 209.377 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 212.814 706.129 Td [(set)]TJ +ET +q +1 0 0 1 227.727 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 231.165 706.129 Td [(mat)]TJ +ET +q +1 0 0 1 251.424 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(gedot)-375(|)-375(Dot)-375(Pro)-31(duct)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-333(function)-334(computes)-333(dot)-333(pro)-28(duct)-333(b)-28(et)28(w)27(een)-333(t)28(w)28(o)-334(v)28(ectors)]TJ/F11 9.9626 Tf 252.332 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -285.961 -11.956 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 8.562 0 Td [(are)-333(real)-334(v)28(ectors)-333(it)-334(computes)-333(dot-pro)-28(duct)-333(as:)]TJ/F11 9.9626 Tf 101.783 -21.289 Td [(dot)]TJ/F14 9.9626 Tf 16.38 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 4.113 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(y)]TJ/F8 9.9626 Tf -189.775 -21.29 Td [(Else)-333(if)]TJ/F11 9.9626 Tf 30.359 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.371 0 Td [(y)]TJ/F8 9.9626 Tf 8.563 0 Td [(are)-333(complex)-334(v)28(ectors)-333(then)-334(it)-333(computes)-333(dot-pro)-28(duct)-333(as:)]TJ/F11 9.9626 Tf 80.747 -21.29 Td [(dot)]TJ/F14 9.9626 Tf 16.38 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F10 6.9738 Tf 5.693 4.113 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.113 Td [(y)]TJ +/F27 9.9626 Tf 254.861 706.129 Td [(default)-383(|)-384(Set)-383(default)-383(storage)-384(format)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -104.156 -18.389 Td [(call)-1050(psb_set_mat_default\050a\051)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -20.935 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.532 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.532 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(a)-285(v)56(ariable)-285(of)]TJ/F30 9.9626 Tf 55.581 0 Td [(class\050psb_T_base_sparse_mat\051)]TJ/F8 9.9626 Tf 149.285 0 Td [(requesting)-285(a)-284(new)-285(default)-285(stor-)]TJ -190.511 -11.955 Td [(age)-333(format.)]TJ 0 -11.956 Td [(T)28(yp)-28(e:)-444(required.)]TJ/F27 9.9626 Tf -24.906 -25.726 Td [(3.2.18)-1150(clone)-383(|)-384(Clone)-383(curren)32(t)-383(ob)-64(ject)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf 0 -18.389 Td [(call)-1050(a%clone\050b,info\051)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -20.935 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.532 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.532 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix.)]TJ 14.355 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -80.358 -32.89 Td [(On)-383(Return)]TJ +0 g 0 G 0 g 0 G + 0 -19.532 Td [(b)]TJ 0 g 0 G -/F30 9.9626 Tf -190.415 -21.29 Td [(psb_gedot\050x,)-525(y,)-525(desc_a,)-525(info)-525([,global]\051)]TJ +/F8 9.9626 Tf 11.346 0 Td [(A)-333(cop)27(y)-333(of)-333(the)-334(in)1(put)-334(ob)-55(ject.)]TJ 0 g 0 G +/F27 9.9626 Tf -11.346 -19.532 Td [(info)]TJ 0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Return)-333(co)-28(de.)]TJ/F27 9.9626 Tf -23.758 -25.727 Td [(3.2.19)-1150(Named)-383(Constan)32(ts)]TJ 0 g 0 G + 0 -18.389 Td [(psb)]TJ ET q -1 0 0 1 183.665 567.173 cm -[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +1 0 0 1 168.641 371.89 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F11 9.9626 Tf 189.642 558.606 Td [(dot)]TJ/F8 9.9626 Tf 13.612 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.927 0 Td [(F)96(unction)]TJ +/F27 9.9626 Tf 172.078 371.691 Td [(dupl)]TJ ET q -1 0 0 1 183.665 554.82 cm -[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +1 0 0 1 195.043 371.89 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F8 9.9626 Tf 189.642 546.252 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ +/F27 9.9626 Tf 198.48 371.691 Td [(o)32(vwrt)]TJ ET q -1 0 0 1 325.649 546.451 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 228.073 371.89 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q +0 g 0 G BT -/F8 9.9626 Tf 328.638 546.252 Td [(gedot)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ +/F8 9.9626 Tf 236.492 371.691 Td [(Duplicate)-315(co)-28(e\016cien)28(ts)-315(should)-315(b)-28(e)-315(o)28(v)28(erwritten)-315(\050i.e.)-438(ignore)-315(du-)]TJ -60.881 -11.955 Td [(plications\051)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.532 Td [(psb)]TJ ET q -1 0 0 1 325.649 534.496 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 168.641 340.403 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F8 9.9626 Tf 328.638 534.297 Td [(gedot)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ +/F27 9.9626 Tf 172.078 340.204 Td [(dupl)]TJ ET q -1 0 0 1 325.649 522.541 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 195.043 340.403 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F8 9.9626 Tf 328.638 522.342 Td [(gedot)]TJ -138.996 -11.956 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ +/F27 9.9626 Tf 198.48 340.204 Td [(add)]TJ ET q -1 0 0 1 325.649 510.586 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 217.467 340.403 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q +0 g 0 G BT -/F8 9.9626 Tf 328.638 510.386 Td [(gedot)]TJ +/F8 9.9626 Tf 225.886 340.204 Td [(Duplicate)-333(co)-28(e\016cien)28(ts)-334(should)-333(b)-28(e)-333(added;)]TJ +0 g 0 G +/F27 9.9626 Tf -75.181 -19.532 Td [(psb)]TJ ET q -1 0 0 1 183.665 506.601 cm -[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +1 0 0 1 168.641 320.871 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 228.067 478.561 Td [(T)83(able)-333(2:)-444(Data)-334(t)28(yp)-28(es)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -128.172 -32.717 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.674 Td [(On)-383(En)32(try)]TJ -0 g 0 G +/F27 9.9626 Tf 172.078 320.672 Td [(dupl)]TJ +ET +q +1 0 0 1 195.043 320.871 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 198.48 320.672 Td [(err)]TJ +ET +q +1 0 0 1 213.856 320.871 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q 0 g 0 G - 0 -19.674 Td [(x)]TJ +BT +/F8 9.9626 Tf 222.274 320.672 Td [(Duplicate)-333(co)-28(e\016cien)28(ts)-334(should)-333(trigger)-333(an)-334(error)-333(conditino)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F27 9.9626 Tf -71.569 -19.532 Td [(psb)]TJ ET q -1 0 0 1 385.864 358.875 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 168.641 301.339 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 389.002 358.675 Td [(T)]TJ +/F27 9.9626 Tf 172.078 301.14 Td [(up)-32(d)]TJ ET q -1 0 0 1 394.86 358.875 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 192.179 301.339 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 397.998 358.675 Td [(vect)]TJ +/F27 9.9626 Tf 195.616 301.14 Td [(d\015t)]TJ ET q -1 0 0 1 419.547 358.875 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 213.489 301.339 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -BT -/F30 9.9626 Tf 422.685 358.675 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-375(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-376(of)-375(t)28(yp)-28(e)-375(sp)-28(eci\014ed)-375(in)-375(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-375(2)]TJ 0 g 0 G - [(.)-570(The)-376(rank)-375(of)]TJ/F11 9.9626 Tf 274.03 0 Td [(x)]TJ/F8 9.9626 Tf 9.432 0 Td [(m)28(ust)-376(b)-27(e)]TJ -283.462 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -83.615 -19.674 Td [(y)]TJ +BT +/F8 9.9626 Tf 221.907 301.14 Td [(Default)-333(up)-28(date)-333(strategy)-334(for)-333(matrix)-333(co)-28(e\016cien)28(ts;)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F27 9.9626 Tf -71.202 -19.533 Td [(psb)]TJ ET q -1 0 0 1 385.864 267.47 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 168.641 281.807 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 389.002 267.27 Td [(T)]TJ +/F27 9.9626 Tf 172.078 281.607 Td [(up)-32(d)]TJ ET q -1 0 0 1 394.86 267.47 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 192.179 281.807 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 397.998 267.27 Td [(vect)]TJ +/F27 9.9626 Tf 195.616 281.607 Td [(src)32(h)]TJ ET q -1 0 0 1 419.547 267.47 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 216.68 281.807 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -BT -/F30 9.9626 Tf 422.685 267.27 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-378(n)27(um)28(b)-28(ers)-378(of)-378(t)28(yp)-28(e)-378(sp)-28(eci\014ed)-378(in)-379(T)84(able)]TJ -0 0 1 rg 0 0 1 RG - [-378(2)]TJ 0 g 0 G - [(.)-580(The)-378(rank)-378(of)]TJ/F11 9.9626 Tf 274.422 0 Td [(y)]TJ/F8 9.9626 Tf 9.01 0 Td [(m)28(ust)-379(b)-27(e)]TJ -283.432 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +BT +/F8 9.9626 Tf 225.098 281.607 Td [(Up)-28(date)-333(strategy)-333(base)-1(d)-333(on)-333(searc)28(h)-334(in)28(to)-333(the)-334(data)-333(structure;)]TJ 0 g 0 G -/F27 9.9626 Tf -84.067 -19.674 Td [(desc)]TJ +/F27 9.9626 Tf -74.393 -19.532 Td [(psb)]TJ ET q -1 0 0 1 121.81 223.885 cm +1 0 0 1 168.641 262.275 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 223.686 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ 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[(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 385.864 295.361 cm +1 0 0 1 436.673 176.72 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 389.002 295.162 Td [(T)]TJ +/F30 9.9626 Tf 439.811 176.521 Td [(T)]TJ ET q -1 0 0 1 394.86 295.361 cm +1 0 0 1 445.669 176.72 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 397.998 295.162 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 176.521 Td [(vect)]TJ ET q -1 0 0 1 419.547 295.361 cm +1 0 0 1 470.356 176.72 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 422.685 295.162 Td [(type)]TJ +/F30 9.9626 Tf 473.495 176.521 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-378(n)27(um)28(b)-28(ers)-378(of)-378(t)28(yp)-28(e)-378(sp)-28(eci\014ed)-378(in)-379(T)84(able)]TJ +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-334(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-335(of)-334(the)-334(t)28(yp)-28(e)-334(indicated)-334(in)-334(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-378(3)]TJ + [-334(1)]TJ 0 g 0 G - [(.)-580(The)-378(rank)-378(of)]TJ/F11 9.9626 Tf 274.422 0 Td [(y)]TJ/F8 9.9626 Tf 9.01 0 Td [(m)28(ust)-379(b)-27(e)]TJ -283.432 -11.956 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ + [(.)-447(The)-334(rank)-335(of)]TJ/F11 9.9626 Tf 288.869 0 Td [(y)]TJ/F8 9.9626 Tf 8.572 0 Td [(m)28(ust)]TJ -297.441 -11.955 Td [(b)-28(e)-333(the)-333(s)-1(ame)-333(of)]TJ/F11 9.9626 Tf 67.027 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -84.067 -18.428 Td [(desc)]TJ +/F27 9.9626 Tf -97.627 -20.33 Td [(desc)]TJ ET q -1 0 0 1 121.81 253.022 cm +1 0 0 1 172.619 132.48 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 252.823 Td [(a)]TJ +/F27 9.9626 Tf 176.057 132.281 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ +0 g 0 G +/F8 9.9626 Tf 109.589 -29.888 Td [(30)]TJ +0 g 0 G +ET + +endstream +endobj +1034 0 obj +<< +/Length 2659 +>> +stream +0 g 0 G +0 g 0 G +BT +/F8 9.9626 Tf 124.802 706.129 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 276.779 205.202 cm +1 0 0 1 276.779 682.418 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 279.917 205.003 Td [(desc)]TJ +/F30 9.9626 Tf 279.917 682.219 Td [(desc)]TJ ET q -1 0 0 1 301.466 205.202 cm +1 0 0 1 301.466 682.418 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 304.604 205.003 Td [(type)]TJ +/F30 9.9626 Tf 304.604 682.219 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -225.631 -18.429 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -225.631 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G 0 g 0 G - 0 -18.428 Td [(res)]TJ + 0 -19.926 Td [(y)]TJ 0 g 0 G -/F8 9.9626 Tf 19.47 0 Td [(is)-333(the)-334(dot)-333(pro)-28(duct)-333(of)-333(v)27(ectors)]TJ/F11 9.9626 Tf 127.467 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -155.659 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-357(as)-1(:)-493(a)-357(n)27(um)28(b)-28(er)-357(or)-358(a)-358(rank-one)-358(ar)1(ra)27(y)-357(of)-358(the)-358(data)-358(t)28(yp)-27(e)-358(indicated)-358(in)]TJ 0 -11.955 Td [(T)83(able)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(submatrix)]TJ/F11 9.9626 Tf 162.364 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -153.727 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG - [-333(2)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G - 141.968 -29.888 Td [(33)]TJ -0 g 0 G +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET - -endstream -endobj -1025 0 obj -<< -/Length 625 ->> -stream +q +1 0 0 1 385.864 592.754 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 389.002 592.555 Td [(T)]TJ +ET +q +1 0 0 1 394.86 592.754 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 397.998 592.555 Td [(vect)]TJ +ET +q +1 0 0 1 419.547 592.754 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 422.685 592.555 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(the)-334(t)28(yp)-28(e)-333(indicated)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(1)]TJ 0 g 0 G + [(.)]TJ 0 g 0 G -BT -/F27 9.9626 Tf 150.705 706.129 Td [(info)]TJ +/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - 141.968 -567.87 Td [(34)]TJ + 141.968 -422.416 Td [(31)]TJ 0 g 0 G ET endstream endobj -1032 0 obj +1044 0 obj << -/Length 6858 +/Length 7709 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.2)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 202.396 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(normi)-375(|)-375(In\014nit)31(y-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -25.091 -19.477 Td [(This)-333(function)-334(computes)-333(the)-333(in\014nit)28(y-norm)-334(of)-333(a)-333(v)27(ector)]TJ/F11 9.9626 Tf 233.182 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -238.876 -11.955 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(a)-334(real)-333(v)28(ector)-334(it)-333(computes)-333(in\014nit)28(y)-334(norm)-333(as:)]TJ/F11 9.9626 Tf 115.269 -23.087 Td [(amax)]TJ/F14 9.9626 Tf 27.741 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.861 -6.275 Td [(i)]TJ/F14 9.9626 Tf 12.341 6.275 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F8 9.9626 Tf -206.698 -26.317 Td [(else)-333(if)]TJ/F11 9.9626 Tf 28.007 0 Td [(x)]TJ/F8 9.9626 Tf 9.014 0 Td [(is)-333(a)-334(complex)-333(v)28(ector)-334(then)-333(it)-333(computes)-334(the)-333(in\014nit)28(y-norm)-333(as:)]TJ/F11 9.9626 Tf 61.447 -23.087 Td [(amax)]TJ/F14 9.9626 Tf 27.74 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.862 -6.275 Td [(i)]TJ/F8 9.9626 Tf 12.34 6.275 Td [(\050)]TJ/F14 9.9626 Tf 3.875 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(r)-28(e)]TJ/F8 9.9626 Tf 9.411 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(j)]TJ/F8 9.9626 Tf 4.981 0 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(im)]TJ/F8 9.9626 Tf 12.18 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(j)]TJ/F8 9.9626 Tf 2.768 0 Td [(\051)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(gedot)-375(|)-375(Dot)-375(Pro)-31(duct)]TJ/F8 9.9626 Tf -55.726 -18.389 Td [(This)-333(function)-334(computes)-333(dot)-333(pro)-28(duct)-333(b)-28(et)28(w)28(e)-1(en)-333(t)28(w)28(o)-334(v)28(ectors)]TJ/F11 9.9626 Tf 252.332 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.371 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -285.96 -11.956 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.014 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 8.563 0 Td [(are)-333(real)-334(v)28(ectors)-333(it)-334(computes)-333(dot-pro)-28(duct)-333(as:)]TJ/F11 9.9626 Tf 101.783 -21.289 Td [(dot)]TJ/F14 9.9626 Tf 16.379 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 4.113 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(y)]TJ/F8 9.9626 Tf -189.774 -21.29 Td [(Else)-333(if)]TJ/F11 9.9626 Tf 30.358 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 8.563 0 Td [(are)-333(complex)-334(v)28(ectors)-333(then)-334(it)-333(computes)-333(dot-pro)-28(duct)-333(as:)]TJ/F11 9.9626 Tf 80.747 -21.29 Td [(dot)]TJ/F14 9.9626 Tf 16.379 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 4.113 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.113 Td [(y)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -241.37 -26.901 Td [(psb_geamax\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ 0 -11.956 Td [(psb_normi\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ +/F30 9.9626 Tf -190.414 -21.29 Td [(psb_gedot\050x,)-525(y,)-525(desc_a,)-525(info)-525([,global]\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 129.083 536.097 cm -[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S +1 0 0 1 234.474 567.173 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q BT -/F11 9.9626 Tf 135.06 527.529 Td [(amax)-7677(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(F)96(unction)]TJ +/F11 9.9626 Tf 240.452 558.606 Td [(dot)]TJ/F8 9.9626 Tf 13.612 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.927 0 Td [(F)96(unction)]TJ ET q -1 0 0 1 129.083 523.743 cm -[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S +1 0 0 1 234.474 554.82 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q BT -/F8 9.9626 Tf 135.06 515.175 Td [(Short)-333(Precision)-334(Real)-1200(Short)-333(Precision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 240.452 546.252 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ ET q -1 0 0 1 372.52 515.374 cm +1 0 0 1 376.459 546.451 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 375.509 515.175 Td [(geamax)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Re)-1(al)-3313(psb)]TJ +/F8 9.9626 Tf 379.447 546.252 Td [(gedot)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ ET q -1 0 0 1 372.52 503.419 cm +1 0 0 1 376.459 534.496 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 375.509 503.22 Td [(geamax)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Short)-333(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 379.447 534.297 Td [(gedot)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ ET q -1 0 0 1 372.52 491.464 cm +1 0 0 1 376.459 522.541 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 375.509 491.265 Td [(geamax)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Com)-1(p)1(lex)-1412(psb)]TJ +/F8 9.9626 Tf 379.447 522.342 Td [(gedot)]TJ -138.995 -11.956 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ ET q -1 0 0 1 372.52 479.509 cm +1 0 0 1 376.459 510.586 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 375.509 479.31 Td [(geamax)]TJ +/F8 9.9626 Tf 379.447 510.386 Td [(gedot)]TJ ET q -1 0 0 1 129.083 475.524 cm -[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S +1 0 0 1 234.474 506.601 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 228.067 447.485 Td [(T)83(able)-333(4:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 278.877 478.561 Td [(T)83(able)-333(2:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -128.172 -36.518 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -128.172 -32.717 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -22.263 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.674 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -22.263 Td [(x)]TJ + 0 -19.674 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 385.864 318.82 cm +1 0 0 1 436.673 358.875 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 389.002 318.621 Td [(T)]TJ +/F30 9.9626 Tf 439.811 358.675 Td [(T)]TJ ET q -1 0 0 1 394.86 318.82 cm +1 0 0 1 445.669 358.875 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 397.998 318.621 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 358.675 Td [(vect)]TJ ET q -1 0 0 1 419.547 318.82 cm +1 0 0 1 470.356 358.875 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 422.685 318.621 Td [(type)]TJ +/F30 9.9626 Tf 473.495 358.675 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-375(n)27(um)28(b)-28(ers)-375(of)-375(t)28(yp)-28(e)-375(sp)-28(eci\014ed)-375(in)-375(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(4)]TJ + [-375(2)]TJ 0 g 0 G - [(.)]TJ + [(.)-570(The)-376(rank)-375(of)]TJ/F11 9.9626 Tf 274.031 0 Td [(x)]TJ/F8 9.9626 Tf 9.432 0 Td [(m)28(ust)-375(b)-28(e)]TJ -283.463 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -22.262 Td [(desc)]TJ -ET +/F27 9.9626 Tf -83.615 -19.674 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ +ET +q +1 0 0 1 436.673 267.47 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 439.811 267.27 Td [(T)]TJ +ET +q +1 0 0 1 445.669 267.47 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 448.807 267.27 Td [(vect)]TJ +ET +q +1 0 0 1 470.356 267.47 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 473.495 267.27 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-378(n)27(um)28(b)-28(ers)-378(of)-378(t)28(yp)-28(e)-378(sp)-28(eci\014ed)-378(in)-379(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-378(2)]TJ +0 g 0 G + [(.)-580(The)-378(rank)-378(of)]TJ/F11 9.9626 Tf 274.422 0 Td [(y)]TJ/F8 9.9626 Tf 9.011 0 Td [(m)28(ust)-378(b)-28(e)]TJ -283.433 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -84.067 -19.674 Td [(desc)]TJ +ET q -1 0 0 1 121.81 284.602 cm +1 0 0 1 172.619 223.885 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 284.403 Td [(a)]TJ +/F27 9.9626 Tf 176.057 223.686 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ ET q -1 0 0 1 276.779 236.781 cm +1 0 0 1 327.588 176.064 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 279.917 236.582 Td [(desc)]TJ +/F30 9.9626 Tf 330.727 175.865 Td [(desc)]TJ ET q -1 0 0 1 301.466 236.781 cm +1 0 0 1 352.275 176.064 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 304.604 236.582 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F30 9.9626 Tf 355.414 175.865 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -225.631 -22.263 Td [(global)]TJ -0 g 0 G -/F8 9.9626 Tf 34.738 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(computation)-358(shoul)1(d)-358(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.955 Td [(across)-333(all)-334(pro)-27(ce)-1(sses.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -193.719 -34.217 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -225.63 -19.674 Td [(global)]TJ 0 g 0 G +/F8 9.9626 Tf 34.737 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(co)-1(mpu)1(tation)-358(should)-357(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.955 Td [(across)-333(all)-334(pro)-27(c)-1(esses.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 166.875 -29.888 Td [(35)]TJ + 71.78 -29.888 Td [(32)]TJ 0 g 0 G ET endstream endobj -1037 0 obj +1050 0 obj << -/Length 4563 +/Length 5125 >> stream 0 g 0 G 0 g 0 G -0 g 0 G BT -/F27 9.9626 Tf 150.705 706.129 Td [(F)96(unction)-384(v)64(alue)]TJ +/F8 9.9626 Tf 124.802 706.129 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(is)-333(the)-334(in\014nit)28(y)-333(norm)-333(of)-334(v)28(ector)]TJ/F11 9.9626 Tf 128.795 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -187.969 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.842 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ari)1(able)]TJ/F30 9.9626 Tf 118.433 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.471 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec-)]TJ -257.748 -11.955 Td [(i\014ed)]TJ 0 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-334(r)1(e)-1(al)-333(n)28(um)28(b)-28(er.)]TJ +/F27 9.9626 Tf -193.719 -31.881 Td [(On)-383(Return)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.925 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 11.9552 Tf -24.906 -21.917 Td [(Notes)]TJ + 0 -19.925 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F8 9.9626 Tf 12.176 -19.926 Td [(1.)]TJ +/F8 9.9626 Tf 78.387 0 Td [(is)-333(the)-334(dot)-333(pro)-28(duct)-333(of)-333(v)28(ec)-1(tor)1(s)]TJ/F11 9.9626 Tf 127.466 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -214.575 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.841 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ariabl)1(e)]TJ/F30 9.9626 Tf 118.434 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.47 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec)-1(-)]TJ -257.747 -11.955 Td [(i\014ed)]TJ 0 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(2)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.925 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.917 Td [(Notes)]TJ +0 g 0 G +/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ 0 g 0 G - [-500(The)-241(computation)-240(of)-241(a)-241(gl)1(obal)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(s)-1(i)1(gni\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.19 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(1)-131(\051)-642(=)-586(p)-75(s)-76(b)]TJ + [-500(The)-241(computation)-240(of)-241(a)-240(global)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(signi\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-265(m)27(ultiple)-265(dot)-265(pro)-28(ducts)-265(at)-266(the)-265(same)-266(time;)-288(in)-265(this)-265(case,)-279(it)-266(is)-265(p)-28(ossible)]TJ 0 -11.955 Td [(to)-333(impro)27(v)28(e)-333(the)-333(run)27(ti)1(m)-1(e)-333(e\016ciency)-333(b)27(y)-333(using)-333(the)-333(follo)27(wing)-333(sc)28(heme:)]TJ 25.189 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(1)-130(\051)-642(=)-625(p)-115(s)-115(b)]TJ ET q -1 0 0 1 277.899 507.075 cm +1 0 0 1 228.651 443.314 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 281.638 506.876 Td [(g)-75(e)-76(a)-75(m)-76(a)-75(x)-181(\050)-148(x)-43(1)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 232.782 443.115 Td [(g)-115(e)-114(d)-115(o)-114(t)-220(\050)-149(x)-43(1)-247(,)-204(y)-43(1)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 367.515 507.075 cm +1 0 0 1 328.66 443.314 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 371.626 506.876 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(2)-131(\051)-642(=)-586(p)-75(s)-76(b)]TJ +/F8 9.9626 Tf 332.771 443.115 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -305.353 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(2)-130(\051)-642(=)-625(p)-115(s)-115(b)]TJ ET q -1 0 0 1 277.899 495.12 cm +1 0 0 1 228.651 431.359 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 281.638 494.921 Td [(g)-75(e)-76(a)-75(m)-76(a)-75(x)-181(\050)-148(x)-43(2)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 232.782 431.16 Td [(g)-115(e)-114(d)-115(o)-114(t)-220(\050)-149(x)-43(2)-247(,)-204(y)-43(2)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 367.515 495.12 cm +1 0 0 1 328.66 431.359 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 371.626 494.921 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(3)-131(\051)-642(=)-586(p)-75(s)-76(b)]TJ +/F8 9.9626 Tf 332.771 431.16 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -305.353 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(3)-130(\051)-642(=)-625(p)-115(s)-115(b)]TJ ET q -1 0 0 1 277.899 483.165 cm +1 0 0 1 228.651 419.404 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 281.638 482.966 Td [(g)-75(e)-76(a)-75(m)-76(a)-75(x)-181(\050)-148(x)-43(3)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 232.782 419.205 Td [(g)-115(e)-114(d)-115(o)-114(t)-220(\050)-149(x)-43(3)-247(,)-204(y)-43(3)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 367.515 483.165 cm +1 0 0 1 328.66 419.404 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 371.626 482.966 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.955 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.101 0 Td [(p)-59(s)-59(b)]TJ +/F8 9.9626 Tf 332.771 419.205 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -305.255 -11.955 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.198 0 Td [(p)-69(s)-69(b)]TJ ET q -1 0 0 1 247.365 471.21 cm +1 0 0 1 196.943 407.449 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 250.944 471.011 Td [(a)-59(m)-59(x)-165(\050)-245(i)-138(c)-139(t)-139(x)-139(t)-439(,)-289(v)-129(r)-128(e)-128(s)-294(\050)-165(1)-165(:)-165(3)-165(\051)-165(\051)]TJ +/F8 9.9626 Tf 200.618 407.25 Td [(s)-69(u)-69(m)-174(\050)-245(i)-139(c)-139(t)-138(x)-139(t)-439(,)-290(v)-128(r)-128(e)-129(s)-293(\050)-165(1)-165(:)-165(3)-165(\051)-166(\051)]TJ 0 g 0 G 0 g 0 G - -75.333 -21.918 Td [(In)-354(th)1(is)-354(w)28(a)28(y)-354(the)-353(global)-354(comm)28(unication,)-359(whic)28(h)-353(for)-354(small)-353(size)-1(s)-353(is)-354(a)-353(latency-)]TJ 0 -11.955 Td [(b)-28(ound)-333(op)-28(eration,)-333(is)-333(in)27(v)28(ok)28(ed)-333(only)-334(once.)]TJ + -75.816 -21.918 Td [(In)-353(this)-354(w)28(a)28(y)-354(the)-353(global)-354(comm)28(unication,)-359(whic)28(h)-353(for)-354(small)-353(sizes)-354(is)-354(a)-353(latency-)]TJ 0 -11.955 Td [(b)-28(ound)-333(op)-28(eration,)-333(is)-333(in)28(v)27(ok)28(ed)-333(only)-333(onc)-1(e.)]TJ 0 g 0 G - 141.968 -346.7 Td [(36)]TJ + 141.968 -282.939 Td [(33)]TJ 0 g 0 G ET endstream endobj -1050 0 obj +1066 0 obj << -/Length 6326 +/Length 8426 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.3)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 202.396 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(geamaxs)-375(|)-375(Generalized)-375(In\014nit)31(y)-375(Norm)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-359(subroutine)-359(computes)-360(a)-359(series)-359(of)-359(in\014nit)28(y)-359(norms)-360(on)-359(the)-359(columns)-359(of)-359(a)-360(d)1(e)-1(n)1(s)-1(e)]TJ 0 -11.956 Td [(matrix)]TJ/F11 9.9626 Tf 32.407 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(:)]TJ/F11 9.9626 Tf 87.106 -11.955 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)]TJ/F14 9.9626 Tf 6.641 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.069 -6.503 Td [(k)]TJ/F14 9.9626 Tf 13.133 6.503 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(k)-31(;)-167(i)]TJ/F8 9.9626 Tf 13.36 0 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(j)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(gedots)-375(|)-375(Generalized)-375(Dot)-375(Pro)-31(duct)]TJ/F8 9.9626 Tf -55.726 -18.389 Td [(This)-392(subroutine)-392(computes)-392(a)-392(series)-392(of)-391(dot)-392(pro)-28(ducts)-392(among)-392(the)-392(columns)-392(of)-391(t)27(w)28(o)]TJ 0 -11.956 Td [(dense)-333(matrices)]TJ/F11 9.9626 Tf 67.109 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(:)]TJ/F11 9.9626 Tf 23.756 -11.955 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.642 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F8 9.9626 Tf 5.693 0 Td [(\050:)]TJ/F11 9.9626 Tf 6.642 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 7.86 0 Td [(\051)]TJ/F10 6.9738 Tf 3.875 4.114 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.114 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(\050:)]TJ/F11 9.9626 Tf 6.642 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 7.86 0 Td [(\051)]TJ -215.343 -15.687 Td [(If)-245(the)-245(matrices)-245(are)-245(complex,)-262(then)-245(the)-245(usual)-245(con)28(v)28(en)27(tion)-245(ap)1(plies)-1(,)-262(i.e.)-415(the)-245(conjugate)]TJ 0 -11.955 Td [(transp)-28(ose)-323(of)]TJ/F11 9.9626 Tf 55.836 0 Td [(x)]TJ/F8 9.9626 Tf 8.913 0 Td [(is)-323(used.)-441(If)]TJ/F11 9.9626 Tf 46.365 0 Td [(x)]TJ/F8 9.9626 Tf 8.913 0 Td [(and)]TJ/F11 9.9626 Tf 19.27 0 Td [(y)]TJ/F8 9.9626 Tf 8.461 0 Td [(are)-323(of)-323(rank)-323(one,)-325(then)]TJ/F11 9.9626 Tf 94.211 0 Td [(r)-28(es)]TJ/F8 9.9626 Tf 17.3 0 Td [(is)-323(a)-323(scalar,)-325(else)-324(it)-323(is)]TJ -259.269 -11.955 Td [(a)-333(rank)-334(one)-333(arra)28(y)83(.)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -215.738 -25.377 Td [(call)-525(psb_geamaxs\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf 0 -18.175 Td [(call)-525(psb_gedots\050res,)-525(x,)-525(y,)-525(desc_a,)-525(info\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 127.118 614.121 cm -[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S +1 0 0 1 228.797 586.966 cm +[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F11 9.9626 Tf 133.096 605.553 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.862 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 234.775 578.398 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.459 0 Td [(Subroutine)]TJ ET q -1 0 0 1 127.118 601.768 cm -[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S +1 0 0 1 228.797 574.612 cm +[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F8 9.9626 Tf 133.096 593.2 Td [(Short)-333(Precision)-334(Real)-1200(Sh)1(ort)-334(Precision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 234.775 566.045 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ ET q -1 0 0 1 370.556 593.399 cm +1 0 0 1 370.782 566.244 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.544 593.2 Td [(geamaxs)]TJ -240.448 -11.956 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ +/F8 9.9626 Tf 373.771 566.045 Td [(gedots)]TJ -138.996 -11.956 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ ET q -1 0 0 1 370.556 581.444 cm +1 0 0 1 370.782 554.289 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.544 581.244 Td [(geamaxs)]TJ -240.448 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Sh)1(ort)-334(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 373.771 554.089 Td [(gedots)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ ET q -1 0 0 1 370.556 569.489 cm +1 0 0 1 370.782 542.333 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.544 569.289 Td [(geamaxs)]TJ -240.448 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 373.771 542.134 Td [(gedots)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ ET q -1 0 0 1 370.556 557.533 cm +1 0 0 1 370.782 530.378 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.544 557.334 Td [(geamaxs)]TJ +/F8 9.9626 Tf 373.771 530.179 Td [(gedots)]TJ ET q -1 0 0 1 127.118 553.548 cm -[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S +1 0 0 1 228.797 526.393 cm +[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 228.067 525.509 Td [(T)83(able)-333(5:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 278.877 498.354 Td [(T)83(able)-333(3:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -128.172 -33.596 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -128.172 -28.356 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -18.428 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.926 Td [(x)]TJ + 0 -18.429 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 385.864 404.441 cm +1 0 0 1 436.673 385.52 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 389.002 404.242 Td [(T)]TJ +/F30 9.9626 Tf 439.811 385.321 Td [(T)]TJ ET q -1 0 0 1 394.86 404.441 cm +1 0 0 1 445.669 385.52 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 397.998 404.242 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 385.321 Td [(vect)]TJ ET q -1 0 0 1 419.547 404.441 cm +1 0 0 1 470.356 385.52 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 422.685 404.242 Td [(type)]TJ +/F30 9.9626 Tf 473.495 385.321 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-375(n)27(um)28(b)-28(ers)-375(of)-375(t)28(yp)-28(e)-375(sp)-28(eci\014ed)-375(in)-375(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(5)]TJ + [-375(3)]TJ 0 g 0 G - [(.)]TJ + [(.)-570(The)-376(rank)-375(of)]TJ/F11 9.9626 Tf 274.031 0 Td [(x)]TJ/F8 9.9626 Tf 9.432 0 Td [(m)28(ust)-375(b)-28(e)]TJ -283.463 -11.956 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -83.615 -18.428 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ +ET +q +1 0 0 1 436.673 295.361 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 439.811 295.162 Td [(T)]TJ +ET +q +1 0 0 1 445.669 295.361 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 448.807 295.162 Td [(vect)]TJ +ET +q +1 0 0 1 470.356 295.361 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 473.495 295.162 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-378(n)27(um)28(b)-28(ers)-378(of)-378(t)28(yp)-28(e)-378(sp)-28(eci\014ed)-378(in)-379(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-378(3)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(desc)]TJ + [(.)-580(The)-378(rank)-378(of)]TJ/F11 9.9626 Tf 274.422 0 Td [(y)]TJ/F8 9.9626 Tf 9.011 0 Td [(m)28(ust)-378(b)-28(e)]TJ -283.433 -11.956 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -84.067 -18.428 Td [(desc)]TJ ET q -1 0 0 1 121.81 372.56 cm +1 0 0 1 172.619 253.022 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 372.361 Td [(a)]TJ +/F27 9.9626 Tf 176.057 252.823 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ ET q -1 0 0 1 276.779 324.74 cm +1 0 0 1 327.588 205.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 279.917 324.54 Td [(desc)]TJ +/F30 9.9626 Tf 330.727 205.003 Td [(desc)]TJ ET q -1 0 0 1 301.466 324.74 cm +1 0 0 1 352.275 205.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 304.604 324.54 Td [(type)]TJ +/F30 9.9626 Tf 355.414 205.003 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -225.631 -19.925 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -225.63 -18.429 Td [(On)-383(Return)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(res)]TJ + 0 -18.428 Td [(res)]TJ 0 g 0 G -/F8 9.9626 Tf 19.47 0 Td [(is)-333(the)-334(in\014nit)28(y)-333(norm)-333(of)-334(the)-333(columns)-333(of)]TJ/F11 9.9626 Tf 166.183 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -166.44 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(Sp)-28(eci\014ed)-289(as:)-422(a)-289(n)28(um)28(b)-28(er)-289(or)-289(a)-289(ran)1(k-one)-289(arra)27(y)-288(of)-289(long)-289(precision)-289(real)-289(n)28(um)28(b)-28(ers.)]TJ +/F8 9.9626 Tf 19.47 0 Td [(is)-333(the)-334(dot)-333(pro)-28(duct)-333(of)-333(v)28(e)-1(ctors)]TJ/F11 9.9626 Tf 127.466 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -155.659 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-358(as:)-493(a)-358(n)28(um)28(b)-28(er)-357(or)-358(a)-358(rank-one)-358(arr)1(a)27(y)-357(of)-358(the)-358(data)-358(t)28(yp)-27(e)-358(indicated)-358(in)]TJ 0 -11.955 Td [(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(2)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(info)]TJ + [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ + 141.968 -29.888 Td [(34)]TJ +0 g 0 G +ET + +endstream +endobj +1071 0 obj +<< +/Length 624 +>> +stream +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F27 9.9626 Tf 99.895 706.129 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - 141.968 -90.64 Td [(37)]TJ + 141.968 -567.87 Td [(35)]TJ 0 g 0 G ET endstream endobj -1059 0 obj +1078 0 obj << -/Length 7148 +/Length 6875 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.4)-1125(psb)]TJ ET q -1 0 0 1 171.761 706.328 cm +1 0 0 1 202.396 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 175.796 706.129 Td [(norm1)-375(|)-375(1-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-333(function)-334(computes)-333(the)-333(1-norm)-334(of)-333(a)-333(v)28(ec)-1(tor)]TJ/F11 9.9626 Tf 207.168 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -212.862 -11.956 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.014 0 Td [(is)-333(a)-334(real)-333(v)28(ector)-334(it)-333(computes)-333(1-norm)-334(as:)]TJ/F11 9.9626 Tf 123.45 -19.151 Td [(asum)]TJ/F14 9.9626 Tf 27.154 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(k)]TJ/F8 9.9626 Tf -196.303 -19.151 Td [(else)-333(if)]TJ/F11 9.9626 Tf 28.006 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(a)-334(complex)-333(v)28(ector)-334(then)-333(it)-333(computes)-334(1-norm)-333(as:)]TJ/F11 9.9626 Tf 70.135 -19.152 Td [(asum)]TJ/F14 9.9626 Tf 27.154 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(r)-28(e)]TJ/F8 9.9626 Tf 9.41 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(1)]TJ/F8 9.9626 Tf 6.683 1.494 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(im)]TJ/F8 9.9626 Tf 12.18 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(1)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(normi)-375(|)-375(In\014nit)31(y-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -55.726 -19.477 Td [(This)-333(function)-334(computes)-333(the)-333(in\014nit)28(y-norm)-334(of)-333(a)-333(v)28(e)-1(ctor)]TJ/F11 9.9626 Tf 233.181 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -238.875 -11.955 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.014 0 Td [(is)-333(a)-334(real)-333(v)28(ector)-334(it)-333(computes)-333(in\014nit)28(y)-334(norm)-333(as:)]TJ/F11 9.9626 Tf 115.269 -23.087 Td [(amax)]TJ/F14 9.9626 Tf 27.741 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.861 -6.275 Td [(i)]TJ/F14 9.9626 Tf 12.341 6.275 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(j)]TJ/F8 9.9626 Tf -206.697 -26.317 Td [(else)-333(if)]TJ/F11 9.9626 Tf 28.006 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(a)-334(complex)-333(v)28(ector)-334(then)-333(it)-333(computes)-334(the)-333(in\014nit)28(y-norm)-333(as:)]TJ/F11 9.9626 Tf 61.446 -23.087 Td [(amax)]TJ/F14 9.9626 Tf 27.741 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.861 -6.275 Td [(i)]TJ/F8 9.9626 Tf 12.341 6.275 Td [(\050)]TJ/F14 9.9626 Tf 3.874 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(r)-28(e)]TJ/F8 9.9626 Tf 9.41 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(j)]TJ/F8 9.9626 Tf 4.981 0 Td [(+)]TJ/F14 9.9626 Tf 9.962 0 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(im)]TJ/F8 9.9626 Tf 12.179 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F8 9.9626 Tf 3.317 1.494 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(j)]TJ/F8 9.9626 Tf 2.767 0 Td [(\051)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -232.086 -17.657 Td [(psb_geasum\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ 0 -11.955 Td [(psb_norm1\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ +/F30 9.9626 Tf -241.369 -26.901 Td [(psb_geamax\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ 0 -11.956 Td [(psb_normi\050x,)-525(desc_a,)-525(info)-525([,global]\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 180.28 566.766 cm -[]0 d 0 J 0.398 w 0 0 m 284.561 0 l S +1 0 0 1 179.892 536.097 cm +[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S Q BT -/F11 9.9626 Tf 186.257 558.198 Td [(asum)-7736(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(F)96(unction)]TJ +/F11 9.9626 Tf 185.87 527.529 Td [(amax)-7677(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(F)96(unction)]TJ ET q -1 0 0 1 180.28 554.412 cm -[]0 d 0 J 0.398 w 0 0 m 284.561 0 l S +1 0 0 1 179.892 523.743 cm +[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S Q BT -/F8 9.9626 Tf 186.257 545.845 Td [(Short)-333(Precision)-334(Real)-1200(Short)-333(Precision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 185.87 515.175 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Real)-3103(psb)]TJ ET q -1 0 0 1 423.717 546.044 cm +1 0 0 1 423.33 515.374 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 426.706 545.845 Td [(geasum)]TJ -240.449 -11.956 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ +/F8 9.9626 Tf 426.319 515.175 Td [(geamax)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ ET q -1 0 0 1 423.717 534.089 cm +1 0 0 1 423.33 503.419 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 426.706 533.889 Td [(geasum)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Short)-333(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 426.319 503.22 Td [(geamax)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Complex)-1200(psb)]TJ ET q -1 0 0 1 423.717 522.133 cm +1 0 0 1 423.33 491.464 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 426.706 521.934 Td [(geasum)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Com)-1(p)1(lex)-1412(psb)]TJ +/F8 9.9626 Tf 426.319 491.265 Td [(geamax)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(psb)]TJ ET q -1 0 0 1 423.717 510.178 cm +1 0 0 1 423.33 479.509 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 426.706 509.979 Td [(geasum)]TJ +/F8 9.9626 Tf 426.319 479.31 Td [(geamax)]TJ ET q -1 0 0 1 180.28 506.193 cm -[]0 d 0 J 0.398 w 0 0 m 284.561 0 l S +1 0 0 1 179.892 475.524 cm +[]0 d 0 J 0.398 w 0 0 m 285.336 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 278.877 478.154 Td [(T)83(able)-333(6:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 278.877 447.485 Td [(T)83(able)-333(4:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -128.172 -29.723 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -128.172 -36.518 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -18.819 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -22.263 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -18.819 Td [(x)]TJ + 0 -22.263 Td [(x)]TJ 0 g 0 G /F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 363.172 cm +1 0 0 1 436.673 318.82 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 362.973 Td [(T)]TJ +/F30 9.9626 Tf 439.811 318.621 Td [(T)]TJ ET q -1 0 0 1 445.669 363.172 cm +1 0 0 1 445.669 318.82 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 362.973 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 318.621 Td [(vect)]TJ ET q -1 0 0 1 470.356 363.172 cm +1 0 0 1 470.356 318.82 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 362.973 Td [(type)]TJ +/F30 9.9626 Tf 473.495 318.621 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.884 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(6)]TJ + [-333(4)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -18.819 Td [(desc)]TJ +/F27 9.9626 Tf -24.906 -22.262 Td [(desc)]TJ ET q -1 0 0 1 172.619 332.398 cm +1 0 0 1 172.619 284.602 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 332.199 Td [(a)]TJ +/F27 9.9626 Tf 176.057 284.403 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 135.659 0 Td [(psb)]TJ ET q -1 0 0 1 327.588 284.577 cm +1 0 0 1 327.588 236.781 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 284.378 Td [(desc)]TJ +/F30 9.9626 Tf 330.727 236.582 Td [(desc)]TJ ET q -1 0 0 1 352.275 284.577 cm +1 0 0 1 352.275 236.781 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 355.414 284.378 Td [(type)]TJ +/F30 9.9626 Tf 355.414 236.582 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -225.63 -18.818 Td [(global)]TJ -0 g 0 G -/F8 9.9626 Tf 34.737 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(co)-1(mpu)1(tation)-358(should)-357(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.956 Td [(across)-333(all)-334(pro)-27(c)-1(esses.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ -0 g 0 G -/F27 9.9626 Tf -193.718 -30.774 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -225.63 -22.263 Td [(global)]TJ 0 g 0 G +/F8 9.9626 Tf 34.737 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(co)-1(mpu)1(tation)-358(should)-357(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.955 Td [(across)-333(all)-334(pro)-27(c)-1(esses.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ 0 g 0 G - 0 -18.819 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -193.718 -34.217 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(is)-333(the)-334(1-norm)-333(of)-333(v)27(ector)]TJ/F11 9.9626 Tf 102.781 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -161.955 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.841 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ariable)]TJ/F30 9.9626 Tf 118.434 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.471 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec-)]TJ -257.748 -11.955 Td [(i\014ed)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-334(r)1(e)-1(al)-333(n)28(um)28(b)-28(er.)]TJ 0 g 0 G - 141.968 -29.888 Td [(38)]TJ +/F8 9.9626 Tf 166.874 -29.888 Td [(36)]TJ 0 g 0 G ET endstream endobj -1064 0 obj +1083 0 obj << -/Length 3878 +/Length 4549 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F27 9.9626 Tf 99.895 706.129 Td [(info)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +/F8 9.9626 Tf 78.387 0 Td [(is)-333(the)-334(in\014ni)1(t)27(y)-333(norm)-333(of)-334(v)28(ector)]TJ/F11 9.9626 Tf 128.795 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -187.969 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.841 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ariabl)1(e)]TJ/F30 9.9626 Tf 118.434 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.47 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec)-1(-)]TJ -257.747 -11.955 Td [(i\014ed)]TJ 0 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-333(real)-334(n)28(um)28(b)-28(er.)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.917 Td [(Notes)]TJ +0 g 0 G +/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ 0 g 0 G - [-500(The)-241(computation)-240(of)-241(a)-240(global)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(signi\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.189 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(1)-130(\051)-642(=)-593(p)-83(s)-82(b)]TJ + [-500(The)-241(computation)-240(of)-241(a)-240(global)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(signi\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.189 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(1)-130(\051)-642(=)-586(p)-76(s)-75(b)]TJ ET q -1 0 0 1 227.371 562.866 cm +1 0 0 1 227.089 507.075 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.181 562.667 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(1)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ +/F8 9.9626 Tf 230.829 506.876 Td [(g)-75(e)-76(a)-75(m)-75(a)-76(x)-181(\050)-148(x)-43(1)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 316.705 562.866 cm +1 0 0 1 316.705 507.075 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 562.667 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(2)-130(\051)-642(=)-593(p)-83(s)-82(b)]TJ +/F8 9.9626 Tf 320.816 506.876 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(2)-130(\051)-642(=)-586(p)-76(s)-75(b)]TJ ET q -1 0 0 1 227.371 550.911 cm +1 0 0 1 227.089 495.12 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.181 550.712 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(2)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ +/F8 9.9626 Tf 230.829 494.921 Td [(g)-75(e)-76(a)-75(m)-75(a)-76(x)-181(\050)-148(x)-43(2)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 316.705 550.911 cm +1 0 0 1 316.705 495.12 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 550.712 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(3)-130(\051)-642(=)-593(p)-83(s)-82(b)]TJ +/F8 9.9626 Tf 320.816 494.921 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(3)-130(\051)-642(=)-586(p)-76(s)-75(b)]TJ ET q -1 0 0 1 227.371 538.956 cm +1 0 0 1 227.089 483.165 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.181 538.757 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(3)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ +/F8 9.9626 Tf 230.829 482.966 Td [(g)-75(e)-76(a)-75(m)-75(a)-76(x)-181(\050)-148(x)-43(3)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 316.705 538.956 cm +1 0 0 1 316.705 483.165 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 538.757 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.956 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.198 0 Td [(p)-69(s)-69(b)]TJ +/F8 9.9626 Tf 320.816 482.966 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.955 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.101 0 Td [(p)-59(s)-59(b)]TJ ET q -1 0 0 1 196.943 527.001 cm +1 0 0 1 196.556 471.21 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q 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[(is)-333(a)-334(complex)-333(v)28(ector)-334(then)-333(it)-333(computes)-334(1-norm)-333(as:)]TJ/F11 9.9626 Tf 69.697 -22.81 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.081 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.642 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(r)-28(e)]TJ/F8 9.9626 Tf 9.411 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F7 6.9738 Tf 4.982 -1.494 Td [(1)]TJ/F8 9.9626 Tf 6.683 1.494 Td [(+)]TJ/F14 9.9626 Tf 9.962 0 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(im)]TJ/F8 9.9626 Tf 12.179 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(1)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(geamaxs)-375(|)-375(Generalized)-375(In\014nit)31(y)-375(Norm)]TJ/F8 9.9626 Tf -55.726 -18.389 Td [(This)-359(subroutine)-359(computes)-360(a)-359(series)-359(of)-359(in\014nit)28(y)-359(norms)-360(on)-359(the)-359(columns)-359(of)-359(a)-359(dense)]TJ 0 -11.956 Td [(matrix)]TJ/F11 9.9626 Tf 32.406 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(:)]TJ/F11 9.9626 Tf 87.106 -11.955 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.642 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.069 -6.503 Td [(k)]TJ/F14 9.9626 Tf 13.133 6.503 Td [(j)]TJ/F11 9.9626 Tf 2.767 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(k)-31(;)-167(i)]TJ/F8 9.9626 Tf 13.36 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(j)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -232.523 -21.762 Td [(call)-525(psb_geasums\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf -215.737 -25.377 Td [(call)-525(psb_geamaxs\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 178.071 508.729 cm -[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S +1 0 0 1 177.927 614.121 cm +[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S Q BT -/F11 9.9626 Tf 184.049 500.161 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.862 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 183.905 605.553 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(Subroutine)]TJ ET q -1 0 0 1 178.071 496.375 cm -[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S +1 0 0 1 177.927 601.768 cm +[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S Q BT -/F8 9.9626 Tf 184.049 487.807 Td [(Short)-333(Precision)-333(R)-1(eal)-1200(S)1(hort)-334(Precision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 183.905 593.2 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Real)-3103(psb)]TJ ET q -1 0 0 1 421.508 488.007 cm +1 0 0 1 421.365 593.399 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 487.807 Td [(geasums)]TJ -240.448 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ +/F8 9.9626 Tf 424.354 593.2 Td [(geamaxs)]TJ -240.449 -11.956 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ ET q -1 0 0 1 421.508 476.051 cm +1 0 0 1 421.365 581.444 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 475.852 Td [(geasums)]TJ -240.448 -11.955 Td [(Short)-333(Precision)-333(R)-1(eal)-1200(S)1(hort)-334(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 424.354 581.244 Td [(geamaxs)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Complex)-1200(psb)]TJ ET q -1 0 0 1 421.508 464.096 cm +1 0 0 1 421.365 569.489 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 463.897 Td [(geasums)]TJ -240.448 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 424.354 569.289 Td [(geamaxs)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(psb)]TJ ET q -1 0 0 1 421.508 452.141 cm +1 0 0 1 421.365 557.533 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 451.942 Td [(geasums)]TJ +/F8 9.9626 Tf 424.354 557.334 Td [(geamaxs)]TJ ET q -1 0 0 1 178.071 448.156 cm -[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S +1 0 0 1 177.927 553.548 cm +[]0 d 0 J 0.398 w 0 0 m 289.266 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 278.877 420.117 Td [(T)83(able)-333(7:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 278.877 525.509 Td [(T)83(able)-333(5:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -128.172 -35.827 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -128.172 -33.596 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -21.709 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -21.71 Td [(x)]TJ + 0 -19.926 Td [(x)]TJ 0 g 0 G /F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 293.25 cm +1 0 0 1 436.673 404.441 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 293.051 Td [(T)]TJ +/F30 9.9626 Tf 439.811 404.242 Td [(T)]TJ ET q -1 0 0 1 445.669 293.25 cm +1 0 0 1 445.669 404.441 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 293.051 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 404.242 Td [(vect)]TJ ET q -1 0 0 1 470.356 293.25 cm +1 0 0 1 470.356 404.441 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 293.051 Td [(type)]TJ +/F30 9.9626 Tf 473.495 404.242 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf -297.884 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(7)]TJ + [-333(5)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -21.709 Td [(desc)]TJ +/F27 9.9626 Tf -24.906 -19.925 Td [(desc)]TJ ET q -1 0 0 1 172.619 259.585 cm +1 0 0 1 172.619 372.56 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 259.386 Td [(a)]TJ +/F27 9.9626 Tf 176.057 372.361 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 135.659 0 Td [(psb)]TJ ET q -1 0 0 1 327.588 211.765 cm +1 0 0 1 327.588 324.74 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 211.565 Td [(desc)]TJ +/F30 9.9626 Tf 330.727 324.54 Td [(desc)]TJ ET q -1 0 0 1 352.275 211.765 cm +1 0 0 1 352.275 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[(On)-383(Return)]TJ 0 g 0 G -ET - -endstream -endobj -1082 0 obj -<< -/Length 624 ->> -stream 0 g 0 G + 0 -19.925 Td [(res)]TJ 0 g 0 G +/F8 9.9626 Tf 19.47 0 Td [(is)-333(the)-334(in\014nit)28(y)-333(norm)-333(of)-334(the)-333(columns)-333(of)]TJ/F11 9.9626 Tf 166.183 0 Td [(x)]TJ/F8 9.9626 Tf 5.693 0 Td [(.)]TJ -166.44 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(Sp)-28(eci\014ed)-289(as:)-422(a)-289(n)28(um)28(b)-28(er)-289(or)-289(a)-289(rank)1(-)-1(on)1(e)-289(arra)27(y)-288(of)-289(long)-289(precision)-289(real)-289(n)28(um)28(b)-28(ers.)]TJ 0 g 0 G -BT -/F27 9.9626 Tf 99.895 706.129 Td [(info)]TJ +/F27 9.9626 Tf -24.906 -19.925 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td 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[(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 320.063 cm +1 0 0 1 385.864 363.172 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 319.864 Td [(T)]TJ +/F30 9.9626 Tf 389.002 362.973 Td [(T)]TJ ET q -1 0 0 1 445.669 320.063 cm +1 0 0 1 394.86 363.172 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 319.864 Td [(vect)]TJ +/F30 9.9626 Tf 397.998 362.973 Td [(vect)]TJ ET q -1 0 0 1 470.356 320.063 cm +1 0 0 1 419.547 363.172 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 319.864 Td [(type)]TJ +/F30 9.9626 Tf 422.685 362.973 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(8)]TJ + [-333(6)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -22.677 Td [(desc)]TJ +/F27 9.9626 Tf -24.907 -18.819 Td [(desc)]TJ ET q -1 0 0 1 172.619 285.431 cm +1 0 0 1 121.81 332.398 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 285.231 Td [(a)]TJ +/F27 9.9626 Tf 125.247 332.199 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 327.588 237.61 cm +1 0 0 1 276.779 284.577 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 237.411 Td [(desc)]TJ +/F30 9.9626 Tf 279.917 284.378 Td [(desc)]TJ ET q -1 0 0 1 352.275 237.61 cm +1 0 0 1 301.466 284.577 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 355.414 237.411 Td [(type)]TJ +/F30 9.9626 Tf 304.604 284.378 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -225.63 -22.677 Td [(global)]TJ +/F27 9.9626 Tf -225.631 -18.818 Td [(global)]TJ 0 g 0 G -/F8 9.9626 Tf 34.737 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(co)-1(mpu)1(tation)-358(should)-357(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.955 Td [(across)-333(all)-334(pro)-27(c)-1(esses.)]TJ 0 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ +/F8 9.9626 Tf 34.738 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(computation)-358(shoul)1(d)-358(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.956 Td [(across)-333(all)-334(pro)-27(ce)-1(sses.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ 0 g 0 G -/F27 9.9626 Tf -193.718 -34.632 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -193.719 -30.774 Td [(On)-383(Return)]TJ 0 g 0 G 0 g 0 G -/F8 9.9626 Tf 166.874 -29.888 Td [(42)]TJ + 0 -18.819 Td [(F)96(unction)-384(v)64(alue)]TJ +0 g 0 G +/F8 9.9626 Tf 78.387 0 Td [(is)-333(the)-334(1-norm)-333(of)-333(v)28(e)-1(ctor)]TJ/F11 9.9626 Tf 102.781 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -161.955 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.841 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ariabl)1(e)]TJ/F30 9.9626 Tf 118.434 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.47 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec)-1(-)]TJ -257.747 -11.955 Td [(i\014ed)]TJ 0 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-333(real)-334(n)28(um)28(b)-28(er.)]TJ +0 g 0 G + 141.968 -29.888 Td [(39)]TJ 0 g 0 G ET endstream endobj -1094 0 obj +1110 0 obj << -/Length 4633 +/Length 3885 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F27 9.9626 Tf 99.895 706.129 Td [(F)96(unction)-384(V)96(alue)]TJ -0 g 0 G -/F8 9.9626 Tf 80.684 0 Td [(is)-333(the)-334(2-norm)-333(of)-333(v)28(e)-1(ctor)]TJ/F11 9.9626 Tf 102.781 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -164.252 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.841 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ariabl)1(e)]TJ/F30 9.9626 Tf 118.434 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.47 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec)-1(-)]TJ -257.747 -11.955 Td [(i\014ed)]TJ 0 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-333(real)-334(n)28(um)28(b)-28(er.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(info)]TJ +/F27 9.9626 Tf 150.705 706.129 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 11.9552 Tf -24.906 -21.918 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +/F8 9.9626 Tf 12.176 -19.925 Td [(1.)]TJ 0 g 0 G - [-500(The)-241(computation)-240(of)-241(a)-240(global)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(signi\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.189 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(1)-130(\051)-642(=)-594(p)-82(s)-83(b)]TJ + [-500(The)-241(computation)-240(of)-241(a)-241(gl)1(obal)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(s)-1(i)1(gni\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.19 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(1)-131(\051)-642(=)-593(p)-83(s)-82(b)]TJ ET q -1 0 0 1 227.381 495.12 cm +1 0 0 1 278.18 562.866 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.194 494.921 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(1)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 281.99 562.667 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(1)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ ET q -1 0 0 1 316.705 495.12 cm +1 0 0 1 367.515 562.866 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 494.921 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(2)-130(\051)-642(=)-594(p)-82(s)-83(b)]TJ +/F8 9.9626 Tf 371.626 562.667 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(2)-131(\051)-642(=)-593(p)-83(s)-82(b)]TJ ET q -1 0 0 1 227.381 483.165 cm +1 0 0 1 278.18 550.911 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.194 482.966 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(2)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 281.99 550.712 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(2)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ ET q -1 0 0 1 316.705 483.165 cm +1 0 0 1 367.515 550.911 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 482.966 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-131(3)-130(\051)-642(=)-594(p)-82(s)-83(b)]TJ +/F8 9.9626 Tf 371.626 550.712 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(3)-131(\051)-642(=)-593(p)-83(s)-82(b)]TJ ET q -1 0 0 1 227.381 471.21 cm +1 0 0 1 278.18 538.956 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 231.194 471.011 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(3)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ +/F8 9.9626 Tf 281.99 538.757 Td [(g)-82(e)-83(a)-82(s)-83(u)-82(m)-188(\050)-149(x)-43(3)-247(,)-274(d)-112(e)-113(s)-113(c)]TJ ET q -1 0 0 1 316.705 471.21 cm +1 0 0 1 367.515 538.956 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 320.816 471.011 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.224 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.348 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.956 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.236 0 Td [(p)-73(s)-72(b)]TJ +/F8 9.9626 Tf 371.626 538.757 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.956 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.198 0 Td [(p)-69(s)-69(b)]TJ ET q -1 0 0 1 197.093 459.255 cm +1 0 0 1 247.753 527.001 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 200.806 459.055 Td [(n)-73(r)-72(m)-73(2)-178(\050)-245(i)-138(c)-139(t)-139(x)-139(t)-439(,)-290(v)-128(r)-128(e)-129(s)-293(\050)-165(1)-165(:)-165(3)-165(\051)-165(\051)]TJ +/F8 9.9626 Tf 251.428 526.801 Td [(s)-69(u)-69(m)-174(\050)-245(i)-139(c)-139(t)-138(x)-139(t)-439(,)-290(v)-128(r)-128(e)-129(s)-293(\050)-165(1)-165(:)-165(3)-165(\051)-165(\051)]TJ 0 g 0 G 0 g 0 G - -76.004 -21.917 Td [(In)-353(this)-354(w)28(a)28(y)-354(the)-353(global)-354(comm)28(unication,)-359(whic)28(h)-353(for)-354(small)-353(sizes)-354(is)-354(a)-353(latency-)]TJ 0 -11.956 Td [(b)-28(ound)-333(op)-28(eration,)-333(is)-333(in)28(v)27(ok)28(ed)-333(only)-333(onc)-1(e.)]TJ + -75.817 -21.917 Td [(In)-354(th)1(is)-354(w)28(a)28(y)-354(the)-353(global)-354(comm)28(unication,)-359(whic)28(h)-353(for)-354(small)-353(size)-1(s)-353(is)-354(a)-353(latency-)]TJ 0 -11.956 Td [(b)-28(ound)-333(op)-28(eration,)-333(is)-333(in)27(v)28(ok)28(ed)-333(only)-334(once.)]TJ 0 g 0 G - 141.968 -334.744 Td [(43)]TJ + 141.968 -402.49 Td [(40)]TJ 0 g 0 G ET endstream endobj -1108 0 obj +1123 0 obj << -/Length 6162 +/Length 7328 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(4.7)-1125(psb)]TJ ET q -1 0 0 1 171.761 706.328 cm +1 0 0 1 151.587 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 175.796 706.129 Td [(genrm2s)-375(|)-375(Generalized)-375(2-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-310(subroutine)-310(computes)-309(a)-310(series)-310(of)-310(2-norms)-310(on)-310(the)-309(c)-1(olu)1(m)-1(n)1(s)-310(of)-310(a)-310(dense)-310(matrix)]TJ/F11 9.9626 Tf 0 -11.956 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(:)]TJ/F11 9.9626 Tf 126.531 -11.955 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.642 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050:)]TJ/F11 9.9626 Tf 6.642 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 7.86 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ +/F16 11.9552 Tf 155.621 706.129 Td [(geasums)-375(|)-375(Generalized)-375(1-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -55.726 -19.22 Td [(This)-310(subroutine)-310(computes)-309(a)-310(series)-310(of)-310(1-norms)-310(on)-310(the)-310(columns)-309(of)-310(a)-310(dense)-310(matrix)]TJ/F11 9.9626 Tf 0 -11.955 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(:)]TJ/F11 9.9626 Tf 119.513 -13.293 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)]TJ/F14 9.9626 Tf 6.641 0 Td [(\040)]TJ/F8 9.9626 Tf 12.73 0 Td [(max)]TJ/F10 6.9738 Tf 7.069 -6.503 Td [(k)]TJ/F14 9.9626 Tf 13.133 6.503 Td [(j)]TJ/F11 9.9626 Tf 2.768 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(k)-31(;)-167(i)]TJ/F8 9.9626 Tf 13.36 0 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(j)]TJ/F8 9.9626 Tf -215.738 -22.73 Td [(This)-333(function)-334(computes)-333(the)-333(1-norm)-334(of)-333(a)-333(v)28(e)-1(ctor)]TJ/F11 9.9626 Tf 207.168 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -212.862 -11.955 Td [(If)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(a)-334(real)-333(v)28(ector)-334(it)-333(computes)-333(1-norm)-334(as:)]TJ/F11 9.9626 Tf 123.012 -22.81 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.641 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.712 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ/F8 9.9626 Tf -196.741 -22.81 Td [(else)-333(if)]TJ/F11 9.9626 Tf 28.006 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(a)-334(complex)-333(v)28(ector)-334(then)-333(it)-333(computes)-334(1-norm)-333(as:)]TJ/F11 9.9626 Tf 69.698 -22.81 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.08 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)]TJ/F14 9.9626 Tf 6.641 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.712 0 Td [(r)-28(e)]TJ/F8 9.9626 Tf 9.41 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(1)]TJ/F8 9.9626 Tf 6.683 1.494 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(im)]TJ/F8 9.9626 Tf 12.18 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\051)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F7 6.9738 Tf 4.982 -1.494 Td [(1)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -207.016 -20.424 Td [(call)-525(psb_genrm2s\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf -232.524 -21.762 Td [(call)-525(psb_geasums\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 178.071 617.58 cm +1 0 0 1 127.261 508.729 cm []0 d 0 J 0.398 w 0 0 m 288.979 0 l S Q BT -/F11 9.9626 Tf 184.049 609.013 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.862 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 133.239 500.161 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(Subroutine)]TJ ET q -1 0 0 1 178.071 605.227 cm +1 0 0 1 127.261 496.375 cm []0 d 0 J 0.398 w 0 0 m 288.979 0 l S Q BT -/F8 9.9626 Tf 184.049 596.659 Td [(Short)-333(Precision)-333(R)-1(eal)-1200(S)1(hort)-334(Precision)-333(Real)-3103(psb)]TJ +/F8 9.9626 Tf 133.239 487.807 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Real)-3103(psb)]TJ ET q -1 0 0 1 421.508 596.858 cm +1 0 0 1 370.699 488.007 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 596.659 Td [(genrm2s)]TJ -240.448 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ +/F8 9.9626 Tf 373.688 487.807 Td [(geasums)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ ET q -1 0 0 1 421.508 584.903 cm +1 0 0 1 370.699 476.051 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 584.704 Td [(genrm2s)]TJ -240.448 -11.955 Td [(Short)-333(Precision)-333(R)-1(eal)-1200(S)1(hort)-334(Precision)-333(Complex)-1200(psb)]TJ +/F8 9.9626 Tf 373.688 475.852 Td [(geasums)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Complex)-1200(psb)]TJ ET q -1 0 0 1 421.508 572.948 cm +1 0 0 1 370.699 464.096 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 572.749 Td [(genrm2s)]TJ -240.448 -11.956 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 373.688 463.897 Td [(geasums)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(psb)]TJ ET q -1 0 0 1 421.508 560.993 cm +1 0 0 1 370.699 452.141 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 424.497 560.793 Td [(genrm2s)]TJ +/F8 9.9626 Tf 373.688 451.942 Td [(geasums)]TJ ET q -1 0 0 1 178.071 557.008 cm +1 0 0 1 127.261 448.156 cm []0 d 0 J 0.398 w 0 0 m 288.979 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 278.877 528.968 Td [(T)83(able)-333(9:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 228.067 420.117 Td [(T)83(able)-333(7:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -128.172 -33.596 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -128.172 -35.827 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -21.709 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.926 Td [(x)]TJ + 0 -21.71 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 407.9 cm +1 0 0 1 385.864 293.25 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 407.701 Td [(T)]TJ +/F30 9.9626 Tf 389.002 293.051 Td [(T)]TJ ET q -1 0 0 1 445.669 407.9 cm +1 0 0 1 394.86 293.25 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 407.701 Td [(vect)]TJ +/F30 9.9626 Tf 397.998 293.051 Td [(vect)]TJ ET q -1 0 0 1 470.356 407.9 cm +1 0 0 1 419.547 293.25 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 407.701 Td [(type)]TJ +/F30 9.9626 Tf 422.685 293.051 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.883 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(9)]TJ + [-333(7)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.926 Td [(desc)]TJ -ET -q -1 0 0 1 172.619 376.02 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 176.057 375.82 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ -ET -q -1 0 0 1 327.588 328.199 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 330.727 328 Td [(desc)]TJ -ET -q -1 0 0 1 352.275 328.199 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 355.414 328 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -225.63 -19.926 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -19.925 Td [(res)]TJ -0 g 0 G -/F8 9.9626 Tf 19.47 0 Td [(con)28(tains)-334(th)1(e)-334(1-norm)-333(of)-333(\050the)-334(columns)-333(of)-78(\051)]TJ/F11 9.9626 Tf 177.75 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -178.008 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-334(r)1(e)-1(al)-333(n)28(um)28(b)-28(er.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -19.926 Td [(info)]TJ -0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(te)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ -0 g 0 G - 141.968 -94.1 Td [(44)]TJ -0 g 0 G -ET - -endstream -endobj -1115 0 obj -<< -/Length 5516 ->> -stream -0 g 0 G -0 g 0 G -BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(norm1)-375(|)-375(1-Norm)-375(of)-375(Sparse)-375(Matrix)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-333(function)-334(computes)-333(the)-333(1-norm)-334(of)-333(a)-333(matrix)]TJ/F11 9.9626 Tf 209.659 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(:)]TJ/F11 9.9626 Tf -76.216 -33.873 Td [(nr)-28(m)]TJ/F8 9.9626 Tf 19.499 0 Td [(1)]TJ/F14 9.9626 Tf 7.749 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(A)]TJ/F14 9.9626 Tf 7.472 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.495 Td [(1)]TJ/F8 9.9626 Tf -198.327 -20.423 Td [(where:)]TJ -0 g 0 G -/F11 9.9626 Tf 0 -19.926 Td [(A)]TJ -0 g 0 G -/F8 9.9626 Tf 12.454 0 Td [(represen)28(ts)-334(the)-333(global)-333(matrix)]TJ/F11 9.9626 Tf 125.834 0 Td [(A)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -ET -q -1 0 0 1 180.183 589.962 cm -[]0 d 0 J 0.398 w 0 0 m 183.136 0 l S -Q -BT -/F11 9.9626 Tf 186.161 581.394 Td [(A)]TJ/F27 9.9626 Tf 120.409 0 Td [(F)96(unction)]TJ -ET -q -1 0 0 1 180.183 577.608 cm -[]0 d 0 J 0.398 w 0 0 m 183.136 0 l S -Q -BT -/F8 9.9626 Tf 186.161 569.04 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ -ET -q -1 0 0 1 322.167 569.24 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 325.156 569.04 Td [(spnrm1)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ -ET -q -1 0 0 1 322.167 557.284 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 325.156 557.085 Td [(spnrm1)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ -ET -q -1 0 0 1 322.167 545.329 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 325.156 545.13 Td [(spnrm1)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ -ET -q -1 0 0 1 322.167 533.374 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 325.156 533.175 Td [(spnrm1)]TJ -ET -q -1 0 0 1 180.183 529.389 cm -[]0 d 0 J 0.398 w 0 0 m 183.136 0 l S -Q -0 g 0 G -BT -/F8 9.9626 Tf 225.577 501.35 Td [(T)83(able)-333(10:)-444(Data)-334(t)28(yp)-28(es)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -125.682 -33.873 Td [(psb_spnrm1\050A,)-525(desc_a,)-525(info\051)]TJ 0 -11.956 Td [(psb_norm1\050A,)-525(desc_a,)-525(info\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -21.917 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -19.925 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(the)-333(global)-333(sparse)-334(matrix)]TJ/F11 9.9626 Tf 196.126 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -189.242 -11.955 Td 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Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -22.677 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(a)]TJ + 0 -22.677 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(the)-333(global)-333(sparse)-334(matrix)]TJ/F11 9.9626 Tf 196.126 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -189.242 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 327.588 346.132 cm +1 0 0 1 385.864 320.063 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 345.932 Td [(Tspmat)]TJ +/F30 9.9626 Tf 389.002 319.864 Td [(T)]TJ ET q -1 0 0 1 362.736 346.132 cm +1 0 0 1 394.86 320.063 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.874 345.932 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -236.091 -19.925 Td [(desc)]TJ +/F30 9.9626 Tf 397.998 319.864 Td [(vect)]TJ ET q -1 0 0 1 172.619 326.206 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 419.547 320.063 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 176.057 326.007 Td [(a)]TJ +/F30 9.9626 Tf 422.685 319.864 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf -297.883 -11.956 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ + [-333(8)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -22.677 Td [(desc)]TJ ET q -1 0 0 1 327.588 278.386 cm +1 0 0 1 121.81 285.431 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 125.247 285.231 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +ET +q +1 0 0 1 276.779 237.61 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 278.186 Td [(desc)]TJ +/F30 9.9626 Tf 279.917 237.411 Td [(desc)]TJ ET q -1 0 0 1 352.275 278.386 cm +1 0 0 1 301.466 237.61 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 355.414 278.186 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -225.63 -19.925 Td [(On)-383(Return)]TJ +/F30 9.9626 Tf 304.604 237.411 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G - 0 -19.925 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -225.631 -22.677 Td [(global)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(is)-333(the)-334(in\014nit)28(y-norm)-333(of)-333(sparse)-334(submatrix)]TJ/F11 9.9626 Tf 176.311 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -237.263 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-334(r)1(e)-1(al)-333(n)28(um)28(b)-28(er.)]TJ +/F8 9.9626 Tf 34.738 0 Td [(Sp)-28(eci\014es)-357(whether)-357(the)-357(computation)-358(shoul)1(d)-358(include)-357(the)-357(global)-357(reduction)]TJ -9.831 -11.955 Td [(across)-333(all)-334(pro)-27(ce)-1(sses.)]TJ 0 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(scalar.)-445(Default:)]TJ/F30 9.9626 Tf 168.812 0 Td [(global=.true.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.926 Td [(info)]TJ +/F27 9.9626 Tf -193.719 -34.632 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(te)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ 0 g 0 G - 141.968 -56.242 Td [(46)]TJ +/F8 9.9626 Tf 166.875 -29.888 Td [(43)]TJ 0 g 0 G ET endstream endobj -1134 0 obj +1142 0 obj << -/Length 7328 +/Length 4643 >> stream 0 g 0 G 0 g 0 G -BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(spmm)-375(|)-375(Sparse)-375(Matrix)-375(b)31(y)-375(Dense)-375(Matrix)-375(Pro)-31(duct)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-333(subroutine)-334(computes)-333(the)-333(Sparse)-334(Matrix)-333(b)28(y)-333(Dense)-334(Matrix)-333(Pro)-28(duct:)]TJ/F11 9.9626 Tf 139.909 -23.911 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(Ax)]TJ/F8 9.9626 Tf 21.79 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -0 g 0 G -/F8 9.9626 Tf 138.581 0 Td [(\0501\051)]TJ -0 g 0 G -/F11 9.9626 Tf -194.21 -17.408 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(A)]TJ/F10 6.9738 Tf 13.882 4.113 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -0 g 0 G -/F8 9.9626 Tf 135.443 0 Td [(\0502\051)]TJ -0 g 0 G -/F11 9.9626 Tf -194.851 -17.408 Td [(y)]TJ/F14 9.9626 Tf 8.01 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(A)]TJ/F10 6.9738 Tf 13.882 4.113 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -0 g 0 G -/F8 9.9626 Tf 134.802 0 Td [(\0503\051)]TJ -0 g 0 G - -316.037 -17.408 Td [(where:)]TJ -0 g 0 G -/F11 9.9626 Tf -14.944 -19.226 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 10.676 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.092 0 Td [(x)]TJ/F7 6.9738 Tf 5.694 -1.495 Td [(:)]TJ/F10 6.9738 Tf 2.256 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ 0 g 0 G -/F11 9.9626 Tf -137.084 -18.081 Td [(y)]TJ -0 g 0 G -/F8 9.9626 Tf 10.224 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.092 0 Td [(y)]TJ/F7 6.9738 Tf 4.885 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ +BT +/F27 9.9626 Tf 150.705 706.129 Td [(F)96(unction)-384(V)96(alue)]TJ 0 g 0 G -/F11 9.9626 Tf -135.822 -18.081 Td [(A)]TJ +/F8 9.9626 Tf 80.683 0 Td [(is)-333(the)-334(2-norm)-333(of)-333(v)27(ector)]TJ/F11 9.9626 Tf 102.781 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -164.252 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 31.842 0 Td [(global)]TJ/F8 9.9626 Tf 32.002 0 Td [(unless)-225(the)-226(optional)-225(v)55(ari)1(able)]TJ/F30 9.9626 Tf 118.433 0 Td [(global=.false.)]TJ/F8 9.9626 Tf 75.471 0 Td [(has)-225(b)-28(een)-226(sp)-27(ec-)]TJ -257.748 -11.955 Td [(i\014ed)]TJ 0 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-334(r)1(e)-1(al)-333(n)28(um)28(b)-28(er.)]TJ 0 g 0 G -/F8 9.9626 Tf 12.454 0 Td [(is)-333(the)-334(global)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 118.943 0 Td [(A)]TJ +/F27 9.9626 Tf -24.906 -19.925 Td [(info)]TJ 0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 11.9552 Tf -24.906 -21.918 Td [(Notes)]TJ 0 g 0 G +/F8 9.9626 Tf 12.176 -19.925 Td [(1.)]TJ 0 g 0 G + [-500(The)-241(computation)-240(of)-241(a)-241(gl)1(obal)-241(result)-241(requires)-240(a)-241(global)-241(comm)28(unication,)-259(whic)28(h)]TJ 12.73 -11.955 Td [(en)28(tails)-421(a)-420(s)-1(i)1(gni\014can)27(t)-420(o)28(v)27(erhead.)-706(It)-420(ma)27(y)-420(b)-28(e)-421(necessary)-420(and/or)-421(advisable)-420(to)]TJ 0 -11.955 Td [(compute)-395(m)28(ultiple)-395(norms)-395(at)-395(the)-395(same)-395(time;)-426(in)-395(this)-395(case,)-410(it)-395(is)-395(p)-28(ossible)-395(to)]TJ 0 -11.955 Td [(impro)28(v)28(e)-334(the)-333(run)28(time)-334(e\016ciency)-333(b)28(y)-334(using)-333(the)-333(follo)28(wing)-334(sc)28(heme:)]TJ 25.19 -17.933 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(1)-131(\051)-642(=)-593(p)-83(s)-83(b)]TJ ET q -1 0 0 1 177.988 532.215 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 278.19 495.12 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F11 9.9626 Tf 183.966 523.647 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(\014)]TJ/F27 9.9626 Tf 71.238 0 Td [(Subroutine)]TJ +/F8 9.9626 Tf 282.003 494.921 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(1)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 177.988 519.862 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 367.515 495.12 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 183.966 511.294 Td [(Short)-333(Precision)-333(R)-1(eal)-3102(psb)]TJ +/F8 9.9626 Tf 371.626 494.921 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(2)-131(\051)-642(=)-593(p)-83(s)-83(b)]TJ ET q -1 0 0 1 319.972 511.493 cm +1 0 0 1 278.19 483.165 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 511.294 Td [(spmm)]TJ -138.995 -11.956 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 282.003 482.966 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(2)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 319.972 499.538 cm +1 0 0 1 367.515 483.165 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 499.338 Td [(spmm)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-333(C)-1(omplex)-1200(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 371.626 482.966 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ -293.397 -11.955 Td [(v)-128(r)-129(e)-128(s)-259(\050)-130(3)-131(\051)-642(=)-593(p)-83(s)-83(b)]TJ ET q -1 0 0 1 319.972 487.583 cm +1 0 0 1 278.19 471.21 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 487.383 Td [(spmm)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ +/F8 9.9626 Tf 282.003 471.011 Td [(g)-83(e)-82(n)-83(r)-83(m)-82(2)-189(\050)-148(x)-43(3)-248(,)-273(d)-113(e)-113(s)-112(c)]TJ ET q -1 0 0 1 319.972 475.627 cm +1 0 0 1 367.515 471.21 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 475.428 Td [(spmm)]TJ +/F8 9.9626 Tf 371.626 471.011 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-415(,)-302(g)-141(l)-142(o)-141(b)-141(a)-141(l)-190(=)-48(.)]TJ/F27 9.9626 Tf 92.223 0 Td [(f)-132(a)-131(l)-132(s)-131(e)]TJ/F8 9.9626 Tf 30.349 0 Td [(.)-178(\051)]TJ/F27 9.9626 Tf -293.299 -11.956 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.235 0 Td [(p)-73(s)-72(b)]TJ ET q -1 0 0 1 177.988 471.642 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 247.903 459.255 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 225.577 443.603 Td [(T)83(able)-333(12:)-444(Data)-334(t)28(yp)-28(es)]TJ -0 g 0 G +/F8 9.9626 Tf 251.616 459.055 Td [(n)-73(r)-72(m)-73(2)-178(\050)-245(i)-138(c)-139(t)-139(x)-139(t)-439(,)-289(v)-129(r)-128(e)-128(s)-294(\050)-165(1)-165(:)-165(3)-165(\051)-165(\051)]TJ 0 g 0 G 0 g 0 G + -76.005 -21.917 Td [(In)-354(th)1(is)-354(w)28(a)28(y)-354(the)-353(global)-354(comm)28(unication,)-359(whic)28(h)-353(for)-354(small)-353(size)-1(s)-353(is)-354(a)-353(latency-)]TJ 0 -11.956 Td [(b)-28(ound)-333(op)-28(eration,)-333(is)-333(in)27(v)28(ok)28(ed)-333(only)-334(once.)]TJ 0 g 0 G -/F30 9.9626 Tf -125.682 -32.649 Td [(call)-525(psb_spmm\050alpha,)-525(a,)-525(x,)-525(beta,)-525(y,)-525(desc_a,)-525(info\051)]TJ 0 -11.955 Td [(call)-525(psb_spmm\050alpha,)-525(a,)-525(x,)-525(beta,)-525(y,desc_a,)-525(info,)-525(&)]TJ 67.995 -11.955 Td [(&)-525(trans,)-525(work\051)]TJ + 141.968 -334.744 Td [(44)]TJ 0 g 0 G -/F27 9.9626 Tf -67.995 -21.044 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +ET + +endstream +endobj +1155 0 obj +<< +/Length 6140 +>> +stream 0 g 0 G -/F27 9.9626 Tf -33.797 -19.575 Td [(On)-383(En)32(try)]TJ 0 g 0 G +BT +/F16 11.9552 Tf 99.895 706.129 Td [(4.9)-1125(psb)]TJ +ET +q +1 0 0 1 151.587 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +Q +BT +/F16 11.9552 Tf 155.621 706.129 Td [(genrm2s)-375(|)-375(Generalized)-375(2-Norm)-375(of)-375(V)94(ector)]TJ/F8 9.9626 Tf -55.726 -18.389 Td [(This)-310(subroutine)-310(computes)-309(a)-310(series)-310(of)-310(2-norms)-310(on)-310(the)-310(columns)-309(of)-310(a)-310(dense)-310(matrix)]TJ/F11 9.9626 Tf 0 -11.956 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(:)]TJ/F11 9.9626 Tf 126.531 -11.955 Td [(r)-28(es)]TJ/F8 9.9626 Tf 14.081 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 6.642 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050:)]TJ/F11 9.9626 Tf 6.642 0 Td [(;)-167(i)]TJ/F8 9.9626 Tf 7.86 0 Td [(\051)]TJ/F14 9.9626 Tf 3.875 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ 0 g 0 G - 0 -19.576 Td [(alpha)]TJ 0 g 0 G -/F8 9.9626 Tf 32.033 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.468 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(.)]TJ -59.004 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(12)]TJ +/F30 9.9626 Tf -207.017 -20.424 Td [(call)-525(psb_genrm2s\050res,)-525(x,)-525(desc_a,)-525(info\051)]TJ 0 g 0 G - [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.575 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(the)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 166.792 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -159.908 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 276.779 211.831 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 127.261 617.58 cm +[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S Q BT -/F30 9.9626 Tf 279.917 211.632 Td [(Tspmat)]TJ +/F11 9.9626 Tf 133.239 609.013 Td [(r)-28(es)-8770(x)]TJ/F27 9.9626 Tf 221.863 0 Td [(Subroutine)]TJ ET q -1 0 0 1 311.927 211.831 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 127.261 605.227 cm +[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S Q BT -/F30 9.9626 Tf 315.065 211.632 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -236.091 -19.575 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F8 9.9626 Tf 133.239 596.659 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Real)-3103(psb)]TJ ET q -1 0 0 1 385.864 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 370.699 596.858 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 389.002 144.236 Td [(T)]TJ +/F8 9.9626 Tf 373.688 596.659 Td [(genrm2s)]TJ -240.449 -11.955 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Real)-3314(psb)]TJ ET q -1 0 0 1 394.86 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 370.699 584.903 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 397.998 144.236 Td [(vect)]TJ +/F8 9.9626 Tf 373.688 584.704 Td [(genrm2s)]TJ -240.449 -11.955 Td [(Short)-333(Precision)-334(Real)-1200(Shor)1(t)-334(Precision)-333(Complex)-1200(psb)]TJ ET q -1 0 0 1 419.547 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 370.699 572.948 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 422.685 144.236 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-342(n)28(um)28(b)-28(ers)-342(of)-342(t)28(yp)-28(e)-342(sp)-28(eci\014ed)-342(in)-341(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-342(12)]TJ -0 g 0 G - [(.)-470(The)-342(rank)-342(of)]TJ/F11 9.9626 Tf 274.694 0 Td [(x)]TJ/F8 9.9626 Tf 9.101 0 Td [(m)28(ust)-342(b)-28(e)]TJ -283.795 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ +/F8 9.9626 Tf 373.688 572.749 Td [(genrm2s)]TJ -240.449 -11.956 Td [(Long)-333(Precision)-334(Real)-1411(Long)-333(Precision)-333(Complex)-1412(psb)]TJ +ET +q +1 0 0 1 370.699 560.993 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 373.688 560.793 Td [(genrm2s)]TJ +ET +q +1 0 0 1 127.261 557.008 cm +[]0 d 0 J 0.398 w 0 0 m 288.979 0 l S +Q 0 g 0 G - 83.26 -29.888 Td [(47)]TJ +BT +/F8 9.9626 Tf 228.067 528.968 Td [(T)83(able)-333(9:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G -ET - -endstream -endobj -1149 0 obj -<< -/Length 6975 ->> -stream 0 g 0 G 0 g 0 G +/F27 9.9626 Tf -128.172 -33.596 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -BT -/F27 9.9626 Tf 150.705 706.129 Td [(b)-32(eta)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 26.94 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.469 0 Td [(\014)]TJ/F8 9.9626 Tf 6.161 0 Td [(.)]TJ -53.664 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)27(yp)-27(e)-334(indicated)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(12)]TJ +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G - [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -18.453 Td [(y)]TJ + 0 -19.926 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.482 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-56(j)1(e)-1(ct)-254(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 592.233 cm +1 0 0 1 385.864 407.9 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 592.034 Td [(T)]TJ +/F30 9.9626 Tf 389.002 407.701 Td [(T)]TJ ET q -1 0 0 1 445.669 592.233 cm +1 0 0 1 394.86 407.9 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 592.034 Td [(vect)]TJ +/F30 9.9626 Tf 397.998 407.701 Td [(vect)]TJ ET q -1 0 0 1 470.356 592.233 cm +1 0 0 1 419.547 407.9 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 592.034 Td [(type)]TJ +/F30 9.9626 Tf 422.685 407.701 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-345(n)28(um)28(b)-28(ers)-345(of)-345(t)28(yp)-28(e)-345(sp)-28(eci\014ed)-345(in)-345(T)84(able)]TJ +/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-345(12)]TJ + [-333(9)]TJ 0 g 0 G - [(.)-479(The)-345(rank)-345(of)]TJ/F11 9.9626 Tf 275.087 0 Td [(y)]TJ/F8 9.9626 Tf 8.678 0 Td [(m)28(ust)-345(b)-28(e)]TJ -283.765 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ + [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -84.067 -18.454 Td [(desc)]TJ +/F27 9.9626 Tf -24.907 -19.926 Td [(desc)]TJ ET q -1 0 0 1 172.619 549.87 cm +1 0 0 1 121.81 376.02 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 549.67 Td [(a)]TJ +/F27 9.9626 Tf 125.247 375.82 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 327.588 502.049 cm +1 0 0 1 276.779 328.199 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 330.727 501.85 Td [(desc)]TJ +/F30 9.9626 Tf 279.917 328 Td [(desc)]TJ ET q -1 0 0 1 352.275 502.049 cm +1 0 0 1 301.466 328.199 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 355.414 501.85 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -225.63 -18.454 Td [(trans)]TJ -0 g 0 G -/F8 9.9626 Tf 30.609 0 Td [(indicates)-333(what)-334(kind)-333(of)-333(op)-28(eration)-333(to)-333(p)-28(erform.)]TJ -0 g 0 G -/F27 9.9626 Tf -5.703 -18.453 Td [(trans)-383(=)-384(N)]TJ -0 g 0 G -/F8 9.9626 Tf 56.124 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ -0 0 1 rg 0 0 1 RG - [-334(1)]TJ -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -56.124 -14.469 Td [(trans)-383(=)-384(T)]TJ +/F30 9.9626 Tf 304.604 328 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 55.128 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ -0 0 1 rg 0 0 1 RG - [-334(2)]TJ -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -55.128 -14.468 Td [(trans)-383(=)-384(C)]TJ -0 g 0 G -/F8 9.9626 Tf 55.433 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-27(ec)-1(i\014)1(e)-1(d)-333(b)28(y)-333(equation)]TJ -0 0 1 rg 0 0 1 RG - [-334(3)]TJ -0 g 0 G - -55.433 -18.453 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(tr)-28(ans)]TJ/F8 9.9626 Tf 27.052 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(N)]TJ/F8 9.9626 Tf -77.005 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-334(v)56(ariable.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -18.454 Td [(w)32(ork)]TJ -0 g 0 G -/F8 9.9626 Tf 29.431 0 Td [(w)28(ork)-334(arr)1(a)27(y)84(.)]TJ -4.525 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-487(as:)-753(a)-487(rank)-488(one)-487(arra)28(y)-488(of)-487(the)-488(same)-487(t)27(yp)-27(e)-488(of)]TJ/F11 9.9626 Tf 239.183 0 Td [(x)]TJ/F8 9.9626 Tf 10.551 0 Td [(and)]TJ/F11 9.9626 Tf 20.907 0 Td [(y)]TJ/F8 9.9626 Tf 10.099 0 Td [(with)-487(the)]TJ -280.74 -11.955 Td [(T)83(AR)28(GET)-333(attribute.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -18.454 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G +/F27 9.9626 Tf -225.631 -19.926 Td [(On)-383(Return)]TJ 0 g 0 G - 0 -18.453 Td [(y)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(matrix)]TJ/F11 9.9626 Tf 147.364 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -138.728 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-475(of)-474(rank)-475(one)-474(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(um)28(b)-28(ers)-474(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(12)]TJ + 0 -19.925 Td [(res)]TJ 0 g 0 G - [(.)]TJ +/F8 9.9626 Tf 19.47 0 Td [(con)28(tains)-334(the)-333(1-norm)-333(of)-334(\050th)1(e)-334(columns)-333(of)-78(\051)]TJ/F11 9.9626 Tf 177.751 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -178.008 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-333(real)-334(n)28(um)28(b)-28(er.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -18.454 Td [(info)]TJ +/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(te)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(t)1(e)-1(d.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - 141.968 -38.108 Td [(48)]TJ + 141.968 -94.1 Td [(45)]TJ 0 g 0 G ET endstream endobj -1155 0 obj +1162 0 obj << -/Length 6787 +/Length 5520 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.10)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(spsm)-375(|)-375(T)94(riangular)-375(System)-375(Solv)31(e)]TJ/F8 9.9626 Tf -25.091 -19.095 Td [(This)-333(subroutine)-334(computes)-333(the)-333(T)83(riangular)-333(System)-334(Solv)28(e:)]TJ/F11 9.9626 Tf 121.693 -35.01 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F11 9.9626 Tf 4.469 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -77.311 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-28(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F11 9.9626 Tf 4.469 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -85.836 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.227 0 Td [(1)]TJ/F11 9.9626 Tf 4.469 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.433 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -85.836 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -79.118 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-28(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -87.643 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.433 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -87.643 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -80.398 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-28(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ -88.923 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.204 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.227 0 Td [(H)]TJ/F11 9.9626 Tf 7.556 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.433 0 Td [(+)]TJ/F11 9.9626 Tf 9.962 0 Td [(\014)-53(y)]TJ/F8 9.9626 Tf -195.672 -37.999 Td [(where:)]TJ -0 g 0 G -/F11 9.9626 Tf -14.944 -21.063 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 10.676 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.092 0 Td [(x)]TJ/F7 6.9738 Tf 5.694 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.256 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ -0 g 0 G -/F11 9.9626 Tf -137.084 -19.948 Td [(y)]TJ -0 g 0 G -/F8 9.9626 Tf 10.224 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.092 0 Td [(y)]TJ/F7 6.9738 Tf 4.885 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ -0 g 0 G -/F11 9.9626 Tf -135.822 -19.948 Td [(T)]TJ -0 g 0 G -/F8 9.9626 Tf 12.187 0 Td [(is)-333(the)-334(global)-333(sparse)-333(blo)-28(c)28(k)-334(triangular)-333(submatrix)]TJ/F11 9.9626 Tf 206.781 0 Td [(T)]TJ -0 g 0 G - -218.968 -21.441 Td [(D)]TJ -0 g 0 G -/F8 9.9626 Tf 13.507 0 Td [(is)-333(the)-334(scaling)-333(diagonal)-333(matrix.)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(norm1)-375(|)-375(1-Norm)-375(of)-375(Sparse)-375(Matrix)]TJ/F8 9.9626 Tf -62.451 -18.389 Td [(This)-333(function)-334(computes)-333(the)-333(1-norm)-334(of)-333(a)-333(matrix)]TJ/F11 9.9626 Tf 209.658 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(:)]TJ/F11 9.9626 Tf -76.215 -33.873 Td [(nr)-28(m)]TJ/F8 9.9626 Tf 19.498 0 Td [(1)]TJ/F14 9.9626 Tf 7.749 0 Td [(\040)-278(k)]TJ/F11 9.9626 Tf 17.711 0 Td [(A)]TJ/F14 9.9626 Tf 7.472 0 Td [(k)]TJ/F7 6.9738 Tf 4.982 -1.495 Td [(1)]TJ/F8 9.9626 Tf -198.327 -20.423 Td [(where:)]TJ 0 g 0 G +/F11 9.9626 Tf 0 -19.926 Td [(A)]TJ 0 g 0 G -/F30 9.9626 Tf -13.507 -23.814 Td [(call)-525(psb_spsm\050alpha,)-525(t,)-525(x,)-525(beta,)-525(y,)-525(desc_a,)-525(info\051)]TJ 0 -11.955 Td [(call)-525(psb_spsm\050alpha,)-525(t,)-525(x,)-525(beta,)-525(y,)-525(desc_a,)-525(info,&)]TJ 67.995 -11.955 Td [(&)-525(trans,)-525(unit,)-525(choice,)-525(diag,)-525(work\051)]TJ +/F8 9.9626 Tf 12.453 0 Td [(represen)28(ts)-334(the)-333(global)-333(matrix)]TJ/F11 9.9626 Tf 125.834 0 Td [(A)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 177.988 335.134 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 230.992 589.962 cm +[]0 d 0 J 0.398 w 0 0 m 183.136 0 l S Q BT -/F11 9.9626 Tf 183.966 326.566 Td [(T)]TJ/F8 9.9626 Tf 7.205 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(D)]TJ/F8 9.9626 Tf 8.525 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(\014)]TJ/F27 9.9626 Tf 56.892 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 236.97 581.394 Td [(A)]TJ/F27 9.9626 Tf 120.41 0 Td [(F)96(unction)]TJ ET q -1 0 0 1 177.988 322.78 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 230.992 577.608 cm +[]0 d 0 J 0.398 w 0 0 m 183.136 0 l S Q BT -/F8 9.9626 Tf 183.966 314.213 Td [(Short)-333(Precision)-333(R)-1(eal)-3102(psb)]TJ +/F8 9.9626 Tf 236.97 569.04 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ ET q -1 0 0 1 319.972 314.412 cm +1 0 0 1 372.977 569.24 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 314.213 Td [(spsm)]TJ -138.995 -11.956 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 375.966 569.04 Td [(spnrm1)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ ET q -1 0 0 1 319.972 302.457 cm +1 0 0 1 372.977 557.284 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 302.257 Td [(spsm)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-333(C)-1(omplex)-1200(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 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3.138 0 l S -Q -BT -/F30 9.9626 Tf 355.414 336.605 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -225.63 -20.649 Td [(trans)]TJ -0 g 0 G -/F8 9.9626 Tf 30.609 0 Td [(sp)-28(ecify)-333(with)]TJ/F17 9.9626 Tf 55.68 0 Td [(unitd)]TJ/F8 9.9626 Tf 25.725 0 Td [(the)-333(op)-28(eration)-333(to)-334(p)-27(e)-1(r)1(form.)]TJ -0 g 0 G -/F27 9.9626 Tf -87.108 -20.65 Td [(trans)-383(=)-384('N')]TJ -0 g 0 G -/F8 9.9626 Tf 62.489 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(no)-333(transp)-28(osed)-333(matrix)]TJ -0 g 0 G -/F27 9.9626 Tf -62.489 -16.303 Td [(trans)-383(=)-384('T')]TJ -0 g 0 G -/F8 9.9626 Tf 61.493 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(transp)-28(osed)-333(matrix.)]TJ -0 g 0 G -/F27 9.9626 Tf -61.493 -16.302 Td [(trans)-383(=)-384('C')]TJ -0 g 0 G -/F8 9.9626 Tf 61.798 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(conjugate)-333(transp)-28(osed)-333(matrix.)]TJ -61.798 -20.65 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(tr)-28(ans)]TJ/F8 9.9626 Tf 27.052 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(N)]TJ/F8 9.9626 Tf -77.005 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-334(v)56(ariable.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -20.65 Td [(unitd)]TJ -0 g 0 G -/F8 9.9626 Tf 31.714 0 Td [(sp)-28(ecify)-333(with)]TJ/F17 9.9626 Tf 55.68 0 Td [(tr)51(ans)]TJ/F8 9.9626 Tf 25.089 0 Td [(the)-333(op)-28(eration)-333(to)-334(p)-27(erform.)]TJ 0 g 0 G -/F27 9.9626 Tf -87.577 -20.649 Td [(unitd)-383(=)-384('U')]TJ -0 g 0 G -/F8 9.9626 Tf 63.443 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(no)-333(scaling)]TJ -0 g 0 G -/F27 9.9626 Tf -63.443 -16.303 Td [(unitd)-383(=)-384('L')]TJ + 0 -19.925 Td 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-11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ 0 g 0 G - 78.747 -29.888 Td [(50)]TJ + 141.968 -56.242 Td [(46)]TJ 0 g 0 G ET endstream endobj -1173 0 obj +1169 0 obj << -/Length 4663 +/Length 5557 >> stream 0 g 0 G 0 g 0 G BT -/F8 9.9626 Tf 124.802 706.129 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(unitd)]TJ/F8 9.9626 Tf 26.665 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(U)]TJ/F8 9.9626 Tf -76.617 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-333(v)55(ariable.)]TJ +/F16 11.9552 Tf 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0 Td [(with)-377(the)-377(T)84(AR)28(GET)]TJ -235.401 -11.955 Td [(attribute.)]TJ + 0 -19.925 Td [(a)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(the)-333(global)-333(sparse)-334(matrix)]TJ/F11 9.9626 Tf 196.126 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -189.242 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +ET +q +1 0 0 1 276.779 346.132 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 279.917 345.932 Td [(Tspmat)]TJ +ET +q +1 0 0 1 311.927 346.132 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 315.065 345.932 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G - 0 -19.925 Td [(y)]TJ +/F27 9.9626 Tf -236.091 -19.925 Td [(desc)]TJ +ET +q +1 0 0 1 121.81 326.206 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 125.247 326.007 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG - [-333(13)]TJ -0 g 0 G - [(.)]TJ +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ +ET +q +1 0 0 1 276.779 278.386 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 279.917 278.186 Td [(desc)]TJ +ET +q +1 0 0 1 301.466 278.386 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 304.604 278.186 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(info)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ +/F27 9.9626 Tf -225.631 -19.925 Td [(On)-383(Return)]TJ 0 g 0 G - 141.968 -73.723 Td [(51)]TJ 0 g 0 G -ET - -endstream -endobj -1178 0 obj -<< -/Length 651 ->> -stream + 0 -19.925 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G +/F8 9.9626 Tf 78.387 0 Td [(is)-333(the)-334(in\014ni)1(t)27(y-norm)-333(of)-333(sparse)-334(submatrix)]TJ/F11 9.9626 Tf 176.311 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -237.263 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(long)-333(precision)-333(real)-334(n)28(um)28(b)-28(er.)]TJ 0 g 0 G -BT -/F16 14.3462 Tf 150.705 706.129 Td [(5)-1125(Comm)31(unication)-375(routines)]TJ/F8 9.9626 Tf 0 -21.821 Td [(The)-283(routines)-283(in)-283(this)-283(c)28(hapter)-283(implemen)28(t)-283(v)55(arious)-283(global)-283(comm)28(unication)-283(op)-28(erators)]TJ 0 -11.955 Td [(on)-344(v)28(ectors)-344(asso)-27(c)-1(iated)-343(with)-344(a)-344(d)1(is)-1(cretization)-343(mesh.)-476(F)84(or)-344(auxiliary)-344(comm)28(unication)]TJ 0 -11.955 Td [(routines)-333(not)-334(tied)-333(to)-333(a)-334(d)1(is)-1(cretization)-333(space)-333(see)]TJ -0 0 1 rg 0 0 1 RG - [-334(6)]TJ +/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ 0 g 0 G - [(.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - 166.874 -569.96 Td [(52)]TJ + 141.968 -56.242 Td [(47)]TJ 0 g 0 G ET endstream endobj -1186 0 obj +1180 0 obj << -/Length 7259 +/Length 7334 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.12)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(halo)-375(|)-375(Halo)-375(Data)-375(Comm)31(unication)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(These)-333(s)-1(u)1(broutines)-334(gathers)-333(the)-333(v)55(alues)-333(of)-334(th)1(e)-334(halo)-333(elemen)28(ts:)]TJ/F11 9.9626 Tf 158.413 -23.188 Td [(x)]TJ/F14 9.9626 Tf 8.462 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F8 9.9626 Tf -179.605 -21.251 Td [(where:)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(spmm)-349(|)-349(Sparse)-349(Matrix)-349(b)31(y)-349(Dense)-349(Matrix)-349(Pro)-31(d-)]TJ -25.091 -13.948 Td [(uct)]TJ/F8 9.9626 Tf -37.36 -18.389 Td [(This)-333(subroutine)-334(computes)-333(the)-333(Sparse)-334(Matrix)-333(b)28(y)-333(Dense)-334(Matrix)-333(Pro)-28(duct:)]TJ/F11 9.9626 Tf 139.908 -23.911 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(Ax)]TJ/F8 9.9626 Tf 21.79 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ 0 g 0 G -/F11 9.9626 Tf 0 -19.391 Td [(x)]TJ +/F8 9.9626 Tf 138.581 0 Td [(\0501\051)]TJ 0 g 0 G -/F8 9.9626 Tf 10.676 0 Td [(is)-333(a)-334(global)-333(dense)-333(submatrix.)]TJ +/F11 9.9626 Tf -194.211 -16.435 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(A)]TJ/F10 6.9738 Tf 13.882 4.114 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.114 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ +0 g 0 G +/F8 9.9626 Tf 135.443 0 Td [(\0502\051)]TJ +0 g 0 G +/F11 9.9626 Tf -194.851 -16.435 Td [(y)]TJ/F14 9.9626 Tf 8.009 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(\013)-4(A)]TJ/F10 6.9738 Tf 13.882 4.114 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.114 Td [(x)]TJ/F8 9.9626 Tf 7.907 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ +0 g 0 G +/F8 9.9626 Tf 134.803 0 Td [(\0503\051)]TJ +0 g 0 G + -316.037 -16.435 Td [(where:)]TJ +0 g 0 G +/F11 9.9626 Tf -14.944 -17.928 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 10.675 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.093 0 Td [(x)]TJ/F7 6.9738 Tf 5.694 -1.495 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ +0 g 0 G +/F11 9.9626 Tf -137.083 -17.432 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 10.223 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.093 0 Td [(y)]TJ/F7 6.9738 Tf 4.884 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.256 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ +0 g 0 G +/F11 9.9626 Tf -135.822 -17.433 Td [(A)]TJ +0 g 0 G +/F8 9.9626 Tf 12.453 0 Td [(is)-333(the)-334(global)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 118.943 0 Td [(A)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 177.988 602.649 cm +1 0 0 1 228.797 525.728 cm []0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F11 9.9626 Tf 183.966 594.081 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F27 9.9626 Tf 107.911 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 234.775 517.16 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(\014)]TJ/F27 9.9626 Tf 71.239 0 Td [(Subroutine)]TJ ET q -1 0 0 1 177.988 590.295 cm +1 0 0 1 228.797 513.374 cm []0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F8 9.9626 Tf 183.966 581.727 Td [(In)28(teger)-9028(psb)]TJ -ET -q -1 0 0 1 319.972 581.926 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 322.961 581.727 Td [(halo)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-333(R)-1(eal)-3102(psb)]TJ +/F8 9.9626 Tf 234.775 504.806 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ ET q -1 0 0 1 319.972 569.971 cm +1 0 0 1 370.782 505.006 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 569.772 Td [(halo)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 373.771 504.806 Td [(spmm)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ ET q -1 0 0 1 319.972 558.016 cm +1 0 0 1 370.782 493.05 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 557.817 Td [(halo)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-333(C)-1(omplex)-1200(p)1(s)-1(b)]TJ +/F8 9.9626 Tf 373.771 492.851 Td [(spmm)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ ET q -1 0 0 1 319.972 546.061 cm +1 0 0 1 370.782 481.095 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 545.862 Td [(halo)]TJ -138.995 -11.956 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ +/F8 9.9626 Tf 373.771 480.896 Td [(spmm)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ ET q -1 0 0 1 319.972 534.106 cm +1 0 0 1 370.782 469.14 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.961 533.906 Td [(halo)]TJ +/F8 9.9626 Tf 373.771 468.941 Td [(spmm)]TJ ET q -1 0 0 1 177.988 530.121 cm +1 0 0 1 228.797 465.155 cm []0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q 0 g 0 G BT -/F8 9.9626 Tf 225.577 502.081 Td [(T)83(able)-333(14:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F8 9.9626 Tf 276.386 437.116 Td [(T)83(able)-333(12:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -124.305 -29.354 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.731 0 Td [(p)-122(s)-123(b)]TJ -ET -q -1 0 0 1 150.256 472.926 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 154.464 472.727 Td [(h)-122(a)-123(l)-122(o)-228(\050)-130(x)-209(,)-874(d)-112(e)-113(s)-113(c)]TJ -ET -q -1 0 0 1 226.044 472.926 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 230.155 472.727 Td [(a)-386(,)-914(i)-152(n)-152(f)-152(o)-258(\051)]TJ/F27 9.9626 Tf -128.883 -11.955 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.731 0 Td [(p)-122(s)-123(b)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -125.681 -30.379 Td [(call)-525(psb_spmm\050alpha,)-525(a,)-525(x,)-525(beta,)-525(y,)-525(desc_a,)-525(info\051)]TJ 0 -11.955 Td [(call)-525(psb_spmm\050alpha,)-525(a,)-525(x,)-525(beta,)-525(y,desc_a,)-525(info,)-525(&)]TJ 67.994 -11.955 Td [(&)-525(trans,)-525(work\051)]TJ +0 g 0 G +/F27 9.9626 Tf -67.994 -19.422 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -18.927 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -18.926 Td [(alpha)]TJ +0 g 0 G +/F8 9.9626 Tf 32.032 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.469 0 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(.)]TJ -59.005 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)27(yp)-27(e)-334(indicated)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(12)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -18.927 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.55 0 Td [(the)-333(lo)-28(cal)-334(p)-27(ortion)-333(of)-334(the)-333(sparse)-334(matri)1(x)]TJ/F11 9.9626 Tf 166.792 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -159.908 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.659 0 Td [(psb)]TJ ET q -1 0 0 1 150.256 460.971 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 327.588 211.183 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 154.464 460.772 Td [(h)-122(a)-123(l)-122(o)-228(\050)-130(x)-209(,)-874(d)-112(e)-113(s)-113(c)]TJ +/F30 9.9626 Tf 330.727 210.983 Td [(Tspmat)]TJ ET q -1 0 0 1 226.044 460.971 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 362.736 211.183 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 230.155 460.772 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-804(w)-43(o)-43(r)-43(k)-247(,)]TJ/F27 9.9626 Tf 91.304 0 Td [(d)-39(a)-39(t)-40(a)]TJ/F8 9.9626 Tf 24.571 0 Td [(\051)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -246.135 -26.961 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.659 Td [(On)-383(En)32(try)]TJ +/F30 9.9626 Tf 365.874 210.983 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G - 0 -19.658 Td [(x)]TJ +/F27 9.9626 Tf -236.091 -18.926 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 88.917 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -80.732 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -167.933 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 385.864 346.872 cm +1 0 0 1 436.673 144.435 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 389.002 346.673 Td [(T)]TJ +/F30 9.9626 Tf 439.811 144.236 Td [(T)]TJ ET q -1 0 0 1 394.86 346.872 cm +1 0 0 1 445.669 144.435 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 397.998 346.673 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 144.236 Td [(vect)]TJ ET q -1 0 0 1 419.547 346.872 cm +1 0 0 1 470.356 144.435 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 422.685 346.673 Td [(type)]TJ +/F30 9.9626 Tf 473.495 144.236 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-342(n)28(um)28(b)-28(ers)-342(of)-342(t)28(yp)-28(e)-342(sp)-28(eci\014ed)-342(in)-341(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(14)]TJ + [-342(12)]TJ +0 g 0 G + [(.)-470(The)-342(rank)-342(of)]TJ/F11 9.9626 Tf 274.695 0 Td [(x)]TJ/F8 9.9626 Tf 9.1 0 Td [(m)28(ust)-342(b)-28(e)]TJ -283.795 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.467 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ +0 g 0 G + 83.259 -29.888 Td [(48)]TJ +0 g 0 G +ET + +endstream +endobj +1195 0 obj +<< +/Length 6993 +>> +stream +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F27 9.9626 Tf 99.895 706.129 Td [(b)-32(eta)]TJ +0 g 0 G +/F8 9.9626 Tf 26.941 0 Td [(the)-333(scalar)]TJ/F11 9.9626 Tf 45.468 0 Td [(\014)]TJ/F8 9.9626 Tf 6.161 0 Td [(.)]TJ -53.663 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(n)28(um)28(b)-28(er)-333(of)-334(the)-333(data)-333(t)28(yp)-28(e)-334(ind)1(ic)-1(ated)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(12)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.658 Td [(desc)]TJ +/F27 9.9626 Tf -24.907 -18.597 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 121.81 315.259 cm +1 0 0 1 385.864 592.09 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 389.002 591.891 Td [(T)]TJ +ET +q +1 0 0 1 394.86 592.09 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 397.998 591.891 Td [(vect)]TJ +ET +q +1 0 0 1 419.547 592.09 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 422.685 591.891 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf -297.883 -11.956 Td [(con)28(taining)-345(n)28(um)28(b)-28(ers)-345(of)-345(t)28(yp)-28(e)-345(sp)-28(eci\014ed)-345(in)-345(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-345(12)]TJ +0 g 0 G + [(.)-479(The)-345(rank)-345(of)]TJ/F11 9.9626 Tf 275.086 0 Td [(y)]TJ/F8 9.9626 Tf 8.678 0 Td [(m)28(ust)-345(b)-28(e)]TJ -283.764 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -84.067 -18.597 Td [(desc)]TJ +ET +q +1 0 0 1 121.81 549.583 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 315.06 Td [(a)]TJ +/F27 9.9626 Tf 125.247 549.383 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 267.438 cm +1 0 0 1 276.779 501.762 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 267.239 Td [(desc)]TJ +/F30 9.9626 Tf 279.917 501.563 Td [(desc)]TJ ET q -1 0 0 1 336.723 267.438 cm +1 0 0 1 301.466 501.762 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 339.861 267.239 Td [(type)]TJ +/F30 9.9626 Tf 304.604 501.563 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.658 Td [(w)32(ork)]TJ +/F27 9.9626 Tf -225.631 -18.597 Td [(trans)]TJ 0 g 0 G -/F8 9.9626 Tf 29.432 0 Td [(the)-333(w)27(ork)-333(arra)28(y)83(.)]TJ -4.525 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(arra)27(y)-333(of)-333(the)-334(same)-333(t)28(yp)-28(e)-333(of)]TJ/F11 9.9626 Tf 220.756 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +/F8 9.9626 Tf 30.609 0 Td [(indicates)-333(what)-334(kind)-333(of)-333(op)-28(eration)-333(to)-334(p)-27(erform.)]TJ 0 g 0 G -/F27 9.9626 Tf -251.357 -19.659 Td [(data)]TJ +/F27 9.9626 Tf -5.702 -18.597 Td [(trans)-383(=)-384(N)]TJ 0 g 0 G -/F8 9.9626 Tf 26.941 0 Td [(index)-333(list)-334(selector.)]TJ -2.034 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(Sp)-28(eci\014ed)-222(as:)-389(an)-222(in)28(teger.)-408(V)84(alues:)]TJ/F30 9.9626 Tf 136.479 0 Td [(psb_comm_halo_)]TJ/F8 9.9626 Tf 73.225 0 Td [(,)]TJ/F30 9.9626 Tf 2.767 0 Td [(psb_comm_mov_)]TJ/F8 9.9626 Tf 67.995 0 Td [(,)]TJ/F30 9.9626 Tf 5.202 0 Td [(psb_comm_ext_)]TJ/F8 9.9626 Tf 67.995 0 Td [(,)]TJ -353.663 -11.955 Td [(default:)]TJ/F30 9.9626 Tf 39.089 0 Td [(psb_comm_halo_)]TJ/F8 9.9626 Tf 73.224 0 Td [(.)-705(Cho)-27(os)-1(es)-420(the)-420(index)-420(list)-420(on)-420(whic)28(h)-420(to)-420(base)-420(the)]TJ -112.313 -11.955 Td [(data)-333(exc)27(hange.)]TJ +/F8 9.9626 Tf 56.124 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-27(e)-1(ci\014ed)-333(b)28(y)-333(equation)]TJ +0 0 1 rg 0 0 1 RG + [-334(1)]TJ 0 g 0 G - 141.968 -29.888 Td [(53)]TJ +0 g 0 G +/F27 9.9626 Tf -56.124 -14.612 Td [(trans)-383(=)-384(T)]TJ +0 g 0 G +/F8 9.9626 Tf 55.128 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-27(e)-1(ci\014)1(e)-1(d)-333(b)28(y)-333(equation)]TJ +0 0 1 rg 0 0 1 RG + [-334(2)]TJ +0 g 0 G +0 g 0 G +/F27 9.9626 Tf -55.128 -14.612 Td [(trans)-383(=)-384(C)]TJ +0 g 0 G +/F8 9.9626 Tf 55.432 0 Td [(the)-333(op)-28(eration)-333(is)-334(sp)-28(eci\014ed)-333(b)28(y)-333(equation)]TJ +0 0 1 rg 0 0 1 RG + [-334(3)]TJ +0 g 0 G + -55.432 -18.597 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(tr)-28(ans)]TJ/F8 9.9626 Tf 27.052 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(N)]TJ/F8 9.9626 Tf -77.004 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-333(v)55(ariable.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.596 Td [(w)32(ork)]TJ +0 g 0 G +/F8 9.9626 Tf 29.432 0 Td [(w)28(ork)-333(arra)27(y)84(.)]TJ -4.525 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-487(as:)-753(a)-487(rank)-488(one)-487(arra)28(y)-488(of)-487(the)-488(same)-487(t)27(yp)-27(e)-488(of)]TJ/F11 9.9626 Tf 239.183 0 Td [(x)]TJ/F8 9.9626 Tf 10.55 0 Td [(and)]TJ/F11 9.9626 Tf 20.908 0 Td [(y)]TJ/F8 9.9626 Tf 10.098 0 Td [(with)-487(the)]TJ -280.739 -11.955 Td [(T)83(AR)28(GET)-333(attribute.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.597 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -18.597 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(matrix)]TJ/F11 9.9626 Tf 147.365 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -138.728 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(12)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.597 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ +0 g 0 G + 141.968 -36.529 Td [(49)]TJ 0 g 0 G ET endstream endobj -1196 0 obj +1202 0 obj << -/Length 3196 +/Length 6783 >> stream 0 g 0 G 0 g 0 G -0 g 0 G BT -/F27 9.9626 Tf 150.705 706.129 Td [(On)-383(Return)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(4.13)-1125(psb)]TJ +ET +q +1 0 0 1 209.121 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +Q +BT +/F16 11.9552 Tf 213.156 706.129 Td [(spsm)-375(|)-375(T)94(riangular)-375(System)-375(Solv)31(e)]TJ/F8 9.9626 Tf -62.451 -19.095 Td [(This)-333(subroutine)-334(computes)-333(the)-333(T)83(riangular)-333(System)-334(S)1(o)-1(l)1(v)27(e:)]TJ/F11 9.9626 Tf 121.692 -35.01 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F11 9.9626 Tf 4.47 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.907 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -77.312 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-27(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F11 9.9626 Tf 4.47 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.907 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -85.837 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F7 6.9738 Tf 6.226 0 Td [(1)]TJ/F11 9.9626 Tf 4.47 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.432 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -85.837 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -79.119 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-27(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.908 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -87.644 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(T)]TJ/F11 9.9626 Tf 6.276 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.433 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -87.644 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.907 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -80.399 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(D)-27(T)]TJ/F13 6.9738 Tf 22.141 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.113 Td [(x)]TJ/F8 9.9626 Tf 7.907 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ -88.924 -14.944 Td [(y)]TJ/F14 9.9626 Tf 15.205 0 Td [(\040)]TJ/F11 9.9626 Tf 19.925 0 Td [(\013)-4(T)]TJ/F13 6.9738 Tf 13.616 4.113 Td [(\000)]TJ/F10 6.9738 Tf 6.226 0 Td [(H)]TJ/F11 9.9626 Tf 7.557 -4.113 Td [(D)-28(x)]TJ/F8 9.9626 Tf 16.432 0 Td [(+)]TJ/F11 9.9626 Tf 9.963 0 Td [(\014)-53(y)]TJ/F8 9.9626 Tf -195.672 -37.999 Td [(where:)]TJ 0 g 0 G +/F11 9.9626 Tf -14.944 -21.063 Td [(x)]TJ 0 g 0 G - 0 -19.925 Td [(x)]TJ +/F8 9.9626 Tf 10.675 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.093 0 Td [(x)]TJ/F7 6.9738 Tf 5.694 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.255 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(result)-333(matrix)]TJ/F11 9.9626 Tf 116.674 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -108.49 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Returned)-271(as:)-414(a)-271(rank)-271(one)-271(or)-272(t)28(w)28(o)-271(arra)28(y)-272(con)28(taining)-271(n)28(um)28(b)-28(ers)-271(of)-272(t)28(yp)-28(e)-271(sp)-28(eci\014ed)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ -0 0 1 rg 0 0 1 RG - [-333(14)]TJ +/F11 9.9626 Tf -137.083 -19.948 Td [(y)]TJ 0 g 0 G - [(.)]TJ +/F8 9.9626 Tf 10.223 0 Td [(is)-333(the)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 116.093 0 Td [(y)]TJ/F7 6.9738 Tf 4.884 -1.494 Td [(:)]TJ/F10 6.9738 Tf 2.256 0 Td [(;)]TJ/F7 6.9738 Tf 2.366 0 Td [(:)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.926 Td [(info)]TJ +/F11 9.9626 Tf -135.822 -19.948 Td [(T)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(submatrix)]TJ/F11 9.9626 Tf 162.364 0 Td [(y)]TJ/F8 9.9626 Tf 5.241 0 Td [(.)]TJ -166.457 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 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[(Long)-333(Precision)-334(Real)-3314(psb)]TJ +/F30 9.9626 Tf 422.685 428.986 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-345(n)28(um)28(b)-28(ers)-345(of)-345(t)28(yp)-28(e)-345(sp)-28(eci\014ed)-345(in)-345(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-345(13)]TJ +0 g 0 G + [(.)-479(The)-345(rank)-345(of)]TJ/F11 9.9626 Tf 275.086 0 Td [(y)]TJ/F8 9.9626 Tf 8.678 0 Td [(m)28(ust)-345(b)-28(e)]TJ -283.764 -11.955 Td [(the)-333(same)-334(of)]TJ/F11 9.9626 Tf 53.466 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -84.067 -20.65 Td [(desc)]TJ ET q -1 0 0 1 370.782 555.201 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 121.81 384.625 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F8 9.9626 Tf 373.771 555.002 Td [(o)28(vrl)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ +/F27 9.9626 Tf 125.247 384.426 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 370.782 543.246 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 276.779 336.805 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 373.771 543.047 Td [(o)28(vrl)]TJ -138.996 -11.956 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ +/F30 9.9626 Tf 279.917 336.605 Td [(desc)]TJ ET q -1 0 0 1 370.782 531.291 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 301.466 336.805 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 373.771 531.091 Td [(o)28(vrl)]TJ +/F30 9.9626 Tf 304.604 336.605 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -225.631 -20.649 Td [(trans)]TJ +0 g 0 G +/F8 9.9626 Tf 30.609 0 Td [(sp)-28(ecify)-333(with)]TJ/F17 9.9626 Tf 55.68 0 Td [(unitd)]TJ/F8 9.9626 Tf 25.726 0 Td [(the)-333(op)-28(eration)-333(to)-334(p)-27(erform.)]TJ +0 g 0 G +/F27 9.9626 Tf -87.108 -20.65 Td [(trans)-383(=)-384('N')]TJ +0 g 0 G +/F8 9.9626 Tf 62.489 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(no)-333(transp)-28(osed)-333(matrix)]TJ +0 g 0 G +/F27 9.9626 Tf -62.489 -16.303 Td [(trans)-383(=)-384('T')]TJ +0 g 0 G +/F8 9.9626 Tf 61.493 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(transp)-28(osed)-333(matrix.)]TJ +0 g 0 G +/F27 9.9626 Tf -61.493 -16.302 Td [(trans)-383(=)-384('C')]TJ +0 g 0 G +/F8 9.9626 Tf 61.797 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(conjugate)-333(transp)-28(osed)-333(matrix.)]TJ -61.797 -20.65 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(tr)-28(ans)]TJ/F8 9.9626 Tf 27.052 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(N)]TJ/F8 9.9626 Tf -77.004 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-333(v)55(ariable.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -20.65 Td [(unitd)]TJ +0 g 0 G +/F8 9.9626 Tf 31.715 0 Td [(sp)-28(ecify)-333(with)]TJ/F17 9.9626 Tf 55.68 0 Td [(tr)51(ans)]TJ/F8 9.9626 Tf 25.089 0 Td [(the)-333(op)-28(eration)-333(to)-334(p)-27(erform.)]TJ +0 g 0 G +/F27 9.9626 Tf -87.577 -20.649 Td [(unitd)-383(=)-384('U')]TJ +0 g 0 G +/F8 9.9626 Tf 63.442 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(no)-333(scaling)]TJ +0 g 0 G +/F27 9.9626 Tf -63.442 -16.303 Td [(unitd)-383(=)-384('L')]TJ +0 g 0 G +/F8 9.9626 Tf 61.519 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(left)-333(scaling)]TJ +0 g 0 G +/F27 9.9626 Tf -61.519 -16.302 Td [(unitd)-383(=)-384('R')]TJ +0 g 0 G +/F8 9.9626 Tf 63.221 0 Td [(the)-333(op)-28(eration)-333(is)-334(with)-333(righ)28(t)-333(s)-1(calin)1(g.)]TJ +0 g 0 G + 78.747 -29.888 Td [(51)]TJ +0 g 0 G +ET + +endstream +endobj +1219 0 obj +<< +/Length 4678 +>> +stream +0 g 0 G +0 g 0 G +BT +/F8 9.9626 Tf 175.611 706.129 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(unitd)]TJ/F8 9.9626 Tf 26.666 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(U)]TJ/F8 9.9626 Tf -76.618 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-334(v)56(ariable.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.925 Td [(c)32(hoice)]TJ +0 g 0 G +/F8 9.9626 Tf 35.374 0 Td [(sp)-28(eci\014es)-333(the)-334(up)-27(date)-334(of)-333(o)28(v)28(erlap)-334(elemen)28(ts)-333(to)-334(b)-27(e)-334(p)-28(erf)1(orme)-1(d)-333(on)-333(exit:)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -5.486 -19.925 Td [(psb_none_)]TJ +0 g 0 G +0 g 0 G + 0 -15.941 Td [(psb_sum_)]TJ +0 g 0 G +0 g 0 G + 0 -15.94 Td [(psb_avg_)]TJ +0 g 0 G +0 g 0 G + 0 -15.94 Td [(psb_square_root_)]TJ/F8 9.9626 Tf -4.982 -19.925 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Default:)]TJ/F30 9.9626 Tf 39.436 0 Td [(psb_avg_)]TJ/F8 9.9626 Tf -39.436 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.925 Td [(diag)]TJ +0 g 0 G +/F8 9.9626 Tf 25.826 0 Td [(the)-333(diagonal)-334(scaling)-333(matrix.)]TJ -0.92 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(diag)]TJ/F8 9.9626 Tf 18.993 0 Td [(\0501\051)-278(=)-278(1\050)]TJ/F11 9.9626 Tf 34.869 0 Td [(noscal)-20(ing)]TJ/F8 9.9626 Tf 42.747 0 Td [(\051)]TJ -136.045 -11.955 Td [(Sp)-28(eci\014ed)-382(as:)-543(a)-382(rank)-383(on)1(e)-383(arra)28(y)-382(c)-1(on)28(taining)-382(n)28(um)28(b)-28(ers)-383(of)-382(the)-382(t)27(yp)-27(e)-383(indicated)]TJ 0 -11.955 Td [(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(13)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.926 Td [(w)32(ork)]TJ +0 g 0 G +/F8 9.9626 Tf 29.431 0 Td [(a)-333(w)27(ork)-333(arra)28(y)83(.)]TJ -4.525 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-377(as:)-531(a)-377(rank)-377(on)1(e)-377(arra)28(y)-377(of)-377(the)-377(same)-377(t)28(yp)-28(e)-377(of)]TJ/F11 9.9626 Tf 225.953 0 Td [(x)]TJ/F8 9.9626 Tf 9.448 0 Td [(with)-377(the)-377(T)84(AR)28(G)-1(E)1(T)]TJ -235.401 -11.955 Td [(attribute.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.926 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.118 0 Td [(y)]TJ/F8 9.9626 Tf 5.241 0 Td [(.)]TJ -167.481 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-475(of)-474(rank)-475(one)-474(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(um)28(b)-28(ers)-474(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(13)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.925 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(te)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(t)1(e)-1(d)1(.)]TJ +0 g 0 G + 141.968 -73.723 Td [(52)]TJ +0 g 0 G +ET + +endstream +endobj +1230 0 obj +<< +/Length 7444 +>> +stream +0 g 0 G +0 g 0 G +BT +/F16 11.9552 Tf 99.895 706.129 Td [(4.14)-1125(psb)]TJ ET q -1 0 0 1 228.797 527.306 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 158.311 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 276.386 499.266 Td [(T)83(able)-333(15:)-444(Data)-334(t)28(yp)-28(es)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(gemlt)-375(|)-375(En)31(trywise)-375(Pro)-31(duct)]TJ/F8 9.9626 Tf -62.451 -19.771 Td [(This)-333(function)-334(computes)-333(the)-333(en)27(try)1(w)-1(i)1(s)-1(e)-333(pro)-28(duct)-333(b)-28(et)28(w)28(een)-334(t)28(w)28(o)-333(v)27(ectors)]TJ/F11 9.9626 Tf 296.14 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(y)]TJ -185.258 -23.403 Td [(dot)]TJ/F14 9.9626 Tf 16.379 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)]TJ/F11 9.9626 Tf 3.874 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)]TJ/F11 9.9626 Tf 3.874 0 Td [(:)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -201.676 -24.145 Td [(psb_gemlt\050x,)-525(y,)-525(desc_a,)-525(info\051)]TJ +0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -124.304 -28.465 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.881 0 Td [(p)-137(s)-138(b)]TJ ET q -1 0 0 1 201.669 471 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 183.665 610.766 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S Q BT -/F8 9.9626 Tf 206.027 470.801 Td [(o)-137(v)-138(r)-137(l)-243(\050)-130(x)-209(,)-874(d)-113(e)-112(s)-113(c)]TJ +/F11 9.9626 Tf 189.642 602.198 Td [(dot)]TJ/F8 9.9626 Tf 13.612 0 Td [(,)]TJ/F11 9.9626 Tf 6.089 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(y)]TJ/F27 9.9626 Tf 88.927 0 Td [(F)96(unction)]TJ ET q -1 0 0 1 276.854 471 cm +1 0 0 1 183.665 598.412 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +Q +BT +/F8 9.9626 Tf 189.642 589.845 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ +ET +q +1 0 0 1 325.649 590.044 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 280.965 470.801 Td [(a)-386(,)-914(i)-152(n)-152(f)-152(o)-258(\051)]TJ/F27 9.9626 Tf -128.883 -11.955 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.881 0 Td [(p)-137(s)-138(b)]TJ +/F8 9.9626 Tf 328.638 589.845 Td [(gemlt)]TJ -138.996 -11.956 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ ET q -1 0 0 1 201.669 459.045 cm +1 0 0 1 325.649 578.089 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 206.027 458.846 Td [(o)-137(v)-138(r)-137(l)-243(\050)-130(x)-209(,)-874(d)-113(e)-112(s)-113(c)]TJ +/F8 9.9626 Tf 328.638 577.889 Td [(gemlt)]TJ -138.996 -11.955 Td [(Short)-333(Precision)-334(Complex)-1200(psb)]TJ ET q -1 0 0 1 276.854 459.045 cm +1 0 0 1 325.649 566.134 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 280.965 458.846 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-846(u)-86(p)-86(d)-86(a)-85(t)-86(e)3(=)-13(u)-101(p)-102(d)-102(a)-102(t)-102(e)]TJ +/F8 9.9626 Tf 328.638 565.934 Td [(gemlt)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Complex)-1411(psb)]TJ ET q -1 0 0 1 415.44 459.045 cm +1 0 0 1 325.649 554.178 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 419.443 458.846 Td [(t)-102(y)-102(p)-101(e)-365(,)-813(w)-52(o)-51(r)-52(k)37(=)38(w)-52(o)-52(r)-51(k)-158(\051)]TJ +/F8 9.9626 Tf 328.638 553.979 Td [(gemlt)]TJ +ET +q +1 0 0 1 183.665 550.193 cm +[]0 d 0 J 0.398 w 0 0 m 176.173 0 l S +Q 0 g 0 G +BT +/F8 9.9626 Tf 225.577 522.154 Td [(T)83(able)-333(14:)-444(Data)-334(t)28(yp)-28(es)]TJ 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -268.738 -25.406 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F27 9.9626 Tf -125.682 -37.309 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.214 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -22.895 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.214 Td [(x)]TJ + 0 -22.895 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 88.917 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -80.732 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(v)27(ector)]TJ/F11 9.9626 Tf 173.627 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -165.442 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-424(as:)-628(an)-424(ob)-56(ject)-424(of)-425(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ +/F30 9.9626 Tf 142.027 0 Td [(psb)]TJ ET q -1 0 0 1 436.673 347.39 cm +1 0 0 1 283.148 391.433 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 439.811 347.191 Td [(T)]TJ +/F30 9.9626 Tf 286.286 391.234 Td [(T)]TJ ET q -1 0 0 1 445.669 347.39 cm +1 0 0 1 292.144 391.433 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.807 347.191 Td [(vect)]TJ +/F30 9.9626 Tf 295.282 391.234 Td [(vect)]TJ ET q -1 0 0 1 470.356 347.39 cm +1 0 0 1 316.831 391.433 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.495 347.191 Td [(type)]TJ +/F30 9.9626 Tf 319.969 391.234 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ +/F8 9.9626 Tf 25.152 0 Td [(con)28(taining)-425(n)28(um)28(b)-28(ers)-425(of)]TJ -220.319 -11.955 Td [(t)28(yp)-28(e)-333(sp)-28(eci\014ed)-333(in)-334(T)84(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(15)]TJ + [-334(2)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.214 Td [(desc)]TJ +/F27 9.9626 Tf -24.907 -22.895 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(v)27(ector)]TJ/F11 9.9626 Tf 173.627 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -164.99 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-424(as:)-628(an)-424(ob)-56(ject)-424(of)-425(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 142.027 0 Td [(psb)]TJ ET q -1 0 0 1 172.619 316.221 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 283.148 308.762 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 176.057 316.022 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 286.286 308.563 Td [(T)]TJ ET q -1 0 0 1 362.845 268.401 cm +1 0 0 1 292.144 308.762 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 268.201 Td [(desc)]TJ +/F30 9.9626 Tf 295.282 308.563 Td [(vect)]TJ ET q -1 0 0 1 387.532 268.401 cm +1 0 0 1 316.831 308.762 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 268.201 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F30 9.9626 Tf 319.969 308.563 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.214 Td [(up)-32(date)]TJ +/F8 9.9626 Tf 25.152 0 Td [(con)28(taining)-425(n)28(um)28(b)-28(ers)-425(of)]TJ -220.319 -11.955 Td [(t)28(yp)-28(e)-333(sp)-28(eci\014ed)-333(in)-334(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-334(2)]TJ 0 g 0 G -/F8 9.9626 Tf 39.67 0 Td [(Up)-28(date)-333(op)-28(erator.)]TJ + [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -14.764 -31.169 Td [(up)-32(date)-383(=)-384(psb)]TJ -ET -q -1 0 0 1 244.786 218.017 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 248.223 217.818 Td [(none)]TJ +/F27 9.9626 Tf -24.907 -22.895 Td [(desc)]TJ ET q -1 0 0 1 272.62 218.017 cm +1 0 0 1 121.81 273.912 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 281.039 217.818 Td [(Do)-333(nothing;)]TJ +/F27 9.9626 Tf 125.247 273.713 Td [(a)]TJ 0 g 0 G -/F27 9.9626 Tf -105.428 -15.229 Td [(up)-32(date)-383(=)-384(psb)]TJ +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 244.786 202.789 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 276.779 226.091 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 248.223 202.589 Td [(add)]TJ +/F30 9.9626 Tf 279.917 225.892 Td [(desc)]TJ ET q -1 0 0 1 267.21 202.789 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 301.466 226.091 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 275.628 202.589 Td [(Sum)-333(o)27(v)28(erlap)-333(en)28(tries,)-334(i.e.)-444(apply)]TJ/F11 9.9626 Tf 136.544 0 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.616 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.616 Td [(;)]TJ +/F30 9.9626 Tf 304.604 225.892 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -250.617 -15.229 Td [(up)-32(date)-383(=)-384(psb)]TJ -ET -q -1 0 0 1 244.786 187.56 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 248.223 187.36 Td [(a)32(vg)]TJ -ET -q -1 0 0 1 265.937 187.56 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -BT -/F8 9.9626 Tf 274.355 187.36 Td [(Av)28(erage)-334(o)28(v)28(erlap)-333(en)27(tries,)-333(i.e.)-444(apply)]TJ/F11 9.9626 Tf 152.346 0 Td [(P)]TJ/F10 6.9738 Tf 6.396 -1.494 Td [(a)]TJ/F11 9.9626 Tf 4.82 1.494 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.616 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.616 Td [(;)]TJ -276.362 -19.214 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(update)]TJ +/F27 9.9626 Tf -225.631 -22.895 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -22.896 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(submatrix)]TJ/F11 9.9626 Tf 162.364 0 Td [(y)]TJ/F8 9.9626 Tf 5.242 0 Td [(.)]TJ -153.727 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-424(as:)-628(an)-424(ob)-56(ject)-424(of)-425(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 142.027 0 Td [(psb)]TJ ET q -1 0 0 1 245.048 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 283.148 132.48 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F11 9.9626 Tf 248.037 144.236 Td [(ty)-36(pe)]TJ/F8 9.9626 Tf 21.258 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(psb)]TJ +/F30 9.9626 Tf 286.286 132.281 Td [(T)]TJ ET q -1 0 0 1 294.367 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 292.144 132.48 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F11 9.9626 Tf 297.356 144.236 Td [(av)-36(g)]TJ +/F30 9.9626 Tf 295.282 132.281 Td [(vect)]TJ ET q -1 0 0 1 313.516 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 316.831 132.48 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 175.611 132.281 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(in)28(teger)-333(v)55(ariable.)]TJ -0 g 0 G - 141.968 -29.888 Td [(56)]TJ -0 g 0 G -ET - -endstream -endobj -1230 0 obj -<< -/Length 5866 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -BT -/F27 9.9626 Tf 99.895 706.129 Td [(w)32(ork)]TJ -0 g 0 G -/F8 9.9626 Tf 29.432 0 Td [(the)-333(w)27(ork)-333(arra)28(y)83(.)]TJ -4.525 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(one)-333(dimensional)-334(ar)1(ra)27(y)-333(of)-333(the)-334(same)-333(t)28(yp)-28(e)-333(of)]TJ/F11 9.9626 Tf 252.609 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -283.21 -19.925 Td [(On)-383(Return)]TJ +/F30 9.9626 Tf 319.969 132.281 Td [(type)]TJ 0 g 0 G -0 g 0 G - 0 -19.925 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(result)-333(matrix)]TJ/F11 9.9626 Tf 116.674 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -108.489 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-474(as:)-727(an)-475(arra)28(y)-474(of)-475(rank)-475(on)1(e)-475(or)-475(t)28(w)28(o)-475(con)28(taining)-474(n)27(u)1(m)27(b)-27(e)-1(r)1(s)-475(of)-475(t)28(yp)-28(e)]TJ 0 -11.955 Td [(sp)-28(eci\014ed)-333(in)-333(T)83(able)]TJ +/F8 9.9626 Tf 25.152 0 Td [(con)28(taining)-425(n)28(um)28(b)-28(ers)-425(of)]TJ -220.319 -11.955 Td [(the)-333(t)27(yp)-27(e)-334(indicated)-333(in)-333(T)83(able)]TJ 0 0 1 rg 0 0 1 RG - [-333(15)]TJ + [-333(14)]TJ 0 g 0 G [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ -0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ -0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ -0 g 0 G - [-500(If)-316(there)-316(is)-317(no)-316(o)28(v)28(erlap)-316(in)-316(the)-317(data)-316(distribution)-316(asso)-28(ciated)-316(with)-316(the)-316(descrip-)]TJ 12.73 -11.955 Td [(tor,)-333(no)-334(op)-27(erations)-334(are)-333(p)-28(erformed;)]TJ -0 g 0 G - -12.73 -19.926 Td [(2.)]TJ -0 g 0 G - [-500(The)-351(op)-27(erator)]TJ/F11 9.9626 Tf 73.737 0 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.616 Td [(T)]TJ/F8 9.9626 Tf 9.77 -3.616 Td [(p)-28(erforms)-350(the)-351(reduction)-351(sum)-350(of)-351(o)28(v)27(erlap)-350(elemen)28(ts)-1(;)-359(it)-351(i)1(s)-351(a)]TJ -78.557 -11.955 Td [(\134prolongation")-365(op)-28(erator)]TJ/F11 9.9626 Tf 108.923 0 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.615 Td [(T)]TJ/F8 9.9626 Tf 9.914 -3.615 Td [(that)-365(replicates)-365(o)27(v)28(erlap)-365(elemen)28(ts,)-373(accoun)27(tin)1(g)]TJ -126.617 -11.955 Td [(for)-333(the)-334(ph)28(ysical)-333(replication)-333(of)-334(data;)]TJ -0 g 0 G - -12.73 -19.925 Td [(3.)]TJ -0 g 0 G - [-500(The)-255(op)-28(erator)]TJ/F11 9.9626 Tf 71.84 0 Td [(P)]TJ/F10 6.9738 Tf 6.397 -1.495 Td [(a)]TJ/F8 9.9626 Tf 7.364 1.495 Td [(p)-28(erforms)-255(a)-256(scaling)-255(on)-256(the)-255(o)28(v)27(erlap)-255(elemen)28(ts)-256(b)28(y)-256(the)-255(amoun)28(t)]TJ -72.871 -11.956 Td 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+0 g 0 G BT -/F8 9.9626 Tf 373.771 486.412 Td [(gather)]TJ +/F8 9.9626 Tf 225.577 544.962 Td [(T)83(able)-333(16:)-444(Data)-334(t)28(yp)-28(es)]TJ +0 g 0 G +0 g 0 G +0 g 0 G +/F27 9.9626 Tf -125.682 -27.831 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -18.278 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -18.278 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(v)27(ector)]TJ/F11 9.9626 Tf 173.627 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -165.442 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-424(as:)-628(an)-424(ob)-56(ject)-424(of)-425(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 142.027 0 Td [(psb)]TJ ET q -1 0 0 1 228.797 482.626 cm -[]0 d 0 J 0.398 w 0 0 m 187.526 0 l S +1 0 0 1 283.148 432.953 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q -0 g 0 G BT -/F8 9.9626 Tf 276.386 454.587 Td [(T)83(able)-333(16:)-444(Data)-334(t)28(yp)-28(es)]TJ -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -124.304 -30.984 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.737 0 Td [(p)-123(s)-123(b)]TJ +/F30 9.9626 Tf 286.286 432.754 Td [(T)]TJ ET q -1 0 0 1 201.095 423.802 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 292.144 432.953 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 205.31 423.603 Td [(g)-123(a)-123(t)-123(h)-123(e)-123(r)-229(\050)-215(g)-110(l)-110(o)-110(b)]TJ +/F30 9.9626 Tf 295.282 432.754 Td [(vect)]TJ ET q -1 0 0 1 270.682 423.802 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 316.831 432.953 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 274.766 423.603 Td [(x)-381(,)-888(l)-127(o)-127(c)]TJ +/F30 9.9626 Tf 319.969 432.754 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 25.152 0 Td [(con)28(taining)-425(n)28(um)28(b)-28(ers)-425(of)]TJ -220.319 -11.955 Td [(t)28(yp)-28(e)-333(sp)-28(eci\014ed)-333(in)-334(T)84(able)]TJ +0 0 1 rg 0 0 1 RG + [-334(2)]TJ +0 g 0 G + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -18.278 Td [(desc)]TJ ET q -1 0 0 1 312.009 423.802 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 121.81 402.72 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F8 9.9626 Tf 316.265 423.603 Td [(x)-415(,)-874(d)-113(e)-112(s)-113(c)]TJ +/F27 9.9626 Tf 125.247 402.521 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(con)28(tains)-334(d)1(ata)-334(structures)-333(for)-333(com)-1(m)28(unications.)]TJ -10.996 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 135.658 0 Td [(psb)]TJ ET q -1 0 0 1 360.541 423.802 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 276.779 354.899 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 364.652 423.603 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-885(r)-124(o)-123(o)-124(t)-230(\051)]TJ/F27 9.9626 Tf -212.57 -11.956 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.737 0 Td [(p)-123(s)-123(b)]TJ +/F30 9.9626 Tf 279.917 354.7 Td [(desc)]TJ ET q -1 0 0 1 201.095 411.847 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 301.466 354.899 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 205.31 411.647 Td [(g)-123(a)-123(t)-123(h)-123(e)-123(r)-229(\050)-215(g)-110(l)-110(o)-110(b)]TJ +/F30 9.9626 Tf 304.604 354.7 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -225.631 -18.278 Td [(\015ag)]TJ +0 g 0 G +/F8 9.9626 Tf 22.645 0 Td [(c)28(hec)28(k)-349(if)-349(an)28(y)-349(of)-349(the)]TJ/F11 9.9626 Tf 84.074 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051)-304(=)-303(0,)-353(and)-349(in)-349(case)-349(returns)-349(error)-349(haltin)1(g)-349(the)-349(compu-)]TJ -94.813 -11.955 Td [(tation.)]TJ 0 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 43.898 0 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -116.542 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(th)1(e)-334(logical)-333(v)55(alue)]TJ/F30 9.9626 Tf 131.784 0 Td [(flag=.true.)]TJ +0 g 0 G +/F27 9.9626 Tf -156.691 -18.278 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -18.278 Td [(y)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(result)-333(submatrix)]TJ/F11 9.9626 Tf 162.364 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -154.179 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-424(as:)-628(an)-424(ob)-56(ject)-424(of)-425(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 142.027 0 Td [(psb)]TJ ET q -1 0 0 1 270.682 411.847 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 283.148 204.424 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 274.766 411.647 Td [(x)-381(,)-888(l)-127(o)-127(c)]TJ +/F30 9.9626 Tf 286.286 204.224 Td [(T)]TJ ET q -1 0 0 1 312.009 411.847 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 292.144 204.424 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 316.265 411.647 Td [(x)-415(,)-874(d)-113(e)-112(s)-113(c)]TJ +/F30 9.9626 Tf 295.282 204.224 Td [(vect)]TJ ET q -1 0 0 1 360.541 411.847 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 316.831 204.424 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 364.652 411.647 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-885(r)-124(o)-123(o)-124(t)-230(\051)]TJ -0 g 0 G +/F30 9.9626 Tf 319.969 204.224 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf 25.152 0 Td [(con)28(taining)-425(n)28(um)28(b)-28(ers)-425(of)]TJ -220.319 -11.955 Td [(the)-333(t)27(yp)-27(e)-334(indicated)-333(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(16)]TJ 0 g 0 G -/F27 9.9626 Tf -213.947 -26.424 Td [(T)32(yp)-32(e:)]TJ + [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +/F27 9.9626 Tf -24.907 -18.278 Td [(info)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.505 Td [(On)-383(En)32(try)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G -0 g 0 G - 0 -19.505 Td [(lo)-32(c)]TJ -ET -q -1 0 0 1 165.713 346.412 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 169.151 346.213 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(dense)-333(matrix)]TJ/F11 9.9626 Tf 176.117 0 Td [(g)-36(l)-20(ob)]TJ -ET -q -1 0 0 1 374.277 346.412 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F11 9.9626 Tf 377.266 346.213 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -207.349 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-56(j)1(e)-1(ct)-254(of)-255(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ -ET -q -1 0 0 1 436.673 298.592 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 439.811 298.392 Td [(T)]TJ -ET -q -1 0 0 1 445.669 298.592 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 448.807 298.392 Td [(vect)]TJ -ET -q -1 0 0 1 470.356 298.592 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 473.495 298.392 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf -297.884 -11.955 Td [(indicated)-333(in)-334(T)84(able)]TJ -0 0 1 rg 0 0 1 RG - [-334(16)]TJ -0 g 0 G - [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -19.505 Td [(desc)]TJ -ET -q -1 0 0 1 172.619 267.131 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 176.057 266.932 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ -ET -q -1 0 0 1 362.845 219.311 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 365.983 219.111 Td [(desc)]TJ -ET -q -1 0 0 1 387.532 219.311 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 390.67 219.111 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -19.505 Td [(ro)-32(ot)]TJ -0 g 0 G -/F8 9.9626 Tf 25.93 0 Td [(The)-291(pro)-28(cess)-291(that)-291(holds)-291(the)-291(global)-291(cop)28(y)83(.)-430(If)]TJ/F11 9.9626 Tf 182.523 0 Td [(r)-28(oot)]TJ/F8 9.9626 Tf 20.794 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-291(all)-291(the)-291(pro)-28(cesses)-291(will)]TJ -222.606 -11.955 Td [(ha)28(v)28(e)-334(a)-333(cop)28(y)-334(of)-333(the)-333(global)-334(v)28(ector.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable)]TJ/F14 9.9626 Tf 142.079 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F14 9.9626 Tf 7.748 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(r)-28(oot)]TJ/F14 9.9626 Tf 20.795 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1,)-333(default)]TJ/F14 9.9626 Tf 44.555 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1.)]TJ -0 g 0 G -/F27 9.9626 Tf -299.782 -19.505 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G -/F8 9.9626 Tf 166.874 -29.888 Td [(60)]TJ + 141.968 -35.732 Td [(57)]TJ 0 g 0 G ET endstream endobj -1266 0 obj +1268 0 obj << -/Length 1455 +/Length 651 >> stream 0 g 0 G 0 g 0 G -0 g 0 G -BT -/F27 9.9626 Tf 99.895 706.129 Td [(glob)]TJ -ET -q -1 0 0 1 121.587 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q BT -/F27 9.9626 Tf 125.024 706.129 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(The)-333(arra)27(y)-333(where)-333(the)-334(lo)-27(cal)-334(parts)-333(m)28(ust)-334(b)-27(e)-334(gathered.)]TJ -11.25 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(or)-334(t)28(w)28(o)-334(arra)28(y)-333(with)-333(the)]TJ/F30 9.9626 Tf 204.4 0 Td [(ALLOCATABLE)]TJ/F8 9.9626 Tf 60.855 0 Td [(attribute.)]TJ -0 g 0 G -/F27 9.9626 Tf -290.162 -19.925 Td [(info)]TJ +/F16 14.3462 Tf 150.705 706.129 Td [(5)-1125(Comm)31(unication)-375(routines)]TJ/F8 9.9626 Tf 0 -21.821 Td [(The)-283(routines)-283(in)-283(this)-283(c)28(hapter)-283(implemen)28(t)-283(v)55(arious)-283(global)-283(comm)28(unication)-283(op)-28(erators)]TJ 0 -11.955 Td [(on)-344(v)28(ectors)-344(asso)-27(c)-1(iated)-343(with)-344(a)-344(d)1(is)-1(cretization)-343(mesh.)-476(F)84(or)-344(auxiliary)-344(comm)28(unication)]TJ 0 -11.955 Td [(routines)-333(not)-334(tied)-333(to)-333(a)-334(d)1(is)-1(cretization)-333(space)-333(see)]TJ +0 0 1 rg 0 0 1 RG + [-334(6)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 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[(These)-333(s)-1(u)1(broutines)-334(gathers)-333(the)-333(v)55(alues)-333(of)-334(th)1(e)-334(halo)-333(elemen)28(ts:)]TJ/F11 9.9626 Tf 158.413 -23.188 Td [(x)]TJ/F14 9.9626 Tf 8.462 0 Td [(\040)]TJ/F11 9.9626 Tf 12.73 0 Td [(x)]TJ/F8 9.9626 Tf -179.605 -21.251 Td [(where:)]TJ 0 g 0 G -/F11 9.9626 Tf -268.562 -21.839 Td [(scatter)]TJ +/F11 9.9626 Tf 0 -19.391 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 35.834 0 Td [(is)-333(the)-334(scatter)-333(function.)]TJ +/F8 9.9626 Tf 10.676 0 Td [(is)-333(a)-334(global)-333(dense)-333(submatrix.)]TJ 0 g 0 G 0 g 0 G 0 g 0 G ET q -1 0 0 1 228.797 539.65 cm +1 0 0 1 177.988 602.649 cm []0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F11 9.9626 Tf 234.775 531.082 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F11 9.9626 Tf 3.317 1.494 Td [(;)-167(y)]TJ/F27 9.9626 Tf 111.399 0 Td [(Subroutine)]TJ +/F11 9.9626 Tf 183.966 594.081 Td [(\013)]TJ/F8 9.9626 Tf 6.41 0 Td [(,)]TJ/F11 9.9626 Tf 6.088 0 Td [(x)]TJ/F27 9.9626 Tf 107.911 0 Td [(Subroutine)]TJ ET q -1 0 0 1 228.797 527.296 cm +1 0 0 1 177.988 590.295 cm []0 d 0 J 0.398 w 0 0 m 187.526 0 l S Q BT -/F8 9.9626 Tf 234.775 518.729 Td [(In)28(teger)-9028(psb)]TJ +/F8 9.9626 Tf 183.966 581.727 Td [(In)28(teger)-9028(psb)]TJ ET q -1 0 0 1 370.782 518.928 cm +1 0 0 1 319.972 581.926 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.771 518.729 Td [(scatter)]TJ -138.996 -11.956 Td [(Short)-333(Precision)-334(Real)-3102(psb)]TJ +/F8 9.9626 Tf 322.961 581.727 Td [(halo)]TJ -138.995 -11.955 Td [(Short)-333(Precision)-333(R)-1(eal)-3102(psb)]TJ ET q -1 0 0 1 370.782 506.973 cm +1 0 0 1 319.972 569.971 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 373.771 506.773 Td [(scatter)]TJ -138.996 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(psb)]TJ +/F8 9.9626 Tf 322.961 569.772 Td [(halo)]TJ -138.995 -11.955 Td [(Long)-333(Precision)-334(Real)-3314(p)1(s)-1(b)]TJ ET q -1 0 0 1 370.782 495.017 cm +1 0 0 1 319.972 558.016 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 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ET q -1 0 0 1 317.987 406.021 cm +1 0 0 1 150.256 460.971 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 322.243 405.822 Td [(x)-415(,)-874(d)-113(e)-112(s)-113(c)]TJ +/F8 9.9626 Tf 154.464 460.772 Td [(h)-122(a)-123(l)-122(o)-228(\050)-130(x)-209(,)-874(d)-112(e)-113(s)-113(c)]TJ ET q -1 0 0 1 366.519 406.021 cm +1 0 0 1 226.044 460.971 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F8 9.9626 Tf 370.63 405.822 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-864(r)-103(o)-103(o)-104(t)-367(,)-808(m)-47(o)-46(l)-47(d)-152(\051)]TJ +/F8 9.9626 Tf 230.155 460.772 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-804(w)-43(o)-43(r)-43(k)-247(,)]TJ/F27 9.9626 Tf 91.304 0 Td [(d)-39(a)-39(t)-40(a)]TJ/F8 9.9626 Tf 24.571 0 Td [(\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F27 9.9626 Tf -219.925 -30.766 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -246.135 -26.961 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -21.84 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.659 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -21.839 Td [(glob)]TJ + 0 -19.658 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 88.917 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -80.732 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)27(o)-254(arra)27(y)-254(or)-255(an)-255(ob)-55(jec)-1(t)-254(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.743 0 Td [(psb)]TJ ET q -1 0 0 1 172.397 331.576 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 385.864 346.872 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 175.834 331.377 Td [(x)]TJ +/F30 9.9626 Tf 389.002 346.673 Td [(T)]TJ +ET +q +1 0 0 1 394.86 346.872 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 397.998 346.673 Td [(vect)]TJ +ET +q +1 0 0 1 419.547 346.872 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 422.685 346.673 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(The)-333(arra)27(y)-333(that)-333(m)28(ust)-334(b)-27(e)-334(scattered)-333(in)28(to)-334(lo)-28(cal)-333(pieces.)]TJ -11.251 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(or)-333(t)28(w)28(o)-334(arra)28(y)84(.)]TJ +/F8 9.9626 Tf -297.883 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)28(yp)-28(e)-334(sp)-27(eci\014ed)-334(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(17)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -21.839 Td [(desc)]TJ + [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.658 Td [(desc)]TJ ET q -1 0 0 1 172.619 261.916 cm +1 0 0 1 121.81 315.259 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 261.717 Td [(a)]TJ +/F27 9.9626 Tf 125.247 315.06 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 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Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-222(as:)-389(a)-222(ob)-56(ject)-222(of)-222(t)28(yp)-28(e)-222(deriv)28(e)-1(d)-222(from)-222(\050in)28(teger\051)]TJ/F30 9.9626 Tf 219.871 0 Td [(psb)]TJ +/F8 9.9626 Tf 206.027 458.846 Td [(o)-137(v)-138(r)-137(l)-243(\050)-130(x)-209(,)-874(d)-113(e)-112(s)-113(c)]TJ ET q -1 0 0 1 411.8 510.604 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 276.854 459.045 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 280.965 458.846 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-846(u)-86(p)-86(d)-86(a)-85(t)-86(e)3(=)-13(u)-101(p)-102(d)-102(a)-102(t)-102(e)]TJ +ET +q +1 0 0 1 415.44 459.045 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 414.939 510.405 Td [(T)]TJ +/F8 9.9626 Tf 419.443 458.846 Td [(t)-102(y)-102(p)-101(e)-365(,)-813(w)-52(o)-51(r)-52(k)37(=)38(w)-52(o)-52(r)-51(k)-158(\051)]TJ +0 g 0 G +0 g 0 G +0 g 0 G +/F27 9.9626 Tf -268.738 -25.406 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.214 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.214 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(matrix)]TJ/F11 9.9626 Tf 88.917 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -80.732 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-255(rank)-254(one)-255(or)-255(t)28(w)28(o)-255(arra)28(y)-255(or)-255(an)-255(ob)-55(ject)-255(of)-255(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 244.742 0 Td [(psb)]TJ ET q -1 0 0 1 420.797 510.604 cm +1 0 0 1 436.673 347.39 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 423.935 510.405 Td [(base)]TJ +/F30 9.9626 Tf 439.811 347.191 Td [(T)]TJ ET q -1 0 0 1 445.484 510.604 cm +1 0 0 1 445.669 347.39 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 448.622 510.405 Td [(vect)]TJ +/F30 9.9626 Tf 448.807 347.191 Td [(vect)]TJ ET q -1 0 0 1 470.171 510.604 cm +1 0 0 1 470.356 347.39 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 473.309 510.405 Td [(type)]TJ/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F30 9.9626 Tf 473.495 347.191 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -343.526 -21.918 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf -297.884 -11.955 Td [(con)28(taining)-333(n)27(um)28(b)-28(ers)-333(of)-333(t)27(yp)-27(e)-334(sp)-27(ec)-1(i)1(\014ed)-334(in)-333(T)83(able)]TJ +0 0 1 rg 0 0 1 RG + [-333(18)]TJ 0 g 0 G + [(.)]TJ 0 g 0 G - 0 -19.926 Td [(desc)]TJ +/F27 9.9626 Tf -24.906 -19.214 Td [(desc)]TJ ET q -1 0 0 1 172.619 468.761 cm +1 0 0 1 172.619 316.221 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 468.561 Td [(a)]TJ +/F27 9.9626 Tf 176.057 316.022 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 362.845 420.94 cm +1 0 0 1 362.845 268.401 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 420.741 Td [(desc)]TJ +/F30 9.9626 Tf 365.983 268.201 Td [(desc)]TJ ET q -1 0 0 1 387.532 420.94 cm +1 0 0 1 387.532 268.401 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 420.741 Td [(type)]TJ +/F30 9.9626 Tf 390.67 268.201 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.926 Td [(info)]TJ -0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 11.9552 Tf -24.906 -21.918 Td [(Notes)]TJ -0 g 0 G -/F8 9.9626 Tf 12.176 -19.925 Td [(1.)]TJ -0 g 0 G - [-500(On)-333(exit)-334(from)-333(this)-333(routine)-333(the)-334(descriptor)-333(is)-333(in)-334(the)-333(assem)28(bled)-334(state.)]TJ -0 g 0 G - 154.698 -220.714 Td [(70)]TJ -0 g 0 G -ET - -endstream -endobj -1334 0 obj -<< -/Length 3277 ->> -stream +/F27 9.9626 Tf -260.887 -19.214 Td [(up)-32(date)]TJ 0 g 0 G +/F8 9.9626 Tf 39.67 0 Td [(Up)-28(date)-333(op)-28(erator.)]TJ 0 g 0 G -BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F27 9.9626 Tf -14.764 -31.169 Td [(up)-32(date)-383(=)-384(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 244.786 218.017 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(cdcp)31(y)-375(|)-375(Copies)-375(a)-375(comm)31(unication)-375(descriptor)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_cdcpy\050desc_in,)-525(desc_out,)-525(info\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -19.925 Td [(desc)]TJ +/F27 9.9626 Tf 248.223 217.818 Td [(none)]TJ ET q -1 0 0 1 121.81 626.17 cm +1 0 0 1 272.62 218.017 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q +0 g 0 G BT -/F27 9.9626 Tf 125.247 625.971 Td [(in)]TJ +/F8 9.9626 Tf 281.039 217.818 Td [(Do)-333(nothing;)]TJ 0 g 0 G -/F8 9.9626 Tf 14.529 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -14.974 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F27 9.9626 Tf -105.428 -15.229 Td [(up)-32(date)-383(=)-384(psb)]TJ ET q -1 0 0 1 312.036 578.35 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 244.786 202.789 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 315.174 578.15 Td [(desc)]TJ +/F27 9.9626 Tf 248.223 202.589 Td [(add)]TJ ET q -1 0 0 1 336.723 578.35 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 267.21 202.789 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q -BT -/F30 9.9626 Tf 339.861 578.15 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -21.917 Td [(On)-383(Return)]TJ 0 g 0 G +BT +/F8 9.9626 Tf 275.628 202.589 Td [(Sum)-333(o)27(v)28(erlap)-333(en)28(tries,)-334(i.e.)-444(apply)]TJ/F11 9.9626 Tf 136.544 0 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.616 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.616 Td [(;)]TJ 0 g 0 G - 0 -19.926 Td [(desc)]TJ +/F27 9.9626 Tf -250.617 -15.229 Td [(up)-32(date)-383(=)-384(psb)]TJ ET q -1 0 0 1 121.81 536.507 cm +1 0 0 1 244.786 187.56 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 536.307 Td [(out)]TJ +/F27 9.9626 Tf 248.223 187.36 Td [(a)32(vg)]TJ +ET +q +1 0 0 1 265.937 187.56 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q 0 g 0 G -/F8 9.9626 Tf 21.53 0 Td [(the)-333(comm)27(unication)-333(descriptor)-333(cop)28(y)83(.)]TJ -21.975 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +BT +/F8 9.9626 Tf 274.355 187.36 Td [(Av)28(erage)-334(o)28(v)28(erlap)-333(en)27(tries,)-333(i.e.)-444(apply)]TJ/F11 9.9626 Tf 152.346 0 Td [(P)]TJ/F10 6.9738 Tf 6.396 -1.494 Td [(a)]TJ/F11 9.9626 Tf 4.82 1.494 Td [(P)]TJ/F10 6.9738 Tf 7.78 3.616 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.616 Td [(;)]TJ -276.362 -19.214 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(update)]TJ ET q -1 0 0 1 312.036 488.686 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 245.048 144.435 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 315.174 488.487 Td [(desc)]TJ +/F11 9.9626 Tf 248.037 144.236 Td [(ty)-36(pe)]TJ/F8 9.9626 Tf 21.258 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(psb)]TJ ET q -1 0 0 1 336.723 488.686 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 294.367 144.435 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 339.861 488.487 Td [(type)]TJ +/F11 9.9626 Tf 297.356 144.236 Td [(av)-36(g)]TJ +ET +q +1 0 0 1 313.516 144.435 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 175.611 132.281 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(in)28(teger)-333(v)55(ariable.)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -19.926 Td [(info)]TJ -0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ -0 g 0 G - 141.968 -330.303 Td [(71)]TJ + 141.968 -29.888 Td [(62)]TJ 0 g 0 G ET endstream endobj -1339 0 obj +1320 0 obj << -/Length 2243 +/Length 5866 >> stream 0 g 0 G 0 g 0 G +0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 171.761 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 175.796 706.129 Td [(cdfree)-375(|)-375(F)94(rees)-375(a)-375(comm)31(unication)-375(descriptor)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(w)32(ork)]TJ 0 g 0 G +/F8 9.9626 Tf 29.432 0 Td [(the)-333(w)27(ork)-333(arra)28(y)83(.)]TJ -4.525 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(one)-333(dimensional)-334(ar)1(ra)27(y)-333(of)-333(the)-334(same)-333(t)28(yp)-28(e)-333(of)]TJ/F11 9.9626 Tf 252.609 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ 0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_cdfree\050desc_a,)-525(info\051)]TJ +/F27 9.9626 Tf -283.21 -19.925 Td [(On)-383(Return)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ + 0 -19.925 Td [(x)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F8 9.9626 Tf 11.028 0 Td [(global)-333(dense)-334(result)-333(matrix)]TJ/F11 9.9626 Tf 116.674 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ -108.489 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 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-43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(t)27(yp)-27(e.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -21.484 Td [(desc)]TJ +/F27 9.9626 Tf -124.304 -33.261 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.99 0 Td [(p)-148(s)-149(b)]TJ ET q -1 0 0 1 121.81 504.47 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 202.107 406.021 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F27 9.9626 Tf 125.247 504.27 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F8 9.9626 Tf 206.575 405.822 Td [(s)-149(c)-148(a)-149(t)-148(t)-148(e)-149(r)-254(\050)-215(g)-110(l)-110(o)-110(b)]TJ ET q -1 0 0 1 312.036 456.649 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 276.66 406.021 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 315.174 456.45 Td [(Tspmat)]TJ +/F8 9.9626 Tf 280.744 405.822 Td [(x)-381(,)-888(l)-127(o)-127(c)]TJ ET q -1 0 0 1 347.183 456.649 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 317.987 406.021 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 350.322 456.45 Td [(type)]TJ +/F8 9.9626 Tf 322.243 405.822 Td [(x)-415(,)-874(d)-113(e)-112(s)-113(c)]TJ +ET +q +1 0 0 1 366.519 406.021 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 370.63 405.822 Td [(a)-386(,)-888(i)-127(n)-127(f)-127(o)-415(,)-864(r)-103(o)-103(o)-104(t)-367(,)-808(m)-47(o)-46(l)-47(d)-152(\051)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -271.348 -21.484 Td [(nl)]TJ 0 g 0 G -/F8 9.9626 Tf 14.529 0 Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(additional)-333(la)28(y)27(ers)-333(desired.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F11 9.9626 Tf 130.428 0 Td [(nl)]TJ/F14 9.9626 Tf 11.916 0 Td [(\025)]TJ/F8 9.9626 Tf 10.516 0 Td [(0.)]TJ +/F27 9.9626 Tf -219.925 -30.766 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F27 9.9626 Tf -177.767 -21.483 Td [(ext)32(yp)-32(e)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 38.398 0 Td [(the)-333(kind)-334(of)-333(estension)-333(required.)]TJ -13.491 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 44.396 0 Td [(.)]TJ -69.579 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-419(as:)-616(an)-420(in)28(teger)-419(v)55(alue)]TJ/F30 9.9626 Tf 135.566 0 Td [(psb_ovt_xhal_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 7.159 0 Td [(psb_ovt_asov_)]TJ/F8 9.9626 Tf 67.995 0 Td [(,)-441(default:)]TJ/F30 9.9626 Tf -278.714 -11.955 Td [(psb_ovt_xhal_)]TJ +/F27 9.9626 Tf -33.797 -21.84 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -23.476 Td [(On)-383(Return)]TJ 0 g 0 G + 0 -21.839 Td [(glob)]TJ +ET +q +1 0 0 1 172.397 331.576 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 175.834 331.377 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(The)-333(arra)27(y)-333(that)-333(m)28(ust)-334(b)-27(e)-334(scattered)-333(in)28(to)-334(lo)-28(cal)-333(pieces.)]TJ -11.251 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(or)-333(t)28(w)28(o)-334(arra)28(y)84(.)]TJ 0 g 0 G - 0 -21.484 Td [(desc)]TJ +/F27 9.9626 Tf -24.906 -21.839 Td [(desc)]TJ ET q -1 0 0 1 121.81 261.126 cm +1 0 0 1 172.619 261.916 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 260.927 Td [(out)]TJ +/F27 9.9626 Tf 176.057 261.717 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 21.53 0 Td [(the)-333(extended)-334(comm)28(unication)-333(descriptor.)]TJ -21.975 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 213.305 cm +1 0 0 1 362.845 214.095 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 213.106 Td [(desc)]TJ +/F30 9.9626 Tf 365.983 213.896 Td [(desc)]TJ ET q -1 0 0 1 336.723 213.305 cm +1 0 0 1 387.532 214.095 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 339.861 213.106 Td [(type)]TJ +/F30 9.9626 Tf 390.67 213.896 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -21.484 Td [(info)]TJ +/F27 9.9626 Tf -260.887 -21.839 Td [(ro)-32(ot)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -23.476 Td [(Notes)]TJ +/F8 9.9626 Tf 25.93 0 Td [(The)-420(pro)-27(ce)-1(ss)-419(that)-420(holds)-419(the)-420(global)-420(cop)28(y)83(.)-703(If)]TJ/F11 9.9626 Tf 194.21 0 Td [(r)-28(oot)]TJ/F8 9.9626 Tf 22.228 0 Td [(=)]TJ/F14 9.9626 Tf 11.949 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-420(all)-419(the)-420(pro)-28(cesses)]TJ -237.16 -11.956 Td [(ha)28(v)28(e)-334(a)-333(cop)28(y)-334(of)-333(the)-333(global)-334(v)28(ector.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-344(as)-1(:)-467(an)-344(in)28(tege)-1(r)-344(v)55(ariabl)1(e)]TJ/F14 9.9626 Tf 142.757 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F14 9.9626 Tf 7.937 0 Td [(\024)]TJ/F11 9.9626 Tf 10.705 0 Td [(r)-28(oot)]TJ/F14 9.9626 Tf 20.983 0 Td [(\024)]TJ/F11 9.9626 Tf 10.704 0 Td [(np)]TJ/F14 9.9626 Tf 13.282 0 Td [(\000)]TJ/F8 9.9626 Tf 10.038 0 Td [(1,)-347(default)]TJ/F30 9.9626 Tf 44.809 0 Td [(psb_root_)]TJ/F8 9.9626 Tf 47.073 0 Td [(,)]TJ -316.037 -11.955 Td [(i.e.)-444(pro)-28(cess)-334(0.)]TJ 0 g 0 G -/F8 9.9626 Tf 166.875 -29.888 Td [(73)]TJ + 141.968 -29.888 Td [(68)]TJ 0 g 0 G ET endstream endobj -1351 0 obj +1372 0 obj << -/Length 1587 +/Length 4181 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F8 9.9626 Tf 162.881 706.129 Td [(1.)]TJ -0 g 0 G - [-500(Sp)-28(ecifying)]TJ/F30 9.9626 Tf 60.092 0 Td [(psb_ovt_xhal_)]TJ/F8 9.9626 Tf 70.801 0 Td [(for)-282(the)]TJ/F30 9.9626 Tf 31.376 0 Td [(extype)]TJ/F8 9.9626 Tf 34.189 0 Td [(argumen)28(t)-282(the)-282(u)1(s)-1(er)-281(will)-282(obtain)-281(a)]TJ -183.728 -11.955 Td [(descriptor)-258(for)-257(a)-258(domain)-257(partition)-258(in)-257(whic)28(h)-258(the)-257(additional)-258(la)28(y)28(ers)-258(are)-257(fetc)27(hed)]TJ 0 -11.955 Td [(as)-415(part)-415(of)-415(an)-415(\050extended\051)-415(halo;)-456(ho)28(w)27(ev)28(er)-415(the)-415(index-to-pro)-28(cess)-415(mapping)-415(is)]TJ 0 -11.956 Td [(iden)28(tical)-334(to)-333(that)-333(of)-333(the)-334(base)-333(descriptor;)]TJ -0 g 0 G - -12.73 -19.925 Td [(2.)]TJ -0 g 0 G - [-500(Sp)-28(ecifying)]TJ/F30 9.9626 Tf 60.957 0 Td [(psb_ovt_asov_)]TJ/F8 9.9626 Tf 71.666 0 Td [(for)-368(the)]TJ/F30 9.9626 Tf 33.108 0 Td [(extype)]TJ/F8 9.9626 Tf 35.053 0 Td [(argumen)28(t)-369(the)-368(user)-369(will)-368(obtain)]TJ -188.054 -11.955 Td [(a)-458(descriptor)-459(with)-458(an)-458(o)28(v)27(erlapp)-27(ed)-459(decomp)-28(osition:)-694(the)-458(additional)-458(la)27(y)28(er)-458(is)]TJ 0 -11.955 Td [(aggregated)-413(to)-413(the)-414(l)1(o)-28(cal)-413(sub)-28(domain)-413(\050and)-413(th)27(u)1(s)-414(is)-413(an)-413(o)28(v)28(erlap\051,)-433(and)-413(a)-414(new)]TJ 0 -11.955 Td [(halo)-333(extending)-334(b)-27(ey)27(ond)-333(the)-333(last)-334(ad)1(ditional)-334(la)28(y)28(er)-333(is)-334(formed.)]TJ -0 g 0 G - 141.968 -524.035 Td [(74)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(mold)]TJ 0 g 0 G +/F8 9.9626 Tf 29.805 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(v)27(ector)-333(storage.)]TJ -4.898 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-273(as:)-414(an)-274(ob)-55(ject)-273(of)-274(a)-273(class)-273(deriv)28(ed)-274(from)]TJ/F30 9.9626 Tf 198.26 0 Td [(psb)]TJ ET - -endstream -endobj -1359 0 obj -<< -/Length 4887 ->> -stream -0 g 0 G -0 g 0 G +q +1 0 0 1 339.381 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F30 9.9626 Tf 342.519 658.308 Td [(T)]TJ ET q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 348.377 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(spall)-375(|)-375(Allo)-31(cates)-375(a)-375(sparse)-375(matrix)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_spall\050a,)-525(desc_a,)-525(info,)-525(nnz\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ +/F30 9.9626 Tf 351.515 658.308 Td [(base)]TJ +ET +q +1 0 0 1 373.064 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 376.202 658.308 Td [(vect)]TJ +ET +q +1 0 0 1 397.751 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 400.89 658.308 Td [(type)]TJ/F8 9.9626 Tf 20.921 0 Td [(;)-293(this)]TJ -297.009 -11.955 Td [(is)-333(only)-334(allo)28(w)28(ed)-333(when)-334(lo)-27(c)]TJ +ET +q +1 0 0 1 231.17 646.552 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 234.159 646.353 Td [(x)-333(is)-334(of)-333(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 52.359 0 Td [(psb)]TJ +ET +q +1 0 0 1 302.837 646.552 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 305.975 646.353 Td [(T)]TJ +ET +q +1 0 0 1 311.833 646.552 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 314.971 646.353 Td [(vect)]TJ +ET +q +1 0 0 1 336.52 646.552 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 339.658 646.353 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf 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[(Sp)-28(eci\014ed)-333(as:)-444(a)-1(n)-333(in)28(teger)-333(v)55(alue.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -22.903 Td [(irw)]TJ +/F27 9.9626 Tf -24.907 -19.201 Td [(vg)]TJ 0 g 0 G -/F8 9.9626 Tf 21.157 0 Td [(the)-333(\014rst)-334(ro)28(w)-333(to)-333(b)-28(e)-334(inserted.)]TJ 3.749 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(sc)-1(alar)1(.)]TJ +/F8 9.9626 Tf 16.757 0 Td [(Data)-333(allo)-28(cation:)-444(eac)27(h)-333(index)]TJ/F11 9.9626 Tf 123.564 0 Td [(i)]TJ/F14 9.9626 Tf 6.2 0 Td [(2)-278(f)]TJ/F8 9.9626 Tf 14.39 0 Td [(1)]TJ/F11 9.9626 Tf 6.642 0 Td [(:)-167(:)-166(:)-167(mg)]TJ/F14 9.9626 Tf 27.14 0 Td [(g)]TJ/F8 9.9626 Tf 8.302 0 Td [(is)-333(allo)-28(cated)-334(t)1(o)-334(pro)-28(cess)]TJ/F11 9.9626 Tf 99.267 0 Td [(v)-36(g)]TJ/F8 9.9626 Tf 10.296 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.433 0 Td [(\051.)]TJ -294.958 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -57.707 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -22.903 Td [(ia)]TJ +/F27 9.9626 Tf -24.907 -19.201 Td [(\015ag)]TJ 0 g 0 G -/F8 9.9626 Tf 13.733 0 Td [(the)-333(ro)27(w)-333(indices)-333(of)-334(th)1(e)-334(co)-28(e\016cien)28(ts)-333(to)-334(b)-27(e)-334(inserted.)]TJ 11.173 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 160.98 0 Td [(nz)]TJ/F8 9.9626 Tf 11.052 0 Td [(.)]TJ +/F8 9.9626 Tf 22.644 0 Td [(Sp)-28(eci\014es)-333(whether)-333(e)-1(n)28(tries)-333(in)]TJ/F11 9.9626 Tf 121.932 0 Td [(v)-36(g)]TJ/F8 9.9626 Tf 13.617 0 Td [(are)-333(zero-)-334(or)-333(one-based.)]TJ -133.286 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)-333(0)]TJ/F11 9.9626 Tf 135.409 0 Td [(;)]TJ/F8 9.9626 Tf 4.428 0 Td [(1,)-333(default)-334(0.)]TJ 0 g 0 G -/F27 9.9626 Tf -196.938 -22.903 Td [(irp)]TJ +/F27 9.9626 Tf -164.744 -19.2 Td [(mg)]TJ 0 g 0 G -/F8 9.9626 Tf 19.247 0 Td [(the)-333(ro)27(w)-333(p)-28(oin)28(ters)-333(of)-333(the)-334(co)-28(e\016cien)28(ts)-333(to)-334(b)-27(e)-334(inserted.)]TJ 5.659 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 160.98 0 Td [(nr)]TJ/F8 9.9626 Tf 12.966 0 Td [(+)-222(1.)]TJ +/F8 9.9626 Tf 20.257 0 Td [(the)-333(\050global\051)-334(n)28(um)28(b)-28(er)-333(of)-333(ro)27(ws)-333(of)-333(the)-334(probl)1(e)-1(m.)]TJ 4.65 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-332(as:)-444(an)-333(in)28(teger)-333(v)56(alue.)-444(I)-1(t)-332(is)-333(required)-332(if)]TJ/F30 9.9626 Tf 203.266 0 Td [(parts)]TJ/F8 9.9626 Tf 29.465 0 Td [(or)]TJ/F30 9.9626 Tf 12.198 0 Td [(repl)]TJ/F8 9.9626 Tf 24.235 0 Td [(is)-333(sp)-27(ec)-1(i)1(\014e)-1(d)1(,)]TJ -269.164 -11.955 Td [(it)-333(is)-334(optional)-333(if)]TJ/F30 9.9626 Tf 67.856 0 Td [(vg)]TJ/F8 9.9626 Tf 13.782 0 Td [(is)-333(sp)-28(eci\014ed.)]TJ 0 g 0 G -/F27 9.9626 Tf -198.852 -22.903 Td [(ja)]TJ +/F27 9.9626 Tf -106.545 -19.201 Td [(parts)]TJ 0 g 0 G -/F8 9.9626 Tf 14.051 0 Td [(the)-333(column)-334(indices)-333(of)-333(the)-334(co)-27(e)-1(\016cien)28(ts)-333(to)-333(b)-28(e)-334(inserted.)]TJ 10.855 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(size)]TJ/F11 9.9626 Tf 160.98 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)]TJ +/F8 9.9626 Tf 30.609 0 Td [(the)-333(subroutine)-334(th)1(at)-334(de\014nes)-333(the)-333(partitioning)-334(sc)28(heme.)]TJ -5.702 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -57.707 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.081 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(subroutine.)]TJ 0 g 0 G -/F27 9.9626 Tf -196.937 -22.903 Td [(v)64(al)]TJ +/F27 9.9626 Tf -24.907 -19.201 Td [(vl)]TJ 0 g 0 G -/F8 9.9626 Tf 19.143 0 Td [(the)-333(co)-28(e\016cien)28(ts)-334(to)-333(b)-28(e)-333(inserted.)]TJ 5.763 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-375(as:)-528(an)-375(arra)28(y)-375(of)-375(size)]TJ/F11 9.9626 Tf 130.933 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)-570(Must)-375(b)-28(e)-375(of)-375(the)-375(same)-375(t)28(yp)-28(e)-375(and)-375(kind)-375(of)]TJ -141.984 -11.956 Td [(the)-333(co)-28(e\016cien)27(ts)-333(of)-333(the)-334(spar)1(s)-1(e)-333(matrix)]TJ/F11 9.9626 Tf 158.517 0 Td [(a)]TJ/F8 9.9626 Tf 5.266 0 Td [(.)]TJ +/F8 9.9626 Tf 14.211 0 Td [(Data)-363(allo)-28(cation:)-504(the)-363(set)-364(of)-363(global)-363(indices)]TJ/F11 9.9626 Tf 182.789 0 Td [(v)-36(l)]TJ/F8 9.9626 Tf 8.355 0 Td [(\0501)-328(:)]TJ/F11 9.9626 Tf 18.15 0 Td [(nl)]TJ/F8 9.9626 Tf 9.149 0 Td [(\051)-363(b)-28(elonging)-363(to)-363(the)-364(callin)1(g)]TJ -207.747 -11.955 Td [(pro)-28(cess.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.074 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ 0 g 0 G - -21.815 -29.887 Td [(76)]TJ + 141.967 -29.888 Td [(70)]TJ 0 g 0 G ET endstream endobj -1373 0 obj +1381 0 obj << -/Length 7378 +/Length 6638 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F27 9.9626 Tf 99.895 706.129 Td [(desc)]TJ +/F27 9.9626 Tf 99.895 706.129 Td [(nl)]TJ +0 g 0 G +/F8 9.9626 Tf 14.529 0 Td [(Data)-223(allo)-28(cation:)-389(in)-222(a)-223(generalized)-223(blo)-28(c)28(k-ro)28(w)-223(distribution)-223(the)-222(n)27(um)28(b)-28(er)-222(of)-223(indices)]TJ 10.378 -11.955 Td [(b)-28(elonging)-333(to)-333(the)-334(curren)28(t)-333(pro)-28(cess.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)-444(Ma)28(y)-334(b)-27(e)-334(sp)-28(eci\014ed)-333(together)-333(with)]TJ/F30 9.9626 Tf 272.479 0 Td [(vl)]TJ/F8 9.9626 Tf 10.46 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -307.846 -20.135 Td [(repl)]TJ +0 g 0 G +/F8 9.9626 Tf 24.499 0 Td [(Data)-351(allo)-28(cation:)-480(build)-351(a)-351(replicated)-351(index)-351(space)-351(\050i.e.)-498(all)-351(pro)-28(cesses)-351(o)27(wn)-351(all)]TJ 0.408 -11.955 Td [(indices\051.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(th)1(e)-334(logical)-333(v)55(alue)]TJ/F30 9.9626 Tf 131.784 0 Td [(.true.)]TJ +0 g 0 G +/F27 9.9626 Tf -156.691 -20.135 Td [(globalc)32(hec)32(k)]TJ +0 g 0 G +/F8 9.9626 Tf 61.948 0 Td [(Data)-333(allo)-28(cation:)-445(d)1(o)-334(global)-333(c)28(hec)27(ks)-333(on)-333(the)-334(lo)-27(cal)-334(index)-333(lists)]TJ/F30 9.9626 Tf 250.201 0 Td [(vl)]TJ/F8 9.9626 Tf -287.242 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(v)55(alue,)-333(default:)]TJ/F30 9.9626 Tf 163.056 0 Td [(.false.)]TJ +0 g 0 G +/F27 9.9626 Tf -187.963 -20.135 Td [(lidx)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Data)-353(allo)-28(cation:)-484(the)-353(set)-353(of)-353(lo)-28(cal)-353(indices)]TJ/F11 9.9626 Tf 176.172 0 Td [(l)-20(idx)]TJ/F8 9.9626 Tf 17.48 0 Td [(\0501)-311(:)]TJ/F11 9.9626 Tf 17.814 0 Td [(nl)]TJ/F8 9.9626 Tf 9.149 0 Td [(\051)-353(to)-353(b)-28(e)-353(assigned)-353(to)-353(the)]TJ -219.466 -11.955 Td [(global)-333(indices)]TJ/F11 9.9626 Tf 62.045 0 Td [(v)-36(l)]TJ/F8 9.9626 Tf 8.355 0 Td [(.)]TJ -70.4 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -22.127 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -20.135 Td [(desc)]TJ ET q -1 0 0 1 121.81 706.328 cm +1 0 0 1 121.81 376.512 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 706.129 Td [(a)]TJ +/F27 9.9626 Tf 125.247 376.313 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(The)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)56(ariable)-334(of)-333(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 137.346 0 Td [(psb)]TJ +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 278.467 658.507 cm +1 0 0 1 312.036 328.692 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 281.605 658.308 Td [(desc)]TJ +/F30 9.9626 Tf 315.174 328.492 Td [(desc)]TJ ET q -1 0 0 1 303.154 658.507 cm +1 0 0 1 336.723 328.692 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 306.292 658.308 Td [(type)]TJ +/F30 9.9626 Tf 339.861 328.492 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -227.319 -31.349 Td [(lo)-32(cal)]TJ +/F27 9.9626 Tf -260.887 -20.135 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 28.055 0 Td [(Whether)-465(the)-464(en)27(tr)1(ie)-1(s)-464(in)-465(the)-465(in)1(dice)-1(s)-464(v)28(ec)-1(tor)1(s)]TJ/F30 9.9626 Tf 194.825 0 Td [(ia)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)]TJ/F30 9.9626 Tf 7.724 0 Td [(ja)]TJ/F8 9.9626 Tf 15.09 0 Td [(are)-465(already)-464(in)-465(lo)-28(cal)]TJ -231.248 -11.955 Td [(n)28(um)28(b)-28(ering.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(v)55(alue;)-333(default:)]TJ/F30 9.9626 Tf 163.056 0 Td [(.false.)]TJ/F8 9.9626 Tf 36.612 0 Td [(.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -22.128 Td [(Notes)]TJ 0 g 0 G -/F27 9.9626 Tf -224.575 -20.589 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 12.177 -20.082 Td [(1.)]TJ 0 g 0 G + [-500(One)-241(of)-241(the)-240(optional)-241(argumen)28(ts)]TJ/F30 9.9626 Tf 144.914 0 Td [(parts)]TJ/F8 9.9626 Tf 26.152 0 Td [(,)]TJ/F30 9.9626 Tf 5.351 0 Td [(vg)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)]TJ/F30 9.9626 Tf 5.351 0 Td [(vl)]TJ/F8 9.9626 Tf 10.46 0 Td [(,)]TJ/F30 9.9626 Tf 5.351 0 Td [(nl)]TJ/F8 9.9626 Tf 12.86 0 Td [(or)]TJ/F30 9.9626 Tf 11.283 0 Td [(repl)]TJ/F8 9.9626 Tf 23.32 0 Td [(m)28(ust)-241(b)-28(e)-241(sp)-27(e)-1(ci\014)1(e)-1(d)1(,)]TJ -242.773 -11.956 Td [(thereb)28(y)-334(c)28(ho)-28(osing)-333(the)-333(initialization)-333(strategy)-334(as)-333(follo)28(ws:)]TJ 0 g 0 G - 0 -19.394 Td [(a)]TJ +/F27 9.9626 Tf 0 -20.135 Td [(parts)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(in)28(to)-333(whic)28(h)-334(co)-27(e)-1(\016cien)28(ts)-333(will)-333(b)-28(e)-334(inserted.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ -ET -q -1 0 0 1 312.036 491.534 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 315.174 491.334 Td [(Tspmat)]TJ -ET -q -1 0 0 1 347.183 491.534 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 350.322 491.334 Td [(type)]TJ +/F8 9.9626 Tf 30.609 0 Td [(In)-337(this)-338(case)-338(w)28(e)-337(ha)28(v)27(e)-337(a)-338(subroutine)-337(sp)-28(ecifying)-337(the)-338(mapping)-337(b)-28(et)28(w)28(een)]TJ -8.691 -11.955 Td [(global)-225(indices)-225(and)-225(pro)-28(cess/lo)-27(c)-1(al)-225(i)1(ndex)-225(pairs.)-409(If)-225(this)-225(optional)-225(ar)1(gume)-1(n)28(t)]TJ 0 -11.955 Td [(is)-316(sp)-28(eci\014ed,)-320(then)-316(it)-317(is)-316(mandatory)-316(to)-317(sp)-28(ecify)-316(the)-316(argumen)28(t)]TJ/F30 9.9626 Tf 251.562 0 Td [(mg)]TJ/F8 9.9626 Tf 13.613 0 Td [(as)-316(w)27(ell.)]TJ -265.175 -11.955 Td [(The)-333(subroutine)-334(m)28(ust)-333(conform)-333(to)-334(the)-333(follo)28(wing)-334(in)28(terface:)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -271.348 -19.394 Td [(desc)]TJ -ET -q -1 0 0 1 121.81 472.14 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 125.247 471.94 Td [(a)]TJ +/F30 9.9626 Tf 10.461 -18.09 Td [(interface)]TJ 15.691 -11.955 Td [(subroutine)-525(psb_parts\050glob_index,mg,np,pv,nv\051)]TJ +0 g 0 G +/F8 9.9626 Tf 93.898 -29.888 Td [(71)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(The)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)56(ariable)-334(of)-333(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 137.346 0 Td [(psb)]TJ ET -q -1 0 0 1 278.467 424.319 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q + +endstream +endobj +1387 0 obj +<< +/Length 10049 +>> +stream +0 g 0 G +0 g 0 G BT -/F30 9.9626 Tf 281.605 424.12 Td [(desc)]TJ +/F30 9.9626 Tf 234.142 706.129 Td [(integer,)-525(intent)-525(\050in\051)-1050(::)-525(glob_index,np,mg)]TJ 0 -11.955 Td [(integer,)-525(intent)-525(\050out\051)-525(::)-525(nv,)-525(pv\050*\051)]TJ -10.461 -11.955 Td [(end)-525(subroutine)-525(psb_parts)]TJ -15.691 -11.956 Td [(end)-525(interface)]TJ/F8 9.9626 Tf -10.461 -17.586 Td [(The)-333(input)-334(argumen)28(ts)-333(are:)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -15.594 Td [(glob)]TJ ET q -1 0 0 1 303.154 424.319 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 219.221 637.283 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 306.292 424.12 Td [(type)]TJ +/F27 9.9626 Tf 222.658 637.083 Td [(index)]TJ 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F8 9.9626 Tf 32.192 0 Td [(The)-333(global)-334(index)-333(to)-333(b)-28(e)-333(mapp)-28(ed;)]TJ 0 g 0 G -/F27 9.9626 Tf -227.319 -31.349 Td [(info)]TJ +/F27 9.9626 Tf -57.321 -13.774 Td [(np)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -20.59 Td [(Notes)]TJ +/F8 9.9626 Tf 17.712 0 Td [(The)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(pro)-28(cesses)-333(in)-334(the)-333(mapping;)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -18.862 Td [(1.)]TJ +/F27 9.9626 Tf -17.712 -13.774 Td [(mg)]TJ 0 g 0 G - [-500(On)-487(en)28(try)-487(to)-488(this)-487(routine)-487(the)-487(descriptor)-487(ma)28(y)-488(b)-27(e)-488(in)-487(either)-487(the)-487(build)-487(or)]TJ 12.73 -11.955 Td [(assem)28(bled)-334(state.)]TJ +/F8 9.9626 Tf 20.258 0 Td [(The)-333(total)-334(n)28(um)28(b)-28(er)-333(of)-333(global)-334(ro)28(ws)-333(in)-334(th)1(e)-334(mapping;)]TJ -20.258 -15.594 Td [(The)-333(output)-334(argumen)28(ts)-333(are:)]TJ 0 g 0 G - -12.73 -19.394 Td [(2.)]TJ +/F27 9.9626 Tf 0 -15.594 Td [(n)32(v)]TJ 0 g 0 G - [-500(On)-363(en)28(try)-362(to)-363(this)-363(routine)-362(the)-363(sparse)-363(matrix)-363(ma)28(y)-363(b)-27(e)-363(in)-363(either)-362(the)-363(build)-363(or)]TJ 12.73 -11.955 Td [(up)-28(date)-333(state.)]TJ +/F8 9.9626 Tf 17.075 0 Td [(The)-333(n)27(um)28(b)-28(er)-333(of)-333(en)28(tries)-334(in)]TJ/F30 9.9626 Tf 111.637 0 Td [(pv)]TJ/F8 9.9626 Tf 10.461 0 Td [(;)]TJ 0 g 0 G - -12.73 -19.394 Td [(3.)]TJ +/F27 9.9626 Tf -139.173 -13.774 Td [(p)32(v)]TJ 0 g 0 G - [-500(If)-230(the)-231(descriptor)-230(is)-231(in)-230(the)-231(build)-230(state,)-251(then)-231(the)-230(sparse)-231(matrix)-230(m)28(ust)-231(also)-230(b)-28(e)-231(in)]TJ 12.73 -11.955 Td [(the)-327(build)-327(state;)-329(the)-328(action)-327(of)-327(the)-327(routine)-327(is)-327(to)-327(\050implicitly\051)-327(call)]TJ/F30 9.9626 Tf 271.731 0 Td [(psb_cdins)]TJ/F8 9.9626 Tf -271.731 -11.956 Td [(to)-419(add)-419(en)28(tries)-419(to)-419(th)1(e)-419(sparsit)27(y)-418(pattern;)-462(eac)28(h)-419(sparse)-419(matrix)-419(en)28(try)-419(implic-)]TJ 0 -11.955 Td [(itly)-359(de\014nes)-360(a)-360(grap)1(h)-360(edge,)-366(that)-360(is)-359(passed)-360(to)-359(the)-360(descriptor)-359(routine)-360(for)-359(the)]TJ 0 -11.955 Td [(appropriate)-333(pro)-28(cessing;)]TJ +/F8 9.9626 Tf 17.075 0 Td [(A)-481(v)28(ector)-481(con)28(taining)-481(the)-481(indi)1(c)-1(es)-480(of)-481(the)-481(pro)-28(cesses)-481(to)-481(whic)28(h)-481(the)]TJ 1.555 -11.955 Td [(global)-468(index)-468(should)-468(b)-28(e)-468(assigend;)-536(eac)28(h)-468(en)28(try)-468(m)28(ust)-469(satisfy)-468(0)]TJ/F14 9.9626 Tf 270.508 0 Td [(\024)]TJ/F11 9.9626 Tf -270.508 -11.956 Td [(pv)]TJ/F8 9.9626 Tf 10.199 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F11 9.9626 Tf 8.603 0 Td [(<)-475(np)]TJ/F8 9.9626 Tf 23.47 0 Td [(;)-511(i)1(f)]TJ/F11 9.9626 Tf 18.163 0 Td [(nv)-511(>)]TJ/F8 9.9626 Tf 28.373 0 Td [(1)-451(w)27(e)-451(ha)28(v)27(e)-451(an)-452(in)1(dex)-452(assigned)-451(to)-452(m)28(ultiple)]TJ -96.115 -11.955 Td [(pro)-28(cesses,)-333(i.e.)-445(w)28(e)-333(ha)27(v)28(e)-333(an)-333(o)27(v)28(erlap)-333(among)-334(t)1(he)-334(sub)-28(domains.)]TJ 0 g 0 G - -12.73 -19.394 Td [(4.)]TJ +/F27 9.9626 Tf -40.548 -15.594 Td [(vg)]TJ 0 g 0 G - [-500(The)-333(input)-334(d)1(ata)-334(can)-333(b)-28(e)-333(passed)-334(in)-333(either)-333(COO)-334(or)-333(CSR)-333(formats;)]TJ +/F8 9.9626 Tf 16.757 0 Td [(In)-398(th)1(is)-398(case)-398(the)-397(asso)-28(ciation)-398(b)-27(e)-1(t)28(w)28(een)-398(an)-397(index)-398(and)-397(a)-398(pro)-27(ces)-1(s)-397(is)-398(sp)-28(ec-)]TJ 5.161 -11.955 Td [(i\014ed)-456(via)-456(an)-456(in)28(tege)-1(r)-456(v)28(ector)]TJ/F30 9.9626 Tf 120.743 0 Td [(vg\0501:mg\051)]TJ/F8 9.9626 Tf 41.842 0 Td [(;)-518(eac)28(h)-456(index)]TJ/F11 9.9626 Tf 59.63 0 Td [(i)]TJ/F14 9.9626 Tf 8.238 0 Td [(2)-482(f)]TJ/F8 9.9626 Tf 16.429 0 Td [(1)]TJ/F11 9.9626 Tf 6.642 0 Td [(:)-167(:)-166(:)-167(mg)]TJ/F14 9.9626 Tf 27.14 0 Td [(g)]TJ/F8 9.9626 Tf 9.526 0 Td [(is)]TJ -290.19 -11.955 Td [(assigned)-449(to)-449(pro)-28(cess)]TJ/F11 9.9626 Tf 89.776 0 Td [(v)-36(g)]TJ/F8 9.9626 Tf 10.296 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051.)-792(The)-449(v)28(ector)]TJ/F30 9.9626 Tf 67.232 0 Td [(vg)]TJ/F8 9.9626 Tf 14.935 0 Td [(m)28(ust)-449(b)-28(e)-449(iden)28(tica)-1(l)-449(on)-449(all)]TJ -189.546 -11.955 Td [(calling)-452(pro)-28(cesses;)-513(it)1(s)-453(en)28(tries)-453(ma)28(y)-453(ha)28(v)28(e)-453(th)1(e)-453(ranges)-453(\0500)]TJ/F11 9.9626 Tf 236.604 0 Td [(:)-167(:)-166(:)-167(np)]TJ/F14 9.9626 Tf 27.281 0 Td [(\000)]TJ/F8 9.9626 Tf 10.754 0 Td [(1\051)-453(or)]TJ -274.639 -11.955 Td [(\0501)]TJ/F11 9.9626 Tf 10.516 0 Td [(:)-167(:)-166(:)-167(np)]TJ/F8 9.9626 Tf 24.276 0 Td [(\051)-347(according)-347(to)-347(the)-347(v)55(alu)1(e)-348(of)]TJ/F30 9.9626 Tf 119.292 0 Td [(flag)]TJ/F8 9.9626 Tf 20.921 0 Td [(.)-486(The)-347(size)]TJ/F11 9.9626 Tf 47.231 0 Td [(mg)]TJ/F8 9.9626 Tf 17.314 0 Td [(ma)28(y)-347(b)-28(e)-347(sp)-28(ec-)]TJ -239.55 -11.955 Td [(i\014ed)-414(via)-414(the)-415(option)1(al)-415(argumen)28(t)]TJ/F30 9.9626 Tf 142.427 0 Td [(mg)]TJ/F8 9.9626 Tf 10.461 0 Td [(;)-455(the)-414(default)-414(is)-414(to)-414(use)-415(the)-414(en)28(tire)]TJ -152.888 -11.956 Td [(v)28(ector)]TJ/F30 9.9626 Tf 29.916 0 Td [(vg)]TJ/F8 9.9626 Tf 10.46 0 Td [(,)-333(th)27(u)1(s)-334(ha)28(ving)]TJ/F30 9.9626 Tf 60.108 0 Td [(mg=size\050vg\051)]TJ/F8 9.9626 Tf 57.534 0 Td [(.)]TJ 0 g 0 G - 0 -19.394 Td [(5.)]TJ +/F27 9.9626 Tf -179.936 -15.593 Td [(vl)]TJ 0 g 0 G - [-500(In)-368(COO)-367(format)-368(the)-367(co)-28(e\016cien)28(ts)-368(to)-368(b)-27(e)-368(inserted)-368(are)-367(represen)28(ted)-368(b)28(y)-368(the)-367(or-)]TJ 12.73 -11.955 Td [(dered)-358(triples)]TJ/F11 9.9626 Tf 58.162 0 Td [(ia)]TJ/F8 9.9626 Tf 8.699 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F11 9.9626 Tf 3.875 0 Td [(;)-167(j)-57(a)]TJ/F8 9.9626 Tf 14.367 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F11 9.9626 Tf 3.875 0 Td [(;)-167(v)-36(a)1(l)]TJ/F8 9.9626 Tf 18.049 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051,)-364(for)]TJ/F11 9.9626 Tf 25.762 0 Td [(i)]TJ/F8 9.9626 Tf 6.608 0 Td [(=)-319(1)]TJ/F11 9.9626 Tf 15.905 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(nz)]TJ/F8 9.9626 Tf 33.191 0 Td [(;)-370(these)-358(triples)-358(should)-358(b)-28(e-)]TJ -210.411 -11.955 Td [(long)-384(to)-385(the)-384(curren)28(t)-385(pro)-28(cess,)-397(i.e.)]TJ/F11 9.9626 Tf 144.426 0 Td [(ia)]TJ/F8 9.9626 Tf 8.698 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)-384(should)-385(b)-28(e)-384(one)-384(of)-385(the)-384(lo)-28(cal)-385(ind)1(ic)-1(es,)]TJ -160.431 -11.955 Td [(but)-333(are)-334(otherwise)-333(arbitrary;)]TJ +/F8 9.9626 Tf 14.211 0 Td [(In)-356(this)-357(case)-356(w)28(e)-357(are)-356(sp)-28(ecifying)-356(the)-357(list)-356(of)-356(indices)]TJ/F30 9.9626 Tf 210.708 0 Td [(vl\0501:nl\051)]TJ/F8 9.9626 Tf 45.393 0 Td [(assigned)-356(to)]TJ -248.394 -11.955 Td [(the)-462(curren)28(t)-462(pro)-27(ce)-1(ss;)-526(th)28(us,)-494(the)-461(global)-462(problem)-462(size)]TJ/F11 9.9626 Tf 229.323 0 Td [(mg)]TJ/F8 9.9626 Tf 18.457 0 Td [(is)-462(giv)28(en)-462(b)28(y)]TJ -247.78 -11.956 Td [(the)-405(range)-405(of)-404(the)-405(aggregate)-405(of)-405(the)-405(in)1(dividual)-405(v)28(ectors)]TJ/F30 9.9626 Tf 233.196 0 Td [(vl)]TJ/F8 9.9626 Tf 14.494 0 Td [(sp)-28(eci\014ed)-405(in)]TJ -247.69 -11.955 Td [(the)-481(calling)-481(p)1(ro)-28(cesses.)-887(The)-481(size)-481(ma)28(y)-481(b)-28(e)-481(sp)-27(eci\014ed)-481(via)-481(the)-481(optional)]TJ 0 -11.955 Td [(argumen)28(t)]TJ/F30 9.9626 Tf 44.85 0 Td [(nl)]TJ/F8 9.9626 Tf 10.461 0 Td [(;)-373(the)-361(default)-360(is)-360(to)-360(use)-360(the)-360(en)28(tire)-361(v)28(ector)]TJ/F30 9.9626 Tf 173.727 0 Td [(vl)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)-367(th)28(us)-360(ha)28(ving)]TJ/F30 9.9626 Tf -239.499 -11.955 Td [(nl=size\050vl\051)]TJ/F8 9.9626 Tf 57.534 0 Td [(.)-419(If)]TJ/F30 9.9626 Tf 16.133 0 Td 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[(T)32(yp)-32(e:)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +/F27 9.9626 Tf -33.797 -19.345 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.639 Td [(On)-383(En)32(try)]TJ 0 g 0 G + 0 -19.344 Td [(nz)]TJ 0 g 0 G - 0 -19.638 Td [(desc)]TJ -ET -q -1 0 0 1 121.81 627.46 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 125.247 627.261 Td [(a)]TJ +/F8 9.9626 Tf 16.438 0 Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(p)-28(oin)28(ts)-333(b)-28(eing)-333(inserte)-1(d)1(.)]TJ 8.469 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue.)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ -ET -q -1 0 0 1 312.036 579.639 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 315.174 579.44 Td [(desc)]TJ -ET -q -1 0 0 1 336.723 579.639 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 339.861 579.44 Td [(type)]TJ +/F27 9.9626 Tf -24.907 -19.344 Td [(ia)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 13.733 0 Td [(the)-333(indices)-334(of)-333(the)-333(starting)-334(v)28(ertex)-333(of)-333(the)-334(edges)-333(b)-28(eing)-333(inserted.)]TJ 11.174 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(arra)27(y)-333(of)-333(length)]TJ/F11 9.9626 Tf 172.547 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.639 Td [(afm)32(t)]TJ +/F27 9.9626 Tf -208.505 -19.344 Td [(ja)]TJ 0 g 0 G -/F8 9.9626 Tf 27.737 0 Td [(the)-333(storage)-334(format)-333(for)-333(the)-334(sparse)-333(matrix.)]TJ -2.83 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(arra)28(y)-333(of)-334(c)28(haracters.)-444(Defalt:)-445('CSR'.)]TJ +/F8 9.9626 Tf 14.051 0 Td [(the)-333(indices)-334(of)-333(the)-333(end)-334(v)28(ertex)-333(of)-334(t)1(he)-334(edges)-333(b)-28(eing)-333(inserted.)]TJ 10.856 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(arra)27(y)-333(of)-333(length)]TJ/F11 9.9626 Tf 172.547 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.639 Td [(up)-32(d)]TJ +/F27 9.9626 Tf -208.505 -19.344 Td [(mask)]TJ 0 g 0 G -/F8 9.9626 Tf 24.395 0 Td [(Pro)28(vide)-333(for)-334(up)-27(dates)-334(to)-333(the)-333(matrix)-334(co)-28(e\016cien)28(ts.)]TJ 0.512 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(in)28(teger,)-333(p)-28(ossible)-333(v)55(alues:)]TJ/F30 9.9626 Tf 164.633 0 Td [(psb_upd_srch_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 6.089 0 Td [(psb_upd_perm_)]TJ +/F8 9.9626 Tf 30.664 0 Td [(Mask)-329(e)-1(n)28(tries)-329(in)]TJ/F30 9.9626 Tf 70.038 0 Td [(ja)]TJ/F8 9.9626 Tf 10.461 0 Td [(,)-330(they)-330(are)-329(inserted)-330(only)-329(when)-329(the)-330(corresp)-28(onding)]TJ/F30 9.9626 Tf 211.627 0 Td [(mask)]TJ/F8 9.9626 Tf -297.883 -11.955 Td [(en)28(tries)-334(are)]TJ/F30 9.9626 Tf 48.54 0 Td [(.true.)]TJ/F8 9.9626 Tf -48.54 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(arra)28(y)-334(of)-333(length)]TJ/F11 9.9626 Tf 165.048 0 Td [(nz)]TJ/F8 9.9626 Tf 11.051 0 Td [(,)-333(default)]TJ/F30 9.9626 Tf 39.574 0 Td [(.true.)]TJ/F8 9.9626 Tf 31.382 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -263.623 -19.639 Td [(dupl)]TJ +/F27 9.9626 Tf -271.962 -19.344 Td [(lidx)]TJ 0 g 0 G -/F8 9.9626 Tf 27.259 0 Td [(Ho)28(w)-334(to)-333(handle)-333(duplicate)-333(co)-28(e\016cien)27(ts.)]TJ -2.352 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-308(as:)-432(in)27(teger,)-313(p)-28(ossible)-309(v)56(alues:)]TJ/F30 9.9626 Tf 163.696 0 Td [(psb_dupl_ovwrt_)]TJ/F8 9.9626 Tf 78.456 0 Td [(,)]TJ/F30 9.9626 Tf 5.891 0 Td [(psb_dupl_add_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf -316.037 -11.955 Td [(psb_dupl_err_)]TJ/F8 9.9626 Tf 67.994 0 Td [(.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(User)-333(de\014ned)-334(lo)-27(cal)-334(indices)-333(for)]TJ/F30 9.9626 Tf 128.85 0 Td [(ja)]TJ/F8 9.9626 Tf 10.461 0 Td [(.)]TJ -138.162 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(length)]TJ/F11 9.9626 Tf 172.547 0 Td [(nz)]TJ/F8 9.9626 Tf 11.052 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -92.901 -19.639 Td [(mold)]TJ +/F27 9.9626 Tf -208.506 -20.465 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 29.805 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(matrix)-334(storage.)]TJ -4.898 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(a)-333(class)-334(deriv)28(ed)-333(from)]TJ/F30 9.9626 Tf 203.349 0 Td [(psb)]TJ -ET -q -1 0 0 1 344.47 297.847 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 347.608 297.647 Td [(T)]TJ -ET -q -1 0 0 1 353.466 297.847 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 356.604 297.647 Td [(base)]TJ -ET -q -1 0 0 1 378.153 297.847 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 381.291 297.647 Td [(sparse)]TJ +0 g 0 G + 0 -19.344 Td [(desc)]TJ ET q -1 0 0 1 413.301 297.847 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 172.619 168.346 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 416.439 297.647 Td [(mat)]TJ/F8 9.9626 Tf 15.691 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -332.235 -21.201 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -19.639 Td [(a)]TJ +/F27 9.9626 Tf 176.057 168.146 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(to)-333(b)-28(e)-333(assem)28(bled.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(the)-333(up)-28(dated)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 209.186 cm +1 0 0 1 362.845 120.525 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 208.986 Td [(Tspmat)]TJ +/F30 9.9626 Tf 365.983 120.326 Td [(desc)]TJ ET q -1 0 0 1 347.183 209.186 cm +1 0 0 1 387.532 120.525 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 350.322 208.986 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -271.348 -19.638 Td [(info)]TJ +/F30 9.9626 Tf 390.67 120.326 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ 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9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - -80.282 -19.926 Td [(2.)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(ila)]TJ 0 g 0 G - [-500(The)-333(sparse)-334(matrix)-333(ma)28(y)-334(b)-27(e)-334(in)-333(either)-333(the)-334(build)-333(or)-333(up)-28(date)-333(state;)]TJ +/F8 9.9626 Tf 16.916 0 Td [(the)-333(lo)-28(cal)-333(indices)-334(of)-333(the)-333(starting)-334(v)28(ertex)-333(of)-334(the)-333(edges)-333(b)-28(eing)-333(inserted.)]TJ 7.991 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 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[(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 89.968 0 Td [(psb)]TJ -ET -q -1 0 0 1 231.089 293.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 234.227 293.219 Td [(T)]TJ -ET -q -1 0 0 1 240.085 293.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 243.223 293.219 Td [(vect)]TJ -ET -q -1 0 0 1 264.772 293.418 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 267.911 293.219 Td [(type)]TJ +/F27 9.9626 Tf -260.887 -21.917 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(,)-333(of)-334(t)28(yp)-28(e)-333(real,)-333(complex)-334(or)-333(in)28(teger.)]TJ 0 g 0 G -/F27 9.9626 Tf -188.937 -31.88 Td [(info)]TJ + 0 -19.926 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ 0 g 0 G - 141.968 -123.08 Td [(83)]TJ + 141.968 -398.049 Td [(78)]TJ 0 g 0 G ET endstream endobj -1430 0 obj +1435 0 obj << -/Length 6841 +/Length 5932 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(6.6)-1125(psb)]TJ ET q -1 0 0 1 171.761 706.328 cm +1 0 0 1 151.587 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 175.796 706.129 Td [(geins)-375(|)-375(Dense)-375(matrix)-375(insertion)-375(routine)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_geins\050m,)-525(irw,)-525(val,)-525(x,)-525(desc_a,)-525(info)-525([,dupl,local]\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -20.681 Td [(T)32(yp)-32(e:)]TJ +/F16 11.9552 Tf 155.621 706.129 Td [(cdbldext)-597(|)-597(Build)-597(an)-598(extended)-597(comm)31(unication)]TJ -25.091 -13.948 Td [(descriptor)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.43 Td [(On)-383(En)32(try)]TJ 0 g 0 G +/F30 9.9626 Tf -30.635 -19.114 Td [(call)-525(psb_cdbldext\050a,desc_a,nl,desc_out,)-525(info,)-525(extype\051)]TJ/F8 9.9626 Tf 14.944 -23.476 Td [(This)-298(subroutine)-297(builds)-298(an)-297(extended)-298(comm)28(unication)-298(descriptor,)-305(based)-297(on)-298(the)]TJ -14.944 -11.955 Td [(input)-389(descriptor)]TJ/F30 9.9626 Tf 74.288 0 Td [(desc_a)]TJ/F8 9.9626 Tf 35.261 0 Td [(and)-389(on)-390(the)-389(stencil)-389(s)-1(p)-27(eci\014ed)-390(through)-389(the)-389(input)-390(sparse)]TJ -109.549 -11.956 Td [(matrix)]TJ/F30 9.9626 Tf 32.407 0 Td [(a)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ 0 g 0 G - 0 -19.431 Td [(m)]TJ +/F27 9.9626 Tf -37.637 -21.094 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 14.529 0 Td [(Num)28(b)-28(er)-333(of)-334(ro)28(ws)-333(in)]TJ/F11 9.9626 Tf 84.516 0 Td [(v)-36(al)]TJ/F8 9.9626 Tf 16.942 0 Td [(to)-333(b)-28(e)-333(inse)-1(r)1(te)-1(d)1(.)]TJ -91.081 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.431 Td [(irw)]TJ +/F27 9.9626 Tf -33.797 -21.483 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F8 9.9626 Tf 21.157 0 Td [(Indices)-444(of)-445(the)-444(ro)27(ws)-444(to)-445(b)-27(e)-445(inserted.)-778(Sp)-28(eci\014cally)84(,)-472(ro)27(w)]TJ/F11 9.9626 Tf 237.973 0 Td [(i)]TJ/F8 9.9626 Tf 7.861 0 Td [(of)]TJ/F11 9.9626 Tf 12.454 0 Td [(v)-36(al)]TJ/F8 9.9626 Tf 18.049 0 Td [(will)-444(b)-28(e)-445(in-)]TJ -272.588 -11.955 Td [(serted)-435(in)28(to)-436(th)1(e)-436(lo)-27(cal)-436(ro)28(w)-435(corresp)-28(onding)-435(to)-435(the)-435(global)-435(ro)28(w)-435(index)]TJ/F11 9.9626 Tf 289.252 0 Td [(ir)-28(w)]TJ/F8 9.9626 Tf 15.605 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051.)]TJ -312.163 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.43 Td [(v)64(al)]TJ + 0 -21.484 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 19.143 0 Td [(the)-333(dense)-334(submatrix)-333(to)-333(b)-28(e)-333(inserted.)]TJ 5.763 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(1)-333(o)-1(r)-333(2)-333(arra)28(y)83(.)-444(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-334(v)56(alue.)]TJ +/F8 9.9626 Tf 10.551 0 Td [(A)-333(sparse)-334(matrix)-333(Scop)-28(e:)]TJ/F27 9.9626 Tf 101.176 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -109.893 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(t)27(yp)-27(e.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -19.43 Td [(desc)]TJ +/F27 9.9626 Tf -24.907 -21.484 Td [(desc)]TJ ET q -1 0 0 1 172.619 414.689 cm +1 0 0 1 121.81 504.47 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 414.49 Td [(a)]TJ +/F27 9.9626 Tf 125.247 504.27 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 362.845 366.869 cm +1 0 0 1 312.036 456.649 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 366.669 Td [(desc)]TJ +/F30 9.9626 Tf 315.174 456.45 Td [(Tspmat)]TJ ET q -1 0 0 1 387.532 366.869 cm +1 0 0 1 347.183 456.649 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 366.669 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F30 9.9626 Tf 350.322 456.45 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.43 Td [(dupl)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 27.259 0 Td [(Ho)28(w)-334(to)-333(handle)-333(duplicate)-333(co)-28(e\016cien)27(ts.)]TJ -2.352 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-308(as:)-432(in)27(teger,)-313(p)-28(ossible)-309(v)56(alues:)]TJ/F30 9.9626 Tf 163.697 0 Td [(psb_dupl_ovwrt_)]TJ/F8 9.9626 Tf 78.455 0 Td [(,)]TJ/F30 9.9626 Tf 5.891 0 Td [(psb_dupl_add_)]TJ/F8 9.9626 Tf 67.995 0 Td [(.)]TJ +/F27 9.9626 Tf -271.348 -21.484 Td [(nl)]TJ 0 g 0 G -/F27 9.9626 Tf -340.944 -19.43 Td [(lo)-32(cal)]TJ +/F8 9.9626 Tf 14.529 0 Td [(the)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(additional)-333(la)28(y)27(ers)-333(desired.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F11 9.9626 Tf 130.428 0 Td [(nl)]TJ/F14 9.9626 Tf 11.916 0 Td [(\025)]TJ/F8 9.9626 Tf 10.516 0 Td [(0.)]TJ 0 g 0 G -/F8 9.9626 Tf 28.054 0 Td [(Whether)-289(the)-289(en)28(tries)-289(in)-289(the)-289(index)-288(v)27(ector)]TJ/F30 9.9626 Tf 172.77 0 Td [(irw)]TJ/F8 9.9626 Tf 15.691 0 Td [(,)-298(are)-289(already)-289(in)-288(lo)-28(cal)-289(n)28(um)28(b)-28(er-)]TJ -191.608 -11.955 Td [(ing.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(logical)-333(v)55(alue;)-333(default:)]TJ/F30 9.9626 Tf 163.055 0 Td [(.false.)]TJ/F8 9.9626 Tf 36.612 0 Td [(.)]TJ +/F27 9.9626 Tf -177.767 -21.483 Td [(ext)32(yp)-32(e)]TJ 0 g 0 G -/F27 9.9626 Tf -224.574 -20.68 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 38.398 0 Td [(the)-333(kind)-334(of)-333(estension)-333(required.)]TJ -13.491 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -57.707 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 44.396 0 Td [(.)]TJ -69.579 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-419(as:)-616(an)-420(in)28(teger)-419(v)55(alue)]TJ/F30 9.9626 Tf 135.566 0 Td [(psb_ovt_xhal_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 7.159 0 Td [(psb_ovt_asov_)]TJ/F8 9.9626 Tf 67.995 0 Td [(,)-441(default:)]TJ/F30 9.9626 Tf -278.714 -11.955 Td [(psb_ovt_xhal_)]TJ 0 g 0 G +/F27 9.9626 Tf -24.907 -23.476 Td [(On)-383(Return)]TJ 0 g 0 G - 0 -19.43 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(the)-333(output)-334(d)1(e)-1(n)1(s)-1(e)-333(matrix.)]TJ 13.879 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-232(as:)-394(a)-233(rank)-233(one)-232(or)-233(t)28(w)28(o)-233(arra)28(y)-233(or)-232(an)-233(ob)-55(ject)-233(of)-233(t)28(yp)-27(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 241.975 0 Td [(psb)]TJ + 0 -21.484 Td [(desc)]TJ ET q -1 0 0 1 433.906 144.435 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 121.81 261.126 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F30 9.9626 Tf 437.044 144.236 Td [(T)]TJ +/F27 9.9626 Tf 125.247 260.927 Td [(out)]TJ +0 g 0 G +/F8 9.9626 Tf 21.53 0 Td [(the)-333(extended)-334(comm)28(unication)-333(descriptor.)]TJ -21.975 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 442.902 144.435 cm +1 0 0 1 312.036 213.305 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 446.04 144.236 Td [(vect)]TJ +/F30 9.9626 Tf 315.174 213.106 Td [(desc)]TJ ET q -1 0 0 1 467.589 144.435 cm +1 0 0 1 336.723 213.305 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 470.727 144.236 Td [(type)]TJ +/F30 9.9626 Tf 339.861 213.106 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(,)]TJ -316.038 -11.955 Td [(of)-333(t)27(yp)-27(e)-334(real,)-333(complex)-333(or)-334(in)28(teger.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -260.887 -21.484 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -23.476 Td [(Notes)]TJ 0 g 0 G - 141.968 -41.843 Td [(84)]TJ +/F8 9.9626 Tf 166.875 -29.888 Td [(79)]TJ 0 g 0 G ET endstream endobj -1434 0 obj +1440 0 obj << -/Length 1111 +/Length 1587 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F27 9.9626 Tf 99.895 706.129 Td [(info)]TJ -0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td 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0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -227.318 -31.88 Td [(mold)]TJ +/F27 9.9626 Tf -260.887 -19.925 Td [(nnz)]TJ 0 g 0 G -/F8 9.9626 Tf 29.805 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(th)1(e)-334(in)28(ternal)-333(v)27(ector)-333(storage.)]TJ -4.899 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-273(as:)-414(an)-274(ob)-55(ject)-273(of)-274(a)-273(class)-273(deriv)28(ed)-274(from)]TJ/F30 9.9626 Tf 198.261 0 Td [(psb)]TJ -ET -q -1 0 0 1 390.19 498.649 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 393.329 498.449 Td [(T)]TJ -ET -q -1 0 0 1 399.186 498.649 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 402.325 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1 312.036 408.985 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 350.177 486.494 Td [(vect)]TJ +/F30 9.9626 Tf 315.174 408.786 Td [(Tspmat)]TJ ET q -1 0 0 1 371.725 486.693 cm +1 0 0 1 347.183 408.985 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 374.864 486.494 Td [(type)]TJ +/F30 9.9626 Tf 350.322 408.786 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -245.08 -21.918 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -271.348 -19.926 Td [(info)]TJ 0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td 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0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 258.995 384.875 Td [(T)]TJ -ET -q -1 0 0 1 264.853 385.075 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 267.992 384.875 Td [(vect)]TJ -ET -q -1 0 0 1 289.541 385.075 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 292.679 384.875 Td [(type)]TJ + [-500(On)-333(exit)-334(from)-333(this)-333(routine)-333(the)-334(sparse)-333(matrix)-333(is)-334(in)-333(the)-333(build)-334(state.)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(,)-333(of)-334(t)28(yp)-28(e)-333(real,)-333(complex)-334(or)-333(in)28(teger.)]TJ + 0 -19.926 Td [(2.)]TJ +0 g 0 G + [-500(The)-333(descriptor)-334(ma)28(y)-333(b)-28(e)-333(in)-334(either)-333(the)-333(build)-333(or)-334(assem)28(bled)-333(state.)]TJ 0 g 0 G -/F27 9.9626 Tf -162.895 -31.88 Td [(info)]TJ + 0 -19.925 Td [(3.)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 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[(;)-167(v)-36(a)1(l)]TJ/F8 9.9626 Tf 18.049 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051,)-364(for)]TJ/F11 9.9626 Tf 25.762 0 Td [(i)]TJ/F8 9.9626 Tf 6.608 0 Td [(=)-319(1)]TJ/F11 9.9626 Tf 15.905 0 Td [(;)-167(:)-166(:)-167(:)-167(;)-166(nz)]TJ/F8 9.9626 Tf 33.191 0 Td [(;)-370(these)-358(triples)-358(should)-358(b)-28(e-)]TJ -210.411 -11.955 Td [(long)-384(to)-385(the)-384(curren)28(t)-385(pro)-28(cess,)-397(i.e.)]TJ/F11 9.9626 Tf 144.426 0 Td [(ia)]TJ/F8 9.9626 Tf 8.698 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)-384(should)-385(b)-28(e)-384(one)-384(of)-385(the)-384(lo)-28(cal)-385(ind)1(ic)-1(es,)]TJ -160.431 -11.955 Td [(but)-333(are)-334(otherwise)-333(arbitrary;)]TJ +0 g 0 G + 141.968 -29.888 Td [(83)]TJ +0 g 0 G +ET + +endstream +endobj +1472 0 obj +<< +/Length 3810 +>> +stream +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F8 9.9626 Tf 162.881 706.129 Td [(6.)]TJ +0 g 0 G + 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9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(arra)28(y)-333(of)-334(c)28(haracters.)-444(Defalt:)-445('CSR'.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F27 9.9626 Tf -24.907 -19.639 Td [(up)-32(d)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F8 9.9626 Tf 24.395 0 Td [(Pro)28(vide)-333(for)-334(up)-27(dates)-334(to)-333(the)-333(matrix)-334(co)-28(e\016cien)28(ts.)]TJ 0.512 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(in)28(teger,)-333(p)-28(ossible)-333(v)55(alues:)]TJ/F30 9.9626 Tf 164.633 0 Td [(psb_upd_srch_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 6.089 0 Td [(psb_upd_perm_)]TJ 0 g 0 G +/F27 9.9626 Tf -263.623 -19.639 Td [(dupl)]TJ 0 g 0 G - 0 -19.925 Td [(x)]TJ +/F8 9.9626 Tf 27.259 0 Td [(Ho)28(w)-334(to)-333(handle)-333(duplicate)-333(co)-28(e\016cien)27(ts.)]TJ -2.352 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-308(as:)-432(in)27(teger,)-313(p)-28(ossible)-309(v)56(alues:)]TJ/F30 9.9626 Tf 163.696 0 Td [(psb_dupl_ovwrt_)]TJ/F8 9.9626 Tf 78.456 0 Td [(,)]TJ/F30 9.9626 Tf 5.891 0 Td [(psb_dupl_add_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf -316.037 -11.955 Td [(psb_dupl_err_)]TJ/F8 9.9626 Tf 67.994 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(An)-333(in)28(te)-1(ger)-333(v)28(ector)-333(of)-334(indices)-333(to)-333(b)-28(e)-334(con)28(v)28(erted.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in,)-383(inout)]TJ/F8 9.9626 Tf 42.645 0 Td [(.)]TJ -76.131 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ +/F27 9.9626 Tf -92.901 -19.639 Td [(mold)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -31.88 Td [(desc)]TJ +/F8 9.9626 Tf 29.805 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(matrix)-334(storage.)]TJ -4.898 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(a)-333(class)-334(deriv)28(ed)-333(from)]TJ/F30 9.9626 Tf 203.349 0 Td [(psb)]TJ ET q -1 0 0 1 121.81 534.514 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 344.47 297.847 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 125.247 534.315 Td [(a)]TJ +/F30 9.9626 Tf 347.608 297.647 Td [(T)]TJ +ET +q +1 0 0 1 353.466 297.847 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 356.604 297.647 Td [(base)]TJ +ET +q +1 0 0 1 378.153 297.847 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 381.291 297.647 Td [(sparse)]TJ +ET +q +1 0 0 1 413.301 297.847 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 416.439 297.647 Td [(mat)]TJ/F8 9.9626 Tf 15.691 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F27 9.9626 Tf -332.235 -21.201 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.639 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(to)-333(b)-28(e)-333(assem)28(bled.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 486.693 cm +1 0 0 1 312.036 209.186 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 486.494 Td [(desc)]TJ +/F30 9.9626 Tf 315.174 208.986 Td [(Tspmat)]TJ ET q -1 0 0 1 336.723 486.693 cm +1 0 0 1 347.183 209.186 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 339.861 486.494 Td [(type)]TJ +/F30 9.9626 Tf 350.322 208.986 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -19.925 Td [(iact)]TJ +/F27 9.9626 Tf -271.348 -19.638 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.281 0 Td [(sp)-28(eci\014es)-333(action)-334(to)-333(b)-28(e)-333(tak)28(en)-334(in)-333(case)-333(of)-334(range)-333(errors.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 257.147 0 Td [(global)]TJ/F8 9.9626 Tf -255.521 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-256(c)28(haracter)-255(v)56(ariable)]TJ/F30 9.9626 Tf 143.584 0 Td [(I)]TJ/F8 9.9626 Tf 5.23 0 Td [(gnore,)]TJ/F30 9.9626 Tf 29.293 0 Td [(W)]TJ/F8 9.9626 Tf 5.23 0 Td [(arning)-255(or)]TJ/F30 9.9626 Tf 41.67 0 Td [(A)]TJ/F8 9.9626 Tf 5.231 0 Td [(b)-28(ort,)-270(default)]TJ/F30 9.9626 Tf 56.741 0 Td [(I)]TJ/F8 9.9626 Tf 5.231 0 Td [(gnore.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.201 Td [(Notes)]TJ 0 g 0 G -/F27 9.9626 Tf -317.117 -21.917 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 166.875 -29.888 Td [(85)]TJ 0 g 0 G +ET + +endstream +endobj +1489 0 obj +<< +/Length 2255 +>> +stream 0 g 0 G - 0 -19.926 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(If)]TJ/F11 9.9626 Tf 10.133 0 Td [(y)]TJ/F8 9.9626 Tf 8.733 0 Td [(is)-350(not)-351(presen)28(t,)-355(then)]TJ/F11 9.9626 Tf 88.586 0 Td [(x)]TJ/F8 9.9626 Tf 9.185 0 Td [(is)-350(o)27(v)28(erwritten)-350(with)-351(th)1(e)-351(translated)-350(in)28(teger)-351(indices.)]TJ -102.758 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(y)]TJ +BT +/F8 9.9626 Tf 162.881 706.129 Td [(1.)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(If)]TJ/F11 9.9626 Tf 10.167 0 Td [(y)]TJ/F8 9.9626 Tf 8.767 0 Td [(is)-354(not)-354(presen)28(t,)-359(then)]TJ/F11 9.9626 Tf 88.732 0 Td [(y)]TJ/F8 9.9626 Tf 8.766 0 Td [(is)-354(o)28(v)28(erwritten)-354(with)-354(the)-354(translated)-353(in)27(teger)-353(indices,)]TJ -102.553 -11.955 Td [(and)]TJ/F11 9.9626 Tf 19.372 0 Td [(x)]TJ/F8 9.9626 Tf 9.015 0 Td [(is)-333(left)-334(unc)28(hanged.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 113.242 0 Td [(global)]TJ/F8 9.9626 Tf -141.629 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ + [-500(On)-406(en)28(try)-406(to)-406(this)-406(routine)-406(the)-406(descriptor)-406(m)28(ust)-406(b)-28(e)-406(in)-406(the)-406(assem)27(b)1(led)-406(s)-1(tate,)]TJ 12.73 -11.955 Td [(i.e.)]TJ/F30 9.9626 Tf 17.158 0 Td [(psb_cdasb)]TJ/F8 9.9626 Tf 50.394 0 Td [(m)28(ust)-334(already)-333(ha)28(v)28(e)-334(b)-27(een)-334(called.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ + -80.282 -19.926 Td [(2.)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ + [-500(The)-333(sparse)-334(matrix)-333(ma)28(y)-334(b)-27(e)-334(in)-333(either)-333(the)-334(build)-333(or)-333(up)-28(date)-333(state;)]TJ 0 g 0 G - 141.968 -115.11 Td [(91)]TJ + 0 -19.925 Td [(3.)]TJ +0 g 0 G + [-500(Duplicate)-250(en)28(tries)-250(are)-249(dete)-1(cted)-249(and)-250(handled)-250(in)-249(b)-28(oth)-250(build)-249(and)-250(up)-28(date)-249(state,)]TJ 12.73 -11.955 Td [(with)-282(the)-283(exception)-282(of)-282(the)-283(error)-282(action)-282(that)-283(is)-282(only)-282(tak)28(en)-283(in)-282(the)-282(build)-283(state,)]TJ 0 -11.955 Td [(i.e.)-444(on)-334(the)-333(\014rst)-333(asse)-1(m)28(bly;)]TJ +0 g 0 G + -12.73 -19.925 Td [(4.)]TJ +0 g 0 G + [-500(If)-224(the)-224(up)-28(date)-223(c)27(hoice)-224(is)]TJ/F30 9.9626 Tf 107.516 0 Td [(psb_upd_perm_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)-246(then)-224(subsequen)28(t)-224(calls)-224(to)]TJ/F30 9.9626 Tf 108.952 0 Td [(psb_spins)]TJ/F8 9.9626 Tf -271.732 -11.956 Td [(to)-246(up)-28(date)-246(the)-246(matrix)-246(m)28(ust)-246(b)-28(e)-246(arranged)-246(in)-246(suc)28(h)-246(a)-246(w)28(a)27(y)-246(as)-246(to)-246(pro)-27(duce)-246(exactly)]TJ 0 -11.955 Td [(the)-228(same)-229(sequence)-228(of)-228(co)-28(e\016cien)27(t)-228(v)56(alues)-229(as)-228(encoun)28(tered)-228(at)-229(the)-228(\014rst)-228(assem)27(b)1(ly;)]TJ +0 g 0 G + -12.73 -19.925 Td [(5.)]TJ +0 g 0 G + [-500(The)-333(output)-334(storage)-333(format)-333(need)-334(not)-333(b)-28(e)-333(the)-333(same)-334(on)-333(all)-333(pro)-28(cesses;)]TJ +0 g 0 G + 0 -19.925 Td [(6.)]TJ +0 g 0 G + [-500(On)-370(exit)-370(from)-370(this)-370(routine)-370(the)-370(matrix)-370(is)-370(in)-370(the)-370(assem)28(bled)-370(state,)-380(an)1(d)-370(th)27(us)]TJ 12.73 -11.956 Td [(is)-333(suitable)-334(for)-333(the)-333(computational)-334(rou)1(tines)-1(.)]TJ +0 g 0 G + 141.968 -444.333 Td [(86)]TJ 0 g 0 G ET endstream endobj -1477 0 obj +1501 0 obj << -/Length 3279 +/Length 3097 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 171.761 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 175.796 706.129 Td [(is)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(6.10)-1125(psb)]TJ ET q -1 0 0 1 185.644 706.328 cm +1 0 0 1 158.311 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 189.679 706.129 Td [(o)31(wned)-375(|)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(spfree)-375(|)-375(F)94(rees)-375(a)-375(sparse)-375(matrix)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -38.974 -18.389 Td [(call)-525(psb_is_owned\050x,)-525(desc_a\051)]TJ +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_spfree\050a,)-525(desc_a,)-525(info\051)]TJ 0 g 0 G /F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G /F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(x)]TJ + 0 -19.925 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(to)-333(b)-28(e)-333(freed.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 312.036 578.35 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 315.174 578.15 Td [(Tspmat)]TJ +ET +q +1 0 0 1 347.183 578.35 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 350.322 578.15 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(In)28(teger)-334(ind)1(e)-1(x.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(scalar)-333(in)28(teger.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -31.88 Td [(desc)]TJ +/F27 9.9626 Tf -271.348 -19.925 Td [(desc)]TJ ET q -1 0 0 1 172.619 546.469 cm +1 0 0 1 121.81 558.424 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 546.27 Td [(a)]TJ +/F27 9.9626 Tf 125.247 558.225 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 362.845 498.649 cm +1 0 0 1 312.036 510.604 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 498.449 Td [(desc)]TJ +/F30 9.9626 Tf 315.174 510.405 Td [(desc)]TJ ET q -1 0 0 1 387.532 498.649 cm +1 0 0 1 336.723 510.604 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 498.449 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -21.917 Td [(On)-383(Return)]TJ +/F30 9.9626 Tf 339.861 510.405 Td [(type)]TJ 0 g 0 G +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G - 0 -19.926 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -260.887 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(A)-302(logical)-301(mask)-302(whic)28(h)-302(is)-302(tru)1(e)-302(if)]TJ/F11 9.9626 Tf 134.085 0 Td [(x)]TJ/F8 9.9626 Tf 8.7 0 Td [(is)-302(o)28(wned)-302(b)28(y)-301(the)-302(curren)28(t)-302(pro-)]TJ -196.265 -11.955 Td [(cess)-334(Scop)-27(e:)]TJ/F27 9.9626 Tf 52.415 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -52.415 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ/F16 11.9552 Tf -74.941 -33.873 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.176 -19.926 Td [(1.)]TJ + 0 -19.926 Td [(info)]TJ 0 g 0 G - [-500(This)-300(routine)-300(r)1(e)-1(tu)1(rns)-300(a)]TJ/F30 9.9626 Tf 111.214 0 Td [(.true.)]TJ/F8 9.9626 Tf 34.368 0 Td [(v)56(alue)-300(for)-300(an)-300(index)-299(that)-300(is)-300(strictly)-300(o)28(wned)-300(b)28(y)]TJ -132.852 -11.955 Td [(the)-333(curren)27(t)-333(pro)-28(cess,)-333(excluding)-333(the)-334(halo)-333(indices)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ 0 g 0 G - 141.968 -264.549 Td [(92)]TJ + 141.968 -330.303 Td [(87)]TJ 0 g 0 G ET endstream endobj -1483 0 obj +1507 0 obj << -/Length 4979 +/Length 3985 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(o)31(wned)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(6.11)-1125(psb)]TJ ET q -1 0 0 1 162.939 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 166.974 706.129 Td [(index)-375(|)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(sprn)-289(|)-289(Reinit)-290(sparse)-289(matrix)-289(structure)-290(for)-289(psblas)]TJ -25.091 -13.948 Td [(routines.)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -67.079 -18.389 Td [(call)-525(psb_owned_index\050y,)-525(x,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf -37.36 -18.389 Td [(call)-525(psb_sprn\050a,)-525(decsc_a,)-525(info,)-525(clear\051)]TJ 0 g 0 G /F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(x)]TJ + 0 -19.926 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(In)28(teger)-334(indices.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in,)-383(inout)]TJ/F8 9.9626 Tf 42.645 0 Td [(.)]TJ -76.131 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(scalar)-333(or)-334(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(to)-333(b)-28(e)-333(reinitialized.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.95 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.914 0 Td [(psb)]TJ +ET +q +1 0 0 1 362.845 564.402 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 365.983 564.203 Td [(Tspmat)]TJ +ET +q +1 0 0 1 397.993 564.402 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 401.131 564.203 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -31.88 Td [(desc)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -271.347 -19.925 Td [(desc)]TJ ET q -1 0 0 1 121.81 546.469 cm +1 0 0 1 172.619 544.477 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 546.27 Td [(a)]TJ +/F27 9.9626 Tf 176.057 544.278 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 498.649 cm +1 0 0 1 362.845 496.656 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 498.449 Td [(desc)]TJ +/F30 9.9626 Tf 365.983 496.457 Td [(desc)]TJ ET q -1 0 0 1 336.723 498.649 cm +1 0 0 1 387.532 496.656 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 339.861 498.449 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -19.925 Td [(iact)]TJ +/F30 9.9626 Tf 390.67 496.457 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 23.281 0 Td [(sp)-28(eci\014es)-333(action)-334(to)-333(b)-28(e)-333(tak)28(en)-334(in)-333(case)-333(of)-334(range)-333(errors.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 257.147 0 Td [(global)]TJ/F8 9.9626 Tf -255.521 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-256(c)28(haracter)-255(v)56(ariable)]TJ/F30 9.9626 Tf 143.584 0 Td [(I)]TJ/F8 9.9626 Tf 5.23 0 Td [(gnore,)]TJ/F30 9.9626 Tf 29.293 0 Td [(W)]TJ/F8 9.9626 Tf 5.23 0 Td [(arning)-255(or)]TJ/F30 9.9626 Tf 41.67 0 Td [(A)]TJ/F8 9.9626 Tf 5.231 0 Td [(b)-28(ort,)-270(default)]TJ/F30 9.9626 Tf 56.741 0 Td [(I)]TJ/F8 9.9626 Tf 5.231 0 Td [(gnore.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -317.117 -21.918 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -260.887 -19.925 Td [(clear)]TJ 0 g 0 G +/F8 9.9626 Tf 28.795 0 Td [(Cho)-28(ose)-333(whether)-333(to)-334(zero)-333(out)-333(m)-1(atr)1(ix)-334(co)-28(e\016cien)28(ts)]TJ -3.888 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Default:)-444(true.)]TJ 0 g 0 G - 0 -19.926 Td [(y)]TJ +/F27 9.9626 Tf -24.907 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(A)-294(logical)-294(mask)-294(whic)28(h)-294(is)-294(true)-294(for)-294(all)-294(corresp)-28(onding)-294(en)28(tries)-294(of)]TJ/F11 9.9626 Tf 259.229 0 Td [(x)]TJ/F8 9.9626 Tf 8.623 0 Td [(that)-294(are)-294(o)28(wned)]TJ -253.973 -11.955 Td [(b)28(y)-333(the)-334(curren)28(t)-333(pro)-28(cess)-334(Scop)-27(e:)]TJ/F27 9.9626 Tf 132.752 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -132.752 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(scalar)-333(or)-334(ran)1(k)-334(one)-333(logical)-333(arra)27(y)84(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ + 0 -19.925 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.034 -11.955 Td [(An)-333(in)28(teger)-334(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detected.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +/F8 9.9626 Tf 12.176 -19.925 Td [(1.)]TJ 0 g 0 G - [-500(This)-475(routine)-474(returns)-475(a)]TJ/F30 9.9626 Tf 118.186 0 Td [(.true.)]TJ/F8 9.9626 Tf 36.111 0 Td [(v)56(alue)-475(for)-475(those)-475(indices)-474(that)-475(are)-475(strictly)]TJ -141.567 -11.955 Td [(o)28(wned)-334(b)28(y)-333(the)-333(curren)27(t)-333(pro)-28(cess,)-333(excluding)-333(the)-334(halo)-333(indices)]TJ + [-500(On)-333(exit)-334(from)-333(this)-333(routine)-334(t)1(he)-334(sparse)-333(matrix)-334(is)-333(in)-333(the)-333(up)-28(date)-334(state.)]TJ 0 g 0 G - 141.968 -141.013 Td [(93)]TJ + 154.698 -206.766 Td [(88)]TJ 0 g 0 G ET endstream endobj -1489 0 obj +1514 0 obj << -/Length 3247 +/Length 5118 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 171.761 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 175.796 706.129 Td [(is)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(6.12)-1125(psb)]TJ ET q -1 0 0 1 185.644 706.328 cm +1 0 0 1 158.311 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 189.679 706.129 Td [(lo)-31(cal)-375(|)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(geall)-375(|)-375(Allo)-31(cates)-375(a)-375(dense)-375(matrix)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -38.974 -18.389 Td [(call)-525(psb_is_local\050x,)-525(desc_a\051)]TJ +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_geall\050x,)-525(desc_a,)-525(info,)-525(n,)-525(lb\051)]TJ 0 g 0 G /F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G /F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(x)]TJ -0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(In)28(teger)-334(ind)1(e)-1(x.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(scalar)-333(in)28(teger.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.907 -31.88 Td [(desc)]TJ + 0 -19.925 Td [(desc)]TJ ET q -1 0 0 1 172.619 546.469 cm +1 0 0 1 121.81 626.17 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 176.057 546.27 Td [(a)]TJ +/F27 9.9626 Tf 125.247 625.971 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.551 0 Td [(The)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)56(ariable)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 137.346 0 Td [(psb)]TJ ET q -1 0 0 1 362.845 498.649 cm +1 0 0 1 278.467 578.35 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 498.449 Td [(desc)]TJ +/F30 9.9626 Tf 281.605 578.15 Td [(desc)]TJ ET q -1 0 0 1 387.532 498.649 cm +1 0 0 1 303.154 578.35 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 498.449 Td [(type)]TJ +/F30 9.9626 Tf 306.292 578.15 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -21.917 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -227.319 -31.88 Td [(n)]TJ 0 g 0 G +/F8 9.9626 Tf 11.347 0 Td [(The)-333(n)27(u)1(m)27(b)-27(e)-1(r)-333(of)-333(columns)-333(of)-334(the)-333(dense)-333(m)-1(atr)1(ix)-334(to)-333(b)-28(e)-333(allo)-28(cated.)]TJ 13.56 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-343(as:)-463(In)27(teger)-343(scalar,)-345(default)-343(1.)-473(It)-343(is)-343(not)-343(a)-343(v)56(alid)-343(argumen)28(t)-343(if)]TJ/F11 9.9626 Tf 294.599 0 Td [(x)]TJ/F8 9.9626 Tf 9.11 0 Td [(is)-343(a)]TJ -303.709 -11.955 Td [(rank-1)-333(arra)28(y)83(.)]TJ 0 g 0 G - 0 -19.926 Td [(F)96(unction)-384(v)64(alue)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(lb)]TJ 0 g 0 G -/F8 9.9626 Tf 78.386 0 Td [(A)-264(logical)-265(mask)-264(whic)27(h)-264(is)-265(true)-264(if)]TJ/F11 9.9626 Tf 131.492 0 Td [(x)]TJ/F8 9.9626 Tf 8.329 0 Td [(is)-265(lo)-27(cal)-265(to)-264(the)-265(curren)28(t)-264(pro)-28(cess)]TJ -193.301 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ/F16 11.9552 Tf -74.941 -33.873 Td [(Notes)]TJ +/F8 9.9626 Tf 14.529 0 Td [(The)-489(lo)28(w)27(er)-489(b)-27(ound)-489(for)-489(the)-490(column)-489(index)-489(range)-489(of)-489(the)-489(dense)-489(matrix)-489(to)-489(b)-28(e)]TJ 10.378 -11.955 Td [(allo)-28(cated.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-343(as:)-463(In)27(teger)-343(scalar,)-345(default)-343(1.)-473(It)-343(is)-343(not)-343(a)-343(v)56(alid)-343(argumen)28(t)-343(if)]TJ/F11 9.9626 Tf 294.599 0 Td [(x)]TJ/F8 9.9626 Tf 9.11 0 Td [(is)-343(a)]TJ -303.709 -11.955 Td [(rank-1)-333(arra)28(y)83(.)]TJ 0 g 0 G -/F8 9.9626 Tf 12.176 -19.926 Td [(1.)]TJ +/F27 9.9626 Tf -24.907 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G - [-500(This)-239(routine)-239(returns)-239(a)]TJ/F30 9.9626 Tf 108.787 0 Td [(.true.)]TJ/F8 9.9626 Tf 33.762 0 Td [(v)56(alue)-239(for)-239(an)-239(index)-239(that)-239(is)-239(lo)-27(cal)-239(to)-239(the)-239(curren)28(t)]TJ -129.819 -11.955 Td [(pro)-28(cess,)-333(including)-333(the)-334(halo)-333(indices)]TJ 0 g 0 G - 141.968 -264.549 Td [(94)]TJ + 0 -19.925 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(The)-333(dense)-334(matrix)-333(to)-333(b)-28(e)-334(all)1(o)-28(cated.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-303(as:)-430(a)-304(rank)-303(one)-304(or)-304(t)28(w)28(o)-304(arra)28(y)-304(with)-303(the)-304(ALLOCA)83(T)83(ABLE)-303(attribute)]TJ 0 -11.955 Td [(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 89.968 0 Td [(psb)]TJ +ET +q +1 0 0 1 231.089 293.418 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 234.227 293.219 Td [(T)]TJ +ET +q +1 0 0 1 240.085 293.418 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 243.223 293.219 Td [(vect)]TJ +ET +q +1 0 0 1 264.772 293.418 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 267.911 293.219 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.921 0 Td [(,)-333(of)-334(t)28(yp)-28(e)-333(real,)-333(complex)-334(or)-333(in)28(teger.)]TJ +0 g 0 G +/F27 9.9626 Tf -188.937 -31.88 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ +0 g 0 G + 141.968 -123.08 Td [(89)]TJ 0 g 0 G ET endstream endobj -1495 0 obj +1520 0 obj << -/Length 4963 +/Length 6852 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(lo)-31(cal)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(6.13)-1125(psb)]TJ ET q -1 0 0 1 152.879 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 156.914 706.129 Td [(index)-375(|)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(geins)-375(|)-375(Dense)-375(matrix)-375(insertion)-375(routine)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -57.019 -18.389 Td [(call)-525(psb_local_index\050y,)-525(x,)-525(desc_a,)-525(info\051)]TJ +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_geins\050m,)-525(irw,)-525(val,)-525(x,)-525(desc_a,)-525(info)-525([,dupl,local]\051)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf 0 -20.681 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.43 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(x)]TJ + 0 -19.431 Td [(m)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(In)28(teger)-334(indices.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in,)-383(inout)]TJ/F8 9.9626 Tf 42.645 0 Td [(.)]TJ -76.131 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(scalar)-333(or)-334(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ +/F8 9.9626 Tf 14.529 0 Td [(Num)28(b)-28(er)-333(of)-334(ro)28(ws)-333(in)]TJ/F11 9.9626 Tf 84.516 0 Td [(v)-36(al)]TJ/F8 9.9626 Tf 16.942 0 Td [(to)-333(b)-28(e)-333(inse)-1(r)1(te)-1(d)1(.)]TJ -91.081 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -31.88 Td [(desc)]TJ +/F27 9.9626 Tf -24.906 -19.431 Td [(irw)]TJ +0 g 0 G +/F8 9.9626 Tf 21.157 0 Td [(Indices)-444(of)-445(the)-444(ro)27(ws)-444(to)-445(b)-27(e)-445(inserted.)-778(Sp)-28(eci\014cally)84(,)-472(ro)27(w)]TJ/F11 9.9626 Tf 237.973 0 Td [(i)]TJ/F8 9.9626 Tf 7.861 0 Td [(of)]TJ/F11 9.9626 Tf 12.454 0 Td [(v)-36(al)]TJ/F8 9.9626 Tf 18.049 0 Td [(will)-444(b)-28(e)-445(in-)]TJ -272.588 -11.955 Td [(serted)-435(in)28(to)-436(th)1(e)-436(lo)-27(cal)-436(ro)28(w)-435(corresp)-28(onding)-435(to)-435(the)-435(global)-435(ro)28(w)-435(index)]TJ/F11 9.9626 Tf 289.252 0 Td [(ir)-28(w)]TJ/F8 9.9626 Tf 15.605 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051.)]TJ -312.163 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.43 Td [(v)64(al)]TJ +0 g 0 G +/F8 9.9626 Tf 19.143 0 Td [(the)-333(dense)-334(submatrix)-333(to)-333(b)-28(e)-333(inserted.)]TJ 5.763 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(1)-333(o)-1(r)-333(2)-333(arra)28(y)83(.)-444(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-334(v)56(alue.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.43 Td [(desc)]TJ ET q -1 0 0 1 121.81 546.469 cm +1 0 0 1 172.619 414.689 cm []0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F27 9.9626 Tf 125.247 546.27 Td [(a)]TJ +/F27 9.9626 Tf 176.057 414.49 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 498.649 cm +1 0 0 1 362.845 366.869 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 498.449 Td [(desc)]TJ +/F30 9.9626 Tf 365.983 366.669 Td [(desc)]TJ ET q -1 0 0 1 336.723 498.649 cm +1 0 0 1 387.532 366.869 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 339.861 498.449 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -260.887 -19.925 Td [(iact)]TJ -0 g 0 G -/F8 9.9626 Tf 23.281 0 Td [(sp)-28(eci\014es)-333(action)-334(to)-333(b)-28(e)-333(tak)28(en)-334(in)-333(case)-333(of)-334(range)-333(errors.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 257.147 0 Td [(global)]TJ/F8 9.9626 Tf -255.521 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-256(c)28(haracter)-255(v)56(ariable)]TJ/F30 9.9626 Tf 143.584 0 Td [(I)]TJ/F8 9.9626 Tf 5.23 0 Td [(gnore,)]TJ/F30 9.9626 Tf 29.293 0 Td [(W)]TJ/F8 9.9626 Tf 5.23 0 Td [(arning)-255(or)]TJ/F30 9.9626 Tf 41.67 0 Td [(A)]TJ/F8 9.9626 Tf 5.231 0 Td [(b)-28(ort,)-270(default)]TJ/F30 9.9626 Tf 56.741 0 Td [(I)]TJ/F8 9.9626 Tf 5.231 0 Td [(gnore.)]TJ -0 g 0 G -/F27 9.9626 Tf -317.117 -21.918 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -19.926 Td [(y)]TJ +/F30 9.9626 Tf 390.67 366.669 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(A)-346(logical)-345(mask)-346(whic)28(h)-346(is)-345(true)-346(for)-345(all)-346(corresp)-28(onding)-345(en)28(tries)-346(of)]TJ/F11 9.9626 Tf 264.883 0 Td [(x)]TJ/F8 9.9626 Tf 9.136 0 Td [(that)-346(are)-345(lo)-28(cal)]TJ -260.14 -11.955 Td [(to)-333(the)-334(curren)28(t)-333(pro)-28(cess)-333(Scop)-28(e:)]TJ/F27 9.9626 Tf 131.092 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -131.092 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(scalar)-333(or)-334(ran)1(k)-334(one)-333(logical)-333(arra)27(y)84(.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(info)]TJ +/F27 9.9626 Tf -260.887 -19.43 Td [(dupl)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +/F8 9.9626 Tf 27.259 0 Td [(Ho)28(w)-334(to)-333(handle)-333(duplicate)-333(co)-28(e\016cien)27(ts.)]TJ -2.352 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-308(as:)-432(in)27(teger,)-313(p)-28(ossible)-309(v)56(alues:)]TJ/F30 9.9626 Tf 163.697 0 Td [(psb_dupl_ovwrt_)]TJ/F8 9.9626 Tf 78.455 0 Td [(,)]TJ/F30 9.9626 Tf 5.891 0 Td [(psb_dupl_add_)]TJ/F8 9.9626 Tf 67.995 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +/F27 9.9626 Tf -340.944 -19.43 Td [(lo)-32(cal)]TJ 0 g 0 G - [-500(This)-308(routine)-309(retur)1(ns)-309(a)]TJ/F30 9.9626 Tf 111.554 0 Td [(.true.)]TJ/F8 9.9626 Tf 34.454 0 Td [(v)56(alue)-309(for)-308(those)-308(indices)-309(that)-308(are)-308(lo)-28(cal)-308(to)-309(the)]TJ -133.278 -11.955 Td [(curren)28(t)-333(pro)-28(cess,)-334(including)-333(the)-333(halo)-333(indices.)]TJ +/F8 9.9626 Tf 28.054 0 Td [(Whether)-289(the)-289(en)28(tries)-289(in)-289(the)-289(index)-288(v)27(ector)]TJ/F30 9.9626 Tf 172.77 0 Td [(irw)]TJ/F8 9.9626 Tf 15.691 0 Td [(,)-298(are)-289(already)-289(in)-288(lo)-28(cal)-289(n)28(um)28(b)-28(er-)]TJ -191.608 -11.955 Td [(ing.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(logical)-333(v)55(alue;)-333(default:)]TJ/F30 9.9626 Tf 163.055 0 Td [(.false.)]TJ/F8 9.9626 Tf 36.612 0 Td [(.)]TJ 0 g 0 G - 141.968 -141.013 Td [(95)]TJ +/F27 9.9626 Tf -224.574 -20.68 Td [(On)-383(Return)]TJ 0 g 0 G -ET - -endstream -endobj -1501 0 obj -<< -/Length 3804 ->> -stream 0 g 0 G + 0 -19.43 Td [(x)]TJ 0 g 0 G -BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 171.761 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 175.796 706.129 Td [(get)]TJ +/F8 9.9626 Tf 11.028 0 Td [(the)-333(output)-334(d)1(e)-1(n)1(s)-1(e)-333(matrix.)]TJ 13.879 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-232(as:)-394(a)-233(rank)-233(one)-232(or)-233(t)28(w)28(o)-233(arra)28(y)-233(or)-232(an)-233(ob)-55(ject)-233(of)-233(t)28(yp)-27(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 241.975 0 Td [(psb)]TJ ET q -1 0 0 1 194.695 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 433.906 144.435 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F16 11.9552 Tf 198.729 706.129 Td [(b)-31(oundary)-375(|)-375(Extract)-375(list)-375(of)-375(b)-32(oundary)-375(elemen)32(ts)]TJ -0 g 0 G -0 g 0 G -/F30 9.9626 Tf -48.024 -18.389 Td [(call)-525(psb_get_boundary\050bndel,)-525(desc,)-525(info\051)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -19.925 Td [(desc)]TJ -0 g 0 G -/F8 9.9626 Tf 26.208 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 437.044 144.236 Td [(T)]TJ ET q -1 0 0 1 362.845 578.35 cm +1 0 0 1 442.902 144.435 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 578.15 Td [(desc)]TJ +/F30 9.9626 Tf 446.04 144.236 Td [(vect)]TJ ET q -1 0 0 1 387.532 578.35 cm +1 0 0 1 467.589 144.435 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 578.15 Td [(type)]TJ +/F30 9.9626 Tf 470.727 144.236 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F8 9.9626 Tf 20.922 0 Td [(,)]TJ -316.038 -11.955 Td [(of)-333(t)27(yp)-27(e)-334(real,)-333(complex)-333(or)-334(in)28(teger.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -21.917 Td [(On)-383(Return)]TJ + 141.968 -41.843 Td [(90)]TJ 0 g 0 G +ET + +endstream +endobj +1524 0 obj +<< +/Length 1111 +>> +stream 0 g 0 G - 0 -19.926 Td [(bndel)]TJ 0 g 0 G -/F8 9.9626 Tf 32.51 0 Td [(The)-268(list)-267(of)-268(b)-27(oundary)-268(elemen)28(ts)-268(on)-267(the)-268(calling)-267(pro)-28(cess,)-281(in)-267(lo)-28(cal)-268(n)28(um)28(b)-28(ering.)]TJ -7.604 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-456(as:)-691(a)-457(rank)-456(one)-457(arra)28(y)-457(with)-456(the)-457(ALLOCA)84(T)83(ABLE)-456(attribute,)-488(of)]TJ 0 -11.955 Td [(t)28(yp)-28(e)-333(in)27(teger.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -31.881 Td [(info)]TJ +BT +/F27 9.9626 Tf 99.895 706.129 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.148 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(An)-333(in)28(te)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ/F16 11.9552 Tf -24.906 -21.917 Td [(Notes)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.176 -19.926 Td [(1.)]TJ +/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ 0 g 0 G - [-500(If)-269(there)-269(are)-269(no)-269(b)-28(oundary)-269(elemen)28(ts)-269(\050i.e.,)-282(if)-269(the)-269(lo)-28(cal)-269(part)-269(of)-269(the)-270(connectivit)28(y)]TJ 12.73 -11.955 Td [(graph)-449(is)-450(self-con)28(tained\051)-450(the)-449(output)-450(v)28(ector)-449(is)-450(set)-449(to)-450(the)-449(\134not)-450(allo)-28(cated")]TJ 0 -11.955 Td [(state.)]TJ + [-500(Dense)-333(v)27(ectors/matrices)-333(do)-333(not)-334(ha)28(v)28(e)-334(an)-333(asso)-28(ciated)-333(state;)]TJ 0 g 0 G - -12.73 -19.925 Td [(2.)]TJ + 0 -19.925 Td [(2.)]TJ 0 g 0 G - [-500(Otherwise)-288(the)-289(size)-288(of)]TJ/F30 9.9626 Tf 105.44 0 Td [(bndel)]TJ/F8 9.9626 Tf 29.024 0 Td [(will)-288(b)-28(e)-288(exactly)-288(e)-1(qu)1(al)-289(to)-288(the)-288(n)28(um)27(b)-27(er)-289(of)-288(b)-28(oun)1(d-)]TJ -121.734 -11.956 Td [(ary)-333(elemen)27(ts.)]TJ + [-500(Duplicate)-292(en)28(tries)-293(are)-292(either)-292(o)28(v)28(erwritten)-292(or)-293(added,)-300(there)-292(is)-292(no)-292(pro)27(vision)-292(for)]TJ 12.73 -11.955 Td [(raising)-333(an)-334(error)-333(condition.)]TJ 0 g 0 G - 141.968 -208.758 Td [(96)]TJ + 141.968 -494.147 Td [(91)]TJ 0 g 0 G ET endstream endobj -1508 0 obj +1534 0 obj << -/Length 3654 +/Length 5226 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(get)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(6.14)-1125(psb)]TJ ET q -1 0 0 1 143.885 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 147.92 706.129 Td [(o)31(v)31(erlap)-375(|)-375(Extract)-375(list)-375(of)-375(o)32(v)31(erlap)-375(elemen)31(ts)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(geasb)-375(|)-375(Assem)31(bly)-375(a)-375(dense)-375(matrix)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -48.025 -18.389 Td [(call)-525(psb_get_overlap\050ovrel,)-525(desc,)-525(info\051)]TJ +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_geasb\050x,)-525(desc_a,)-525(info,)-525(mold\051)]TJ 0 g 0 G /F27 9.9626 Tf 0 -21.918 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G /F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G 0 -19.925 Td [(desc)]TJ +ET +q +1 0 0 1 172.619 626.17 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 176.057 625.971 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 26.209 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -1.302 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(The)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(v)56(ariable)-334(of)-333(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 137.347 0 Td [(psb)]TJ +ET +q +1 0 0 1 329.276 578.35 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT 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9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(preconditioner)-333(data)-333(structure)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 197.537 0 Td [(psb)]TJ ET -q -1 0 0 1 389.467 408.985 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q + +endstream +endobj +1544 0 obj +<< +/Length 3466 +>> +stream +0 g 0 G +0 g 0 G BT -/F30 9.9626 Tf 392.606 408.786 Td [(prec)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(6.16)-1125(psb)]TJ ET q -1 0 0 1 414.155 408.985 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 209.121 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F30 9.9626 Tf 417.293 408.786 Td [(type)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(gelp)-525(|)-526(Applies)-525(a)-526(left)-525(p)-31(erm)31(utation)-525(to)-526(a)-525(dense)]TJ -25.091 -13.948 Td [(matrix)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -287.509 -19.926 Td 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[(A)-333(c)27(har)1(ac)-1(ter)-333(that)-333(sp)-28(eci\014es)-333(whether)-334(to)-333(p)-28(erm)28(ute)]TJ/F11 9.9626 Tf 204.179 0 Td [(A)]TJ/F8 9.9626 Tf 10.793 0 Td [(or)]TJ/F11 9.9626 Tf 12.204 0 Td [(A)]TJ/F10 6.9738 Tf 7.472 3.616 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.616 Td [(.)]TJ -246.626 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(single)-333(c)28(haracter)-334(with)-333(v)56(alue)-334('N')-333(for)]TJ/F11 9.9626 Tf 217.435 0 Td [(A)]TJ/F8 9.9626 Tf 10.792 0 Td [(or)-333('T')-334(for)]TJ/F11 9.9626 Tf 43.504 0 Td [(A)]TJ/F10 6.9738 Tf 7.472 3.615 Td [(T)]TJ/F8 9.9626 Tf 6.276 -3.615 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -310.386 -31.881 Td [(ip)-32(erm)]TJ +0 g 0 G +/F8 9.9626 Tf 34.364 0 Td [(An)-333(in)28(tege)-1(r)-333(arra)28(y)-333(con)27(tain)1(ing)-334(p)-28(erm)28(utation)-333(information.)]TJ -9.457 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(one-dimensional)-334(arra)28(y)84(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -31.881 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(The)-333(dense)-334(matrix)-333(to)-333(b)-28(e)-333(p)-28(erm)27(u)1(te)-1(d)1(.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(one)-333(or)-333(t)27(w)28(o)-333(dimensional)-334(arra)28(y)84(.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -33.873 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(info)]TJ +0 g 0 G +/F8 9.9626 Tf 23.758 0 Td [(Error)-333(co)-28(de.)]TJ 1.149 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.034 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detected.)]TJ 0 g 0 G - -63.207 -242.632 Td [(100)]TJ + 141.967 -212.744 Td [(94)]TJ 0 g 0 G ET endstream endobj -1534 0 obj +1549 0 obj << -/Length 5762 +/Length 6552 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(Sorting)-375(utilities)-375(|)]TJ 0 -19.593 Td [(psb)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(6.17)-1125(psb)]TJ ET q -1 0 0 1 120.951 686.736 cm +1 0 0 1 158.311 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 686.536 Td [(msort)-375(|)-375(Sorting)-375(b)31(y)-375(the)-375(Merge-sort)-375(algorithm)]TJ -25.091 -12.601 Td [(psb)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(glob)]TJ ET q -1 0 0 1 120.951 674.134 cm +1 0 0 1 187.811 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 673.935 Td [(qsort)-375(|)-375(Sorting)-375(b)31(y)-375(the)-375(Quic)31(ksort)-375(algorithm)]TJ -25.091 -12.602 Td [(psb)]TJ +/F16 11.9552 Tf 191.846 706.129 Td [(to)]TJ ET q -1 0 0 1 120.951 661.532 cm +1 0 0 1 204.608 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 661.333 Td [(hsort)-375(|)-375(Sorting)-375(b)31(y)-375(the)-375(Heapsort)-375(algorithm)]TJ +/F16 11.9552 Tf 208.643 706.129 Td [(lo)-31(c)-359(|)-359(Global)-358(to)-359(lo)-31(cal)-359(indices)-359(con)32(v)31(ertion)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -25.091 -22.511 Td [(call)-525(psb_msort\050x,ix,dir,flag\051)]TJ 0 -11.955 Td [(call)-525(psb_qsort\050x,ix,dir,flag\051)]TJ 0 -11.955 Td [(call)-525(psb_hsort\050x,ix,dir,flag\051)]TJ/F8 9.9626 Tf 14.944 -21.865 Td [(These)-332(serial)-332(rou)1(tines)-332(sort)-332(a)-332(sequence)]TJ/F11 9.9626 Tf 162.708 0 Td [(X)]TJ/F8 9.9626 Tf 12.34 0 Td [(in)28(to)-332(ascending)-332(or)-331(descending)-332(order.)]TJ -189.992 -11.955 Td [(The)-320(argumen)28(t)-321(meaning)-320(is)-320(iden)28(tical)-320(for)-320(the)-321(thr)1(e)-1(e)-320(calls;)-324(the)-321(on)1(ly)-321(di\013erence)-320(is)-320(the)]TJ 0 -11.955 Td [(algorithm)-333(used)-334(to)-333(accomplish)-333(the)-334(task)-333(\050see)-334(Usage)-333(Notes)-333(b)-28(elo)28(w\051.)]TJ +/F30 9.9626 Tf -108.748 -18.389 Td [(call)-525(psb_glob_to_loc\050x,)-525(y,)-525(desc_a,)-525(info,)-525(iact,owned\051)]TJ 0 -11.956 Td [(call)-525(psb_glob_to_loc\050x,)-525(desc_a,)-525(info,)-525(iact,owned\051)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -21.865 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf 0 -21.201 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -22.511 Td [(On)-383(En)32(try)]TJ -0 g 0 G +/F27 9.9626 Tf -33.797 -19.639 Td [(On)-383(En)32(try)]TJ 0 g 0 G - 0 -22.511 Td [(x)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(The)-333(sequence)-334(to)-333(b)-28(e)-333(sorted.)]TJ 13.879 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger,)-333(real)-334(or)-333(complex)-333(arra)27(y)-333(of)-333(rank)-333(1.)]TJ + 0 -19.639 Td [(x)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -22.511 Td [(ix)]TJ +/F8 9.9626 Tf 11.028 0 Td [(An)-333(in)28(te)-1(ger)-333(v)28(ector)-333(of)-334(indices)-333(to)-333(b)-28(e)-334(con)28(v)28(erted.)]TJ 13.879 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in,)-383(inout)]TJ/F8 9.9626 Tf 42.645 0 Td [(.)]TJ -76.131 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ 0 g 0 G -/F8 9.9626 Tf 14.211 0 Td [(A)-333(v)27(ector)-333(of)-333(indices.)]TJ 10.696 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)-333(of)-333(\050at)-333(le)-1(ast\051)-333(the)-333(same)-334(size)-333(as)]TJ/F11 9.9626 Tf 258.559 0 Td [(X)]TJ/F8 9.9626 Tf 9.035 0 Td [(.)]TJ +/F27 9.9626 Tf -24.907 -31.594 Td [(desc)]TJ +ET +q +1 0 0 1 121.81 536.09 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 125.247 535.891 Td [(a)]TJ 0 g 0 G -/F27 9.9626 Tf -292.501 -22.511 Td [(dir)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(comm)27(unication)-333(descriptor.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -51.024 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 312.036 488.27 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 315.174 488.07 Td [(desc)]TJ +ET +q +1 0 0 1 336.723 488.27 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 339.861 488.07 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 19.248 0 Td [(The)-333(desired)-334(ordering.)]TJ 5.659 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue:)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -22.511 Td [(In)32(teger)-383(and)-384(real)-383(data:)]TJ +/F27 9.9626 Tf -260.887 -19.638 Td [(iact)]TJ 0 g 0 G -/F30 9.9626 Tf 114.397 0 Td [(psb_sort_up_)]TJ/F8 9.9626 Tf 62.764 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_sort_down_)]TJ/F8 9.9626 Tf 73.224 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf -306.867 -11.955 Td [(psb_asort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(;)-333(default)]TJ/F30 9.9626 Tf 39.574 0 Td [(psb_sort_up_)]TJ/F8 9.9626 Tf 62.764 0 Td [(.)]TJ +/F8 9.9626 Tf 23.281 0 Td [(sp)-28(eci\014es)-333(action)-334(to)-333(b)-28(e)-333(tak)28(en)-334(in)-333(case)-333(of)-334(range)-333(errors.)-444(Scop)-28(e:)]TJ/F27 9.9626 Tf 257.147 0 Td [(global)]TJ/F8 9.9626 Tf -255.521 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-255(as:)-405(a)-256(c)28(haracter)-255(v)56(ariable)]TJ/F30 9.9626 Tf 143.584 0 Td [(I)]TJ/F8 9.9626 Tf 5.23 0 Td [(gnore,)]TJ/F30 9.9626 Tf 29.293 0 Td [(W)]TJ/F8 9.9626 Tf 5.23 0 Td [(arning)-255(or)]TJ/F30 9.9626 Tf 41.67 0 Td [(A)]TJ/F8 9.9626 Tf 5.231 0 Td [(b)-28(ort,)-270(default)]TJ/F30 9.9626 Tf 56.741 0 Td [(I)]TJ/F8 9.9626 Tf 5.231 0 Td [(gnore.)]TJ 0 g 0 G -/F27 9.9626 Tf -202.711 -17.233 Td [(Complex)-383(data:)]TJ +/F27 9.9626 Tf -317.117 -19.639 Td [(o)32(wned)]TJ 0 g 0 G -/F30 9.9626 Tf 78.338 0 Td [(psb_lsort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_lsort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(;)]TJ -364.927 -11.955 Td [(default)]TJ/F30 9.9626 Tf 33.485 0 Td [(psb_lsort_up_)]TJ/F8 9.9626 Tf 67.995 0 Td [(.)]TJ +/F8 9.9626 Tf 36.647 0 Td [(Sp)-28(ec\014es)-333(v)55(alid)-333(range)-333(of)-334(i)1(nput)-334(Scop)-27(e:)]TJ/F27 9.9626 Tf 158.933 0 Td [(global)]TJ/F8 9.9626 Tf -170.673 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(If)-294(true,)-302(then)-294(only)-295(indices)-294(strictly)-294(o)28(wned)-295(b)28(y)-294(the)-294(curren)28(t)-295(pro)-27(ces)-1(s)-294(are)-294(consid-)]TJ 0 -11.955 Td [(ered)-333(v)55(alid,)-333(if)-333(false)-334(then)-333(halo)-333(indices)-334(are)-333(also)-333(accepted.)-445(Default:)-444(false.)]TJ 0 g 0 G -/F27 9.9626 Tf -148.305 -22.511 Td [(\015ag)]TJ +/F27 9.9626 Tf -24.907 -21.202 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 22.645 0 Td [(Whether)-333(to)-334(k)28(eep)-333(the)-333(original)-334(v)56(alues)-333(in)]TJ/F11 9.9626 Tf 170.582 0 Td [(I)-78(X)]TJ/F8 9.9626 Tf 14.197 0 Td [(.)]TJ -182.517 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.956 Td [(Sp)-28(eci\014ed)-222(as:)-389(an)-222(in)28(teger)-222(v)55(alue)]TJ/F30 9.9626 Tf 125.446 0 Td [(psb_sort_ovw_idx_)]TJ/F8 9.9626 Tf 91.13 0 Td [(or)]TJ/F30 9.9626 Tf 11.097 0 Td [(psb_sort_keep_idx_)]TJ/F8 9.9626 Tf 94.147 0 Td [(;)]TJ -321.82 -11.955 Td [(default)]TJ/F30 9.9626 Tf 33.486 0 Td [(psb_sort_ovw_idx_)]TJ/F8 9.9626 Tf 88.915 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -147.308 -24.503 Td [(On)-383(Return)]TJ + 0 -19.639 Td [(x)]TJ 0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(If)]TJ/F11 9.9626 Tf 10.133 0 Td [(y)]TJ/F8 9.9626 Tf 8.733 0 Td [(is)-350(not)-351(presen)28(t,)-355(then)]TJ/F11 9.9626 Tf 88.586 0 Td [(x)]TJ/F8 9.9626 Tf 9.185 0 Td [(is)-350(o)27(v)28(erwritten)-350(with)-351(th)1(e)-351(translated)-350(in)28(teger)-351(indices.)]TJ -102.758 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-333(in)27(teger)-333(arra)28(y)83(.)]TJ 0 g 0 G - 0 -22.511 Td [(x)]TJ +/F27 9.9626 Tf -24.907 -19.639 Td [(y)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(The)-333(sequence)-334(of)-333(v)55(alues,)-333(in)-333(the)-334(c)28(hosen)-333(ordering.)]TJ 13.879 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 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[-500(If)-343(there)-343(are)-344(no)-343(o)28(v)28(erlap)-344(elemen)28(ts)-343(the)-343(output)-344(v)28(ector)-343(is)-343(set)-344(to)-343(the)-343(\134not)-343(allo-)]TJ 12.73 -11.955 Td [(cated")-333(state.)]TJ +0 g 0 G + -12.73 -19.925 Td [(2.)]TJ +0 g 0 G + [-500(Otherwise)-284(the)-284(size)-283(of)]TJ/F30 9.9626 Tf 105.261 0 Td [(ovrel)]TJ/F8 9.9626 Tf 28.979 0 Td [(will)-284(b)-27(e)-284(exactly)-284(equal)-284(to)-284(th)1(e)-284(n)28(um)27(b)-27(er)-284(of)-284(o)28(v)28(erlap)]TJ -121.51 -11.955 Td [(elemen)28(ts.)]TJ 0 g 0 G - 139.477 -170.9 Td [(112)]TJ + 139.477 -220.714 Td [(103)]TJ 0 g 0 G ET endstream endobj -1601 0 obj +1606 0 obj << -/Length 5146 +/Length 5828 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(6.25)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(sum)-375(|)-375(Global)-375(sum)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(sp)]TJ +ET +q +1 0 0 1 226.74 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +Q +BT +/F16 11.9552 Tf 230.775 706.129 Td [(getro)31(w)-433(|)-433(E)-1(xtract)-433(ro)31(w\050s\051)-433(from)-434(a)-433(sparse)-433(ma-)]TJ -42.71 -13.948 Td [(trix)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_sum\050icontxt,)-525(dat,)-525(root\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-318(subroutine)-319(implemen)28(ts)-318(a)-319(sum)-318(reduction)-318(op)-28(eration)-318(based)-319(on)-318(the)-318(under-)]TJ -14.944 -11.955 Td [(lying)-333(comm)27(unication)-333(library)84(.)]TJ +/F30 9.9626 Tf -37.36 -18.389 Td [(call)-525(psb_sp_getrow\050row,)-525(a,)-525(nz,)-525(ia,)-525(ja,)-525(val,)-525(info,)-525(&)]TJ 73.225 -11.955 Td [(&)-525(append,)-525(nzin,)-525(lrw\051)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -19.926 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -73.225 -20.298 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.277 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(icon)32(txt)]TJ + 0 -19.277 Td [(ro)32(w)]TJ 0 g 0 G -/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyin)1(g)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ +/F8 9.9626 Tf 23.384 0 Td [(The)-333(\050\014rst\051)-334(ro)28(w)-333(to)-334(b)-27(e)-334(extracted.)]TJ 1.523 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.95 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)]TJ/F11 9.9626 Tf 104.69 0 Td [(>)]TJ/F8 9.9626 Tf 10.517 0 Td [(0.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(dat)]TJ +/F27 9.9626 Tf -140.114 -19.277 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 21.371 0 Td [(The)-333(lo)-28(cal)-334(con)28(tribution)-333(to)-333(the)-334(global)-333(sum.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-464(a)-464(rank)-463(1)-464(or)-464(2)-464(arra)28(y)83(.)-1299(T)28(yp)-28(e,)-497(kind,)-496(rank)-464(and)-463(size)-464(m)27(ust)-463(agree)-464(on)-464(all)]TJ 0 -11.955 Td [(pro)-28(cesses.)]TJ +/F8 9.9626 Tf 10.551 0 Td [(the)-333(matrix)-334(from)-333(whic)28(h)-333(to)-334(get)-333(ro)28(ws.)]TJ 14.356 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.95 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.95 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf -25.183 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 362.845 488.266 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 365.983 488.067 Td [(Tspmat)]TJ +ET +q +1 0 0 1 397.993 488.266 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 401.131 488.067 Td [(type)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(ro)-32(ot)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 25.931 0 Td [(Pro)-28(cess)-310(to)-309(hold)-310(the)-310(\014nal)-310(sum,)-314(or)]TJ/F14 9.9626 Tf 144.053 0 Td [(\000)]TJ/F8 9.9626 Tf 7.748 0 Td [(1)-310(to)-310(mak)28(e)-310(it)-309(a)27(v)56(ailable)-310(on)-310(all)-309(pro)-28(cesses.)]TJ -152.825 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.428 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.748 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.962 0 Td [(1,)-333(default)-334(-1.)]TJ +/F27 9.9626 Tf -271.347 -19.277 Td [(app)-32(end)]TJ 0 g 0 G -/F27 9.9626 Tf -251.325 -21.918 Td [(On)-383(Return)]TJ +/F8 9.9626 Tf 41.58 0 Td [(Whether)-333(to)-334(app)-27(end)-334(or)-333(o)28(v)28(erwrite)-334(existing)-333(output.)]TJ -16.674 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf -25.184 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(logical)-333(v)55(alue)-333(default:)-444(false)-334(\050o)28(v)28(erwrite\051.)]TJ 0 g 0 G +/F27 9.9626 Tf -24.906 -19.277 Td [(nzin)]TJ 0 g 0 G - 0 -19.925 Td [(dat)]TJ +/F8 9.9626 Tf 25.986 0 Td [(Input)-333(size)-334(to)-333(b)-28(e)-333(app)-28(ended)-333(to.)]TJ -1.08 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 27.951 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -27.951 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf -25.184 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-398(as:)-573(an)-398(in)28(teger)]TJ/F11 9.9626 Tf 107.908 0 Td [(>)]TJ/F8 9.9626 Tf 11.588 0 Td [(0.)-638(When)-398(app)-28(end)-398(is)-397(true,)-414(s)-1(p)-27(eci\014es)-398(ho)28(w)-398(man)27(y)]TJ -119.496 -11.955 Td [(en)28(tries)-334(in)-333(the)-333(output)-333(v)27(ectors)-333(are)-333(already)-334(\014lled.)]TJ 0 g 0 G -/F8 9.9626 Tf 21.372 0 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9.9626 Tf -287.509 -19.926 Td [(On)-383(Return)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 32.469 0 Td [(dat)]TJ/F8 9.9626 Tf 18.273 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.012 -11.956 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ 0 g 0 G - -12.73 -19.925 Td [(2.)]TJ + 0 -19.925 Td [(F)96(unction)-384(v)64(alue)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 33.209 0 Td [(dat)]TJ/F8 9.9626 Tf 19.012 0 Td [(argumen)28(t)-333(m)-1(a)28(y)-333(also)-333(b)-28(e)-334(a)-333(long)-333(in)28(teger)-334(scalar.)]TJ +/F8 9.9626 Tf 78.386 0 Td [(The)-332(memory)-331(o)-28(ccupation)-332(of)-331(the)-332(ob)-55(jec)-1(t)-331(sp)-28(eci\014ed)-332(in)-331(the)-332(calling)]TJ -53.48 -11.955 Td [(sequence,)-333(in)-334(b)28(ytes.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td 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73.224 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf -306.867 -11.955 Td [(psb_asort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(;)-333(default)]TJ/F30 9.9626 Tf 39.574 0 Td [(psb_sort_up_)]TJ/F8 9.9626 Tf 62.764 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(ro)-32(ot)]TJ +/F27 9.9626 Tf -202.711 -17.233 Td [(Complex)-383(data:)]TJ 0 g 0 G -/F8 9.9626 Tf 25.93 0 Td [(Pro)-28(cess)-276(to)-276(hold)-276(the)-276(\014nal)-276(v)56(alue,)-287(or)]TJ/F14 9.9626 Tf 146.411 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-276(to)-276(mak)28(e)-276(it)-276(a)28(v)55(ailable)-276(on)-276(all)-276(pr)1(o)-28(cesses)-1(.)]TJ -155.183 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.427 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.749 0 Td [(<)]TJ/F8 9.9626 Tf 7.748 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1,)-333(default)-334(-1.)]TJ +/F30 9.9626 Tf 78.338 0 Td [(psb_lsort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_lsort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_up_)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)]TJ/F30 9.9626 Tf 5.203 0 Td [(psb_asort_down_)]TJ/F8 9.9626 Tf 78.455 0 Td [(;)]TJ -364.927 -11.955 Td [(default)]TJ/F30 9.9626 Tf 33.485 0 Td [(psb_lsort_up_)]TJ/F8 9.9626 Tf 67.995 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -251.325 -33.873 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -148.305 -22.511 Td [(\015ag)]TJ 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32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(tege)-1(r,)-341(real)-339(or)-340(complex)-340(v)56(ariable,)-342(whic)28(h)-339(m)-1(a)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-464(a)-464(ran)1(k)-464(1)-464(or)-464(2)-464(arra)28(y)83(.)-1299(T)28(yp)-28(e,)-497(kind)1(,)-497(rank)-464(and)-463(size)-464(m)27(ust)-463(agree)-464(on)-464(all)]TJ 0 -11.956 Td [(pro)-28(cesses.)]TJ/F16 11.9552 Tf -24.907 -21.917 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ + 0 -22.511 Td [(x)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 32.469 0 Td [(dat)]TJ/F8 9.9626 Tf 18.272 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.011 -11.955 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ +/F8 9.9626 Tf 11.028 0 Td [(The)-333(sequence)-334(of)-333(v)55(alues,)-333(in)-333(the)-334(c)28(hosen)-333(ordering.)]TJ 13.879 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger,)-333(real)-334(or)-333(complex)-333(arra)27(y)-333(of)-333(rank)-333(1.)]TJ 0 g 0 G - -12.73 -19.925 Td [(2.)]TJ +/F27 9.9626 Tf -24.907 -22.511 Td [(ix)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 33.208 0 Td [(dat)]TJ/F8 9.9626 Tf 19.012 0 Td [(argumen)28(t)-334(ma)28(y)-333(also)-334(b)-27(e)-334(a)-333(long)-333(in)28(teger)-334(scalar.)]TJ +/F8 9.9626 Tf 14.211 0 Td [(A)-333(v)27(ector)-333(of)-333(indices.)]TJ 10.696 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-332(in)27(teger)-332(arra)28(y)-333(of)-332(rank)-333(1,)-332(whose)-333(en)28(tries)-332(are)-333(mo)28(v)28(ed)-333(to)-332(the)-333(same)-332(p)-28(osition)]TJ 0 -11.955 Td [(as)-333(the)-334(corresp)-28(on)1(ding)-334(en)28(tries)-333(in)]TJ/F11 9.9626 Tf 136.959 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(.)]TJ 0 g 0 G - 99.987 -97.177 Td [(116)]TJ + -3.176 -43.727 Td [(107)]TJ 0 g 0 G ET endstream endobj -1626 0 obj +1628 0 obj << -/Length 5248 +/Length 6992 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(amn)-375(|)-375(Global)-375(minim)31(um)-375(absolute)-375(v)63(alue)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(Notes)]TJ 0 g 0 G +/F8 9.9626 Tf 12.176 -19.925 Td [(1.)]TJ 0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_amn\050icontxt,)-525(dat,)-525(root\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-336(s)-1(u)1(broutine)-337(implemen)28(ts)-337(a)-336(minim)28(um)-337(absolute)-336(v)55(alue)-336(reduction)-336(op)-28(eration)]TJ -14.944 -11.955 Td [(based)-333(on)-334(the)-333(underlying)-333(comm)28(unication)-334(library)84(.)]TJ + [-500(F)83(or)-466(in)28(te)-1(ger)-466(or)-467(real)-466(data)-467(the)-467(sorting)-466(can)-467(b)-28(e)-466(p)-28(erformed)-467(in)-466(the)-467(up/do)28(wn)]TJ 12.73 -11.956 Td [(direction,)-333(on)-334(the)-333(natural)-333(or)-333(absolute)-334(v)56(alues;)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -19.926 Td [(T)32(yp)-32(e:)]TJ + -12.73 -19.925 Td [(2.)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ + [-500(F)83(or)-397(complex)-398(data)-398(the)-397(sorting)-398(can)-398(b)-27(e)-398(done)-398(in)-397(a)-398(lexicographic)-398(order)-397(\050i.e.:)]TJ 12.73 -11.955 Td 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[(for)-333(quic)28(ks)-1(or)1(t)-334(or)-333(heapsort;)]TJ 0 g 0 G - 0 -19.925 Td [(icon)32(txt)]TJ + -12.73 -19.925 Td [(4.)]TJ 0 g 0 G -/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyin)1(g)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ + [-500(If)]TJ/F11 9.9626 Tf 21.89 0 Td [(f)-108(l)-19(ag)]TJ/F8 9.9626 Tf 22.261 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(psb)]TJ +ET +q +1 0 0 1 232.104 542.941 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 235.093 542.742 Td [(sor)-28(t)]TJ +ET +q +1 0 0 1 253.559 542.941 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 256.548 542.742 Td [(ov)-36(w)]TJ +ET +q +1 0 0 1 274.562 542.941 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 277.55 542.742 Td [(idx)]TJ +ET +q +1 0 0 1 292.46 542.941 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 297.966 542.742 Td [(then)-253(the)-252(en)27(tries)-252(in)]TJ/F11 9.9626 Tf 80.169 0 Td [(ix)]TJ/F8 9.9626 Tf 9.126 0 Td [(\0501)-278(:)]TJ/F11 9.9626 Tf 17.158 0 Td [(n)]TJ/F8 9.9626 Tf 5.98 0 Td [(\051)-253(where)]TJ/F11 9.9626 Tf 34.397 0 Td [(n)]TJ/F8 9.9626 Tf 8.498 0 Td [(is)-253(the)-252(size)]TJ -277.683 -11.956 Td [(of)]TJ/F11 9.9626 Tf 11.911 0 Td [(x)]TJ/F8 9.9626 Tf 9.579 0 Td [(are)-390(initialized)-390(to)]TJ/F11 9.9626 Tf 76.439 0 Td [(ix)]TJ/F8 9.9626 Tf 9.127 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)]TJ/F14 9.9626 Tf 7.582 0 Td [(\040)]TJ/F11 9.9626 Tf 13.67 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(;)-418(th)28(us,)-405(u)1(p)-28(on)-390(return)-390(from)-390(the)-390(subroutine,)]TJ -139.046 -11.955 Td [(for)-333(eac)27(h)-333(index)]TJ/F11 9.9626 Tf 64.505 0 Td [(i)]TJ/F8 9.9626 Tf 6.752 0 Td [(w)28(e)-333(ha)27(v)28(e)-333(in)]TJ/F11 9.9626 Tf 49.256 0 Td [(ix)]TJ/F8 9.9626 Tf 9.126 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)-333(the)-333(p)-28(osition)-333(that)-333(the)-334(item)]TJ/F11 9.9626 Tf 123.751 0 Td [(x)]TJ/F8 9.9626 Tf 5.694 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(\051)-333(o)-28(ccupied)]TJ -273.697 -11.955 Td [(in)-333(the)-334(original)-333(data)-333(sequence;)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(dat)]TJ + -12.73 -19.925 Td [(5.)]TJ 0 g 0 G -/F8 9.9626 Tf 21.371 0 Td [(The)-333(lo)-28(cal)-334(con)28(tribution)-333(to)-333(the)-334(global)-333(minim)28(um.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-464(a)-464(rank)-463(1)-464(or)-464(2)-464(arra)28(y)83(.)-1299(T)28(yp)-28(e,)-497(kind,)-496(rank)-464(and)-463(size)-464(m)27(ust)-463(agree)-464(on)-464(all)]TJ 0 -11.955 Td [(pro)-28(cesses.)]TJ + [-500(If)]TJ/F11 9.9626 Tf 23.404 0 Td [(f)-108(l)-19(ag)]TJ/F8 9.9626 Tf 23.446 0 Td [(=)]TJ/F11 9.9626 Tf 11.701 0 Td [(psb)]TJ +ET +q +1 0 0 1 235.988 487.15 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 238.977 486.951 Td [(sor)-28(t)]TJ +ET +q +1 0 0 1 257.443 487.15 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 260.432 486.951 Td [(k)-31(ee)-1(p)]TJ +ET +q +1 0 0 1 280.82 487.15 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F11 9.9626 Tf 283.809 486.951 Td [(idx)]TJ +ET +q +1 0 0 1 298.718 487.15 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 305.739 486.951 Td [(the)-405(routine)-404(will)-405(assume)-405(that)-404(the)-405(en)28(tries)-405(in)]TJ/F11 9.9626 Tf -130.128 -11.955 Td [(ix)]TJ/F8 9.9626 Tf 9.127 0 Td [(\050:\051)-333(ha)28(v)27(e)-333(already)-333(b)-28(een)-333(initialized)-334(b)28(y)-333(the)-333(use)-1(r;)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(ro)-32(ot)]TJ + -21.857 -19.926 Td [(6.)]TJ 0 g 0 G -/F8 9.9626 Tf 25.931 0 Td [(Pro)-28(cess)-276(to)-276(hold)-276(the)-276(\014nal)-275(v)55(alue,)-287(or)]TJ/F14 9.9626 Tf 146.411 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-276(to)-276(mak)28(e)-276(it)-276(a)28(v)55(ailable)-276(on)-276(all)-276(p)1(ro)-28(cesses.)]TJ -155.184 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.428 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.748 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.962 0 Td [(1,)-333(default)-334(-1.)]TJ + [-500(The)-376(three)-375(sorting)-376(algorithms)-376(ha)28(v)28(e)-376(a)-376(similar)]TJ/F11 9.9626 Tf 208.295 0 Td [(O)]TJ/F8 9.9626 Tf 7.876 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(n)]TJ/F8 9.9626 Tf 7.64 0 Td [(log)]TJ/F11 9.9626 Tf 14.529 0 Td [(n)]TJ/F8 9.9626 Tf 5.98 0 Td [(\051)-376(exp)-27(ec)-1(t)1(e)-1(d)-375(running)]TJ -235.465 -11.955 Td [(time;)-349(in)-343(the)-344(a)28(v)28(erage)-344(case)-344(qu)1(ic)27(ksort)-343(will)-344(b)-28(e)-343(the)-344(fastest)-343(and)-344(merge-sort)-343(the)]TJ 0 -11.955 Td [(slo)28(w)27(est.)-444(Ho)28(w)27(ev)28(er)-333(note)-333(that:)]TJ 0 g 0 G -/F27 9.9626 Tf -251.325 -33.873 Td [(On)-383(Return)]TJ + 4.207 -19.925 Td [(\050a\051)]TJ 0 g 0 G + [-500(The)-419(w)28(orst)-419(case)-419(run)1(ning)-419(time)-419(for)-419(qui)1(c)27(ksort)-418(is)]TJ/F11 9.9626 Tf 221.058 0 Td [(O)]TJ/F8 9.9626 Tf 7.876 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(n)]TJ/F7 6.9738 Tf 5.98 3.615 Td [(2)]TJ/F8 9.9626 Tf 4.469 -3.615 Td [(\051;)-461(the)-419(algorithm)]TJ -225.547 -11.955 Td [(implemen)28(ted)-319(here)-319(follo)28(ws)-319(the)-319(w)27(ell-kno)28(wn)-319(median-of-three)-319(heuristics,)]TJ 0 -11.956 Td [(but)-333(the)-334(w)28(orst)-333(case)-334(ma)28(y)-333(still)-334(app)1(ly;)]TJ 0 g 0 G - 0 -19.926 Td [(dat)]TJ + -18.265 -15.94 Td [(\050b\051)]TJ 0 g 0 G -/F8 9.9626 Tf 21.372 0 Td [(On)-333(destination)-333(pro)-28(cess\050es\051,)-334(the)-333(result)-333(of)-334(the)-333(minim)28(um)-334(op)-27(eration.)]TJ 3.535 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -71.51 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-333(a)-334(rank)-333(1)-333(or)-334(2)-333(arra)28(y)83(.)]TJ 0 -11.956 Td [(T)28(yp)-28(e,)-333(kind,)-334(r)1(ank)-334(and)-333(size)-333(m)27(ust)-333(agree)-333(on)-334(all)-333(pro)-28(cesses.)]TJ/F16 11.9552 Tf -24.907 -21.917 Td [(Notes)]TJ + [-500(The)-222(w)28(orst)-223(case)-222(running)-222(time)-222(for)-223(merge-sort)-222(and)-222(heap-sort)-222(is)]TJ/F11 9.9626 Tf 273.309 0 Td [(O)]TJ/F8 9.9626 Tf 7.876 0 Td [(\050)]TJ/F11 9.9626 Tf 3.875 0 Td [(n)]TJ/F8 9.9626 Tf 7.64 0 Td [(log)]TJ/F11 9.9626 Tf 14.529 0 Td [(n)]TJ/F8 9.9626 Tf 5.98 0 Td [(\051)]TJ -294.944 -11.955 Td [(as)-333(the)-334(a)28(v)28(erage)-334(case;)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ + -17.158 -15.94 Td [(\050c\051)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 32.469 0 Td [(dat)]TJ/F8 9.9626 Tf 18.273 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.012 -11.955 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ + [-500(The)-358(merge-sort)-358(algorithm)-357(is)-358(implemen)28(ted)-358(to)-358(tak)28(e)-358(adv)56(an)28(tage)-358(of)-358(sub-)]TJ 17.158 -11.955 Td [(sequences)-401(that)-400(ma)28(y)-401(b)-28(e)-400(already)-401(in)-400(the)-401(desired)-400(ordering)-400(prior)-401(to)-400(the)]TJ 0 -11.956 Td [(subroutine)-246(call;)-275(this)-246(situation)-246(is)-247(relativ)28(ely)-246(common)-246(when)-246(dealing)-246(with)]TJ 0 -11.955 Td [(groups)-301(of)-301(indices)-301(of)-302(sparse)-301(matrix)-301(en)28(tries,)-308(th)28(us)-301(merge-sort)-302(is)-301(the)-301(pre-)]TJ 0 -11.955 Td [(ferred)-249(c)28(hoice)-249(when)-249(a)-249(sorting)-248(is)-249(needed)-249(b)28(y)-249(other)-249(routines)-249(in)-249(t)1(he)-249(library)83(.)]TJ 0 g 0 G - -12.73 -19.925 Td [(2.)]TJ + 117.559 -205.23 Td [(108)]TJ +0 g 0 G +ET + +endstream +endobj +1641 0 obj +<< +/Length 182 +>> +stream 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 33.209 0 Td [(dat)]TJ/F8 9.9626 Tf 19.012 0 Td [(argumen)28(t)-333(m)-1(a)28(y)-333(also)-333(b)-28(e)-334(a)-333(long)-333(in)28(teger)-334(scalar.)]TJ 0 g 0 G - 99.986 -97.177 Td [(117)]TJ +BT +/F16 14.3462 Tf 99.895 706.129 Td [(7)-1125(P)31(arallel)-375(en)31(vironmen)32(t)-375(routines)]TJ +0 g 0 G +/F8 9.9626 Tf 164.384 -615.691 Td [(109)]TJ 0 g 0 G ET endstream endobj -1632 0 obj +1646 0 obj << -/Length 6223 +/Length 5584 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 150.705 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(7.1)-1125(psb)]TJ ET q -1 0 0 1 171.761 706.328 cm +1 0 0 1 202.396 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 175.796 706.129 Td [(nrm2)-375(|)-375(Global)-375(2-norm)-375(reduction)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(init)-375(|)-375(Initializes)-375(PSBLAS)-375(parallel)-375(en)31(vironmen)31(t)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_nrm2\050icontxt,)-525(dat,)-525(root\051)]TJ/F8 9.9626 Tf 14.944 -19.604 Td [(This)-425(subroutine)-425(implem)-1(en)28(ts)-425(a)-425(2-norm)-426(v)56(alue)-425(reduction)-426(op)-27(eration)-426(based)-425(on)]TJ -14.944 -11.955 Td [(the)-333(underlying)-333(com)-1(m)28(unication)-333(library)83(.)]TJ +/F30 9.9626 Tf -55.726 -18.389 Td [(call)-525(psb_init\050icontxt,)-525(np,)-525(basectxt,)-525(ids\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-294(subroutine)-294(initial)1(iz)-1(es)-293(the)-294(PSBLAS)-294(parallel)-294(en)28(vironmen)28(t,)-302(de\014ning)-294(a)-294(vir-)]TJ -14.944 -11.955 Td [(tual)-333(parallel)-334(mac)28(hine.)]TJ 0 g 0 G -/F27 9.9626 Tf 0 -18.074 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf 0 -19.926 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G /F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -19 Td [(icon)32(txt)]TJ +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyi)1(ng)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(ariable.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19 Td [(dat)]TJ + 0 -19.925 Td [(np)]TJ 0 g 0 G -/F8 9.9626 Tf 21.371 0 Td [(The)-333(lo)-28(cal)-333(c)-1(on)28(tribution)-333(to)-333(the)-334(gl)1(obal)-334(minim)28(um.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-421(as:)-619(a)-421(real)-421(v)55(ariable,)-443(whic)28(h)-421(ma)28(y)-421(b)-28(e)-421(a)-421(scalar,)-443(or)-420(a)-421(rank)-421(1)-421(arra)28(y)83(.)]TJ 0 -11.955 Td [(Kind,)-333(rank)-333(and)-334(size)-333(m)28(ust)-334(agree)-333(on)-333(all)-334(pro)-27(ces)-1(ses.)]TJ +/F8 9.9626 Tf 17.711 0 Td [(Num)28(b)-28(er)-333(of)-334(pro)-27(cess)-1(es)-333(in)-333(the)-334(P)1(SBLA)-1(S)-333(virtual)-333(parallel)-333(mac)27(hin)1(e)-1(.)]TJ 7.196 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue.)-778(Defau)1(lt:)-445(use)-333(all)-334(a)28(v)56(ailable)-333(pro)-28(cesses.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19 Td [(ro)-32(ot)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(basectxt)]TJ 0 g 0 G -/F8 9.9626 Tf 25.93 0 Td [(Pro)-28(cess)-276(to)-276(hold)-276(the)-276(\014nal)-276(v)56(alue,)-287(or)]TJ/F14 9.9626 Tf 146.411 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-276(to)-276(mak)28(e)-276(it)-276(a)28(v)55(ailable)-276(on)-276(all)-276(pr)1(o)-28(cesses)-1(.)]TJ -155.183 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.427 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.749 0 Td [(<)]TJ/F8 9.9626 Tf 7.748 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1,)-333(default)-334(-1.)]TJ +/F8 9.9626 Tf 46.736 0 Td [(the)-356(initial)-357(comm)28(unication)-356(con)28(text.)-514(The)-356(new)-357(con)28(text)-356(will)-357(b)-27(e)-357(de\014ned)]TJ -21.829 -11.955 Td [(from)-333(the)-334(pro)-27(cesse)-1(s)-333(participating)-333(in)-333(the)-334(initial)-333(one.)]TJ 0 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)-778(Defau)1(lt:)-445(use)-333(MPI)]TJ +ET +q +1 0 0 1 389.991 466.768 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 392.98 466.569 Td [(COMM)]TJ +ET +q +1 0 0 1 426.787 466.768 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 429.775 466.569 Td [(W)28(ORLD.)]TJ 0 g 0 G -/F27 9.9626 Tf -251.325 -31.559 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -279.07 -19.925 Td [(ids)]TJ 0 g 0 G +/F8 9.9626 Tf 19.048 0 Td [(Iden)28(tities)-497(of)-497(the)-497(pro)-28(cesses)-497(to)-497(use)-497(for)-497(the)-497(new)-498(con)28(text;)-579(the)-497(argumen)28(t)-497(is)]TJ 5.858 -11.956 Td [(ignored)-428(when)]TJ/F30 9.9626 Tf 63.346 0 Td [(np)]TJ/F8 9.9626 Tf 14.723 0 Td [(is)-428(not)-428(sp)-27(eci\014ed.)-728(This)-428(allo)28(ws)-428(the)-428(pro)-27(ces)-1(ses)-427(in)-428(the)-428(new)]TJ -78.069 -11.955 Td [(en)28(vironmen)28(t)-334(to)-333(b)-28(e)-333(in)-333(an)-334(order)-333(di\013eren)28(t)-334(from)-333(the)-333(original)-333(one.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)84(.)-778(Default:)-444(use)-334(the)-333(indices)-333(\0500)]TJ/F11 9.9626 Tf 254.159 0 Td [(:)-167(:)-166(:)-167(np)]TJ/F14 9.9626 Tf 26.489 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1\051.)]TJ 0 g 0 G - 0 -19 Td [(dat)]TJ +/F27 9.9626 Tf -315.517 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 21.371 0 Td [(On)-333(destination)-334(p)1(ro)-28(cess\050es)-1(\051)1(,)-334(the)-333(result)-333(of)-334(the)-333(2-norm)-333(reduction.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(real)-333(v)55(ariabl)1(e)-1(,)-333(whic)28(h)-333(ma)27(y)-333(b)-28(e)-333(a)-333(scalar,)-334(or)-333(a)-333(rank)-334(1)-333(arra)28(y)83(.)]TJ 0 -11.955 Td [(Kind,)-333(rank)-333(and)-334(size)-333(m)28(ust)-334(agree)-333(on)-333(all)-334(pro)-27(ces)-1(ses.)]TJ/F16 11.9552 Tf -24.907 -19.603 Td [(Notes)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -18.075 Td [(1.)]TJ + 0 -19.925 Td [(icon)32(txt)]TJ 0 g 0 G - [-500(This)-416(reduction)-416(is)-416(appropriate)-416(to)-416(compute)-416(the)-417(r)1(e)-1(sult)1(s)-417(of)-416(m)28(ultiple)-416(\050lo)-28(cal\051)]TJ 12.73 -11.955 Td [(NRM2)-333(op)-28(erations)-333(at)-334(the)-333(same)-333(time)-1(.)]TJ +/F8 9.9626 Tf 39.989 0 Td [(the)-457(c)-1(omm)28(unication)-457(con)28(te)-1(x)1(t)-458(iden)28(tifying)-458(the)-457(virtual)-458(p)1(arallel)-458(mac)28(hine.)]TJ -15.083 -11.956 Td [(Note)-335(that)-335(this)-335(is)-336(alw)28(a)28(ys)-335(a)-335(duplicate)-335(of)]TJ/F30 9.9626 Tf 169.953 0 Td [(basectxt)]TJ/F8 9.9626 Tf 41.843 0 Td [(,)-336(so)-335(that)-335(library)-335(comm)28(u-)]TJ -211.796 -11.955 Td [(nications)-305(are)-305(completely)-306(separated)-305(from)-305(other)-305(comm)28(unication)-305(op)-28(erations.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.51 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ/F16 11.9552 Tf -24.906 -21.917 Td [(Notes)]TJ 0 g 0 G - -12.73 -18.999 Td [(2.)]TJ +/F8 9.9626 Tf 12.176 -19.926 Td [(1.)]TJ 0 g 0 G - [-500(Denoting)-283(b)28(y)]TJ/F11 9.9626 Tf 68.601 0 Td [(dat)]TJ/F10 6.9738 Tf 14.049 -1.495 Td [(i)]TJ/F8 9.9626 Tf 6.139 1.495 Td [(the)-283(v)55(alue)-283(of)-283(the)-283(v)55(ariabl)1(e)]TJ/F11 9.9626 Tf 106.289 0 Td [(dat)]TJ/F8 9.9626 Tf 16.871 0 Td [(on)-283(pro)-28(cess)]TJ/F11 9.9626 Tf 47.569 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(,)-293(the)-283(output)]TJ/F11 9.9626 Tf 54.504 0 Td [(r)-28(es)]TJ/F8 9.9626 Tf -304.724 -11.956 Td [(is)-333(equiv)55(alen)28(t)-333(to)-334(the)-333(computation)-333(of)]TJ/F11 9.9626 Tf 122.07 -25.714 Td [(r)-28(es)]TJ/F8 9.9626 Tf 16.848 0 Td [(=)]TJ/F1 9.9626 Tf 10.516 14.335 Td [(s)]TJ -ET -q -1 0 0 1 335.008 204.589 cm -[]0 d 0 J 0.398 w 0 0 m 34.569 0 l S -Q -BT -/F1 9.9626 Tf 335.008 199.519 Td [(X)]TJ/F10 6.9738 Tf 5.786 -21.219 Td [(i)]TJ/F11 9.9626 Tf 10.265 11.754 Td [(dat)]TJ/F7 6.9738 Tf 14.05 3.432 Td [(2)]TJ/F10 6.9738 Tf 0 -6.209 Td [(i)]TJ/F11 9.9626 Tf 4.469 2.777 Td [(;)]TJ/F8 9.9626 Tf -193.967 -30.717 Td [(with)-333(care)-334(tak)28(en)-333(to)-334(a)28(v)28(oid)-333(unnecessary)-334(o)28(v)28(er\015o)28(w.)]TJ + [-500(A)-333(call)-334(to)-333(this)-333(routine)-334(m)28(ust)-333(precede)-334(an)28(y)-333(other)-333(PSBLAS)-334(call.)]TJ 0 g 0 G - -12.73 -19 Td [(3.)]TJ + 0 -19.925 Td [(2.)]TJ 0 g 0 G - [-500(The)]TJ/F30 9.9626 Tf 32.47 0 Td [(dat)]TJ/F8 9.9626 Tf 18.272 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.012 -11.955 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ + [-500(It)-262(is)-262(an)-262(error)-262(to)-262(sp)-28(ecify)-262(a)-262(v)56(alue)-262(for)]TJ/F11 9.9626 Tf 159.87 0 Td [(np)]TJ/F8 9.9626 Tf 13.602 0 Td [(greater)-262(than)-262(the)-262(n)28(um)28(b)-28(er)-262(of)-262(pro)-28(cesses)]TJ -160.742 -11.955 Td [(a)28(v)55(ailable)-333(in)-333(the)-334(und)1(e)-1(r)1(lying)-334(base)-333(parallel)-333(en)27(viron)1(m)-1(en)28(t.)]TJ 0 g 0 G - 139.477 -37.944 Td [(118)]TJ + 139.477 -97.177 Td [(110)]TJ 0 g 0 G ET endstream endobj -1640 0 obj +1652 0 obj << -/Length 5346 +/Length 4667 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(7.2)-1125(psb)]TJ ET q -1 0 0 1 120.951 706.328 cm +1 0 0 1 151.587 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 124.986 706.129 Td [(snd)-375(|)-375(Send)-375(data)]TJ +/F16 11.9552 Tf 155.621 706.129 Td [(info)-453(|)-453(Return)-453(information)-453(ab)-31(out)-453(PSBLAS)-453(par-)]TJ -25.091 -13.948 Td [(allel)-375(en)31(vironmen)31(t)]TJ 0 g 0 G 0 g 0 G -/F30 9.9626 Tf -25.091 -18.389 Td [(call)-525(psb_snd\050icontxt,)-525(dat,)-525(dst,)-525(m\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-333(subroutine)-334(sends)-333(a)-333(pac)27(k)28(et)-333(of)-333(data)-334(to)-333(a)-333(destination.)]TJ +/F30 9.9626 Tf -30.635 -18.389 Td [(call)-525(psb_info\050icontxt,)-525(iam,)-525(np\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-456(subroutine)-456(returns)-456(inf)1(orma)-1(t)1(ion)-456(ab)-28(out)-456(the)-456(PSBLAS)-456(paral)1(le)-1(l)-455(en)27(viron-)]TJ -14.944 -11.955 Td [(men)28(t,)-334(de\014nin)1(g)-334(a)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ 0 g 0 G -/F27 9.9626 Tf -14.944 -19.926 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf 0 -19.925 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous:)-445(see)-333(usage)-333(notes.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +/F27 9.9626 Tf -33.797 -19.926 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G 0 -19.925 Td [(icon)32(txt)]TJ 0 g 0 G /F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyin)1(g)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(dat)]TJ +/F27 9.9626 Tf -24.907 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 21.371 0 Td [(The)-333(data)-334(to)-333(b)-28(e)-333(sen)28(t.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-381(a)-381(rank)-381(1)-381(or)-381(2)-381(arra)27(y)84(,)-393(or)-381(a)-381(c)27(har)1(ac)-1(ter)-381(or)-381(logical)-381(scalar.)-969(T)28(yp)-27(e)-1(,)-393(ki)1(nd)-381(and)]TJ 0 -11.955 Td [(rank)-327(m)27(ust)-327(agree)-328(on)-327(sender)-328(and)-327(receiv)27(er)-327(pro)-28(cess;)-329(if)]TJ/F11 9.9626 Tf 220.724 0 Td [(m)]TJ/F8 9.9626 Tf 12.01 0 Td [(is)-328(not)-327(sp)-28(eci\014ed,)-329(size)]TJ -232.734 -11.955 Td [(m)28(ust)-334(agree)-333(as)-333(w)27(ell.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.926 Td [(dst)]TJ + 0 -19.925 Td [(iam)]TJ 0 g 0 G -/F8 9.9626 Tf 20.321 0 Td [(Destination)-333(pro)-28(cess.)]TJ 4.586 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)-333(0)]TJ/F11 9.9626 Tf 138.176 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(dst)-278(<)]TJ/F8 9.9626 Tf 23.969 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.207 0 Td [(\000)]TJ/F8 9.9626 Tf 9.962 0 Td [(1.)]TJ +/F8 9.9626 Tf 23.281 0 Td [(Iden)28(ti\014er)-333(of)-334(curren)28(t)-333(pro)-28(cess)-333(in)-334(the)-333(PSBLAS)-333(virtual)-334(par)1(allel)-334(mac)28(hine.)]TJ 1.626 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)]TJ/F14 9.9626 Tf 134.302 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F14 9.9626 Tf 7.749 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(iam)]TJ/F14 9.9626 Tf 20.213 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1)]TJ 0 g 0 G -/F27 9.9626 Tf -239.002 -31.881 Td [(m)]TJ +/F27 9.9626 Tf -239.121 -19.926 Td [(np)]TJ 0 g 0 G -/F8 9.9626 Tf 14.529 0 Td [(Num)28(b)-28(er)-333(of)-334(ro)28(ws.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf 43.455 0 Td [(.)]TJ -73.066 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)-333(0)]TJ/F11 9.9626 Tf 138.176 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(m)-278(<)]TJ/F8 9.9626 Tf 19.264 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(siz)-44(e)]TJ/F8 9.9626 Tf 17.812 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(dat;)]TJ/F8 9.9626 Tf 18.477 0 Td [(1\051.)]TJ -226.384 -11.956 Td [(When)]TJ/F11 9.9626 Tf 29.071 0 Td [(dat)]TJ/F8 9.9626 Tf 17.383 0 Td [(is)-335(a)-334(rank)-335(2)-335(arra)28(y)84(,)-335(sp)-28(eci\014es)-335(the)-335(n)28(um)28(b)-28(er)-334(of)-335(ro)28(ws)-335(to)-335(b)-27(e)-335(sen)28(t)-335(inde-)]TJ -46.454 -11.955 Td [(p)-28(enden)28(tly)-285(of)-285(the)-286(leading)-285(dimension)]TJ/F11 9.9626 Tf 153.742 0 Td [(siz)-44(e)]TJ/F8 9.9626 Tf 17.812 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(dat;)]TJ/F8 9.9626 Tf 18.477 0 Td 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[-500(F)83(or)-500(pro)-27(cesse)-1(s)-500(in)-500(th)1(e)-501(v)1(irtual)-500(parallel)-500(mac)27(hin)1(e)-501(th)1(e)-501(id)1(e)-1(n)28(ti\014er)-500(will)-500(satisfy)]TJ 12.73 -11.955 Td [(0)]TJ/F14 9.9626 Tf 7.749 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(iam)]TJ/F14 9.9626 Tf 20.213 0 Td [(\024)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1;)]TJ 0 g 0 G -/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ + -84.893 -19.925 Td [(2.)]TJ 0 g 0 G - [-500(This)-402(subroutine)-403(implies)-402(a)-402(s)-1(yn)1(c)27(hronization,)-419(but)-403(on)1(ly)-403(b)-28(et)28(w)28(een)-403(the)-402(calling)]TJ 12.73 -11.955 Td [(pro)-28(cess)-333(and)-333(the)-334(destination)-333(pro)-28(cess)]TJ/F11 9.9626 Tf 157.521 0 Td [(dst)]TJ/F8 9.9626 Tf 13.453 0 Td [(.)]TJ + [-500(If)-432(the)-433(user)-432(has)-433(requested)-432(on)]TJ/F30 9.9626 Tf 143.13 0 Td [(psb_init)]TJ/F8 9.9626 Tf 46.151 0 Td 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9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(logical)-333(v)55(ariabl)1(e)-1(,)-333(default)-333(v)55(al)1(ue:)-445(true.)]TJ/F16 11.9552 Tf -24.907 -19.925 Td [(Notes)]TJ 0 g 0 G - -10.792 -105.147 Td [(120)]TJ +/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ 0 g 0 G -ET - -endstream -endobj -1652 0 obj -<< -/Length 6381 ->> -stream + [-500(This)-241(routine)-241(ma)28(y)-241(b)-28(e)-241(called)-241(ev)28(en)-241(if)-241(a)-241(previous)-241(call)-241(to)]TJ/F30 9.9626 Tf 233.304 0 Td [(psb_info)]TJ/F8 9.9626 Tf 44.244 0 Td [(has)-241(returned)]TJ -264.818 -11.955 Td [(with)]TJ/F11 9.9626 Tf 22.962 0 Td [(iam)]TJ/F8 9.9626 Tf 20.663 0 Td [(=)]TJ/F14 9.9626 Tf 10.966 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1;)-374(indeed,)-367(it)-360(it)-361(is)-360(the)-361(only)-360(routine)-360(that)-361(ma)28(y)-360(b)-28(e)-361(called)-360(with)]TJ 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[(execution.)]TJ 14.944 -11.956 Td [(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-353(9)]TJ + [-500(A)-305(call)-306(to)-305(this)-305(routine)-305(with)]TJ/F30 9.9626 Tf 128.752 0 Td [(close=.true.)]TJ/F8 9.9626 Tf 65.806 0 Td [(implies)-305(a)-306(call)-305(to)]TJ/F30 9.9626 Tf 71.445 0 Td [(MPI_Finalize)]TJ/F8 9.9626 Tf 62.764 0 Td [(,)]TJ -316.037 -11.956 Td [(after)-333(whic)28(h)-334(no)-333(parallel)-333(routine)-334(ma)28(y)-333(b)-28(e)-333(called.)]TJ 0 g 0 G - [-353(sho)28(ws)-353(the)-353(la)28(y)27(out)-353(of)-353(a)-353(generic)]TJ/F30 9.9626 Tf 170.683 0 Td [(psb_foo)]TJ/F8 9.9626 Tf 40.129 0 Td [(routine)-353(with)-353(resp)-28(ect)-353(to)-353(the)]TJ -225.756 -11.955 Td [(PSBLAS-2.0)-326(error)-326(handl)1(ing)-326(p)-28(olicy)83(.)-442(It)-325(is)-326(p)-28(ossible)-326(to)-326(see)-326(ho)28(w,)-327(whenev)27(er)-325(an)-326(error)]TJ 0 -11.955 Td [(condition)-379(is)-378(detected,)-390(the)]TJ/F30 9.9626 Tf 115.439 0 Td [(info)]TJ/F8 9.9626 Tf 24.694 0 Td [(v)56(ariable)-379(is)-379(set)-379(to)-378(the)-379(corresp)-28(onding)-378(error)-379(co)-28(de)]TJ -140.133 -11.955 Td [(whic)28(h)-376(is,)-387(then,)-386(pushed)-376(on)-376(top)-376(of)-376(the)-376(stac)28(k)-376(b)28(y)-376(means)-376(of)-376(the)]TJ/F30 9.9626 Tf 264.703 0 Td [(psb_errpush)]TJ/F8 9.9626 Tf 57.533 0 Td [(.)-572(An)]TJ -322.236 -11.955 Td [(error)-331(condition)-331(ma)28(y)-331(b)-28(e)-331(directly)-331(detected)-331(inside)-331(a)-331(routine)-331(or)-331(indirectly)-331(c)27(hec)28(king)]TJ 0 -11.956 Td [(the)-462(error)-461(co)-28(de)-461(returned)-462(returned)-461(b)28(y)-462(a)-461(called)-462(routine.)-829(Whenev)28(er)-461(an)-462(error)-461(is)]TJ 0 -11.955 Td [(encoun)28(tered,)-459(after)-434(it)-434(has)-434(b)-27(een)-434(pushed)-434(on)-434(stac)28(k,)-459(the)-434(program)-433(exec)-1(u)1(tion)-434(skips)]TJ 0 -11.955 Td [(to)-356(a)-356(p)-27(oin)28(t)-356(where)-356(the)-356(error)-355(c)-1(on)1(dition)-356(is)-356(handled;)-367(the)-355(e)-1(r)1(ror)-356(condition)-356(is)-356(hand)1(le)-1(d)]TJ 0 -11.955 Td [(either)-392(b)28(y)-392(returning)-392(con)28(trol)-392(to)-392(the)-392(caller)-392(r)1(outine)-392(or)-392(b)28(y)-392(calling)-392(the)]TJ/F30 9.9626 Tf 291.408 0 Td [(psb\134_error)]TJ/F8 9.9626 Tf -291.408 -11.955 Td [(routine)-478(whic)28(h)-479(prin)28(ts)-478(the)-478(con)28(ten)27(t)-478(of)-478(the)-478(error)-479(stac)28(k)-478(and)-478(ab)-28(orts)-478(the)-478(program)]TJ 0 -11.955 Td [(execution,)-330(accordin)1(g)-329(to)-329(th)1(e)-329(c)28(hoice)-329(made)-328(b)27(y)-328(the)-329(user)-328(with)]TJ/F30 9.9626 Tf 252.028 0 Td [(psb_set_erraction)]TJ/F8 9.9626 Tf 88.916 0 Td [(.)]TJ -340.944 -11.956 Td [(The)-347(default)-346(is)-347(to)-346(prin)28(t)-347(the)-347(error)-346(and)-347(terminate)-346(the)-347(program,)-350(but)-346(the)-347(user)-346(ma)27(y)]TJ 0 -11.955 Td [(c)28(ho)-28(ose)-333(to)-334(handle)-333(the)-333(error)-334(explicitly)84(.)]TJ 14.944 -11.955 Td [(Figure)]TJ -0 0 1 rg 0 0 1 RG - [-479(10)]TJ + -12.73 -19.925 Td [(3.)]TJ 0 g 0 G - [-479(rep)-28(orts)-479(a)-479(sample)-480(error)-479(message)-479(generated)-479(b)28(y)-480(the)-479(PSBLAS-2.0)]TJ -14.944 -11.955 Td [(library)83(.)-451(This)-335(error)-336(has)-335(b)-28(een)-336(generated)-335(b)27(y)-335(the)-336(fact)-335(that)-336(the)-335(use)-1(r)-335(has)-336(c)28(hosen)-336(the)]TJ 0 -11.955 Td [(in)28(v)55(alid)-367(\134F)28(OO")-368(storage)-367(format)-368(to)-367(represen)27(t)-367(the)-368(sparse)-367(matrix.)-547(F)83(rom)-367(this)-368(error)]TJ 0 -11.955 Td [(message)-248(it)-248(is)-248(p)-27(oss)-1(ib)1(le)-248(to)-248(see)-248(that)-248(the)-248(error)-247(has)-248(b)-28(een)-248(detected)-248(inside)-248(the)]TJ/F30 9.9626 Tf 301.869 0 Td [(psb_cest)]TJ/F8 9.9626 Tf -301.869 -11.956 Td [(subroutine)-333(called)-334(b)28(y)]TJ/F30 9.9626 Tf 91.408 0 Td [(psb_spasb)]TJ/F8 9.9626 Tf 50.394 0 Td [(...)-444(b)27(y)-333(pro)-28(cess)-333(0)-333(\050i.e.)-445(the)-333(ro)-28(ot)-333(pro)-28(cess\051.)]TJ + [-500(If)-391(the)-390(user)-391(whishes)-391(to)-390(use)-391(m)28(ultiple)-391(comm)28(unication)-391(con)28(texts)-391(in)-390(the)-391(same)]TJ 12.73 -11.955 Td [(program,)-485(or)-455(to)-455(en)28(ter)-455(and)-454(exit)-455(m)27(u)1(ltiple)-455(times)-455(in)28(to)-455(the)-455(parallel)-455(en)28(viron-)]TJ 0 -11.955 Td [(men)28(t,)-494(this)-462(routine)-462(ma)28(y)-462(b)-28(e)-462(called)-462(to)-462(selectiv)28(ely)-462(close)-462(the)-462(con)27(texts)-462(with)]TJ/F30 9.9626 Tf 0 -11.955 Td [(close=.false.)]TJ/F8 9.9626 Tf 67.994 0 Td [(,)-244(while)-223(on)-222(the)-222(last)-222(call)-223(it)-222(should)-222(b)-28(e)-222(called)-222(with)]TJ/F30 9.9626 Tf 194.327 0 Td [(close=.true.)]TJ/F8 9.9626 Tf -262.321 -11.955 Td [(to)-333(sh)27(u)1(tdo)27(wn)-333(in)-333(a)-334(clean)-333(w)28(a)28(y)-334(the)-333(en)28(tire)-334(parallel)-333(en)28(vironmen)28(t.)]TJ 0 g 0 G - 22.582 -211.304 Td [(121)]TJ + 139.477 -212.744 Td [(112)]TJ 0 g 0 G ET endstream endobj -1659 0 obj +1665 0 obj << -/Length 7207 +/Length 2621 >> stream 0 g 0 G 0 g 0 G -0 g 0 G -0 g 0 G -0 g 0 G BT -/F53 8.9664 Tf 159.61 680.066 Td [(s)-60(u)-60(b)-60(r)-60(o)-59(u)-60(t)-60(i)-60(n)-60(e)]TJ/F46 8.9664 Tf 61.471 0 Td [(p)-132(s)-132(b)]TJ -ET -q -1 0 0 1 239.064 680.265 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S -Q -BT -/F46 8.9664 Tf 243.014 680.066 Td [(f)-132(o)-132(o)-241(\050)-155(s)-47(o)-47(m)-46(e)-769(a)-105(r)-106(g)-105(s)-376(,)-939(i)-156(n)-156(f)-157(o)-265(\051)]TJ -65.126 -10.959 Td [(.)-248(.)-249(.)]TJ/F53 8.9664 Tf -0.604 -10.959 Td [(i)-181(f)]TJ/F46 8.9664 Tf 10.409 0 Td [(\050)-259(e)-152(r)-151(r)-151(o)-151(r)-897(d)-129(e)-129(t)-129(e)-130(c)-129(t)-129(e)-130(d)-237(\051)]TJ/F53 8.9664 Tf 93.291 0 Td [(t)-30(h)-30(e)-29(n)]TJ/F46 8.9664 Tf -87.332 -10.959 Td [(i)-156(n)-157(f)-156(o)-65(=)-38(e)-129(r)-129(r)-128(c)-129(o)-129(d)-129(e)-129(1)]TJ/F53 8.9664 Tf -0.133 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.487 0 Td [(p)-124(s)-124(b)]TJ -ET -q -1 0 0 1 238.765 636.429 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S -Q -BT -/F46 8.9664 Tf 242.641 636.23 Td [(e)-124(r)-124(r)-124(p)-123(u)-124(s)-124(h)-232(\050)-330(')-242(p)-132(s)-133(b)]TJ -ET -q -1 0 0 1 310.944 636.429 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S -Q -BT -/F46 8.9664 Tf 314.894 636.23 Td [(f)-132(o)-132(o)-353(')-332(,)-855(e)-129(r)-129(r)-129(c)-129(o)-129(d)-128(e)-129(1)-237(\051)]TJ/F53 8.9664 Tf -122.23 -10.959 Td [(g)-46(o)-47(t)-46(o)]TJ/F46 8.9664 Tf 27.969 0 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf -44.989 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ/F46 8.9664 Tf 2.244 -10.959 Td [(.)-248(.)-249(.)]TJ/F53 8.9664 Tf -0.957 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.399 0 Td [(p)-114(s)-114(b)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(7.4)-1125(psb)]TJ ET q -1 0 0 1 221.826 592.594 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 151.587 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 225.613 592.394 Td [(b)-114(a)-114(r)-223(\050)-155(s)-47(o)-46(m)-47(e)-769(a)-105(r)-105(g)-105(s)-376(,)-939(i)-157(n)-156(f)-157(o)-264(\051)]TJ/F53 8.9664 Tf -48.329 -10.958 Td [(i)-181(f)]TJ/F46 8.9664 Tf 10.409 0 Td [(\050)-265(i)-156(n)-157(f)-156(o)-939(.)]TJ/F53 8.9664 Tf 37.83 0 Td [(n)-11(e)]TJ/F46 8.9664 Tf 12.445 0 Td [(.)-910(z)-127(e)-127(r)-128(o)-236(\051)]TJ/F53 8.9664 Tf 43.016 0 Td [(t)-30(h)-30(e)-29(n)]TJ/F46 8.9664 Tf -87.332 -10.959 Td [(i)-156(n)-157(f)-156(o)-65(=)-38(e)-129(r)-129(r)-128(c)-129(o)-129(d)-129(e)-129(2)]TJ/F53 8.9664 Tf -0.133 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.487 0 Td [(p)-124(s)-124(b)]TJ +/F16 11.9552 Tf 155.621 706.129 Td [(get)]TJ ET q -1 0 0 1 238.765 559.717 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 174.52 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 242.641 559.518 Td [(e)-124(r)-124(r)-124(p)-123(u)-124(s)-124(h)-232(\050)-330(')-242(p)-132(s)-133(b)]TJ +/F16 11.9552 Tf 178.555 706.129 Td [(mpi)]TJ ET q -1 0 0 1 310.944 559.717 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 201.778 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 314.894 559.518 Td [(f)-132(o)-132(o)-353(')-332(,)-855(e)-129(r)-129(r)-129(c)-129(o)-129(d)-128(e)-129(2)-237(\051)]TJ/F53 8.9664 Tf -122.23 -10.959 Td [(g)-46(o)-47(t)-46(o)]TJ/F46 8.9664 Tf 27.969 0 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf -44.989 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ/F46 8.9664 Tf 2.244 -10.959 Td [(.)-248(.)-249(.)]TJ -18.077 -10.959 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf 27.419 0 Td [(c)-57(o)-57(n)-57(t)-56(i)-57(n)-57(u)-57(e)]TJ -9.946 -10.959 Td [(i)-181(f)]TJ/F46 8.9664 Tf 15.938 0 Td [(\050)-273(e)-164(r)-165(r)]TJ +/F16 11.9552 Tf 205.813 706.129 Td [(comm)-375(|)-375(Get)-375(the)-375(MPI)-375(comm)31(unicator)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -105.918 -18.389 Td [(icomm)-525(=)-525(psb_get_mpi_comm\050icontxt\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-450(function)-451(retu)1(rns)-451(the)-450(MPI)-450(comm)27(uni)1(c)-1(ator)-450(asso)-28(ciated)-450(with)-450(a)-451(PSBLAS)]TJ -14.944 -11.955 Td [(con)28(text)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -19.926 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(icon)32(txt)]TJ +0 g 0 G +/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyin)1(g)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -21.918 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(F)96(unction)-384(v)64(alue)]TJ +0 g 0 G +/F8 9.9626 Tf 78.387 0 Td [(The)-314(MPI)-314(comm)28(unicator)-314(ass)-1(o)-27(ciated)-314(with)-314(the)-315(PS)1(B)-1(LAS)-314(vir)1(tual)]TJ -53.48 -11.955 Td [(parallel)-333(mac)27(hin)1(e)-1(.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ/F16 11.9552 Tf -74.942 -33.873 Td [(Notes)]TJ/F8 9.9626 Tf 37.587 0 Td [(The)-369(subroutine)-368(v)27(ersion)]TJ/F30 9.9626 Tf 104.726 0 Td [(psb_get_mpicomm)]TJ/F8 9.9626 Tf 82.129 0 Td [(is)-369(still)-369(a)28(v)56(ailable)-369(but)-369(is)-368(dep-)]TJ -224.442 -11.955 Td [(recated.)]TJ +0 g 0 G + 164.384 -320.34 Td [(113)]TJ +0 g 0 G ET -q -1 0 0 1 215.536 504.923 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S -Q + +endstream +endobj +1669 0 obj +<< +/Length 3470 +>> +stream +0 g 0 G +0 g 0 G BT -/F46 8.9664 Tf 219.774 504.723 Td [(a)-164(c)-165(t)-946(.)]TJ/F53 8.9664 Tf 27.965 0 Td [(e)-22(q)]TJ/F46 8.9664 Tf 12.346 0 Td [(.)-923(a)-141(c)-141(t)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(7.5)-1125(psb)]TJ ET q -1 0 0 1 287.553 504.923 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 202.396 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 291.582 504.723 Td [(a)-141(b)-141(o)-141(r)-141(t)-249(\051)]TJ/F53 8.9664 Tf 39.166 0 Td [(t)-30(h)-29(e)-30(n)]TJ -142.758 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.681 0 Td [(p)-146(s)-145(b)]TJ +/F16 11.9552 Tf 206.431 706.129 Td [(get)]TJ ET q -1 0 0 1 234.014 493.964 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 225.33 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 238.084 493.764 Td [(e)-146(r)-145(r)-146(o)-145(r)-254(\050)-252(i)-144(c)-143(o)-144(n)-143(t)-143(x)-144(t)-252(\051)]TJ/F53 8.9664 Tf -50.844 -10.959 Td [(r)-58(e)-58(t)-58(u)-58(r)-58(n)]TJ -10.529 -10.958 Td [(e)-117(l)-117(s)-117(e)]TJ 10.529 -10.959 Td [(r)-58(e)-58(t)-58(u)-58(r)-58(n)]TJ -11.596 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ -16.588 -21.918 Td [(e)2(n)2(d)-675(s)-60(u)-59(b)-60(r)-60(o)-60(u)-60(t)-60(i)-60(n)-60(e)]TJ/F46 8.9664 Tf 84.142 0 Td [(p)-132(s)-132(b)]TJ +/F16 11.9552 Tf 229.365 706.129 Td [(mpi)]TJ ET q -1 0 0 1 261.181 428.21 cm -[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +1 0 0 1 252.587 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F46 8.9664 Tf 265.131 428.011 Td [(f)-132(o)-132(o)]TJ +/F16 11.9552 Tf 256.622 706.129 Td [(rank)-375(|)-375(Get)-375(the)-375(MPI)-375(rank)]TJ 0 g 0 G 0 g 0 G -ET -q -1 0 0 1 150.705 701.884 cm -[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S -Q -q -1 0 0 1 150.904 410.576 cm -[]0 d 0 J 0.398 w 0 0 m 0 291.308 l S -Q -q -1 0 0 1 497.088 410.576 cm -[]0 d 0 J 0.398 w 0 0 m 0 291.308 l S -Q -q -1 0 0 1 150.705 410.576 cm -[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S -Q -BT -/F8 9.9626 Tf 150.705 382.537 Td [(Figure)-329(9:)-443(The)-329(la)27(y)28(out)-329(of)-330(a)-329(generic)]TJ/F30 9.9626 Tf 147.445 0 Td [(psb)]TJ -ET -q -1 0 0 1 314.468 382.736 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q -BT -/F30 9.9626 Tf 317.606 382.537 Td [(foo)]TJ/F8 9.9626 Tf 18.974 0 Td [(routine)-329(with)-330(resp)-28(ect)-329(to)-329(PSBLAS-2.0)]TJ -185.875 -11.955 Td [(error)-333(handling)-333(p)-28(olicy)83(.)]TJ +/F30 9.9626 Tf -105.917 -18.389 Td [(rank)-525(=)-525(psb_get_mpi_rank\050icontxt,)-525(id\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td 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-11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(arra)27(y)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -31.881 Td [(a)]TJ -ET -q -1 0 0 1 106.152 353.748 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S -Q -BT -/F27 9.9626 Tf 109.589 353.548 Td [(err)]TJ + 0 -19.926 Td [(dat)]TJ 0 g 0 G -/F8 9.9626 Tf 19.669 0 Td [(addional)-333(info)-333(for)-334(error)-333(co)-28(de)]TJ -4.456 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(string.)]TJ +/F8 9.9626 Tf 21.371 0 Td [(On)-333(pro)-28(cesses)-334(other)-333(than)-333(ro)-28(ot,)-333(the)-334(dat)1(a)-334(to)-333(b)-28(e)-333(broadcast.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(tege)-1(r,)-341(real)-339(or)-340(complex)-340(v)56(ariable,)-342(whic)28(h)-339(m)-1(a)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-346(a)-346(rank)-347(1)-346(or)-346(2)-346(arra)28(y)83(,)-349(or)-347(a)-346(c)28(haracter)-346(or)-346(logical)-347(scalar.)-829(T)28(yp)-28(e,)-349(kind,)-350(rank)]TJ 0 -11.956 Td [(and)-333(size)-334(m)28(ust)-333(agree)-334(on)-333(all)-333(pro)-28(cesses.)]TJ 0 g 0 G - 139.477 -227.245 Td [(123)]TJ + 139.477 -170.9 Td [(118)]TJ 0 g 0 G ET endstream endobj -1696 0 obj +1691 0 obj << -/Length 1400 +/Length 5157 >> stream 0 g 0 G 0 g 0 G -0 g 0 G -0 g 0 G -BT -/F16 14.3462 Tf 150.705 680.226 Td [(psb)]TJ -ET -q -1 0 0 1 175.972 680.425 cm -[]0 d 0 J 0.398 w 0 0 m 4.842 0 l S -Q BT -/F16 14.3462 Tf 180.814 680.226 Td [(error|Prin)31(ts)-375(the)-375(error)-375(stac)32(k)-375(con)31(ten)31(t)-375(and)]TJ -30.109 -17.933 Td [(ab)-31(orts)-375(execution)]TJ/F27 9.9626 Tf 1.377 -35.768 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.921 0 Td [(p)-141(s)-142(b)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(7.10)-1125(psb)]TJ ET q -1 0 0 1 201.829 626.724 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 158.311 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F8 9.9626 Tf 206.228 626.525 Td [(e)-142(r)-141(r)-141(o)-142(r)-247(\050)-245(i)-140(c)-139(o)-140(n)-139(t)-140(x)-140(t)-245(\051)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(sum)-375(|)-375(Global)-375(sum)]TJ 0 g 0 G 0 g 0 G +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_sum\050icontxt,)-525(dat,)-525(root\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-318(subroutine)-319(implemen)28(ts)-318(a)-319(sum)-318(reduction)-318(op)-28(eration)-318(based)-319(on)-318(the)-318(under-)]TJ -14.944 -11.955 Td 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g 0 G +/F27 9.9626 Tf -24.907 -19.926 Td [(ro)-32(ot)]TJ +0 g 0 G +/F8 9.9626 Tf 25.931 0 Td [(Pro)-28(cess)-310(to)-309(hold)-310(the)-310(\014nal)-310(sum,)-314(or)]TJ/F14 9.9626 Tf 144.053 0 Td [(\000)]TJ/F8 9.9626 Tf 7.748 0 Td [(1)-310(to)-310(mak)28(e)-310(it)-309(a)27(v)56(ailable)-310(on)-310(all)-309(pro)-28(cesses.)]TJ -152.825 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.428 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.748 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.962 0 Td [(1,)-333(default)-334(-1.)]TJ +0 g 0 G +/F27 9.9626 Tf -251.325 -21.918 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(dat)]TJ +0 g 0 G +/F8 9.9626 Tf 21.372 0 Td [(On)-333(destination)-333(pro)-28(cess\050es\051,)-334(the)-333(result)-333(of)-334(the)-333(sum)-333(op)-28(eration.)]TJ 3.535 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -71.51 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-333(a)-334(rank)-333(1)-333(or)-334(2)-333(arra)28(y)83(.)]TJ 0 -11.955 Td [(T)28(yp)-28(e,)-333(kind,)-334(r)1(ank)-334(and)-333(size)-333(m)27(ust)-333(agree)-333(on)-334(all)-333(pro)-28(cesses.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +0 g 0 G +/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +0 g 0 G + [-500(The)]TJ/F30 9.9626 Tf 32.469 0 Td [(dat)]TJ/F8 9.9626 Tf 18.273 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.012 -11.956 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ +0 g 0 G + -12.73 -19.925 Td [(2.)]TJ 0 g 0 G -/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger.)]TJ + [-500(The)]TJ/F30 9.9626 Tf 33.209 0 Td [(dat)]TJ/F8 9.9626 Tf 19.012 0 Td [(argumen)28(t)-333(m)-1(a)28(y)-333(also)-333(b)-28(e)-334(a)-333(long)-333(in)28(teger)-334(scalar.)]TJ 0 g 0 G - 139.476 -430.483 Td [(124)]TJ + 99.986 -109.132 Td [(119)]TJ 0 g 0 G ET endstream endobj -1702 0 obj +1697 0 obj << -/Length 1631 +/Length 5196 >> stream 0 g 0 G 0 g 0 G -0 g 0 G -0 g 0 G -BT -/F16 14.3462 Tf 99.895 680.226 Td [(psb)]TJ -ET -q -1 0 0 1 125.163 680.425 cm -[]0 d 0 J 0.398 w 0 0 m 4.842 0 l S -Q -BT -/F16 14.3462 Tf 130.004 680.226 Td [(set)]TJ -ET -q -1 0 0 1 150.979 680.425 cm -[]0 d 0 J 0.398 w 0 0 m 4.842 0 l S -Q -BT -/F16 14.3462 Tf 155.821 680.226 Td [(errv)31(erb)-31(osit)31(y|Sets)-375(the)-375(v)31(erb)-31(osit)31(y)-375(of)-375(error)]TJ -55.926 -17.933 Td [(messages.)]TJ/F27 9.9626 Tf 1.377 -35.768 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 30.082 0 Td 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[(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue)]TJ/F14 9.9626 Tf 130.427 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)]TJ/F11 9.9626 Tf 7.749 0 Td [(<)]TJ/F8 9.9626 Tf 7.748 0 Td [(=)]TJ/F11 9.9626 Tf 10.517 0 Td [(r)-28(oot)-278(<)]TJ/F8 9.9626 Tf 28.543 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1,)-333(default)-334(-1.)]TJ 0 g 0 G - 0 -19.925 Td [(a)]TJ +/F27 9.9626 Tf -251.325 -33.873 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.926 Td [(dat)]TJ +0 g 0 G +/F8 9.9626 Tf 21.371 0 Td [(On)-333(destination)-334(p)1(ro)-28(cess\050es)-1(\051)1(,)-334(the)-333(result)-333(of)-334(the)-333(maxim)28(um)-334(op)-27(eration.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(tege)-1(r,)-341(real)-339(or)-340(complex)-340(v)56(ariable,)-342(whic)28(h)-339(m)-1(a)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-464(a)-464(ran)1(k)-464(1)-464(or)-464(2)-464(arra)28(y)83(.)-1299(T)28(yp)-28(e,)-497(kind)1(,)-497(rank)-464(and)-463(size)-464(m)27(ust)-463(agree)-464(on)-464(all)]TJ 0 -11.956 Td [(pro)-28(cesses.)]TJ/F16 11.9552 Tf -24.907 -21.917 Td [(Notes)]TJ +0 g 0 G +/F8 9.9626 Tf 12.177 -19.926 Td [(1.)]TJ +0 g 0 G + [-500(The)]TJ/F30 9.9626 Tf 32.469 0 Td [(dat)]TJ/F8 9.9626 Tf 18.272 0 Td [(argumen)28(t)-259(is)-259(b)-28(oth)-259(input)-259(and)-259(output,)-274(and)-259(its)-259(v)55(alue)-259(ma)28(y)-259(b)-28(e)-259(c)28(hanged)]TJ -38.011 -11.955 Td [(ev)28(en)-334(on)-333(pro)-28(cesses)-333(di\013eren)28(t)-334(from)-333(the)-333(\014nal)-334(result)-333(destination.)]TJ +0 g 0 G + -12.73 -19.925 Td [(2.)]TJ +0 g 0 G + [-500(The)]TJ/F30 9.9626 Tf 33.208 0 Td [(dat)]TJ/F8 9.9626 Tf 19.012 0 Td [(argumen)28(t)-334(ma)28(y)-333(also)-334(b)-27(e)-334(a)-333(long)-333(in)28(teger)-334(scalar.)]TJ +0 g 0 G + 99.987 -97.177 Td [(122)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)-333(read)-333(from)-334(\014le.)]TJ 14.356 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.081 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET -q -1 0 0 1 362.845 452.82 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S -Q + +endstream +endobj +1716 0 obj +<< +/Length 5259 +>> +stream +0 g 0 G +0 g 0 G BT -/F30 9.9626 Tf 365.983 452.621 Td [(Tspmat)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(7.14)-1125(psb)]TJ ET q -1 0 0 1 397.993 452.82 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 158.311 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F30 9.9626 Tf 401.131 452.621 Td [(type)]TJ +/F16 11.9552 Tf 162.346 706.129 Td [(amn)-375(|)-375(Global)-375(minim)31(um)-375(absolute)-375(v)63(alue)]TJ +0 g 0 G +0 g 0 G +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_amn\050icontxt,)-525(dat,)-525(root\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-336(s)-1(u)1(broutine)-337(implemen)28(ts)-337(a)-336(minim)28(um)-337(absolute)-336(v)55(alue)-336(reduction)-336(op)-28(eration)]TJ -14.944 -11.955 Td [(based)-333(on)-334(the)-333(underlying)-333(comm)28(unication)-334(library)84(.)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -19.926 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(icon)32(txt)]TJ +0 g 0 G +/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyin)1(g)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 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[(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(te)-1(ger,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-340(ma)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-464(a)-464(rank)-463(1)-464(or)-464(2)-464(arra)28(y)83(.)-1299(T)28(yp)-28(e,)-497(kind,)-496(rank)-464(and)-463(size)-464(m)27(ust)-463(agree)-464(on)-464(all)]TJ 0 -11.955 Td [(pro)-28(cesses.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.926 Td [(ro)-32(ot)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 25.931 0 Td [(Pro)-28(cess)-276(to)-276(hold)-276(the)-276(\014nal)-275(v)55(alue,)-287(or)]TJ/F14 9.9626 Tf 146.411 0 Td [(\000)]TJ/F8 9.9626 Tf 7.749 0 Td [(1)-276(to)-276(mak)28(e)-276(it)-276(a)28(v)55(ailable)-276(on)-276(all)-276(p)1(ro)-28(cesses.)]TJ -155.184 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.135 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 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[(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ +/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ 0 g 0 G - 139.477 -318.348 Td [(130)]TJ + [-500(This)-402(subroutine)-403(implies)-402(a)-402(s)-1(yn)1(c)27(hronization,)-419(but)-403(on)1(ly)-403(b)-28(et)28(w)28(een)-403(the)-402(calling)]TJ 12.73 -11.955 Td [(pro)-28(cess)-333(and)-333(the)-334(destination)-333(pro)-28(cess)]TJ/F11 9.9626 Tf 157.521 0 Td [(dst)]TJ/F8 9.9626 Tf 13.453 0 Td [(.)]TJ +0 g 0 G + -31.497 -105.147 Td [(125)]TJ 0 g 0 G ET endstream endobj -1740 0 obj +1735 0 obj << -/Length 3705 +/Length 5375 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(mm)]TJ -ET -q -1 0 0 1 123.118 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 127.153 706.129 Td [(arra)31(y)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(7.17)-1125(psb)]TJ ET q -1 0 0 1 158.747 706.328 cm +1 0 0 1 209.121 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 162.782 706.129 Td [(read)-504(|)-504(Read)-504(a)-504(dense)-504(arra)32(y)-504(from)-504(a)-504(\014le)-504(in)-504(the)]TJ -62.887 -13.948 Td [(MatrixMark)31(et)-375(format)]TJ/F27 9.9626 Tf 1.377 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.373 0 Td [(m)-87(m)]TJ -ET -q -1 0 0 1 149.57 668.014 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 153.421 667.814 Td [(a)-86(r)-87(r)-86(a)-87(y)]TJ -ET -q -1 0 0 1 181.351 668.014 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S -Q -BT -/F8 9.9626 Tf 185.201 667.814 Td [(r)-86(e)-87(a)-86(d)-192(\050)-121(b)-191(,)-910(i)-150(r)-149(e)-150(t)-460(,)-896(i)-135(u)-135(n)-135(i)-135(t)-431(,)-890(f)-129(i)-129(l)-129(e)-129(n)-129(a)-129(m)-129(e)-234(\051)]TJ +/F16 11.9552 Tf 213.156 706.129 Td [(rcv)-375(|)-375(Receiv)31(e)-375(data)]TJ 0 g 0 G 0 g 0 G +/F30 9.9626 Tf -62.451 -18.389 Td [(call)-525(psb_rcv\050icontxt,)-525(dat,)-525(src,)-525(m\051)]TJ/F8 9.9626 Tf 14.944 -21.918 Td [(This)-333(subroutine)-334(receiv)28(es)-333(a)-334(pac)28(k)28(et)-333(of)-334(data)-333(to)-333(a)-334(destination.)]TJ 0 g 0 G -/F27 9.9626 Tf -85.306 -17.933 Td [(T)32(yp)-32(e:)]TJ +/F27 9.9626 Tf -14.944 -19.926 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous:)-444(s)-1(ee)-333(usage)-333(notes.)]TJ 0 g 0 G /F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(\014lename)]TJ + 0 -19.925 Td [(icon)32(txt)]TJ 0 g 0 G -/F8 9.9626 Tf 46.513 0 Td [(The)-333(name)-334(of)-333(the)-333(\014le)-334(to)-333(b)-28(e)-333(read.)]TJ -21.606 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-435(as:)-648(a)-435(c)27(h)1(arac)-1(ter)-435(v)56(ariable)-435(con)28(taining)-436(a)-435(v)56(alid)-435(\014le)-435(name,)-461(or)]TJ/F30 9.9626 Tf 297.915 0 Td [(-)]TJ/F8 9.9626 Tf 5.231 0 Td [(,)-461(in)]TJ -303.146 -11.956 Td [(whic)28(h)-302(cas)-1(e)-302(the)-302(default)-302(input)-302(unit)-302(5)-303(\050i.e.)-434(standard)-302(input)-302(in)-302(Unix)-302(jargon\051)-302(is)]TJ 0 -11.955 Td [(used.)-444(Default:)]TJ/F30 9.9626 Tf 66.058 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +/F8 9.9626 Tf 39.989 0 Td [(the)-333(comm)27(unication)-333(con)28(text)-333(iden)27(tifyi)1(ng)-334(the)-333(virtual)-333(parallel)-334(mac)28(hine.)]TJ -15.082 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(ariable.)]TJ 0 g 0 G -/F27 9.9626 Tf -96.195 -19.925 Td [(iunit)]TJ +/F27 9.9626 Tf -24.907 -19.925 Td [(src)]TJ 0 g 0 G -/F8 9.9626 Tf 28.532 0 Td [(The)-333(F)83(ortran)-333(\014le)-334(un)1(it)-334(n)28(um)28(b)-28(er.)]TJ -3.625 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)-444(Only)-333(me)-1(ani)1(ngful)-334(if)-333(\014lename)-333(is)-334(not)]TJ/F30 9.9626 Tf 286.288 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +/F8 9.9626 Tf 19.311 0 Td [(Source)-333(pro)-28(cess.)]TJ 5.596 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.756 0 Td [(.)]TJ -62.134 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue)-333(0)]TJ/F11 9.9626 Tf 138.176 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(sr)-28(c)-277(<)]TJ/F8 9.9626 Tf 24.269 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(np)]TJ/F14 9.9626 Tf 13.206 0 Td [(\000)]TJ/F8 9.9626 Tf 9.963 0 Td [(1.)]TJ 0 g 0 G -/F27 9.9626 Tf -316.425 -21.918 Td [(On)-383(Return)]TJ +/F27 9.9626 Tf -239.302 -31.88 Td [(m)]TJ 0 g 0 G +/F8 9.9626 Tf 14.529 0 Td [(Num)28(b)-28(er)-333(of)-334(ro)28(ws.)]TJ 10.378 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(global)]TJ/F8 9.9626 Tf 29.757 0 Td [(.)]TJ -62.135 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf 43.455 0 Td [(.)]TJ -73.066 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue)-333(0)]TJ/F11 9.9626 Tf 138.176 0 Td [(<)]TJ/F8 9.9626 Tf 7.749 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(m)-278(<)]TJ/F8 9.9626 Tf 19.263 0 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(siz)-44(e)]TJ/F8 9.9626 Tf 17.813 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(dat;)]TJ/F8 9.9626 Tf 18.477 0 Td [(1\051.)]TJ -226.384 -11.955 Td [(When)]TJ/F11 9.9626 Tf 29.071 0 Td [(dat)]TJ/F8 9.9626 Tf 17.383 0 Td [(is)-335(a)-334(rank)-335(2)-335(arra)28(y)84(,)-335(sp)-28(eci\014es)-335(the)-335(n)28(um)28(b)-28(er)-334(of)-335(ro)28(ws)-335(to)-335(b)-27(e)-335(sen)28(t)-335(inde-)]TJ -46.454 -11.955 Td [(p)-28(enden)28(tly)-285(of)-285(the)-286(leadin)1(g)-286(dimension)]TJ/F11 9.9626 Tf 153.741 0 Td [(siz)-44(e)]TJ/F8 9.9626 Tf 17.813 0 Td [(\050)]TJ/F11 9.9626 Tf 3.874 0 Td [(dat;)]TJ/F8 9.9626 Tf 18.477 0 Td [(1\051;)-301(m)27(u)1(s)-1(t)-285(ha)28(v)28(e)-285(the)-286(same)-285(v)55(al)1(ue)]TJ -193.905 -11.955 Td [(on)-333(sending)-334(and)-333(receiving)-333(pro)-28(cesses.)]TJ 0 g 0 G - 0 -19.925 Td [(b)]TJ +/F27 9.9626 Tf -24.907 -21.918 Td [(On)-383(Return)]TJ 0 g 0 G -/F8 9.9626 Tf 11.347 0 Td [(Rigth)-333(hand)-333(s)-1(i)1(de\050s)-1(\051.)]TJ 13.56 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-310(arra)28(y)-310(of)-310(t)28(yp)-28(e)-310(real)-310(or)-310(complex,)-315(rank)-309(1)-310(or)-310(2)-310(and)-310(ha)28(ving)-310(the)-310(ALLOCA)83(T-)]TJ 0 -11.955 Td [(ABLE)-334(attribute;)-334(will)-333(b)-28(e)-334(allo)-28(cated)-333(and)-334(\014lled)-334(in)-333(if)-334(the)-334(input)-333(\014le)-334(con)28(tains)-334(a)]TJ 0 -11.955 Td [(righ)28(t)-333(hand)-334(side,)-333(otherwise)-333(will)-334(b)-27(e)-334(left)-333(in)-333(the)-334(UNALLOCA)84(TED)-334(state.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(iret)]TJ + 0 -19.926 Td [(dat)]TJ 0 g 0 G -/F8 9.9626 Tf 22.589 0 Td [(Error)-333(co)-28(de.)]TJ 2.318 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detected.)]TJ +/F8 9.9626 Tf 21.371 0 Td [(The)-333(data)-334(to)-333(b)-28(e)-333(receiv)28(ed.)]TJ 3.536 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -71.509 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-339(as:)-458(an)-339(in)28(teg)-1(er,)-341(real)-340(or)-339(complex)-340(v)56(ariable,)-342(whic)28(h)-339(m)-1(a)28(y)-339(b)-28(e)-340(a)-340(scalar,)]TJ 0 -11.955 Td [(or)-381(a)-381(rank)-381(1)-381(or)-381(2)-381(arra)28(y)83(,)-393(or)-381(a)-381(c)27(h)1(aracte)-1(r)-381(or)-381(logical)-381(scalar.)-968(T)27(yp)-27(e,)-393(kind)-381(and)]TJ 0 -11.956 Td [(rank)-327(m)27(ust)-327(agree)-328(on)-327(sender)-328(and)-327(receiv)27(er)-327(pro)-28(cess;)-329(if)]TJ/F11 9.9626 Tf 220.724 0 Td [(m)]TJ/F8 9.9626 Tf 12.01 0 Td [(is)-328(not)-327(sp)-28(eci\014ed,)-328(s)-1(ize)]TJ -232.734 -11.955 Td [(m)28(ust)-334(agree)-333(as)-333(w)27(ell.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ +0 g 0 G +/F8 9.9626 Tf 12.177 -19.925 Td [(1.)]TJ +0 g 0 G + [-500(This)-402(subroutine)-403(implies)-402(a)-402(sync)27(hronization,)-419(but)-403(on)1(ly)-403(b)-28(et)28(w)28(een)-403(th)1(e)-403(calling)]TJ 12.73 -11.955 Td [(pro)-28(cess)-333(and)-333(the)-334(source)-333(pro)-28(cess)]TJ/F11 9.9626 Tf 136.516 0 Td [(sr)-28(c)]TJ/F8 9.9626 Tf 13.753 0 Td [(.)]TJ +0 g 0 G + -10.792 -105.147 Td [(126)]TJ +0 g 0 G +ET + +endstream +endobj +1742 0 obj +<< +/Length 6381 +>> +stream +0 g 0 G +0 g 0 G +BT +/F16 14.3462 Tf 99.895 706.129 Td [(8)-1125(Error)-375(handling)]TJ/F8 9.9626 Tf 0 -21.821 Td [(The)-446(PSBLAS)-446(library)-446(error)-446(handling)-446(p)-28(olicy)-446(has)-446(b)-28(een)-446(completely)-446(rewritten)-446(in)]TJ 0 -11.955 Td [(v)28(ersion)-448(2.0.)-788(The)-448(idea)-448(b)-27(ehind)-448(the)-448(design)-448(of)-447(this)-448(new)-448(error)-448(handling)-447(strategy)]TJ 0 -11.955 Td [(is)-491(to)-492(k)28(eep)-491(error)-491(me)-1(ssages)-491(on)-491(a)-492(stac)28(k)-491(allo)28(wing)-492(the)-491(user)-491(to)-491(trace)-492(bac)28(k)-491(up)-492(to)]TJ 0 -11.956 Td [(the)-401(p)-27(oin)27(t)-400(where)-401(the)-400(\014rst)-401(error)-400(me)-1(ssage)-400(has)-401(b)-28(een)-400(generated.)-646(Ev)27(ery)-400(routine)-401(in)]TJ 0 -11.955 Td [(the)-442(PS)1(B)-1(LAS)1(-)-1(2.0)-441(library)-441(has,)-469(as)-442(last)-441(non-optional)-441(argume)-1(n)28(t,)-468(an)-442(in)28(teger)]TJ/F30 9.9626 Tf 322.79 0 Td [(info)]TJ/F8 9.9626 Tf -322.79 -11.955 Td [(v)56(ariable;)-385(whenev)28(er,)-376(inside)-368(the)-367(routine,)-376(an)-368(error)-367(is)-368(detected,)-376(this)-367(v)55(ariable)-367(is)-368(set)]TJ 0 -11.955 Td [(to)-381(a)-380(v)55(alue)-380(corresp)-28(onding)-380(to)-381(a)-380(sp)-28(eci\014c)-381(error)-380(co)-28(de.)-586(Then)-381(this)-380(error)-381(co)-28(de)-380(is)-381(also)]TJ 0 -11.955 Td [(pushed)-245(on)-245(the)-245(error)-245(stac)28(k)-245(and)-245(then)-245(either)-245(con)27(trol)-245(is)-245(return)1(e)-1(d)-245(to)-245(the)-245(caller)-245(routine)]TJ 0 -11.955 Td [(or)-372(the)-372(execution)-371(is)-372(ab)-28(orted,)-381(dep)-28(ending)-372(on)-371(the)-372(users)-372(c)28(hoice.)-560(A)28(t)-372(the)-372(time)-371(when)]TJ 0 -11.956 Td [(the)-364(execution)-363(is)-364(ab)-28(orted,)-371(an)-364(error)-364(message)-363(is)-364(prin)28(ted)-364(on)-364(standard)-363(output)-364(with)]TJ 0 -11.955 Td [(a)-448(lev)28(el)-448(of)-447(v)27(erb)-27(osit)27(y)-447(than)-448(can)-448(b)-27(e)-448(c)28(hosen)-448(b)28(y)-448(the)-448(user.)-787(If)-448(the)-448(execution)-447(is)-448(not)]TJ 0 -11.955 Td [(ab)-28(orted,)-328(then,)-329(the)-328(caller)-327(routine)-328(c)28(hec)28(ks)-328(the)-328(v)56(alue)-328(retur)1(ned)-328(in)-328(the)]TJ/F30 9.9626 Tf 285.46 0 Td [(info)]TJ/F8 9.9626 Tf 24.185 0 Td [(v)56(ariable)]TJ -309.645 -11.955 Td [(and,)-359(if)-354(not)-354(zero,)-359(an)-353(e)-1(r)1(ror)-354(condition)-354(is)-354(raised.)-506(This)-354(pro)-28(cess)-354(con)28(tin)28(ues)-354(on)-354(all)-354(the)]TJ 0 -11.955 Td [(lev)28(els)-297(of)-297(nested)-296(calls)-297(un)28(til)-297(the)-296(lev)28(e)-1(l)-296(where)-297(the)-296(user)-297(decides)-297(to)-296(ab)-28(ort)-297(the)-296(program)]TJ 0 -11.955 Td [(execution.)]TJ 14.944 -11.956 Td [(Figure)]TJ +0 0 1 rg 0 0 1 RG + [-353(9)]TJ +0 g 0 G + [-353(sho)28(ws)-353(the)-353(la)28(y)27(out)-353(of)-353(a)-353(generic)]TJ/F30 9.9626 Tf 170.683 0 Td [(psb_foo)]TJ/F8 9.9626 Tf 40.129 0 Td [(routine)-353(with)-353(resp)-28(ect)-353(to)-353(the)]TJ -225.756 -11.955 Td [(PSBLAS-2.0)-326(error)-326(handl)1(ing)-326(p)-28(olicy)83(.)-442(It)-325(is)-326(p)-28(ossible)-326(to)-326(see)-326(ho)28(w,)-327(whenev)27(er)-325(an)-326(error)]TJ 0 -11.955 Td [(condition)-379(is)-378(detected,)-390(the)]TJ/F30 9.9626 Tf 115.439 0 Td [(info)]TJ/F8 9.9626 Tf 24.694 0 Td [(v)56(ariable)-379(is)-379(set)-379(to)-378(the)-379(corresp)-28(onding)-378(error)-379(co)-28(de)]TJ -140.133 -11.955 Td [(whic)28(h)-376(is,)-387(then,)-386(pushed)-376(on)-376(top)-376(of)-376(the)-376(stac)28(k)-376(b)28(y)-376(means)-376(of)-376(the)]TJ/F30 9.9626 Tf 264.703 0 Td [(psb_errpush)]TJ/F8 9.9626 Tf 57.533 0 Td [(.)-572(An)]TJ -322.236 -11.955 Td [(error)-331(condition)-331(ma)28(y)-331(b)-28(e)-331(directly)-331(detected)-331(inside)-331(a)-331(routine)-331(or)-331(indirectly)-331(c)27(hec)28(king)]TJ 0 -11.956 Td [(the)-462(error)-461(co)-28(de)-461(returned)-462(returned)-461(b)28(y)-462(a)-461(called)-462(routine.)-829(Whenev)28(er)-461(an)-462(error)-461(is)]TJ 0 -11.955 Td [(encoun)28(tered,)-459(after)-434(it)-434(has)-434(b)-27(een)-434(pushed)-434(on)-434(stac)28(k,)-459(the)-434(program)-433(exec)-1(u)1(tion)-434(skips)]TJ 0 -11.955 Td [(to)-356(a)-356(p)-27(oin)28(t)-356(where)-356(the)-356(error)-355(c)-1(on)1(dition)-356(is)-356(handled;)-367(the)-355(e)-1(r)1(ror)-356(condition)-356(is)-356(hand)1(le)-1(d)]TJ 0 -11.955 Td [(either)-392(b)28(y)-392(returning)-392(con)28(trol)-392(to)-392(the)-392(caller)-392(r)1(outine)-392(or)-392(b)28(y)-392(calling)-392(the)]TJ/F30 9.9626 Tf 291.408 0 Td [(psb\134_error)]TJ/F8 9.9626 Tf -291.408 -11.955 Td [(routine)-478(whic)28(h)-479(prin)28(ts)-478(the)-478(con)28(ten)27(t)-478(of)-478(the)-478(error)-479(stac)28(k)-478(and)-478(ab)-28(orts)-478(the)-478(program)]TJ 0 -11.955 Td [(execution,)-330(accordin)1(g)-329(to)-329(th)1(e)-329(c)28(hoice)-329(made)-328(b)27(y)-328(the)-329(user)-328(with)]TJ/F30 9.9626 Tf 252.028 0 Td [(psb_set_erraction)]TJ/F8 9.9626 Tf 88.916 0 Td [(.)]TJ -340.944 -11.956 Td [(The)-347(default)-346(is)-347(to)-346(prin)28(t)-347(the)-347(error)-346(and)-347(terminate)-346(the)-347(program,)-350(but)-346(the)-347(user)-346(ma)27(y)]TJ 0 -11.955 Td [(c)28(ho)-28(ose)-333(to)-334(handle)-333(the)-333(error)-334(explicitly)84(.)]TJ 14.944 -11.955 Td [(Figure)]TJ +0 0 1 rg 0 0 1 RG + [-479(10)]TJ +0 g 0 G + [-479(rep)-28(orts)-479(a)-479(sample)-480(error)-479(message)-479(generated)-479(b)28(y)-480(the)-479(PSBLAS-2.0)]TJ -14.944 -11.955 Td [(library)83(.)-451(This)-335(error)-336(has)-335(b)-28(een)-336(generated)-335(b)27(y)-335(the)-336(fact)-335(that)-336(the)-335(use)-1(r)-335(has)-336(c)28(hosen)-336(the)]TJ 0 -11.955 Td [(in)28(v)55(alid)-367(\134F)28(OO")-368(storage)-367(format)-368(to)-367(represen)27(t)-367(the)-368(sparse)-367(matrix.)-547(F)83(rom)-367(this)-368(error)]TJ 0 -11.955 Td [(message)-248(it)-248(is)-248(p)-27(oss)-1(ib)1(le)-248(to)-248(see)-248(that)-248(the)-248(error)-247(has)-248(b)-28(een)-248(detected)-248(inside)-248(the)]TJ/F30 9.9626 Tf 301.869 0 Td [(psb_cest)]TJ/F8 9.9626 Tf -301.869 -11.956 Td [(subroutine)-333(called)-334(b)28(y)]TJ/F30 9.9626 Tf 91.408 0 Td [(psb_spasb)]TJ/F8 9.9626 Tf 50.394 0 Td [(...)-444(b)27(y)-333(pro)-28(cess)-333(0)-333(\050i.e.)-445(the)-333(ro)-28(ot)-333(pro)-28(cess\051.)]TJ 0 g 0 G - 139.477 -294.437 Td [(131)]TJ + 22.582 -211.304 Td [(127)]TJ 0 g 0 G ET endstream endobj -1747 0 obj +1749 0 obj << -/Length 4185 +/Length 7207 >> stream 0 g 0 G 0 g 0 G +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F53 8.9664 Tf 159.61 680.066 Td [(s)-60(u)-60(b)-60(r)-60(o)-59(u)-60(t)-60(i)-60(n)-60(e)]TJ/F46 8.9664 Tf 61.471 0 Td [(p)-132(s)-132(b)]TJ +ET +q +1 0 0 1 239.064 680.265 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 243.014 680.066 Td [(f)-132(o)-132(o)-241(\050)-155(s)-47(o)-47(m)-46(e)-769(a)-105(r)-106(g)-105(s)-376(,)-939(i)-156(n)-156(f)-157(o)-265(\051)]TJ -65.126 -10.959 Td [(.)-248(.)-249(.)]TJ/F53 8.9664 Tf -0.604 -10.959 Td [(i)-181(f)]TJ/F46 8.9664 Tf 10.409 0 Td [(\050)-259(e)-152(r)-151(r)-151(o)-151(r)-897(d)-129(e)-129(t)-129(e)-130(c)-129(t)-129(e)-130(d)-237(\051)]TJ/F53 8.9664 Tf 93.291 0 Td [(t)-30(h)-30(e)-29(n)]TJ/F46 8.9664 Tf -87.332 -10.959 Td [(i)-156(n)-157(f)-156(o)-65(=)-38(e)-129(r)-129(r)-128(c)-129(o)-129(d)-129(e)-129(1)]TJ/F53 8.9664 Tf -0.133 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.487 0 Td [(p)-124(s)-124(b)]TJ +ET +q +1 0 0 1 238.765 636.429 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 242.641 636.23 Td [(e)-124(r)-124(r)-124(p)-123(u)-124(s)-124(h)-232(\050)-330(')-242(p)-132(s)-133(b)]TJ +ET +q +1 0 0 1 310.944 636.429 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 314.894 636.23 Td [(f)-132(o)-132(o)-353(')-332(,)-855(e)-129(r)-129(r)-129(c)-129(o)-129(d)-128(e)-129(1)-237(\051)]TJ/F53 8.9664 Tf -122.23 -10.959 Td [(g)-46(o)-47(t)-46(o)]TJ/F46 8.9664 Tf 27.969 0 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf -44.989 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ/F46 8.9664 Tf 2.244 -10.959 Td [(.)-248(.)-249(.)]TJ/F53 8.9664 Tf -0.957 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.399 0 Td [(p)-114(s)-114(b)]TJ +ET +q +1 0 0 1 221.826 592.594 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 225.613 592.394 Td [(b)-114(a)-114(r)-223(\050)-155(s)-47(o)-46(m)-47(e)-769(a)-105(r)-105(g)-105(s)-376(,)-939(i)-157(n)-156(f)-157(o)-264(\051)]TJ/F53 8.9664 Tf -48.329 -10.958 Td [(i)-181(f)]TJ/F46 8.9664 Tf 10.409 0 Td [(\050)-265(i)-156(n)-157(f)-156(o)-939(.)]TJ/F53 8.9664 Tf 37.83 0 Td [(n)-11(e)]TJ/F46 8.9664 Tf 12.445 0 Td [(.)-910(z)-127(e)-127(r)-128(o)-236(\051)]TJ/F53 8.9664 Tf 43.016 0 Td [(t)-30(h)-30(e)-29(n)]TJ/F46 8.9664 Tf -87.332 -10.959 Td [(i)-156(n)-157(f)-156(o)-65(=)-38(e)-129(r)-129(r)-128(c)-129(o)-129(d)-129(e)-129(2)]TJ/F53 8.9664 Tf -0.133 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.487 0 Td [(p)-124(s)-124(b)]TJ +ET +q +1 0 0 1 238.765 559.717 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 242.641 559.518 Td [(e)-124(r)-124(r)-124(p)-123(u)-124(s)-124(h)-232(\050)-330(')-242(p)-132(s)-133(b)]TJ +ET +q +1 0 0 1 310.944 559.717 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 314.894 559.518 Td [(f)-132(o)-132(o)-353(')-332(,)-855(e)-129(r)-129(r)-129(c)-129(o)-129(d)-128(e)-129(2)-237(\051)]TJ/F53 8.9664 Tf -122.23 -10.959 Td [(g)-46(o)-47(t)-46(o)]TJ/F46 8.9664 Tf 27.969 0 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf -44.989 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ/F46 8.9664 Tf 2.244 -10.959 Td [(.)-248(.)-249(.)]TJ -18.077 -10.959 Td [(9)-82(9)-82(9)-83(9)]TJ/F53 8.9664 Tf 27.419 0 Td [(c)-57(o)-57(n)-57(t)-56(i)-57(n)-57(u)-57(e)]TJ -9.946 -10.959 Td [(i)-181(f)]TJ/F46 8.9664 Tf 15.938 0 Td [(\050)-273(e)-164(r)-165(r)]TJ +ET +q +1 0 0 1 215.536 504.923 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q +BT +/F46 8.9664 Tf 219.774 504.723 Td [(a)-164(c)-165(t)-946(.)]TJ/F53 8.9664 Tf 27.965 0 Td [(e)-22(q)]TJ/F46 8.9664 Tf 12.346 0 Td [(.)-923(a)-141(c)-141(t)]TJ +ET +q +1 0 0 1 287.553 504.923 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S +Q BT -/F16 11.9552 Tf 150.705 706.129 Td [(mm)]TJ +/F46 8.9664 Tf 291.582 504.723 Td [(a)-141(b)-141(o)-141(r)-141(t)-249(\051)]TJ/F53 8.9664 Tf 39.166 0 Td [(t)-30(h)-29(e)-30(n)]TJ -142.758 -10.959 Td [(c)-142(a)-141(l)-142(l)]TJ/F46 8.9664 Tf 27.681 0 Td [(p)-146(s)-145(b)]TJ ET q -1 0 0 1 173.928 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 234.014 493.964 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S Q BT -/F16 11.9552 Tf 177.963 706.129 Td [(mat)]TJ +/F46 8.9664 Tf 238.084 493.764 Td [(e)-146(r)-145(r)-146(o)-145(r)-254(\050)-252(i)-144(c)-143(o)-144(n)-143(t)-143(x)-144(t)-252(\051)]TJ/F53 8.9664 Tf -50.844 -10.959 Td [(r)-58(e)-58(t)-58(u)-58(r)-58(n)]TJ -10.529 -10.958 Td [(e)-117(l)-117(s)-117(e)]TJ 10.529 -10.959 Td [(r)-58(e)-58(t)-58(u)-58(r)-58(n)]TJ -11.596 -10.959 Td [(e)2(n)2(d)-796(i)-181(f)]TJ -16.588 -21.918 Td [(e)2(n)2(d)-675(s)-60(u)-59(b)-60(r)-60(o)-60(u)-60(t)-60(i)-60(n)-60(e)]TJ/F46 8.9664 Tf 84.142 0 Td [(p)-132(s)-132(b)]TJ ET q -1 0 0 1 201.746 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 261.181 428.21 cm +[]0 d 0 J 0.398 w 0 0 m 2.765 0 l S Q BT -/F16 11.9552 Tf 205.781 706.129 Td [(write)-531(|)-532(W)94(rite)-531(a)-532(sparse)-531(matrix)-532(to)-531(a)-532(\014le)-531(in)-531(the)]TJ -55.076 -13.948 Td [(MatrixMark)31(et)-375(format)]TJ/F27 9.9626 Tf 1.377 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.175 0 Td [(m)-67(m)]TJ +/F46 8.9664 Tf 265.131 428.011 Td [(f)-132(o)-132(o)]TJ +0 g 0 G +0 g 0 G ET q -1 0 0 1 199.787 668.014 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 150.705 701.884 cm +[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S +Q +q +1 0 0 1 150.904 410.576 cm +[]0 d 0 J 0.398 w 0 0 m 0 291.308 l S +Q +q +1 0 0 1 497.088 410.576 cm +[]0 d 0 J 0.398 w 0 0 m 0 291.308 l S +Q +q +1 0 0 1 150.705 410.576 cm +[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S Q BT -/F8 9.9626 Tf 203.439 667.814 Td [(m)-67(a)-66(t)]TJ +/F8 9.9626 Tf 150.705 382.537 Td [(Figure)-329(9:)-443(The)-329(la)27(y)28(out)-329(of)-330(a)-329(generic)]TJ/F30 9.9626 Tf 147.445 0 Td [(psb)]TJ ET q -1 0 0 1 223.186 668.014 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 314.468 382.736 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 226.839 667.814 Td [(w)-67(r)-66(i)-67(t)-66(e)-173(\050)-139(a)-227(,)-885(m)-124(t)-123(i)-124(t)-124(l)-123(e)-409(,)-910(i)-150(r)-149(e)-150(t)-460(,)-896(i)-135(u)-135(n)-135(i)-135(t)-431(,)-890(f)-129(i)-129(l)-129(e)-129(n)-129(a)-129(m)-129(e)-234(\051)]TJ -0 g 0 G -0 g 0 G +/F30 9.9626 Tf 317.606 382.537 Td [(foo)]TJ/F8 9.9626 Tf 18.974 0 Td [(routine)-329(with)-330(resp)-28(ect)-329(to)-329(PSBLAS-2.0)]TJ -185.875 -11.955 Td [(error)-333(handling)-333(p)-28(olicy)83(.)]TJ 0 g 0 G -/F27 9.9626 Tf -76.134 -17.933 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ 0 g 0 G 0 g 0 G - 0 -19.925 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)-333(to)-333(b)-28(e)-333(written.)]TJ 14.356 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.081 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.914 0 Td [(psb)]TJ +/F30 9.9626 Tf 8.368 -39.475 Td [(==========================================================)]TJ 0 -11.955 Td [(Process:)-525(0.)-1050(PSBLAS)-525(Error)-525(\0504010\051)-525(in)-525(subroutine:)-525(df_sample)]TJ 0 -11.955 Td [(Error)-525(from)-525(call)-525(to)-525(subroutine)-525(mat)-525(dist)]TJ 0 -11.955 Td [(==========================================================)]TJ 0 -11.955 Td [(Process:)-525(0.)-1050(PSBLAS)-525(Error)-525(\0504010\051)-525(in)-525(subroutine:)-525(mat_distv)]TJ 0 -11.956 Td [(Error)-525(from)-525(call)-525(to)-525(subroutine)-525(psb_spasb)]TJ 0 -11.955 Td [(==========================================================)]TJ 0 -11.955 Td [(Process:)-525(0.)-1050(PSBLAS)-525(Error)-525(\0504010\051)-525(in)-525(subroutine:)-525(psb_spasb)]TJ 0 -11.955 Td [(Error)-525(from)-525(call)-525(to)-525(subroutine)-525(psb_cest)]TJ 0 -11.955 Td [(==========================================================)]TJ 0 -11.955 Td [(Process:)-525(0.)-1050(PSBLAS)-525(Error)-525(\050136\051)-525(in)-525(subroutine:)-525(psb_cest)]TJ 0 -11.956 Td [(Format)-525(FOO)-525(is)-525(unknown)]TJ 0 -11.955 Td [(==========================================================)]TJ 0 -11.955 Td [(Aborting...)]TJ ET q -1 0 0 1 362.845 586.32 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 150.705 343.417 cm +[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S +Q +q +1 0 0 1 150.904 165.307 cm +[]0 d 0 J 0.398 w 0 0 m 0 178.111 l S +Q +q +1 0 0 1 497.088 165.307 cm +[]0 d 0 J 0.398 w 0 0 m 0 178.111 l S +Q +q +1 0 0 1 150.705 165.307 cm +[]0 d 0 J 0.398 w 0 0 m 346.583 0 l S Q BT -/F30 9.9626 Tf 365.983 586.121 Td [(Tspmat)]TJ +/F8 9.9626 Tf 150.705 137.267 Td [(Figure)-386(10:)-551(A)-386(sample)-386(PSBLAS-2.0)-387(err)1(or)-387(message.)-603(Pro)-28(cess)-387(0)-386(detected)-386(an)-387(error)]TJ 0 -11.955 Td [(condition)-333(inside)-334(t)1(he)-334(psb)]TJ ET q -1 0 0 1 397.993 586.32 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 255.468 125.512 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 401.131 586.121 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -271.347 -19.926 Td [(m)32(title)]TJ -0 g 0 G -/F8 9.9626 Tf 34.737 0 Td [(Matrix)-333(title.)]TJ -9.831 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(A)-299(c)28(harac)28(h)27(t)1(e)-1(r)-298(v)55(ariable)-299(hold)1(ing)-299(a)-299(descriptiv)28(e)-299(title)-299(for)-299(the)-299(matrix)-298(to)-299(b)-28(e)-299(writ-)]TJ 0 -11.955 Td [(ten)-333(to)-334(\014le.)]TJ -0 g 0 G -/F27 9.9626 Tf -24.906 -19.925 Td [(\014lename)]TJ -0 g 0 G -/F8 9.9626 Tf 46.513 0 Td [(The)-333(name)-334(of)-333(the)-333(\014le)-334(to)-333(b)-28(e)-333(written)-333(to.)]TJ -21.607 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.761 -11.955 Td [(Sp)-28(eci\014ed)-435(as:)-648(a)-435(c)27(haracter)-435(v)56(ariable)-435(con)27(tain)1(ing)-436(a)-435(v)56(alid)-435(\014le)-435(name)-1(,)-460(or)]TJ/F30 9.9626 Tf 297.916 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(,)-461(in)]TJ -303.146 -11.955 Td [(whic)28(h)-281(case)-280(the)-281(d)1(e)-1(f)1(ault)-281(output)-280(unit)-280(6)-281(\050i.e.)-427(stand)1(ard)-281(output)-280(in)-280(Unix)-281(jargon\051)]TJ 0 -11.955 Td [(is)-333(used.)-445(Default:)]TJ/F30 9.9626 Tf 76.076 0 Td [(-)]TJ/F8 9.9626 Tf 5.231 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -106.213 -19.925 Td [(iunit)]TJ -0 g 0 G -/F8 9.9626 Tf 28.532 0 Td [(The)-333(F)83(ortran)-333(\014le)-334(u)1(nit)-334(n)28(um)28(b)-28(er.)]TJ -3.626 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.761 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)-444(Only)-334(meaningf)1(ul)-334(if)-333(\014lename)-333(is)-334(not)]TJ/F30 9.9626 Tf 286.289 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -316.425 -21.918 Td [(On)-383(Return)]TJ -0 g 0 G -0 g 0 G - 0 -19.925 Td [(iret)]TJ +/F8 9.9626 Tf 258.457 125.312 Td [(cest)-333(subroutine)]TJ 0 g 0 G -/F8 9.9626 Tf 22.589 0 Td [(Error)-333(co)-28(de.)]TJ 2.318 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-333(in)28(teger)-334(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detected.)]TJ 0 g 0 G - 139.476 -262.557 Td [(132)]TJ + 56.631 -34.874 Td [(128)]TJ 0 g 0 G ET endstream endobj -1753 0 obj +1779 0 obj << -/Length 3381 +/Length 3730 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(mm)]TJ +/F16 11.9552 Tf 99.895 706.129 Td [(8.1)-1125(psb)]TJ ET q -1 0 0 1 123.118 706.328 cm +1 0 0 1 151.587 706.328 cm []0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F16 11.9552 Tf 127.153 706.129 Td [(arra)31(y)]TJ +/F16 11.9552 Tf 155.621 706.129 Td [(errpush)-469(|)-468(Pushes)-469(an)-469(error)-468(co)-31(de)-469(on)31(to)-468(the)-469(error)]TJ -25.091 -13.948 Td [(stac)31(k)]TJ/F27 9.9626 Tf -29.258 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.712 0 Td [(p)-120(s)-121(b)]TJ ET q -1 0 0 1 158.747 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S +1 0 0 1 150.181 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F16 11.9552 Tf 162.782 706.129 Td [(write)-438(|)-438(W)93(rite)-438(a)-438(dense)-438(arra)31(y)-438(from)-438(a)-438(\014le)-439(in)-438(the)]TJ -62.887 -13.948 Td [(MatrixMark)31(et)-375(format)]TJ/F27 9.9626 Tf 1.377 -24.367 Td 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0 G +/F8 9.9626 Tf 11.346 0 Td [(Rigth)-333(hand)-334(sid)1(e)-1(\050s\051.)]TJ 13.56 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(An)-282(arr)1(a)27(y)-281(of)-282(t)28(yp)-28(e)-281(real)-282(or)-281(complex,)-292(rank)-282(2)-281(and)-282(ha)28(ving)-281(the)-282(ALLOCA)83(T)84(ABLE)]TJ 0 -11.956 Td [(attribute;)-409(will)-384(b)-28(e)-384(allo)-28(cated)-384(and)-383(\014lled)-384(in)-384(if)-384(the)-384(input)-384(\014le)-384(con)28(tains)-384(a)-384(righ)28(t)]TJ 0 -11.955 Td [(hand)-333(side,)-334(otherwise)-333(will)-333(b)-28(e)-333(left)-334(in)-333(the)-333(UNALLOCA)83(TED)-333(state.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.925 Td [(m)32(title)]TJ +0 g 0 G +/F8 9.9626 Tf 34.737 0 Td [(Matrix)-333(title.)]TJ -9.831 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(A)-405(c)28(harac)28(h)28(ter)-405(v)56(ariable)-405(of)-405(length)-404(72)-405(holding)-405(a)-404(cop)27(y)-404(of)-405(the)-405(matrix)-404(title)-405(as)]TJ 0 -11.956 Td [(sp)-28(eci\014ed)-333(b)28(y)-334(the)-333(Harw)28(ell-Bo)-28(eing)-333(format)-334(and)-333(con)28(tained)-333(in)-334(the)-333(input)-333(\014le.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -19.925 Td [(iret)]TJ +0 g 0 G +/F8 9.9626 Tf 22.589 0 Td [(Error)-333(co)-28(de.)]TJ 2.317 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(An)-333(in)27(t)1(e)-1(ger)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detec)-1(ted.)]TJ +0 g 0 G + 139.477 -194.811 Td [(134)]TJ +0 g 0 G +ET + +endstream +endobj +1817 0 obj +<< +/Length 5264 +>> +stream +0 g 0 G +0 g 0 G +BT +/F16 11.9552 Tf 99.895 706.129 Td [(9.2)-1125(h)31(b)]TJ ET q -1 0 0 1 395.279 298.012 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 145.908 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F30 9.9626 Tf 398.417 297.812 Td [(T)]TJ +/F16 11.9552 Tf 149.943 706.129 Td [(write)-573(|)-574(W)94(rite)-574(a)-573(sparse)-574(matrix)-573(to)-574(a)-573(\014le)-574(in)-573(the)]TJ -19.412 -13.948 Td [(Harw)31(ell{Bo)-31(eing)-375(format)]TJ/F27 9.9626 Tf -29.259 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.734 0 Td [(h)-123(b)]TJ ET q -1 0 0 1 404.275 298.012 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 145.117 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 407.413 297.812 Td [(base)]TJ +/F8 9.9626 Tf 149.328 667.814 Td [(w)-123(r)-122(i)-123(t)-123(e)-228(\050)-139(a)-228(,)-910(i)-150(r)-149(e)-150(t)-460(,)-896(i)-135(u)-135(n)-135(i)-135(t)-431(,)-877(f)-116(i)-116(l)-116(e)-116(n)-116(a)-116(m)-117(e)-393(,)-821(k)-60(e)-60(y)-281(,)-853(r)-92(h)-91(s)-345(,)-902(m)-141(t)-142(i)-141(t)-141(l)-141(e)-247(\051)]TJ +0 g 0 G +0 g 0 G +0 g 0 G +/F27 9.9626 Tf -49.433 -17.933 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)-333(to)-333(b)-28(e)-333(written.)]TJ 14.356 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.899 0 Td [(.)]TJ -67.082 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 428.962 298.012 cm +1 0 0 1 312.036 586.32 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 432.101 297.812 Td [(vect)]TJ +/F30 9.9626 Tf 315.174 586.121 Td [(Tspmat)]TJ ET q -1 0 0 1 453.65 298.012 cm +1 0 0 1 347.183 586.32 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 456.788 297.812 Td [(type)]TJ/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F30 9.9626 Tf 350.322 586.121 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -271.348 -19.926 Td [(b)]TJ +0 g 0 G +/F8 9.9626 Tf 11.347 0 Td [(Rigth)-333(hand)-333(s)-1(i)1(de.)]TJ 13.56 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-282(ar)1(ra)27(y)-281(of)-282(t)28(yp)-28(e)-281(real)-282(or)-281(complex,)-292(rank)-282(1)-281(and)-282(ha)28(ving)-281(the)-282(ALLOCA)83(T)84(ABLE)]TJ 0 -11.955 Td [(attribute;)-409(will)-384(b)-28(e)-384(allo)-28(cated)-384(an)1(d)-384(\014lled)-384(in)-384(if)-384(the)-384(input)-384(\014le)-384(con)28(tains)-384(a)-384(righ)28(t)]TJ 0 -11.955 Td [(hand)-333(side.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.926 Td [(\014lename)]TJ +0 g 0 G +/F8 9.9626 Tf 46.513 0 Td [(The)-333(name)-334(of)-333(the)-333(\014le)-334(to)-333(b)-28(e)-333(written)-333(to.)]TJ -21.606 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-435(as:)-648(a)-435(c)27(h)1(arac)-1(ter)-435(v)56(ariable)-435(con)28(taining)-436(a)-435(v)56(alid)-435(\014le)-435(name,)-461(or)]TJ/F30 9.9626 Tf 297.915 0 Td [(-)]TJ/F8 9.9626 Tf 5.231 0 Td [(,)-461(in)]TJ -303.146 -11.955 Td [(whic)28(h)-281(case)-280(the)-280(default)-281(output)-280(unit)-280(6)-281(\050i.e.)-426(s)-1(t)1(andard)-281(output)-280(in)-280(Unix)-281(jargon\051)]TJ 0 -11.955 Td [(is)-333(used.)-445(Default:)]TJ/F30 9.9626 Tf 76.076 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -106.213 -19.926 Td [(iunit)]TJ +0 g 0 G +/F8 9.9626 Tf 28.532 0 Td [(The)-333(F)83(ortran)-333(\014le)-334(un)1(it)-334(n)28(um)28(b)-28(er.)]TJ -3.625 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(alue.)-444(Only)-333(me)-1(ani)1(ngful)-334(if)-333(\014lename)-333(is)-334(not)]TJ/F30 9.9626 Tf 286.288 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -316.425 -19.925 Td [(k)32(ey)]TJ +0 g 0 G +/F8 9.9626 Tf 22.008 0 Td [(Matrix)-333(k)28(ey)83(.)]TJ 2.899 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.611 -11.956 Td [(A)-385(c)28(harac)28(h)28(ter)-385(v)56(ariable)-385(of)-385(length)-384(8)-385(holding)-385(the)-384(m)-1(atri)1(x)-385(k)28(ey)-385(as)-385(sp)-28(eci\014ed)-384(b)27(y)]TJ 0 -11.955 Td [(the)-333(Harw)27(ell-Bo)-27(eing)-334(format)-333(and)-333(to)-334(b)-27(e)-334(written)-333(to)-333(\014le.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.925 Td [(m)32(title)]TJ +0 g 0 G +/F8 9.9626 Tf 34.738 0 Td [(Matrix)-333(title.)]TJ -9.831 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(Optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(A)-318(c)28(harac)28(h)28(ter)-318(v)56(ariable)-318(of)-317(length)-318(72)-317(holding)-318(the)-317(m)-1(atr)1(ix)-318(title)-318(as)-317(sp)-28(eci\014ed)-318(b)28(y)]TJ 0 -11.956 Td [(the)-333(Harw)27(ell-Bo)-27(eing)-334(format)-333(and)-333(to)-334(b)-27(e)-334(written)-333(to)-333(\014le.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -21.917 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.926 Td [(iret)]TJ +0 g 0 G +/F8 9.9626 Tf 22.589 0 Td [(Error)-333(co)-28(de.)]TJ 2.318 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detecte)-1(d)1(.)]TJ +0 g 0 G + 139.477 -139.02 Td [(135)]TJ 0 g 0 G -/F27 9.9626 Tf -327.004 -22.878 Td [(imold)]TJ +ET + +endstream +endobj +1824 0 obj +<< +/Length 3666 +>> +stream 0 g 0 G -/F8 9.9626 Tf 32.987 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(in)27(teger)-333(v)28(ector)-334(storage.)]TJ -8.081 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-222(as:)-389(an)-222(ob)-56(ject)-222(of)-222(a)-222(class)-223(deriv)28(ed)-222(from)-222(\050in)28(teger\051)]TJ/F30 9.9626 Tf 233.542 0 Td [(psb)]TJ +0 g 0 G +BT +/F16 11.9552 Tf 150.705 706.129 Td [(9.3)-1125(mm)]TJ ET q -1 0 0 1 425.471 227.312 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 204.563 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F30 9.9626 Tf 428.61 227.113 Td [(T)]TJ +/F16 11.9552 Tf 208.598 706.129 Td [(mat)]TJ ET q -1 0 0 1 434.468 227.312 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 232.381 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT -/F30 9.9626 Tf 437.606 227.113 Td [(base)]TJ +/F16 11.9552 Tf 236.416 706.129 Td [(read)-409(|)-409(Read)-409(a)-409(sparse)-409(matrix)-409(from)-409(a)-410(\014le)-409(in)]TJ -55.076 -13.948 Td [(the)-375(MatrixMark)31(et)-375(format)]TJ/F27 9.9626 Tf -29.258 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.009 0 Td [(m)-50(m)]TJ ET q -1 0 0 1 459.155 227.312 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 199.288 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 462.293 227.113 Td [(vect)]TJ +/F8 9.9626 Tf 202.775 667.814 Td [(m)-50(a)-50(t)]TJ ET q -1 0 0 1 483.842 227.312 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 222.024 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 486.98 227.113 Td [(type)]TJ/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +/F8 9.9626 Tf 225.51 667.814 Td [(r)-50(e)-50(a)-50(d)-155(\050)-139(a)-228(,)-911(i)-149(r)-150(e)-149(t)-461(,)-896(i)-134(u)-135(n)-135(i)-135(t)-431(,)-890(f)-129(i)-129(l)-129(e)-129(n)-129(a)-129(m)-129(e)-235(\051)]TJ 0 g 0 G -/F27 9.9626 Tf -357.196 -24.133 Td [(On)-383(Return)]TJ 0 g 0 G 0 g 0 G - 0 -22.879 Td [(prec)]TJ +/F27 9.9626 Tf -74.805 -17.933 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 26.408 0 Td [(the)-333(preconditioner.)]TJ -1.502 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(precondtioner)-333(data)-333(structure)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Async)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.925 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(\014lename)]TJ +0 g 0 G +/F8 9.9626 Tf 46.513 0 Td [(The)-333(name)-334(of)-333(the)-333(\014le)-334(to)-333(b)-28(e)-333(read.)]TJ -21.607 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.184 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-435(as:)-648(a)-435(c)28(haracte)-1(r)-435(v)56(ariable)-435(con)28(taining)-435(a)-436(v)56(alid)-435(\014le)-435(name,)-461(or)]TJ/F30 9.9626 Tf 297.915 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(,)-461(in)]TJ -303.145 -11.956 Td [(whic)28(h)-302(case)-303(the)-302(default)-302(input)-302(unit)-302(5)-303(\050i.e.)-434(standard)-302(input)-302(in)-302(Unix)-302(jargon\051)-302(is)]TJ 0 -11.955 Td [(used.)-444(Default:)]TJ/F30 9.9626 Tf 66.057 0 Td [(-)]TJ/F8 9.9626 Tf 5.231 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -96.195 -19.925 Td [(iunit)]TJ +0 g 0 G +/F8 9.9626 Tf 28.532 0 Td [(The)-333(F)83(ortran)-333(\014le)-334(u)1(nit)-334(n)28(um)28(b)-28(er.)]TJ -3.625 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(in)28(teger)-333(v)55(alue.)-444(Only)-333(me)-1(an)1(ingful)-334(if)-333(\014lename)-333(is)-334(not)]TJ/F30 9.9626 Tf 286.288 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -316.425 -21.918 Td [(On)-383(Return)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(sparse)-334(matrix)-333(read)-333(from)-334(\014le.)]TJ 14.356 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(required)]TJ/F8 9.9626 Tf 41.898 0 Td [(.)]TJ -67.081 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 194.77 0 Td [(psb)]TJ +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ ET q -1 0 0 1 386.7 132.48 cm +1 0 0 1 362.845 452.82 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 389.838 132.281 Td [(prec)]TJ +/F30 9.9626 Tf 365.983 452.621 Td [(Tspmat)]TJ ET q -1 0 0 1 411.387 132.48 cm +1 0 0 1 397.993 452.82 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 414.525 132.281 Td [(type)]TJ -0 g 0 G -0 g 0 G -/F8 9.9626 Tf -99.437 -41.843 Td [(136)]TJ -0 g 0 G -ET - -endstream -endobj -1780 0 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-19.925 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.925 Td [(\014lename)]TJ +0 g 0 G +/F8 9.9626 Tf 46.513 0 Td [(The)-333(name)-334(of)-333(the)-333(\014le)-334(to)-333(b)-28(e)-333(read.)]TJ -21.606 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 25.183 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -65.76 -11.955 Td [(Sp)-28(eci\014ed)-435(as:)-648(a)-435(c)27(h)1(arac)-1(ter)-435(v)56(ariable)-435(con)28(taining)-436(a)-435(v)56(alid)-435(\014le)-435(name,)-461(or)]TJ/F30 9.9626 Tf 297.915 0 Td [(-)]TJ/F8 9.9626 Tf 5.231 0 Td [(,)-461(in)]TJ -303.146 -11.956 Td [(whic)28(h)-302(cas)-1(e)-302(the)-302(default)-302(input)-302(unit)-302(5)-303(\050i.e.)-434(standard)-302(input)-302(in)-302(Unix)-302(jargon\051)-302(is)]TJ 0 -11.955 Td [(used.)-444(Default:)]TJ/F30 9.9626 Tf 66.058 0 Td [(-)]TJ/F8 9.9626 Tf 5.23 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -96.195 -19.925 Td [(iunit)]TJ +0 g 0 G +/F8 9.9626 Tf 28.532 0 Td 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[(ABLE)-334(attribute;)-334(will)-333(b)-28(e)-334(allo)-28(cated)-333(and)-334(\014lled)-334(in)-333(if)-334(the)-334(input)-333(\014le)-334(con)28(tains)-334(a)]TJ 0 -11.955 Td [(righ)28(t)-333(hand)-334(side,)-333(otherwise)-333(will)-334(b)-27(e)-334(left)-333(in)-333(the)-334(UNALLOCA)84(TED)-334(state.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.925 Td [(iret)]TJ +0 g 0 G +/F8 9.9626 Tf 22.589 0 Td [(Error)-333(co)-28(de.)]TJ 2.318 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(An)-333(in)28(tege)-1(r)-333(v)56(alue;)-334(0)-333(means)-333(no)-334(error)-333(has)-333(b)-28(een)-333(detected.)]TJ +0 g 0 G + 139.477 -294.437 Td [(137)]TJ +0 g 0 G +ET + +endstream +endobj +1837 0 obj +<< +/Length 4197 +>> +stream +0 g 0 G +0 g 0 G +BT +/F16 11.9552 Tf 150.705 706.129 Td [(9.5)-1125(mm)]TJ ET q -1 0 0 1 449.109 522.559 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 204.563 706.328 cm +[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S Q BT 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[(write)-481(|)-481(W)94(rite)-481(a)-481(sparse)-480(matrix)-481(to)-481(a)-481(\014le)-481(in)]TJ -55.076 -13.948 Td [(the)-375(MatrixMark)31(et)-375(format)]TJ/F27 9.9626 Tf -29.258 -24.367 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.175 0 Td [(m)-67(m)]TJ ET q -1 0 0 1 393.01 466.768 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 199.787 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 396.148 466.569 Td [(desc)]TJ +/F8 9.9626 Tf 203.439 667.814 Td [(m)-67(a)-66(t)]TJ ET q -1 0 0 1 417.697 466.768 cm -[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +1 0 0 1 223.186 668.014 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F30 9.9626 Tf 420.835 466.569 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F8 9.9626 Tf 226.839 667.814 Td [(w)-67(r)-66(i)-67(t)-66(e)-173(\050)-139(a)-227(,)-885(m)-124(t)-123(i)-124(t)-124(l)-123(e)-409(,)-910(i)-150(r)-149(e)-150(t)-460(,)-896(i)-135(u)-135(n)-135(i)-135(t)-431(,)-890(f)-129(i)-129(l)-129(e)-129(n)-129(a)-129(m)-129(e)-234(\051)]TJ 0 g 0 G -/F27 9.9626 Tf -291.052 -19.925 Td [(trans)]TJ 0 g 0 G -/F8 9.9626 Tf 30.609 0 Td [(Scop)-28(e:)]TJ -5.702 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(c)28(haracter.)]TJ 0 g 0 G -/F27 9.9626 Tf -24.907 -19.925 Td [(w)32(ork)]TJ +/F27 9.9626 Tf -76.134 -17.933 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 29.431 0 Td [(an)-333(optional)-334(w)28(ork)-333(space)-333(Scop)-28(e:)]TJ/F27 9.9626 Tf 135.963 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -140.487 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 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[(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(c)28(haracter)-333(s)-1(t)1(ring,)-334(see)-333(usage)-334(notes.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.907 -19.926 Td [(On)-383(Exit)]TJ 0 g 0 G 0 g 0 G 0 -19.925 Td [(prec)]TJ 0 g 0 G -/F8 9.9626 Tf 26.408 0 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -33.88 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(preconditioner)-333(data)-333(structure)]TJ +/F8 9.9626 Tf 26.408 0 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -33.88 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(preconditioner)-333(data)-333(structure)]TJ 0 0 1 rg 0 0 1 RG /F30 9.9626 Tf 197.537 0 Td [(psb)]TJ ET q -1 0 0 1 338.658 502.634 cm +1 0 0 1 338.658 446.843 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 341.796 502.434 Td [(prec)]TJ +/F30 9.9626 Tf 341.796 446.644 Td [(prec)]TJ ET q -1 0 0 1 363.345 502.634 cm +1 0 0 1 363.345 446.843 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 366.483 502.434 Td [(type)]TJ +/F30 9.9626 Tf 366.483 446.644 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -287.51 -19.925 Td [(info)]TJ +/F27 9.9626 Tf -287.51 -19.926 Td [(info)]TJ 0 g 0 G -/F8 9.9626 Tf 23.758 0 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -31.23 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Error)-333(co)-28(de:)-444(if)-334(no)-333(error,)-333(0)-334(is)-333(returned.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ/F8 9.9626 Tf 37.234 0 Td [(Releases)-334(all)-333(in)28(ternal)-333(storage.)]TJ +/F8 9.9626 Tf 23.758 0 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -31.23 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(out)]TJ/F8 9.9626 Tf 16.549 0 Td [(.)]TJ -50.035 -11.955 Td [(Error)-333(co)-28(de:)-444(if)-334(no)-333(error,)-333(0)-334(is)-333(returned.)]TJ/F16 11.9552 Tf -24.907 -21.918 Td [(Notes)]TJ/F8 9.9626 Tf 37.059 0 Td [(Legal)-316(inputs)-315(to)-316(this)-316(subroutine)-315(are)-316(in)28(terpreted)-316(dep)-28(ending)-315(on)-316(the)]TJ/F11 9.9626 Tf 283.149 0 Td [(pty)-36(pe)]TJ/F8 9.9626 Tf -320.208 -11.955 Td [(string)-333(as)-334(follo)28(ws)]TJ +0 0 1 rg 0 0 1 RG +/F7 6.9738 Tf 69.933 3.615 Td [(4)]TJ 0 g 0 G - 127.15 -334.288 Td [(141)]TJ +/F8 9.9626 Tf 4.469 -3.615 Td [(:)]TJ 0 g 0 G -ET - -endstream -endobj -1808 0 obj -<< -/Length 608 ->> -stream +/F27 9.9626 Tf -74.402 -19.925 Td [(NONE)]TJ +0 g 0 G +/F8 9.9626 Tf 39.048 0 Td [(No)-333(preconditioning,)-333(i.e.)-445(the)-333(preconditioner)-333(is)-334(just)-333(a)-333(cop)27(y)-333(op)-28(erator.)]TJ +0 g 0 G +/F27 9.9626 Tf -39.048 -19.926 Td [(DIA)32(G)]TJ 0 g 0 G +/F8 9.9626 Tf 35.464 0 Td [(Diagonal)-441(scaling;)-496(eac)28(h)-442(en)28(try)-441(of)-442(th)1(e)-442(input)-441(v)28(ec)-1(tor)-441(is)-441(m)27(ultip)1(lied)-442(b)28(y)-441(the)]TJ -10.557 -11.955 Td [(recipro)-28(cal)-346(of)-346(the)-346(sum)-346(of)-345(the)-346(absolute)-346(v)55(alues)-346(of)-346(the)-346(co)-27(e\016cien)27(ts)-346(in)-346(th)1(e)-346(c)-1(or)1(-)]TJ 0 -11.955 Td [(resp)-28(onding)-333(ro)28(w)-334(of)-333(matrix)]TJ/F11 9.9626 Tf 113.602 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(;)]TJ +0 g 0 G +/F27 9.9626 Tf -145.981 -19.925 Td [(BJA)32(C)]TJ +0 g 0 G +/F8 9.9626 Tf 35.672 0 Td [(Precondition)-249(b)28(y)-249(a)-249(factorization)-248(of)-249(the)-249(blo)-28(c)28(k-diagonal)-249(of)-249(matrix)]TJ/F11 9.9626 Tf 269.665 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(,)-266(where)]TJ -287.902 -11.956 Td [(blo)-28(c)28(k)-457(b)-28(oundaries)-457(are)-457(determined)-457(b)28(y)-457(the)-457(data)-457(allo)-28(cation)-457(b)-28(oundaries)-457(for)]TJ 0 -11.955 Td [(eac)28(h)-347(pro)-28(cess;)-353(requires)-346(no)-347(comm)28(unication.)-484(Only)-347(the)-346(incomplete)-347(factoriza-)]TJ 0 -11.955 Td [(tion)]TJ/F11 9.9626 Tf 20.479 0 Td [(I)-78(LU)]TJ/F8 9.9626 Tf 19.83 0 Td [(\0500\051)-333(is)-334(curren)28(tly)-333(implemen)28(ted.)]TJ 0 g 0 G +ET +q +1 0 0 1 99.895 129.78 cm +[]0 d 0 J 0.398 w 0 0 m 137.482 0 l S +Q BT -/F16 14.3462 Tf 150.705 706.129 Td [(11)-1125(Iterativ)31(e)-375(Metho)-31(ds)]TJ/F8 9.9626 Tf 0 -21.821 Td [(In)-519(thi)1(s)-519(c)28(hapter)-519(w)28(e)-519(pro)28(vide)-519(routi)1(nes)-519(for)-519(preconditioners)-518(and)-519(iterativ)28(e)-519(meth-)]TJ 0 -11.955 Td [(o)-28(ds.)-647(The)-401(in)28(terfaces)-401(for)-401(Kr)1(ylo)27(v)-401(sub)1(s)-1(p)1(ac)-1(e)-400(metho)-28(ds)-401(are)-401(a)28(v)55(ailable)-400(in)-401(the)-401(mo)-28(dule)]TJ/F30 9.9626 Tf 0 -11.955 Td [(psb_krylov_mod)]TJ/F8 9.9626 Tf 73.225 0 Td [(.)]TJ +/F32 5.9776 Tf 110.987 123.138 Td [(4)]TJ/F31 7.9701 Tf 4.151 -2.812 Td [(The)-354(string)-354(is)-355(case-insensitiv)30(e)]TJ 0 g 0 G - 91.158 -569.96 Td [(142)]TJ +0 g 0 G +/F8 9.9626 Tf 149.141 -29.888 Td [(141)]TJ 0 g 0 G ET endstream endobj -1815 0 obj +1865 0 obj << -/Length 8313 +/Length 7738 >> stream 0 g 0 G 0 g 0 G BT -/F16 11.9552 Tf 99.895 706.129 Td [(psb)]TJ -ET -q -1 0 0 1 120.951 706.328 cm -[]0 d 0 J 0.398 w 0 0 m 4.035 0 l S -Q -BT -/F16 11.9552 Tf 124.986 706.129 Td [(krylo)31(v)-375(|)-375(Krylo)31(v)-375(Metho)-31(ds)-375(Driv)31(er)-375(Routine)]TJ/F8 9.9626 Tf -25.091 -18.389 Td [(This)-343(subroutine)-342(is)-343(a)-343(driv)28(er)-343(that)-342(pro)27(vid)1(e)-1(s)-342(a)-343(general)-343(in)28(terface)-343(for)-342(all)-343(the)-343(Krylo)28(v-)]TJ 0 -11.956 Td [(Subspace)-333(family)-334(metho)-27(ds)-334(implemen)28(ted)-333(in)-334(PSBLAS)-333(v)28(ersion)-333(2.)]TJ 14.944 -11.955 Td [(The)-333(stopping)-334(criterion)-333(can)-333(tak)28(e)-334(the)-333(follo)28(wing)-334(v)56(alues:)]TJ +/F16 11.9552 Tf 150.705 706.129 Td [(10.2)-1125(build)-375(|)-375(Builds)-375(a)-375(preconditioner)]TJ 0 g 0 G -/F27 9.9626 Tf -14.944 -19.102 Td [(1)]TJ 0 g 0 G -/F8 9.9626 Tf 10.71 0 Td [(norm)28(wise)-334(bac)28(kw)28(ard)-333(error)-334(in)-333(the)-333(in\014nit)28(y)-334(norm;)-333(the)-333(iteration)-334(i)1(s)-334(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 109.583 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 38.11 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ -ET -q -1 0 0 1 248.849 621.14 cm -[]0 d 0 J 0.398 w 0 0 m 70.572 0 l S -Q -BT -/F8 9.9626 Tf 248.849 611.815 Td [(\050)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(A)]TJ/F14 9.9626 Tf 7.472 0 Td [(kk)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(k)]TJ/F8 9.9626 Tf 7.195 0 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F8 9.9626 Tf 4.981 0 Td [(\051)]TJ/F11 9.9626 Tf 7.837 6.834 Td [(<)-278(eps)]TJ +/F30 9.9626 Tf 0 -19.764 Td [(call)-525(prec%build\050a,)-525(desc_a,)-525(info[,amold,vmold,imold]\051)]TJ 0 g 0 G -/F27 9.9626 Tf -223.488 -29.952 Td [(2)]TJ +/F27 9.9626 Tf 0 -24.132 Td [(T)32(yp)-32(e:)]TJ 0 g 0 G -/F8 9.9626 Tf 10.71 0 Td [(Relativ)28(e)-334(residual)-333(in)-333(the)-333(2-)-1(n)1(orm)-1(;)-333(the)-333(iteration)-333(is)-334(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 135.515 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 12.178 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ -ET -q -1 0 0 1 274.781 565.11 cm -[]0 d 0 J 0.398 w 0 0 m 18.708 0 l S -Q -BT -/F14 9.9626 Tf 274.781 555.785 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ/F11 9.9626 Tf 8.432 8.328 Td [(<)-278(eps)]TJ +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ 0 g 0 G -/F27 9.9626 Tf -197.556 -29.952 Td [(3)]TJ +/F27 9.9626 Tf -33.797 -22.879 Td [(On)-383(En)32(try)]TJ 0 g 0 G -/F8 9.9626 Tf 10.71 0 Td [(Relativ)28(e)-334(residual)-333(reduction)-333(in)-333(the)-334(2-norm;)-333(the)-333(iteration)-334(is)-333(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 133.171 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 14.522 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ -ET -q -1 0 0 1 272.436 509.08 cm -[]0 d 0 J 0.398 w 0 0 m 23.396 0 l S -Q -BT -/F14 9.9626 Tf 272.436 499.755 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F7 6.9738 Tf 4.494 -1.494 Td [(0)]TJ/F14 9.9626 Tf 4.47 1.494 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ/F11 9.9626 Tf 8.432 8.328 Td [(<)-278(eps)]TJ/F8 9.9626 Tf -199.9 -30.505 Td [(The)-443(b)-27(eha)28(viour)-443(is)-442(con)27(troll)1(e)-1(d)-442(b)28(y)-443(the)-442(istop)-442(argumen)27(t)-442(\050see)-443(later\051.)-771(In)-443(the)-442(ab)-28(o)28(v)27(e)]TJ 0 -11.955 Td [(form)28(ulae,)]TJ/F11 9.9626 Tf 43.127 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.495 Td [(i)]TJ/F8 9.9626 Tf 5.856 1.495 Td [(is)-255(the)-255(ten)28(tativ)28(e)-255(solution)-255(and)]TJ/F11 9.9626 Tf 122.117 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.495 Td [(i)]TJ/F8 9.9626 Tf 6.084 1.495 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(b)]TJ/F14 9.9626 Tf 4.925 0 Td [(\000)]TJ/F11 9.9626 Tf 8.399 0 Td [(Ax)]TJ/F10 6.9738 Tf 13.166 -1.495 Td [(i)]TJ/F8 9.9626 Tf 5.856 1.495 Td [(the)-255(corresp)-28(ondin)1(g)-255(residual)]TJ -230.235 -11.956 Td [(at)-333(the)]TJ/F11 9.9626 Tf 29.335 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(-th)-333(iteration.)]TJ/F27 9.9626 Tf -31.39 -17.52 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.763 0 Td [(p)-126(s)-125(b)]TJ +0 g 0 G + 0 -22.879 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(system)-334(sparse)-333(matrix.)-445(Scop)-27(e:)]TJ/F27 9.9626 Tf 148.886 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -134.53 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(,)-333(target.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(a)-334(sparse)-333(matrix)-334(d)1(ata)-334(structure)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 194.05 0 Td [(psb)]TJ ET q -1 0 0 1 150.386 434.852 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 385.981 580.809 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 154.627 434.653 Td [(k)-126(r)-125(y)-126(l)-125(o)-126(v)-231(\050)-146(m)-40(e)-41(t)-40(h)-40(o)-40(d)-242(,)-194(a)-228(,)-255(p)-94(r)-94(e)-94(c)-349(,)-176(b)-191(,)-185(x)-209(,)-243(e)-81(p)-81(s)-323(,)-274(d)-113(e)-112(s)-113(c)]TJ +/F30 9.9626 Tf 389.119 580.61 Td [(Tspmat)]TJ ET q -1 0 0 1 351.575 434.852 cm -[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +1 0 0 1 421.128 580.809 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F8 9.9626 Tf 355.686 434.653 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-302(,)-48(&)]TJ -226.788 -11.956 Td [(&)-579(i)-67(t)-67(m)-68(a)-67(x)-296(,)-311(i)-150(t)-149(e)-150(r)-460(,)]TJ/F27 9.9626 Tf 79.244 0 Td [(e)-65(r)-65(r)]TJ/F8 9.9626 Tf 18.889 0 Td [(,)-305(i)-144(t)-144(r)-144(a)-145(c)-144(e)-449(,)-319(i)-158(r)-158(s)-158(t)-477(,)-287(i)-126(s)-126(t)-126(o)-127(p)-413(,)-230(c)-69(o)-69(n)-69(d)-174(\051)]TJ -0 g 0 G -0 g 0 G -0 g 0 G -/F27 9.9626 Tf -127.136 -26.454 Td [(T)32(yp)-32(e:)]TJ -0 g 0 G -/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ -0 g 0 G -/F27 9.9626 Tf -33.797 -19.513 Td [(On)-383(En)32(try)]TJ -0 g 0 G -0 g 0 G - 0 -19.514 Td [(metho)-32(d)]TJ -0 g 0 G -/F8 9.9626 Tf 43.012 0 Td [(a)-235(string)-235(that)-235(de\014nes)-236(th)1(e)-236(iterativ)28(e)-235(metho)-28(d)-235(to)-235(b)-28(e)-235(used.)-412(Supp)-27(orted)-235(v)55(alues)]TJ -18.105 -11.955 Td [(are:)]TJ -0 g 0 G -/F27 9.9626 Tf 0 -19.513 Td [(CG:)]TJ -0 g 0 G -/F8 9.9626 Tf 25.446 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ -0 g 0 G -/F27 9.9626 Tf -25.446 -15.529 Td [(CGS:)]TJ -0 g 0 G -/F8 9.9626 Tf 31.811 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ -0 g 0 G -/F27 9.9626 Tf -31.811 -15.528 Td [(GCR:)]TJ -0 g 0 G -/F8 9.9626 Tf 34.039 0 Td [(the)-333(Generalized)-334(Conjugate)-333(Residual)-333(metho)-28(d;)]TJ -0 g 0 G -/F27 9.9626 Tf -34.039 -15.529 Td [(F)32(CG:)]TJ -0 g 0 G -/F8 9.9626 Tf 32.337 0 Td [(the)-333(Flexible)-334(Conjugate)-333(Gradien)28(t)-333(metho)-28(d)]TJ -0 0 1 rg 0 0 1 RG -/F7 6.9738 Tf 177.626 3.616 Td [(5)]TJ -0 g 0 G -/F8 9.9626 Tf 4.469 -3.616 Td [(;)]TJ -0 g 0 G -/F27 9.9626 Tf -214.432 -15.528 Td [(BICG:)]TJ -0 g 0 G -/F8 9.9626 Tf 37.941 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ -0 g 0 G -/F27 9.9626 Tf -37.941 -15.529 Td [(BICGST)96(AB:)]TJ -0 g 0 G -/F8 9.9626 Tf 68.133 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ -0 g 0 G -/F27 9.9626 Tf -68.133 -15.528 Td [(BICGST)96(ABL:)]TJ -0 g 0 G -/F8 9.9626 Tf 75.024 0 Td [(the)-222(Bi-Conjugate)-222(Gradien)27(t)-222(Stabilized)-222(metho)-28(d)-222(with)-222(restart-)]TJ -53.106 -11.955 Td [(ing;)]TJ -0 g 0 G -/F27 9.9626 Tf -21.918 -15.529 Td [(R)32(GMRES:)]TJ +/F30 9.9626 Tf 424.267 580.61 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 58.807 0 Td [(the)-333(Generalized)-334(Minimal)-333(Residual)-333(metho)-28(d)-333(with)-334(restarting.)]TJ +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -83.714 -19.513 Td [(a)]TJ +/F27 9.9626 Tf -294.483 -22.879 Td [(prec)]TJ 0 g 0 G -/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 178.968 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -172.084 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 26.408 0 Td [(the)-333(preconditioner.)]TJ -1.501 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.378 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(inout)]TJ/F8 9.9626 Tf 26.097 0 Td [(.)]TJ -59.582 -11.956 Td [(Sp)-28(eci\014ed)-222(as:)-389(an)-222(already)-222(initialized)-222(precondtioner)-222(data)-223(structure)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 273.115 0 Td [(psb)]TJ ET q -1 0 0 1 312.036 137.958 cm +1 0 0 1 465.045 510.11 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 315.174 137.759 Td [(Tspmat)]TJ +/F30 9.9626 Tf 468.184 509.91 Td [(prec)]TJ ET q -1 0 0 1 347.183 137.958 cm +1 0 0 1 489.733 510.11 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 350.322 137.759 Td [(type)]TJ +/F30 9.9626 Tf 492.871 509.91 Td [(type)]TJ 0 g 0 G -/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G +/F27 9.9626 Tf -342.166 -34.833 Td [(desc)]TJ ET q -1 0 0 1 99.895 129.78 cm -[]0 d 0 J 0.398 w 0 0 m 137.482 0 l S +1 0 0 1 172.619 475.276 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S Q BT -/F32 5.9776 Tf 110.987 123.138 Td [(5)]TJ/F31 7.9701 Tf 4.151 -2.812 Td [(Note:)-472(the)-355(implemen)30(tation)-354(is)-355(f)1(or)]TJ/F33 7.9701 Tf 120.25 0 Td [(F)-148(C)-70(G)]TJ/F31 7.9701 Tf 19.732 0 Td [(\0501\051.)]TJ -0 g 0 G -0 g 0 G -/F8 9.9626 Tf 9.159 -29.888 Td [(143)]TJ -0 g 0 G -ET - -endstream -endobj -1827 0 obj -<< -/Length 7123 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -BT -/F27 9.9626 Tf 150.705 706.129 Td [(prec)]TJ +/F27 9.9626 Tf 176.057 475.077 Td [(a)]TJ 0 g 0 G -/F8 9.9626 Tf 26.408 0 Td [(The)-333(data)-334(structure)-333(con)28(taining)-333(the)-334(preconditioner.)]TJ -1.502 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +/F8 9.9626 Tf 10.55 0 Td [(the)-333(problem)-334(comm)28(unication)-333(descriptor.)-445(Scop)-27(e:)]TJ/F27 9.9626 Tf 208.247 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -219.243 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(,)-333(target.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(comm)28(unication)-333(des)-1(crip)1(tor)-334(data)-333(structure)]TJ 0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 247.683 0 Td [(psb)]TJ ET q -1 0 0 1 362.845 658.507 cm +1 0 0 1 439.613 439.41 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 658.308 Td [(prec)]TJ +/F30 9.9626 Tf 442.751 439.211 Td [(desc)]TJ ET q -1 0 0 1 387.532 658.507 cm +1 0 0 1 464.3 439.41 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 390.67 658.308 Td [(type)]TJ +/F30 9.9626 Tf 467.438 439.211 Td [(type)]TJ 0 g 0 G /F8 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -260.887 -22.202 Td [(b)]TJ +/F27 9.9626 Tf -337.655 -22.879 Td [(amold)]TJ 0 g 0 G -/F8 9.9626 Tf 11.346 0 Td [(The)-333(RHS)-334(v)28(ector.)]TJ 13.56 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(ar)1(ra)27(y)-333(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 223.496 0 Td [(psb)]TJ +/F8 9.9626 Tf 35.374 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(matrix)-334(storage.)]TJ -10.467 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.378 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.451 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(optional)]TJ/F8 9.9626 Tf 40.577 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.485 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-444(an)-334(ob)-55(ject)-334(of)-333(a)-333(class)-334(deriv)28(ed)-333(from)]TJ/F30 9.9626 Tf 203.348 0 Td [(psb)]TJ ET q -1 0 0 1 415.426 588.484 cm +1 0 0 1 395.279 368.711 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 418.564 588.285 Td [(T)]TJ +/F30 9.9626 Tf 398.417 368.512 Td [(T)]TJ ET q -1 0 0 1 424.422 588.484 cm +1 0 0 1 404.275 368.711 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 427.56 588.285 Td [(vect)]TJ +/F30 9.9626 Tf 407.413 368.512 Td [(base)]TJ ET q -1 0 0 1 449.109 588.484 cm +1 0 0 1 428.962 368.711 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 452.247 588.285 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +/F30 9.9626 Tf 432.101 368.512 Td [(sparse)]TJ +ET +q +1 0 0 1 464.11 368.711 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 467.248 368.512 Td [(mat)]TJ/F8 9.9626 Tf 15.691 0 Td [(.)]TJ 0 g 0 G -/F27 9.9626 Tf -322.464 -22.202 Td [(x)]TJ +/F27 9.9626 Tf -332.234 -22.879 Td [(vmold)]TJ 0 g 0 G -/F8 9.9626 Tf 11.028 0 Td [(The)-333(initial)-334(guess.)]TJ 13.878 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(ar)1(ra)27(y)-333(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 223.496 0 Td [(psb)]TJ +/F8 9.9626 Tf 35.851 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(v)27(ector)-333(storage.)]TJ -10.945 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(ob)-55(ject)-334(of)-333(a)-333(class)-334(deriv)28(ed)-333(from)]TJ/F30 9.9626 Tf 203.349 0 Td [(psb)]TJ ET q -1 0 0 1 415.426 518.461 cm +1 0 0 1 395.279 298.012 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 418.564 518.262 Td [(T)]TJ +/F30 9.9626 Tf 398.417 297.812 Td [(T)]TJ ET q -1 0 0 1 424.422 518.461 cm +1 0 0 1 404.275 298.012 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 427.56 518.262 Td [(vect)]TJ +/F30 9.9626 Tf 407.413 297.812 Td [(base)]TJ ET q -1 0 0 1 449.109 518.461 cm +1 0 0 1 428.962 298.012 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 452.247 518.262 Td [(type)]TJ -0 g 0 G -/F8 9.9626 Tf 20.922 0 Td [(.)]TJ -0 g 0 G -/F27 9.9626 Tf -322.464 -22.203 Td [(eps)]TJ +/F30 9.9626 Tf 432.101 297.812 Td [(vect)]TJ +ET +q +1 0 0 1 453.65 298.012 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 456.788 297.812 Td [(type)]TJ/F8 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F8 9.9626 Tf 21.116 0 Td [(The)-333(stopping)-334(tolerance.)]TJ 3.79 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(real)-333(n)28(um)27(b)-27(er.)]TJ +/F27 9.9626 Tf -327.004 -22.878 Td [(imold)]TJ 0 g 0 G -/F27 9.9626 Tf -24.906 -22.203 Td [(desc)]TJ +/F8 9.9626 Tf 32.987 0 Td [(The)-333(desired)-334(dynamic)-333(t)28(yp)-28(e)-333(for)-334(the)-333(in)28(ternal)-333(in)27(teger)-333(v)28(ector)-334(storage.)]TJ -8.081 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf 23.073 0 Td [(.)]TJ -55.452 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf 40.576 0 Td [(.)]TJ -70.188 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-222(as:)-389(an)-222(ob)-56(ject)-222(of)-222(a)-222(class)-223(deriv)28(ed)-222(from)-222(\050in)28(teger\051)]TJ/F30 9.9626 Tf 233.542 0 Td [(psb)]TJ ET q -1 0 0 1 172.619 426.236 cm -[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +1 0 0 1 425.471 227.312 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F27 9.9626 Tf 176.057 426.036 Td [(a)]TJ -0 g 0 G -/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ -0 0 1 rg 0 0 1 RG -/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +/F30 9.9626 Tf 428.61 227.113 Td [(T)]TJ ET q -1 0 0 1 362.845 378.415 cm +1 0 0 1 434.468 227.312 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F30 9.9626 Tf 365.983 378.216 Td [(desc)]TJ +/F30 9.9626 Tf 437.606 227.113 Td [(base)]TJ ET q -1 0 0 1 387.532 378.415 cm +1 0 0 1 459.155 227.312 cm []0 d 0 J 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-62.451 -18.389 Td [(This)-343(subroutine)-342(is)-343(a)-343(driv)28(er)-343(that)-342(pro)27(vid)1(e)-1(s)-342(a)-343(general)-343(in)28(terface)-343(for)-342(all)-343(the)-343(Krylo)28(v-)]TJ 0 -11.956 Td [(Subspace)-333(family)-334(metho)-27(ds)-334(implemen)28(ted)-333(in)-334(PSBLAS)-333(v)28(ersion)-333(2.)]TJ 14.944 -11.955 Td [(The)-333(stopping)-334(criterion)-333(can)-333(tak)28(e)-334(the)-333(follo)28(wing)-334(v)56(alues:)]TJ +0 g 0 G +/F27 9.9626 Tf -14.944 -19.102 Td [(1)]TJ +0 g 0 G +/F8 9.9626 Tf 10.71 0 Td [(norm)28(wise)-334(bac)28(kw)28(ard)-333(error)-334(in)-333(the)-333(in\014nit)28(y)-334(norm;)-333(the)-333(iteration)-334(i)1(s)-334(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 109.583 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 38.11 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ +ET +q +1 0 0 1 248.849 621.14 cm +[]0 d 0 J 0.398 w 0 0 m 70.572 0 l S +Q +BT +/F8 9.9626 Tf 248.849 611.815 Td [(\050)]TJ/F14 9.9626 Tf 3.874 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(A)]TJ/F14 9.9626 Tf 7.472 0 Td [(kk)]TJ/F11 9.9626 Tf 9.963 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.494 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.494 Td [(k)]TJ/F8 9.9626 Tf 7.195 0 Td [(+)]TJ/F14 9.9626 Tf 9.963 0 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F8 9.9626 Tf 4.981 0 Td [(\051)]TJ/F11 9.9626 Tf 7.837 6.834 Td [(<)-278(eps)]TJ +0 g 0 G +/F27 9.9626 Tf -223.488 -29.952 Td [(2)]TJ +0 g 0 G +/F8 9.9626 Tf 10.71 0 Td [(Relativ)28(e)-334(residual)-333(in)-333(the)-333(2-)-1(n)1(orm)-1(;)-333(the)-333(iteration)-333(is)-334(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 135.515 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 12.178 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ +ET +q +1 0 0 1 274.781 565.11 cm +[]0 d 0 J 0.398 w 0 0 m 18.708 0 l S +Q +BT +/F14 9.9626 Tf 274.781 555.785 Td [(k)]TJ/F11 9.9626 Tf 4.981 0 Td [(b)]TJ/F14 9.9626 Tf 4.276 0 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ/F11 9.9626 Tf 8.432 8.328 Td [(<)-278(eps)]TJ +0 g 0 G +/F27 9.9626 Tf -197.556 -29.952 Td [(3)]TJ +0 g 0 G +/F8 9.9626 Tf 10.71 0 Td [(Relativ)28(e)-334(residual)-333(reduction)-333(in)-333(the)-334(2-norm;)-333(the)-333(iteration)-334(is)-333(stopp)-28(ed)-333(when)]TJ/F11 9.9626 Tf 133.171 -26.078 Td [(er)-28(r)]TJ/F8 9.9626 Tf 16.949 0 Td [(=)]TJ/F14 9.9626 Tf 14.522 6.74 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F10 6.9738 Tf 4.494 -1.495 Td [(i)]TJ/F14 9.9626 Tf 3.317 1.495 Td [(k)]TJ +ET +q +1 0 0 1 272.436 509.08 cm +[]0 d 0 J 0.398 w 0 0 m 23.396 0 l S +Q +BT +/F14 9.9626 Tf 272.436 499.755 Td [(k)]TJ/F11 9.9626 Tf 4.982 0 Td [(r)]TJ/F7 6.9738 Tf 4.494 -1.494 Td [(0)]TJ/F14 9.9626 Tf 4.47 1.494 Td [(k)]TJ/F7 6.9738 Tf 4.981 -1.494 Td [(2)]TJ/F11 9.9626 Tf 8.432 8.328 Td [(<)-278(eps)]TJ/F8 9.9626 Tf -199.9 -30.505 Td [(The)-443(b)-27(eha)28(viour)-443(is)-442(con)27(troll)1(e)-1(d)-442(b)28(y)-443(the)-442(istop)-442(argumen)27(t)-442(\050see)-443(later\051.)-771(In)-443(the)-442(ab)-28(o)28(v)27(e)]TJ 0 -11.955 Td [(form)28(ulae,)]TJ/F11 9.9626 Tf 43.127 0 Td [(x)]TJ/F10 6.9738 Tf 5.694 -1.495 Td [(i)]TJ/F8 9.9626 Tf 5.856 1.495 Td [(is)-255(the)-255(ten)28(tativ)28(e)-255(solution)-255(and)]TJ/F11 9.9626 Tf 122.117 0 Td [(r)]TJ/F10 6.9738 Tf 4.495 -1.495 Td [(i)]TJ/F8 9.9626 Tf 6.084 1.495 Td [(=)]TJ/F11 9.9626 Tf 10.516 0 Td [(b)]TJ/F14 9.9626 Tf 4.925 0 Td [(\000)]TJ/F11 9.9626 Tf 8.399 0 Td [(Ax)]TJ/F10 6.9738 Tf 13.166 -1.495 Td [(i)]TJ/F8 9.9626 Tf 5.856 1.495 Td [(the)-255(corresp)-28(ondin)1(g)-255(residual)]TJ -230.235 -11.956 Td [(at)-333(the)]TJ/F11 9.9626 Tf 29.335 0 Td [(i)]TJ/F8 9.9626 Tf 3.432 0 Td [(-th)-333(iteration.)]TJ/F27 9.9626 Tf -31.39 -17.52 Td [(c)-138(a)-138(l)-139(l)]TJ/F8 9.9626 Tf 29.763 0 Td [(p)-126(s)-125(b)]TJ +ET +q +1 0 0 1 150.386 434.852 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 154.627 434.653 Td [(k)-126(r)-125(y)-126(l)-125(o)-126(v)-231(\050)-146(m)-40(e)-41(t)-40(h)-40(o)-40(d)-242(,)-194(a)-228(,)-255(p)-94(r)-94(e)-94(c)-349(,)-176(b)-191(,)-185(x)-209(,)-243(e)-81(p)-81(s)-323(,)-274(d)-113(e)-112(s)-113(c)]TJ +ET +q +1 0 0 1 351.575 434.852 cm +[]0 d 0 J 0.398 w 0 0 m 2.989 0 l S +Q +BT +/F8 9.9626 Tf 355.686 434.653 Td [(a)-386(,)-288(i)-127(n)-127(f)-127(o)-302(,)-48(&)]TJ -226.788 -11.956 Td [(&)-579(i)-67(t)-67(m)-68(a)-67(x)-296(,)-311(i)-150(t)-149(e)-150(r)-460(,)]TJ/F27 9.9626 Tf 79.244 0 Td [(e)-65(r)-65(r)]TJ/F8 9.9626 Tf 18.889 0 Td [(,)-305(i)-144(t)-144(r)-144(a)-145(c)-144(e)-449(,)-319(i)-158(r)-158(s)-158(t)-477(,)-287(i)-126(s)-126(t)-126(o)-127(p)-413(,)-230(c)-69(o)-69(n)-69(d)-174(\051)]TJ +0 g 0 G +0 g 0 G +0 g 0 G +/F27 9.9626 Tf -127.136 -26.454 Td [(T)32(yp)-32(e:)]TJ +0 g 0 G +/F8 9.9626 Tf 33.797 0 Td [(Sync)28(hronous.)]TJ +0 g 0 G +/F27 9.9626 Tf -33.797 -19.513 Td [(On)-383(En)32(try)]TJ +0 g 0 G +0 g 0 G + 0 -19.514 Td [(metho)-32(d)]TJ +0 g 0 G +/F8 9.9626 Tf 43.012 0 Td [(a)-235(string)-235(that)-235(de\014nes)-236(th)1(e)-236(iterativ)28(e)-235(metho)-28(d)-235(to)-235(b)-28(e)-235(used.)-412(Supp)-27(orted)-235(v)55(alues)]TJ -18.105 -11.955 Td [(are:)]TJ +0 g 0 G +/F27 9.9626 Tf 0 -19.513 Td [(CG:)]TJ +0 g 0 G +/F8 9.9626 Tf 25.446 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ +0 g 0 G +/F27 9.9626 Tf -25.446 -15.529 Td [(CGS:)]TJ +0 g 0 G +/F8 9.9626 Tf 31.811 0 Td [(the)-333(Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ +0 g 0 G +/F27 9.9626 Tf -31.811 -15.528 Td [(GCR:)]TJ +0 g 0 G +/F8 9.9626 Tf 34.039 0 Td [(the)-333(Generalized)-334(Conjugate)-333(Residual)-333(metho)-28(d;)]TJ +0 g 0 G +/F27 9.9626 Tf -34.039 -15.529 Td [(F)32(CG:)]TJ +0 g 0 G +/F8 9.9626 Tf 32.337 0 Td [(the)-333(Flexible)-334(Conjugate)-333(Gradien)28(t)-333(metho)-28(d)]TJ +0 0 1 rg 0 0 1 RG +/F7 6.9738 Tf 177.626 3.616 Td [(5)]TJ +0 g 0 G +/F8 9.9626 Tf 4.469 -3.616 Td [(;)]TJ +0 g 0 G +/F27 9.9626 Tf -214.432 -15.528 Td [(BICG:)]TJ +0 g 0 G +/F8 9.9626 Tf 37.941 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(metho)-28(d;)]TJ +0 g 0 G +/F27 9.9626 Tf -37.941 -15.529 Td [(BICGST)96(AB:)]TJ +0 g 0 G +/F8 9.9626 Tf 68.133 0 Td [(the)-333(Bi-Conjugate)-334(Gradien)28(t)-333(Stabilized)-333(metho)-28(d;)]TJ +0 g 0 G +/F27 9.9626 Tf -68.133 -15.528 Td [(BICGST)96(ABL:)]TJ +0 g 0 G +/F8 9.9626 Tf 75.024 0 Td [(the)-222(Bi-Conjugate)-222(Gradien)27(t)-222(Stabilized)-222(metho)-28(d)-222(with)-222(restart-)]TJ -53.106 -11.955 Td [(ing;)]TJ +0 g 0 G +/F27 9.9626 Tf -21.918 -15.529 Td [(R)32(GMRES:)]TJ +0 g 0 G +/F8 9.9626 Tf 58.807 0 Td [(the)-333(Generalized)-334(Minimal)-333(Residual)-333(metho)-28(d)-333(with)-334(restarting.)]TJ +0 g 0 G +/F27 9.9626 Tf -83.714 -19.513 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.551 0 Td [(the)-333(lo)-28(cal)-333(p)-28(ortion)-333(of)-334(global)-333(sparse)-333(matrix)]TJ/F11 9.9626 Tf 178.968 0 Td [(A)]TJ/F8 9.9626 Tf 7.472 0 Td [(.)]TJ -172.084 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.611 0 Td [(required)]TJ/F8 9.9626 Tf -29.611 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.547 0 Td [(.)]TJ -43.033 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 312.036 137.958 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 315.174 137.759 Td [(Tspmat)]TJ +ET +q +1 0 0 1 347.183 137.958 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 350.322 137.759 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.921 0 Td [(.)]TJ +0 g 0 G +ET +q +1 0 0 1 99.895 129.78 cm +[]0 d 0 J 0.398 w 0 0 m 137.482 0 l S +Q +BT +/F32 5.9776 Tf 110.987 123.138 Td [(5)]TJ/F31 7.9701 Tf 4.151 -2.812 Td [(Note:)-472(the)-355(implemen)30(tation)-354(is)-355(f)1(or)]TJ/F33 7.9701 Tf 120.25 0 Td [(F)-148(C)-70(G)]TJ/F31 7.9701 Tf 19.732 0 Td [(\0501\051.)]TJ +0 g 0 G +0 g 0 G +/F8 9.9626 Tf 9.159 -29.888 Td [(149)]TJ +0 g 0 G +ET + +endstream +endobj +1917 0 obj << -/D [1848 0 R /XYZ 150.705 590.562 null] +/Length 7123 >> -% 737 0 obj +stream +0 g 0 G +0 g 0 G +0 g 0 G +BT +/F27 9.9626 Tf 150.705 706.129 Td [(prec)]TJ +0 g 0 G +/F8 9.9626 Tf 26.408 0 Td [(The)-333(data)-334(structure)-333(con)28(taining)-333(the)-334(preconditioner.)]TJ -1.502 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.956 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 362.845 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 365.983 658.308 Td [(prec)]TJ +ET +q +1 0 0 1 387.532 658.507 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 390.67 658.308 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -260.887 -22.202 Td [(b)]TJ +0 g 0 G +/F8 9.9626 Tf 11.346 0 Td [(The)-333(RHS)-334(v)28(ector.)]TJ 13.56 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(ar)1(ra)27(y)-333(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 223.496 0 Td [(psb)]TJ +ET +q +1 0 0 1 415.426 588.484 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 418.564 588.285 Td [(T)]TJ +ET +q +1 0 0 1 424.422 588.484 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 427.56 588.285 Td [(vect)]TJ +ET +q +1 0 0 1 449.109 588.484 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 452.247 588.285 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -322.464 -22.202 Td [(x)]TJ +0 g 0 G +/F8 9.9626 Tf 11.028 0 Td [(The)-333(initial)-334(guess.)]TJ 13.878 -11.956 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(inout)]TJ/F8 9.9626 Tf 26.096 0 Td [(.)]TJ -59.582 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(rank)-333(one)-334(ar)1(ra)27(y)-333(or)-333(an)-334(ob)-55(ject)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 223.496 0 Td [(psb)]TJ +ET +q +1 0 0 1 415.426 518.461 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 418.564 518.262 Td [(T)]TJ +ET +q +1 0 0 1 424.422 518.461 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 427.56 518.262 Td [(vect)]TJ +ET +q +1 0 0 1 449.109 518.461 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 452.247 518.262 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -322.464 -22.203 Td [(eps)]TJ +0 g 0 G +/F8 9.9626 Tf 21.116 0 Td [(The)-333(stopping)-334(tolerance.)]TJ 3.79 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(real)-333(n)28(um)27(b)-27(er.)]TJ +0 g 0 G +/F27 9.9626 Tf -24.906 -22.203 Td [(desc)]TJ +ET +q +1 0 0 1 172.619 426.236 cm +[]0 d 0 J 0.398 w 0 0 m 3.437 0 l S +Q +BT +/F27 9.9626 Tf 176.057 426.036 Td [(a)]TJ +0 g 0 G +/F8 9.9626 Tf 10.55 0 Td [(con)28(tains)-334(data)-333(structures)-333(for)-333(c)-1(omm)28(unications.)]TJ -10.996 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(lo)-32(cal)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(required)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Sp)-28(eci\014ed)-333(as:)-445(a)-333(structured)-333(data)-333(of)-334(t)28(yp)-28(e)]TJ +0 0 1 rg 0 0 1 RG +/F30 9.9626 Tf 170.915 0 Td [(psb)]TJ +ET +q +1 0 0 1 362.845 378.415 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 365.983 378.216 Td [(desc)]TJ +ET +q +1 0 0 1 387.532 378.415 cm +[]0 d 0 J 0.398 w 0 0 m 3.138 0 l S +Q +BT +/F30 9.9626 Tf 390.67 378.216 Td [(type)]TJ +0 g 0 G +/F8 9.9626 Tf 20.922 0 Td [(.)]TJ +0 g 0 G +/F27 9.9626 Tf -260.887 -22.203 Td [(itmax)]TJ +0 g 0 G +/F8 9.9626 Tf 33.783 0 Td [(The)-333(maxim)27(um)-333(n)28(um)28(b)-28(er)-333(of)-334(iterations)-333(to)-333(p)-28(erform.)]TJ -8.877 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.955 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(itmax)]TJ/F8 9.9626 Tf 29.505 0 Td [(=)-278(1000.)]TJ -68.941 -11.956 Td [(Sp)-28(eci\014ed)-333(as:)-445(an)-333(in)28(teger)-333(v)55(ariable)]TJ/F11 9.9626 Tf 142.079 0 Td [(itmax)]TJ/F14 9.9626 Tf 29.505 0 Td [(\025)]TJ/F8 9.9626 Tf 10.516 0 Td [(1.)]TJ +0 g 0 G +/F27 9.9626 Tf -207.006 -22.202 Td [(itrace)]TJ +0 g 0 G +/F8 9.9626 Tf 33.25 0 Td [(If)]TJ/F11 9.9626 Tf 8.912 0 Td [(>)]TJ/F8 9.9626 Tf 10.516 0 Td [(0)-228(prin)28(t)-228(out)-228(an)-228(i)1(nformational)-228(message)-228(ab)-28(out)-228(con)28(v)28(ergence)-228(ev)27(ery)]TJ/F11 9.9626 Tf 265.015 0 Td [(itr)-28(ace)]TJ/F8 9.9626 Tf -292.787 -11.955 Td [(iterations.)-444(If)-334(=)-278(0)-333(prin)28(t)-333(a)-334(message)-333(in)-333(cas)-1(e)-333(of)-333(con)28(v)27(ergence)-333(failure.)]TJ 0 -11.955 Td [(Scop)-28(e:)]TJ/F27 9.9626 Tf 32.379 0 Td [(global)]TJ/F8 9.9626 Tf -32.379 -11.956 Td [(T)28(yp)-28(e:)]TJ/F27 9.9626 Tf 29.612 0 Td [(optional)]TJ/F8 9.9626 Tf -29.612 -11.955 Td [(In)28(ten)28(t:)]TJ/F27 9.9626 Tf 33.486 0 Td [(in)]TJ/F8 9.9626 Tf 9.548 0 Td [(.)]TJ -43.034 -11.955 Td [(Default:)]TJ/F11 9.9626 Tf 39.436 0 Td [(itr)-28(ace)]TJ/F8 9.9626 Tf 28.785 0 Td [(=)]TJ/F14 9.9626 Tf 10.516 0 Td [(\000)]TJ/F8 9.9626 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[ ‹/‹1‹2È ‹3‹9‹5 sÏ‹6‹8‹>‹: ˆù‹;‹=‹@‹A‹D‹? ž5‹BÈ0‹`‹a‹b‹E ·_‹F‹G‹HÈ‹I‹J‹K‹L‹M‹N‹O‹P‹Q‹R‹S‹T‹U‹V‹W‹X‹Y‹Z‹[‹\‹]‹^‹_÷‹c ÓÃ÷÷÷Þÿ÷ +÷w÷÷÷ ÷÷  4÷ ÷÷÷÷Þ÷÷÷÷÷Z÷È1÷÷!÷°÷÷÷ ÷#÷(÷"/÷$÷&÷'÷*÷/÷)Dj÷+÷-÷.÷5÷0Rù÷1÷3÷4÷7÷<÷6a»÷8÷:÷;÷B÷=r]÷>÷@÷AÈ2÷F÷CÛ÷D÷H÷I÷M÷G„×÷J÷L÷O÷P÷Q÷R÷U÷N˜õ÷S÷X÷V·l÷W÷Z÷[÷\÷]÷`÷Y»ï÷^÷b]÷aÓ÷cÈ3q€]]Ž]]]] ] +±] ]] ž] ]]]]];]]]]]È ]]]] ]8ü]]"]$]!U ]#È4]']%gž]&]7](h+])]*],]4]6]A]8ƒÎ]9]@]B]C]D]E]F]G]H]I]J]K]L]M]N]O]P]Q]R]S]T]U?]Vè]W7]X^‹]Y|B]Z½Ò][ÛÐ]\C]]!¨]^†ž]_¦‹]`Èf]a +]bIÕ]cºÈÜSשÈ'lÈVãȤnÈ´£ÈÈ5È6È7È8È9È:È;Ì5®ÛÛÛÛÛÛÛ Û +Û Û Û ÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛÛ Û!Û"Û#Û$Û%Û&Û'Û(Û)Û*Û+Û,Û-Û.Û/Û0Û1Û2Û3Û4Û5Û6Û7Û8Û9Û:Û;Û<Û=Û>Û?Û@ÛAÛBÛCÛDÛEÛFÛGÛHÛIÛJÛKÛLÛMÛNÛOÛPÛQÛRÛSÛTÛUÛVÛWÛXÛYÛZÛ[Û\Û]Û^Û_Û`ÛaÛbÛc>‡v>>>>>>>>> > +> > > >>>>>>>…A’" endstream endobj startxref -1298040 +1348130 %%EOF diff --git a/docs/src/Makefile b/docs/src/Makefile index 65574507..78c2bc85 100644 --- a/docs/src/Makefile +++ b/docs/src/Makefile @@ -113,6 +113,7 @@ DATE = $(shell date +%Y-%m-%d) # LATEX = latex LTX2HTML = latex2html -local_icons +LTX2HTML = htlatex PDFLATEX = pdflatex ACRO = evince XPDF = xpdf @@ -138,11 +139,12 @@ PDF = $(join $(BASEFILE),.pdf) PS = $(join $(BASEFILE),.ps) GXS = $(join $(BASEFILE),.gxs) GLX = $(join $(BASEFILE),.glx) -TARGETPDF= ../psblas-3.6.pdf +TARGETPDF= ../psblas-3.7.pdf BASEHTML = $(patsubst %.tex,%,$(HTMLFILE)) -HTML = $(join $(HTMLFILE),.html) +HTML = $(join $(BASEHTML),.html) HTMLDIR = ../html HTMLFLAGS = -noaddress +HTMLFLAGS = "html,3" FIGURES = $(sort $(wildcard $(FIGDIR)/*)) GLOFILES:= $(sort $(wildcard lib/*.gdf)) @@ -159,9 +161,9 @@ TEXLNFIL = $(addprefix $(PWD)/,$(TEXFILES)) #============================================================================ all: pdf html - + pdf: $(PDF) copypdf -html: $(HTML) +html: $(HTML) copyhtml $(PDF): $(TEXFILES) $(LIBFILES) $(FIGURES) Makefile $(header) @@ -184,19 +186,21 @@ copypdf: $(HTML): $(TEXFILES) $(LIBFILES) $(FIGURES) Makefile $(header) $(initialize) - $(latex-filter) + $(pdflatex-filter) ifneq ($(BIBFILES),) $(bibtex) - $(latex-filter) + $(pdflatex-filter) endif ifneq ($(GLOFILES),) $(glosstex) - $(latex-filter) + $(pdflatex-filter) endif # $(makeindex) - $(latex-filter) $(ltx2html-filter) +copyhtml: + $(ltx2html-cpy) + $(PS): $(PDF) $(PDF2PS) $< $(PS) @@ -285,6 +289,7 @@ define initialize @ln -sf $(TEXLNFIL) tmp @ln -sf $(PWD)/lib/* tmp @ln -sf $(PWD)/$(FIGDIR) tmp + @ln -sf $(PWD)/$(FIGDIR)/*png tmp endef #---------------------------------------------------------------------------- @@ -328,7 +333,16 @@ define ltx2html-filter @echo "----- latex -------------------------------------------------------" @echo -n "Starting: "; date @echo - cd tmp; ($(LTX2HTML) $(HTMLFLAGS) -dir ../$(HTMLDIR) $(HTMLFILE) 2>&1) | $(FILTER) +# cd tmp; ($(LTX2HTML) $(HTMLFLAGS) -dir ../$(HTMLDIR) $(HTMLFILE) 2>&1) | $(FILTER) + cd tmp; ($(LTX2HTML) $(HTMLFILE) $(HTMLFLAGS) 2>&1) | $(FILTER) +endef + +define ltx2html-cpy + @echo + @echo "----- latex -------------------------------------------------------" + @echo -n "Starting: "; date + @echo + cd tmp; (cp *.css *.html *.png ../$(HTMLDIR)); (cp $(HTML) ../$(HTMLDIR)/index.html) endef #---------------------------------------------------------------------------- diff --git a/docs/src/commrout.tex b/docs/src/commrout.tex index 1c66b2fb..bdfd7c1c 100644 --- a/docs/src/commrout.tex +++ b/docs/src/commrout.tex @@ -8,8 +8,7 @@ The routines in this chapter implement various global communication operators on vectors associated with a discretization mesh. For auxiliary communication routines not tied to a discretization space see~\ref{sec:toolsrout}. -\clearpage\subsection*{psb\_halo --- Halo Data Communication} -\addcontentsline{toc}{subsection}{psb\_halo} +\clearpage\subsection{psb\_halo --- Halo Data Communication} These subroutines gathers the values of the halo @@ -88,7 +87,7 @@ An integer value that contains an error code. \begin{figure}[h] \begin{center} \ifcase\pdfoutput -\includegraphics[scale=0.45]{figures/try8x8.eps} +\includegraphics[scale=0.45]{try8x8.png} \or \includegraphics[scale=0.45]{figures/try8x8} \fi @@ -162,8 +161,7 @@ following: %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_ovrl --- Overlap Update} -\addcontentsline{toc}{subsection}{psb\_ovrl} +\clearpage\subsection{psb\_ovrl --- Overlap Update} These subroutines applies an overlap operator to the input vector: @@ -267,7 +265,7 @@ their instances. \begin{figure}[h] \begin{center} \ifcase\pdfoutput -\includegraphics[scale=0.65]{figures/try8x8_ov.eps} +\includegraphics[scale=0.65]{try8x8_ov.png} \or {\includegraphics[scale=0.65]{figures/try8x8_ov}} \fi @@ -354,8 +352,7 @@ following (showing a transition among the two subdomains) % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_gather --- Gather Global Dense Matrix} -\addcontentsline{toc}{subsection}{psb\_gather} +\clearpage\subsection{psb\_gather --- Gather Global Dense Matrix} These subroutines collect the portions of global dense matrix distributed over all process into one single array stored on one @@ -456,8 +453,7 @@ An integer value; 0 means no error has been detected. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_scatter --- Scatter Global Dense Matrix} -\addcontentsline{toc}{subsection}{psb\_scatter} +\clearpage\subsection{psb\_scatter --- Scatter Global Dense Matrix} These subroutines scatters the portions of global dense matrix owned by a process to all the processes in the processes grid. diff --git a/docs/src/datastruct.tex b/docs/src/datastruct.tex index 210476ea..72ee814b 100644 --- a/docs/src/datastruct.tex +++ b/docs/src/datastruct.tex @@ -182,8 +182,7 @@ state, which can take the following values: \subsubsection{Descriptor Methods} -\subsubsection*{get\_local\_rows --- Get number of local rows} -\addcontentsline{toc}{paragraph}{get\_local\_rows} +\subsubsection{get\_local\_rows --- Get number of local rows} \begin{verbatim} nr = desc%get_local_rows() @@ -208,8 +207,7 @@ Scope: {\bf local}.\\ \end{description} -\subsubsection*{get\_local\_cols --- Get number of local cols} -\addcontentsline{toc}{paragraph}{get\_local\_cols} +\subsubsection{get\_local\_cols --- Get number of local cols} \begin{verbatim} nc = desc%get_local_cols() @@ -235,8 +233,7 @@ Scope: {\bf local}.\\ \end{description} -\subsubsection*{get\_global\_rows --- Get number of global rows} -\addcontentsline{toc}{paragraph}{get\_global\_rows} +\subsubsection{get\_global\_rows --- Get number of global rows} \begin{verbatim} nr = desc%get_global_rows() @@ -258,8 +255,7 @@ Scope: {\bf local}.\\ global index space. \end{description} -\subsubsection*{get\_global\_cols --- Get number of global cols} -\addcontentsline{toc}{paragraph}{get\_global\_cols} +\subsubsection{get\_global\_cols --- Get number of global cols} \begin{verbatim} nr = desc%get_global_cols() @@ -282,8 +278,7 @@ Scope: {\bf local}.\\ \end{description} -\subsubsection*{get\_global\_indices --- Get vector of global indices} -\addcontentsline{toc}{paragraph}{get\_global\_indices} +\subsubsection{get\_global\_indices --- Get vector of global indices} \begin{verbatim} myidx = desc%get_global_indices([owned]) @@ -306,13 +301,12 @@ Type: {\bf optional}; default: \verb|.true.|.\\ \begin{description} \item[\bf On Return] \item[Function value] The global indices, returned as an allocatable - integer array of rank 1. + integer array of kind \verb|psb_lpk_| and rank 1. \end{description} -\subsubsection*{get\_context --- Get communication context} -\addcontentsline{toc}{paragraph}{get\_context} +\subsubsection{get\_context --- Get communication context} \begin{verbatim} ictxt = desc%get_context() @@ -333,8 +327,7 @@ Scope: {\bf local}.\\ \item[Function value] The communication context. \end{description} -\subsubsection*{Clone --- clone current object} -\addcontentsline{toc}{paragraph}{Clone} +\subsubsection{Clone --- clone current object} \begin{verbatim} call desc%clone(descout,info) @@ -357,8 +350,7 @@ Scope: {\bf local}.\\ \end{description} -\subsubsection*{CNV --- convert internal storage format} -\addcontentsline{toc}{paragraph}{CNV} +\subsubsection{CNV --- convert internal storage format} \begin{verbatim} call desc%cnv(mold) @@ -369,7 +361,7 @@ call desc%cnv(mold) \item[\bf On Entry] \item[desc] the communication descriptor.\\ Scope: {\bf local}.\\ -\item[mold] the desred integer storage format.\\ +\item[mold] the desired integer storage format.\\ Scope: {\bf local}.\\ % Type: {\bf required}.\\ % Intent: {\bf in}.\\ @@ -381,9 +373,8 @@ accelerators. -\subsubsection*{psb\_cd\_get\_large\_threshold --- Get threshold for +\subsubsection{psb\_cd\_get\_large\_threshold --- Get threshold for index mapping switch} -\addcontentsline{toc}{paragraph}{psb\_cd\_get\_large\_threshold} \begin{verbatim} ith = psb_cd_get_large_threshold() @@ -398,9 +389,9 @@ ith = psb_cd_get_large_threshold() -\subsubsection*{psb\_cd\_set\_large\_threshold --- Set threshold for +\subsubsection{psb\_cd\_set\_large\_threshold --- Set threshold for index mapping switch} -\addcontentsline{toc}{paragraph}{psb\_cd\_set\_large\_threshold} +%\addcontentsline{toc}{paragraph}{psb\_cd\_set\_large\_threshold} \begin{verbatim} call psb_cd_set_large_threshold(ith) @@ -421,6 +412,76 @@ has no effect on communication descriptors that have already been initialized. Moreover the threshold must have the same value on all processes. + +\subsubsection{get\_p\_adjcncy --- Get process adjacency list} +%\addcontentsline{toc}{paragraph}{get\_p\_adjcncy} + +\begin{verbatim} +list = desc%get_p_adjcncy() +\end{verbatim} + +\begin{description} +\item[Type:] Asynchronous. +\item[\bf On Return] +\item[Function value] The current list of adjacent processes, + i.e. processes with which the current one has to exchange halo + data. + +\end{description} + +\subsubsection{set\_p\_adjcncy --- Set process adjacency list} +%\addcontentsline{toc}{paragraph}{set\_p\_adjcncy} + +\begin{verbatim} +call desc%set_p_adjcncy(list) +\end{verbatim} + +\begin{description} +\item[Type:] Asynchronous. +\item[\bf On Entry] +\item[list] the list of adjacent processes.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ +Intent: {\bf in}.\\ +Specified as: a one-dimensional array of integers of kind \verb|psb_ipk_|. +\end{description} +Note: this method can be called after a call to \verb|psb_cdall| and +before a call to \verb|psb_cdasb|. The user is specifying here some +knowledge about which processes are topological neighbours of the +current process. The availability of this information may speed up the +execution of the assembly call \verb|psb_cdasb|. + + +\subsubsection{fnd\_owner --- Find the owner process of a set of indices} +%\addcontentsline{toc}{paragraph}{fnd\_owner} + +\begin{verbatim} +call desc%fnd_owner(idx,iprc,info) +\end{verbatim} + +\begin{description} +\item[Type:] Synchronous. +\item[\bf On Entry] +\item[idx] the list of global indices for which we need the owning processes.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ +Intent: {\bf in}.\\ +Specified as: a one-dimensional array of integers of kind \verb|psb_lpk_|. +\item[\bf On Return] +\item[iprc] the list of processes owning the indices in \verb|idx|.\\ +Scope: {\bf local}.\\ +Type: {\bf required}.\\ +Intent: {\bf in}.\\ +Specified as: an allocatable one-dimensional array of integers of kind \verb|psb_ipk_|. +\end{description} +Note: this method may or may not actually require communications, depending on +the exact internal data storage; given that the choice of storage may +be altered by runtime parameters, it is necessary for safety that this +method is called by all processes. + + + + \subsubsection{Named Constants} \label{sec:cd_constants} \begin{description} @@ -521,8 +582,8 @@ variants are obtained by conversion to/from it. \subsubsection{Sparse Matrix Methods} -\subsubsection*{get\_nrows --- Get number of rows in a sparse matrix} -\addcontentsline{toc}{paragraph}{get\_nrows} +\subsubsection{get\_nrows --- Get number of rows in a sparse matrix} +%\addcontentsline{toc}{paragraph}{get\_nrows} \begin{verbatim} nr = a%get_nrows() @@ -544,9 +605,9 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{get\_ncols --- Get number of columns in a sparse +\subsubsection{get\_ncols --- Get number of columns in a sparse matrix} -\addcontentsline{toc}{paragraph}{get\_ncols} +%\addcontentsline{toc}{paragraph}{get\_ncols} \begin{verbatim} nc = a%get_ncols() @@ -568,9 +629,9 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{get\_nnzeros --- Get number of nonzero elements +\subsubsection{get\_nnzeros --- Get number of nonzero elements in a sparse matrix} -\addcontentsline{toc}{paragraph}{get\_nnzeros} +%\addcontentsline{toc}{paragraph}{get\_nnzeros} \begin{verbatim} nz = a%get_nnzeros() @@ -598,9 +659,9 @@ Scope: {\bf local}\\ value for the same matrix may be different for different storage choices. \end{enumerate} -\subsubsection*{get\_size --- Get maximum number of nonzero elements +\subsubsection{get\_size --- Get maximum number of nonzero elements in a sparse matrix} -\addcontentsline{toc}{paragraph}{get\_size } +%\addcontentsline{toc}{paragraph}{get\_size } \begin{verbatim} maxnz = a%get_size() @@ -622,9 +683,9 @@ Scope: {\bf local}\\ be stored in sparse matrix \verb|a| using its current memory allocation. \end{description} -\subsubsection*{sizeof --- Get memory occupation in bytes +\subsubsection{sizeof --- Get memory occupation in bytes of a sparse matrix} -\addcontentsline{toc}{paragraph}{sizeof } +%\addcontentsline{toc}{paragraph}{sizeof } \begin{verbatim} memory_size = a%sizeof() @@ -646,8 +707,8 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{get\_fmt --- Short description of the dynamic type} -\addcontentsline{toc}{paragraph}{get\_fmt } +\subsubsection{get\_fmt --- Short description of the dynamic type} +%\addcontentsline{toc}{paragraph}{get\_fmt } \begin{verbatim} write(*,*) a%get_fmt() @@ -670,8 +731,8 @@ Scope: {\bf local}\\ \verb|CSR| and \verb|CSC|. \end{description} -\subsubsection*{is\_bld, is\_upd, is\_asb --- Status check} -\addcontentsline{toc}{paragraph}{is\_bld, is\_upd, is\_asb } +\subsubsection{is\_bld, is\_upd, is\_asb --- Status check} +%\addcontentsline{toc}{paragraph}{is\_bld, is\_upd, is\_asb } \begin{verbatim} if (a%is_bld()) then @@ -695,9 +756,9 @@ Scope: {\bf local}\\ matrix is in the Build, Update or Assembled state, respectively. \end{description} -\subsubsection*{is\_lower, is\_upper, is\_triangle, is\_unit --- +\subsubsection{is\_lower, is\_upper, is\_triangle, is\_unit --- Format check} -\addcontentsline{toc}{paragraph}{is\_lower, is\_upper, is\_triangle, is\_unit} +%\addcontentsline{toc}{paragraph}{is\_lower, is\_upper, is\_triangle, is\_unit} \begin{verbatim} if (a%is_triangle()) then @@ -725,8 +786,8 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{cscnv --- Convert to a different storage format} -\addcontentsline{toc}{paragraph}{cscnv} +\subsubsection{cscnv --- Convert to a different storage format} +%\addcontentsline{toc}{paragraph}{cscnv} \begin{verbatim} call a%cscnv(b,info [, type, mold, dupl]) @@ -758,8 +819,8 @@ employed to interface with special devices, such as GPUs and other accelerators. -\subsubsection*{csclip --- Reduce to a submatrix} -\addcontentsline{toc}{paragraph}{csclip} +\subsubsection{csclip --- Reduce to a submatrix} +%\addcontentsline{toc}{paragraph}{csclip} \begin{verbatim} call a%csclip(b,info[,& & imin,imax,jmin,jmax,rscale,cscale]) @@ -786,8 +847,8 @@ A variable of type \verb|psb_Tspmat_type|. \item[info] Return code. \end{description} -\subsubsection*{clean\_zeros --- Eliminate zero coefficients} -\addcontentsline{toc}{paragraph}{clean\_zeros} +\subsubsection{clean\_zeros --- Eliminate zero coefficients} +%\addcontentsline{toc}{paragraph}{clean\_zeros} \begin{verbatim} call a%clean_zeros(info) \end{verbatim} @@ -810,8 +871,8 @@ A variable of type \verb|psb_Tspmat_type|. \item[info] Return code. \end{description} -\subsubsection*{get\_diag --- Get main diagonal} -\addcontentsline{toc}{paragraph}{get\_diag} +\subsubsection{get\_diag --- Get main diagonal} +%\addcontentsline{toc}{paragraph}{get\_diag} \begin{verbatim} call a%get_diag(d,info) \end{verbatim} @@ -832,8 +893,8 @@ A one-dimensional array of the appropriate type. \end{description} -\subsubsection*{clip\_diag --- Cut out main diagonal} -\addcontentsline{toc}{paragraph}{clip\_diag} +\subsubsection{clip\_diag --- Cut out main diagonal} +%\addcontentsline{toc}{paragraph}{clip\_diag} \begin{verbatim} call a%clip_diag(b,info) \end{verbatim} @@ -854,8 +915,8 @@ A variable of type \verb|psb_Tspmat_type|. \end{description} -\subsubsection*{tril --- Return the lower triangle} -\addcontentsline{toc}{paragraph}{tril} +\subsubsection{tril --- Return the lower triangle} +%\addcontentsline{toc}{paragraph}{tril} \begin{verbatim} call a%tril(l,info[,& & diag,imin,imax,jmin,jmax,rscale,cscale,u]) @@ -888,8 +949,8 @@ A variable of type \verb|psb_Tspmat_type|. \item[info] Return code. \end{description} -\subsubsection*{triu --- Return the upper triangle} -\addcontentsline{toc}{paragraph}{triu} +\subsubsection{triu --- Return the upper triangle} +%\addcontentsline{toc}{paragraph}{triu} \begin{verbatim} call a%triu(u,info[,& & diag,imin,imax,jmin,jmax,rscale,cscale,l]) @@ -925,8 +986,8 @@ A variable of type \verb|psb_Tspmat_type|. -\subsubsection*{psb\_set\_mat\_default --- Set default storage format} -\addcontentsline{toc}{paragraph}{psb\_set\_mat\_default} +\subsubsection{psb\_set\_mat\_default --- Set default storage format} +%\addcontentsline{toc}{paragraph}{psb\_set\_mat\_default} \begin{verbatim} @@ -945,8 +1006,8 @@ Type: required. -\subsubsection*{clone --- Clone current object} -\addcontentsline{toc}{paragraph}{clone} +\subsubsection{clone --- Clone current object} +%\addcontentsline{toc}{paragraph}{clone} \begin{verbatim} call a%clone(b,info) @@ -1042,8 +1103,8 @@ private memory. \end{figure} \subsubsection{Vector Methods} -\subsubsection*{get\_nrows --- Get number of rows in a dense vector} -\addcontentsline{toc}{paragraph}{get\_nrows} +\subsubsection{get\_nrows --- Get number of rows in a dense vector} +%\addcontentsline{toc}{paragraph}{get\_nrows} \begin{verbatim} nr = v%get_nrows() @@ -1065,9 +1126,9 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{sizeof --- Get memory occupation in bytes +\subsubsection{sizeof --- Get memory occupation in bytes of a dense vector} -\addcontentsline{toc}{paragraph}{sizeof } +%\addcontentsline{toc}{paragraph}{sizeof } \begin{verbatim} memory_size = v%sizeof() @@ -1089,8 +1150,8 @@ Scope: {\bf local}\\ \end{description} -\subsubsection*{set --- Set contents of the vector} -\addcontentsline{toc}{paragraph}{set } +\subsubsection{set --- Set contents of the vector} +%\addcontentsline{toc}{paragraph}{set } \begin{verbatim} call v%set(alpha[,first,last]) @@ -1127,8 +1188,8 @@ constant having the appropriate type and kind. Scope: {\bf local}\\ \end{description} -\subsubsection*{get\_vect --- Get a copy of the vector contents} -\addcontentsline{toc}{paragraph}{get\_vect } +\subsubsection{get\_vect --- Get a copy of the vector contents} +%\addcontentsline{toc}{paragraph}{get\_vect } \begin{verbatim} extv = v%get_vect([n]) @@ -1157,8 +1218,8 @@ Type: {\bf optional}; default: entire vector.\\ array is the same as the internal size of the vector. \end{description} -\subsubsection*{clone --- Clone current object} -\addcontentsline{toc}{paragraph}{clone} +\subsubsection{clone --- Clone current object} +%\addcontentsline{toc}{paragraph}{clone} \begin{verbatim} call x%clone(y,info) \end{verbatim} diff --git a/docs/src/error.tex b/docs/src/error.tex index bbef2da4..a483d3d1 100644 --- a/docs/src/error.tex +++ b/docs/src/error.tex @@ -119,9 +119,10 @@ Aborting... \end{figure} -\clearpage\subroutine{psb\_errpush}{Pushes an error code onto the error +\clearpage\subsection{psb\_errpush --- Pushes an error code onto the error stack} + \begin{lstlisting} call psb_errpush(err_c, r_name, i_err, a_err) \end{lstlisting} @@ -149,7 +150,7 @@ Type: {\bf optional}\\ Specified as: a string.\\ \end{description} -\clearpage\subroutine{psb\_error}{Prints the error stack content and aborts +\clearpage\subsection{psb\_error --- Prints the error stack content and aborts execution} \begin{lstlisting} @@ -168,8 +169,9 @@ Specified as: an integer. -\clearpage\subroutine{psb\_set\_errverbosity}{Sets the verbosity of error - messages.} +\clearpage\subsection{psb\_set\_errverbosity --- Sets the verbosity of error + messages} + \begin{lstlisting} call psb_set_errverbosity(v) @@ -185,9 +187,8 @@ Intent: {\bf in}.\\ Specified as: an integer. \end{description} -\clearpage\subroutine{psb\_set\_erraction}{Set the type of action to be - taken upon error condition.} - +\clearpage\subsection{psb\_set\_erraction --- Set the type of action to be + taken upon error condition} \begin{lstlisting} call psb_set_erraction(err_act) @@ -205,27 +206,6 @@ Specified as: an integer. Possible values: \verb|psb_act_ret|, \end{description} - -%% \clearpage\subroutine{psb\_errcomm}{Error communication routine} - -%% \begin{lstlisting} -%% call psb_errcomm(icontxt, err) -%% \end{lstlisting} - -%% \begin{description} -%% \item[\bf On Entry] -%% \item[icontxt] the communication context.\\ -%% Scope: {\bf global} \\ -%% Type: {\bf required}\\ -%% Intent: {\bf in}.\\ -%% Specified as: an integer. -%% \item[err] the error code to be communicated\\ -%% Scope: {\bf global} \\ -%% Type: {\bf required}\\ -%% Intent: {\bf inout}.\\ -%% Specified as: an integer.\\ -%% \end{description} - %%% Local Variables: %%% mode: latex %%% TeX-master: "userguide" diff --git a/docs/src/figures/points.png b/docs/src/figures/points.png new file mode 100644 index 00000000..097201d3 Binary files /dev/null and b/docs/src/figures/points.png differ diff --git a/docs/src/figures/psblas.png b/docs/src/figures/psblas.png new file mode 100644 index 00000000..c904340d Binary files /dev/null and b/docs/src/figures/psblas.png differ diff --git a/docs/src/figures/try8x8.png b/docs/src/figures/try8x8.png new file mode 100644 index 00000000..4ff4882c Binary files /dev/null and b/docs/src/figures/try8x8.png differ diff --git a/docs/src/figures/try8x8_ov.png b/docs/src/figures/try8x8_ov.png new file mode 100644 index 00000000..a5025abe Binary files /dev/null and b/docs/src/figures/try8x8_ov.png differ diff --git a/docs/src/intro.tex b/docs/src/intro.tex index d0fb9b8c..0ee391a5 100644 --- a/docs/src/intro.tex +++ b/docs/src/intro.tex @@ -101,7 +101,7 @@ further details on our communication layer see Sec.~\ref{sec:parenv}. \begin{figure}[h] \begin{center} \ifcase\pdfoutput -\includegraphics[scale=0.65]{figures/psblas.eps} +\includegraphics[scale=0.65]{psblas.png} \or \includegraphics[scale=0.65]{figures/psblas} \fi @@ -218,7 +218,7 @@ local rows) is $|{\cal I}_i| + |{\cal B}_i| +|{\cal H}_i|$. \begin{center} \ifcase\pdfoutput %\rotatebox{-90}{ -\includegraphics[scale=0.65]{figures/points.eps}%} +\includegraphics[scale=0.65]{points.png}%} \or \rotatebox{-90}{\includegraphics[scale=0.65]{figures/points}} \fi diff --git a/docs/src/methods.tex b/docs/src/methods.tex index 6a80f92c..4b2f8b66 100644 --- a/docs/src/methods.tex +++ b/docs/src/methods.tex @@ -11,9 +11,8 @@ the module \verb|psb_krylov_mod|. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_krylov \label{krylov} --- Krylov Methods Driver +\clearpage\subsection{psb\_krylov \label{krylov} --- Krylov Methods Driver Routine} -\addcontentsline{toc}{subsection}{psb\_krylov} This subroutine is a driver that provides a general interface for all the Krylov-Subspace family methods implemented in PSBLAS version 2. diff --git a/docs/src/penv.tex b/docs/src/penv.tex index 9fd2c968..9465c8b3 100644 --- a/docs/src/penv.tex +++ b/docs/src/penv.tex @@ -1,10 +1,10 @@ + \section{Parallel environment routines} \label{sec:parenv} -\clearpage\subsection*{psb\_init --- Initializes PSBLAS parallel +\clearpage\subsection{psb\_init --- Initializes PSBLAS parallel environment} -\addcontentsline{toc}{subsection}{psb\_init} \begin{verbatim} call psb_init(icontxt, np, basectxt, ids) @@ -61,9 +61,8 @@ Specified as: an integer variable. \end{enumerate} -\clearpage\subsection*{psb\_info --- Return information about PSBLAS parallel +\clearpage\subsection{psb\_info --- Return information about PSBLAS parallel environment} -\addcontentsline{toc}{subsection}{psb\_info} \begin{verbatim} call psb_info(icontxt, iam, np) @@ -109,9 +108,8 @@ Specified as: an integer variable. \ \end{enumerate} -\clearpage\subsection*{psb\_exit --- Exit from PSBLAS parallel +\clearpage\subsection{psb\_exit --- Exit from PSBLAS parallel environment} -\addcontentsline{toc}{subsection}{psb\_exit} \begin{verbatim} call psb_exit(icontxt) @@ -153,14 +151,13 @@ Specified as: a logical variable, default value: true. \end{enumerate} -\clearpage\subsection*{psb\_get\_mpicomm --- Get the MPI communicator} -\addcontentsline{toc}{subsection}{psb\_get\_mpicomm} +\clearpage\subsection{psb\_get\_mpi\_comm --- Get the MPI communicator} \begin{verbatim} -icomm = psb_get_mpicomm(icontxt) +icomm = psb_get_mpi_comm(icontxt) \end{verbatim} -This subroutine returns the MPI communicator associated with a PSBLAS context +This function returns the MPI communicator associated with a PSBLAS context \begin{description} \item[Type:] Asynchronous. \item[\bf On Entry ] @@ -180,15 +177,17 @@ Type: {\bf required}.\\ Intent: {\bf out}.\\ \end{description} +{\par\noindent\large\bfseries Notes} +The subroutine version \verb|psb_get_mpicomm| is still available but +is deprecated. -\clearpage\subsection*{psb\_get\_rank --- Get the MPI rank} -\addcontentsline{toc}{subsection}{psb\_get\_rank} +\clearpage\subsection{psb\_get\_mpi\_rank --- Get the MPI rank} \begin{verbatim} -rank = psb_get_rank(icontxt, id) +rank = psb_get_mpi_rank(icontxt, id) \end{verbatim} -This subroutine returns the MPI rank of the PSBLAS process $id$ +This function returns the MPI rank of the PSBLAS process $id$ \begin{description} \item[Type:] Asynchronous. \item[\bf On Entry ] @@ -213,11 +212,13 @@ Type: {\bf required}.\\ Intent: {\bf out}.\\ \end{description} +{\par\noindent\large\bfseries Notes} +The subroutine version \verb|psb_get_rank| is still available but is +deprecated. -\clearpage\subsection*{psb\_wtime --- Wall clock timing} -\addcontentsline{toc}{subsection}{psb\_wtime} +\clearpage\subsection{psb\_wtime --- Wall clock timing} \begin{verbatim} time = psb_wtime() @@ -233,9 +234,8 @@ Returned as: a \verb|real(psb_dpk_)| variable. \end{description} -\clearpage\subsection*{psb\_barrier --- Sinchronization point parallel +\clearpage\subsection{psb\_barrier --- Sinchronization point parallel environment} -\addcontentsline{toc}{subsection}{psb\_barrier} \begin{verbatim} call psb_barrier(icontxt) @@ -255,8 +255,7 @@ Specified as: an integer variable. \end{description} -\clearpage\subsection*{psb\_abort --- Abort a computation} -\addcontentsline{toc}{subsection}{psb\_abort} +\clearpage\subsection{psb\_abort --- Abort a computation} \begin{verbatim} call psb_abort(icontxt) @@ -278,8 +277,7 @@ Specified as: an integer variable. -\clearpage\subsection*{psb\_bcast --- Broadcast data} -\addcontentsline{toc}{subsection}{psb\_bcast} +\clearpage\subsection{psb\_bcast --- Broadcast data} \begin{verbatim} call psb_bcast(icontxt, dat, root) @@ -324,8 +322,7 @@ Type, kind, rank and size must agree on all processes. \end{description} -\clearpage\subsection*{psb\_sum --- Global sum} -\addcontentsline{toc}{subsection}{psb\_sum} +\clearpage\subsection{psb\_sum --- Global sum} \begin{verbatim} call psb_sum(icontxt, dat, root) @@ -379,8 +376,7 @@ Type, kind, rank and size must agree on all processes. -\clearpage\subsection*{psb\_max --- Global maximum} -\addcontentsline{toc}{subsection}{psb\_max} +\clearpage\subsection{psb\_max --- Global maximum} \begin{verbatim} call psb_max(icontxt, dat, root) @@ -433,8 +429,7 @@ Type, kind, rank and size must agree on all processes. \item The \verb|dat| argument may also be a long integer scalar. \end{enumerate} -\clearpage\subsection*{psb\_min --- Global minimum} -\addcontentsline{toc}{subsection}{psb\_min} +\clearpage\subsection{psb\_min --- Global minimum} \begin{verbatim} call psb_min(icontxt, dat, root) @@ -487,8 +482,7 @@ Type, kind, rank and size must agree on all processes. \item The \verb|dat| argument may also be a long integer scalar. \end{enumerate} -\clearpage\subsection*{psb\_amx --- Global maximum absolute value} -\addcontentsline{toc}{subsection}{psb\_amx} +\clearpage\subsection{psb\_amx --- Global maximum absolute value} \begin{verbatim} call psb_amx(icontxt, dat, root) @@ -541,8 +535,7 @@ Type, kind, rank and size must agree on all processes. \item The \verb|dat| argument may also be a long integer scalar. \end{enumerate} -\clearpage\subsection*{psb\_amn --- Global minimum absolute value} -\addcontentsline{toc}{subsection}{psb\_amn} +\clearpage\subsection{psb\_amn --- Global minimum absolute value} \begin{verbatim} call psb_amn(icontxt, dat, root) @@ -595,8 +588,7 @@ Type, kind, rank and size must agree on all processes. \item The \verb|dat| argument may also be a long integer scalar. \end{enumerate} -\clearpage\subsection*{psb\_nrm2 --- Global 2-norm reduction} -\addcontentsline{toc}{subsection}{psb\_nrm2} +\clearpage\subsection{psb\_nrm2 --- Global 2-norm reduction} \begin{verbatim} call psb_nrm2(icontxt, dat, root) @@ -656,8 +648,7 @@ Kind, rank and size must agree on all processes. -\clearpage\subsection*{psb\_snd --- Send data} -\addcontentsline{toc}{subsection}{psb\_snd} +\clearpage\subsection{psb\_snd --- Send data} \begin{verbatim} call psb_snd(icontxt, dat, dst, m) @@ -708,8 +699,7 @@ same value on sending and receiving processes. \end{enumerate} -\clearpage\subsection*{psb\_rcv --- Receive data} -\addcontentsline{toc}{subsection}{psb\_rcv} +\clearpage\subsection{psb\_rcv --- Receive data} \begin{verbatim} call psb_rcv(icontxt, dat, src, m) diff --git a/docs/src/precs.tex b/docs/src/precs.tex index 6c58bbc0..b976b7ad 100644 --- a/docs/src/precs.tex +++ b/docs/src/precs.tex @@ -23,9 +23,7 @@ backward compatibility %% package, which will characterize release 2.1 of our library. - -\clearpage\subsection*{init --- Initialize a preconditioner} -\addcontentsline{toc}{subsection}{prec\%init} +\clearpage\subsection{init --- Initialize a preconditioner} \begin{verbatim} call prec%init(icontxt,ptype, info) @@ -86,8 +84,7 @@ $ptype$ string as follows\footnote{The string is case-insensitive}: \end{description} -\clearpage\subsection*{build --- Builds a preconditioner} -\addcontentsline{toc}{subsection}{prec\%build} +\clearpage\subsection{build --- Builds a preconditioner} \begin{verbatim} call prec%build(a, desc_a, info[,amold,vmold,imold]) @@ -152,9 +149,8 @@ accelerators. -\clearpage\subsection*{apply --- Preconditioner application +\clearpage\subsection{apply --- Preconditioner application routine} -\addcontentsline{toc}{subsection}{prec\%apply} \begin{verbatim} call prec%apply(x,y,desc_a,info,trans,work) @@ -207,9 +203,8 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{descr --- Prints a description of current +\clearpage\subsection{descr --- Prints a description of current preconditioner} -\addcontentsline{toc}{subsection}{prec\%descr} \begin{verbatim} call prec%descr() @@ -240,9 +235,8 @@ all processes will print. Default: 0. -\clearpage\subsection*{clone --- clone current +\clearpage\subsection{clone --- clone current preconditioner} -\addcontentsline{toc}{subsection}{clone} \begin{verbatim} call prec%clone(precout,info) \end{verbatim} @@ -264,8 +258,7 @@ Scope: {\bf local}.\\ \end{description} -\clearpage\subsection*{free --- Free a preconditioner} -\addcontentsline{toc}{subsection}{prec\%free} +\clearpage\subsection{free --- Free a preconditioner} \begin{verbatim} call prec%free(info) diff --git a/docs/src/psbrout.tex b/docs/src/psbrout.tex index d8288093..fbe0d3da 100644 --- a/docs/src/psbrout.tex +++ b/docs/src/psbrout.tex @@ -5,8 +5,7 @@ % DENSE MATRIX SUM % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_geaxpby --- General Dense Matrix Sum} -\addcontentsline{toc}{subsection}{psb\_geaxpby} +\clearpage\subsection{psb\_geaxpby --- General Dense Matrix Sum} This subroutine is an interface to the computational kernel for dense matrix sum: @@ -111,8 +110,7 @@ An integer value; 0 means no error has been detected. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_gedot --- Dot Product} -\addcontentsline{toc}{subsection}{psb\_gedot} +\clearpage\subsection{psb\_gedot --- Dot Product} This function computes dot product between two vectors $x$ and $y$.\\ @@ -229,8 +227,7 @@ An integer value; 0 means no error has been detected. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_gedots --- Generalized Dot Product} -\addcontentsline{toc}{subsection}{psb\_gedots} +\clearpage\subsection{psb\_gedots --- Generalized Dot Product} This subroutine computes a series of dot products among the columns of two dense matrices $x$ and $y$: @@ -303,8 +300,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_normi --- Infinity-Norm of Vector} -\addcontentsline{toc}{subsection}{psb\_normi} +\clearpage\subsection{psb\_normi --- Infinity-Norm of Vector} This function computes the infinity-norm of a vector $x$.\\ @@ -407,8 +403,7 @@ An integer value; 0 means no error has been detected. % %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_geamaxs --- Generalized Infinity Norm} -\addcontentsline{toc}{subsection}{psb\_geamaxs} +\clearpage\subsection{psb\_geamaxs --- Generalized Infinity Norm} This subroutine computes a series of infinity norms on the columns of a dense matrix $x$: @@ -469,8 +464,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_norm1 --- 1-Norm of Vector} -\addcontentsline{toc}{subsection}{psb\_norm1} +\clearpage\subsection{psb\_norm1 --- 1-Norm of Vector} This function computes the 1-norm of a vector $x$.\\ If $x$ is a real vector @@ -557,8 +551,7 @@ An integer value; 0 means no error has been detected. \end{enumerate} -\clearpage\subsection*{psb\_geasums --- Generalized 1-Norm of Vector} -\addcontentsline{toc}{subsection}{psb\_geasums} +\clearpage\subsection{psb\_geasums --- Generalized 1-Norm of Vector} This subroutine computes a series of 1-norms on the columns of a dense matrix $x$: @@ -631,8 +624,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_norm2 --- 2-Norm of Vector} -\addcontentsline{toc}{subsection}{psb\_norm2} +\clearpage\subsection{psb\_norm2 --- 2-Norm of Vector} This function computes the 2-norm of a vector $x$.\\ If $x$ is a real vector @@ -730,8 +722,7 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{psb\_genrm2s --- Generalized 2-Norm of Vector} -\addcontentsline{toc}{subsection}{psb\_genrm2s} +\clearpage\subsection{psb\_genrm2s --- Generalized 2-Norm of Vector} This subroutine computes a series of 2-norms on the columns of a dense matrix $x$: @@ -798,8 +789,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_norm1 --- 1-Norm of Sparse Matrix} -\addcontentsline{toc}{subsection}{psb\_norm1} +\clearpage\subsection{psb\_norm1 --- 1-Norm of Sparse Matrix} This function computes the 1-norm of a matrix $A$:\\ @@ -863,8 +853,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_normi --- Infinity Norm of Sparse Matrix} -\addcontentsline{toc}{subsection}{psb\_normi} +\clearpage\subsection{psb\_normi --- Infinity Norm of Sparse Matrix} This function computes the infinity-norm of a matrix $A$:\\ @@ -928,9 +917,8 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_spmm --- Sparse Matrix by Dense Matrix +\clearpage\subsection{psb\_spmm --- Sparse Matrix by Dense Matrix Product} -\addcontentsline{toc}{subsection}{psb\_spmm} This subroutine computes the Sparse Matrix by Dense Matrix Product: @@ -1081,8 +1069,7 @@ An integer value; 0 means no error has been detected. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\clearpage\subsection*{psb\_spsm --- Triangular System Solve} -\addcontentsline{toc}{subsection}{psb\_spsm} +\clearpage\subsection{psb\_spsm --- Triangular System Solve} This subroutine computes the Triangular System Solve: @@ -1244,8 +1231,216 @@ Intent: {\bf out}.\\ An integer value; 0 means no error has been detected. \end{description} +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% +% +% VECTOR VECTOR OPERATIONS +% +%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + + +\clearpage\subsection{psb\_gemlt --- Entrywise Product} + +This function computes the entrywise product between two vectors $x$ and +$y$ +\[dot \leftarrow x(i) y(i).\] + +\begin{verbatim} +psb_gemlt(x, y, desc_a, info) +\end{verbatim} +%% \syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy} +\begin{table}[h] + \begin{center} + \begin{tabular}{ll} + \hline + $dot$, $x$, $y$ & {\bf Function}\\ + \hline + Short Precision Real & psb\_gemlt \\ + Long Precision Real & psb\_gemlt \\ + Short Precision Complex & psb\_gemlt \\ + Long Precision Complex & psb\_gemlt \\ + \hline + \end{tabular} + \end{center} + \caption{Data types\label{tab:f90mlt}} +\end{table} + +\begin{description} + \item[Type:] Synchronous. + \item[\bf On Entry] + \item[x] the local portion of global dense vector + $x$.\\ + %% This function computes the location of the first element of + %% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf in}.\\ + Specified as: an object of type \vdata\ + containing numbers of type specified in + Table~\ref{tab:f90dot}. + \item[y] the local portion of global dense vector + $y$. \\ + %% This function computes the location of the first element of + %% local subarray used, based on $iy, jy$ and the field $matrix\_data$ of $desc\_a$ . \\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf in}.\\ + Specified as: an object of type \vdata\ + containing numbers of type specified in + Table~\ref{tab:f90dot}. + \item[desc\_a] contains data structures for communications.\\ + Scope: {\bf local} \\ + Type: {\bf required}\\ + Intent: {\bf in}.\\ + Specified as: an object of type \descdata. + \item[\bf On Return] + \item[y] the local portion of result submatrix $y$.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf inout}.\\ + Specified as: an object of type \vdata\ containing numbers of the type + indicated in Table~\ref{tab:f90mlt}. + \item[info] Error code.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf out}.\\ + An integer value; 0 means no error has been detected. +\end{description} + +\clearpage\subsection{psb\_gediv --- Entrywise Division} + +This function computes the entrywise division between two vectors $x$ and +$y$ +\[/ \leftarrow x(i)/y(i).\] +\begin{verbatim} +psb_gediv(x, y, desc_a, info, [flag) +\end{verbatim} +%% \syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy} +\begin{table}[h] + \begin{center} + \begin{tabular}{ll} + \hline + $/$, $x$, $y$ & {\bf Function}\\ + \hline + Short Precision Real & psb\_gediv \\ + Long Precision Real & psb\_gediv \\ + Short Precision Complex & psb\_gediv \\ + Long Precision Complex & psb\_gediv \\ + \hline + \end{tabular} + \end{center} + \caption{Data types\label{tab:f90div}} +\end{table} + +\begin{description} + \item[Type:] Synchronous. + \item[\bf On Entry] + \item[x] the local portion of global dense vector + $x$.\\ + %% This function computes the location of the first element of + %% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf in}.\\ + Specified as: an object of type \vdata\ + containing numbers of type specified in + Table~\ref{tab:f90dot}. + \item[y] the local portion of global dense vector + $y$. \\ + %% This function computes the location of the first element of + %% local subarray used, based on $iy, jy$ and the field $matrix\_data$ of $desc\_a$ . \\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf in}.\\ + Specified as: an object of type \vdata\ + containing numbers of type specified in + Table~\ref{tab:f90dot}. + \item[desc\_a] contains data structures for communications.\\ + Scope: {\bf local} \\ + Type: {\bf required}\\ + Intent: {\bf in}.\\ + Specified as: an object of type \descdata. + \item[flag] check if any of the $y(i) = 0$, and in case returns error halting the computation.\\ + Scope: {\bf local} \\ + Type: {\bf optional} + Intent: {\bf in}.\\ + Specified as: the logical value \verb|flag=.true.| + \item[\bf On Return] + \item[x] the local portion of result submatrix $x$.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf inout}.\\ + Specified as: an object of type \vdata\ containing numbers of the type + indicated in Table~\ref{tab:f90mlt}. + \item[info] Error code.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf out}.\\ + An integer value; 0 means no error has been detected. +\end{description} + +\clearpage\subsection{psb\_geinv --- Entrywise Inversion} +This function computes the entrywise inverse of a vector $x$ and puts it into +$y$ +\[/ \leftarrow 1/x(i).\] + +\begin{verbatim} +psb_geinv(x, y, desc_a, info, [flag) +\end{verbatim} +%% \syntax*{psb\_gedot}{x, y, desc\_a, info, jx, jy} +\begin{table}[h] + \begin{center} + \begin{tabular}{ll} + \hline + $/$, $x$, $y$ & {\bf Function}\\ + \hline + Short Precision Real & psb\_geinv \\ + Long Precision Real & psb\_geinv \\ + Short Precision Complex & psb\_geinv \\ + Long Precision Complex & psb\_geinv \\ + \hline + \end{tabular} + \end{center} + \caption{Data types\label{tab:f90inv}} +\end{table} + +\begin{description} + \item[Type:] Synchronous. + \item[\bf On Entry] + \item[x] the local portion of global dense vector + $x$.\\ + %% This function computes the location of the first element of + %% local subarray used, based on $jx$ and the field $matrix\_data$ of $desc\_a$ . \\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf in}.\\ + Specified as: an object of type \vdata\ + containing numbers of type specified in + Table~\ref{tab:f90dot}. + \item[desc\_a] contains data structures for communications.\\ + Scope: {\bf local} \\ + Type: {\bf required}\\ + Intent: {\bf in}.\\ + Specified as: an object of type \descdata. + \item[flag] check if any of the $x(i) = 0$, and in case returns error halting the computation.\\ + Scope: {\bf local} \\ + Type: {\bf optional} + Intent: {\bf in}.\\ + Specified as: the logical value \verb|flag=.true.| + \item[\bf On Return] + \item[y] the local portion of result submatrix $x$.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf out}.\\ + Specified as: an object of type \vdata\ containing numbers of the type + indicated in Table~\ref{tab:f90inv}. + \item[info] Error code.\\ + Scope: {\bf local} \\ + Type: {\bf required} \\ + Intent: {\bf out}.\\ + An integer value; 0 means no error has been detected. +\end{description} %%% Local Variables: %%% mode: latex diff --git a/docs/src/toolsrout.tex b/docs/src/toolsrout.tex index 68554c40..95639b84 100644 --- a/docs/src/toolsrout.tex +++ b/docs/src/toolsrout.tex @@ -5,8 +5,7 @@ % %% psb_cdall %% % -\subsection*{psb\_cdall --- Allocates a communication descriptor} -\addcontentsline{toc}{subsection}{psb\_cdall} +\subsection{psb\_cdall --- Allocates a communication descriptor} \begin{verbatim} call psb_cdall(icontxt, desc_a, info,mg=mg,parts=parts) @@ -196,9 +195,8 @@ An integer value; 0 means no error has been detected. % %% psb_cdins %% % -\clearpage\subsection*{psb\_cdins --- Communication descriptor insert +\clearpage\subsection{psb\_cdins --- Communication descriptor insert routine} -\addcontentsline{toc}{subsection}{psb\_cdins} \begin{verbatim} call psb_cdins(nz, ia, ja, desc_a, info [,ila,jla]) @@ -292,9 +290,8 @@ nor the end vertex belong to the current process. % %% psb_cdasb %% % -\clearpage\subsection*{psb\_cdasb --- Communication descriptor assembly +\clearpage\subsection{psb\_cdasb --- Communication descriptor assembly routine} -\addcontentsline{toc}{subsection}{psb\_cdasb} \begin{verbatim} call psb_cdasb(desc_a, info [, mold]) @@ -334,14 +331,20 @@ An integer value; 0 means no error has been detected. \item On exit from this routine the descriptor is in the assembled state. \end{enumerate} - - +This call will set up all the necessary information for the halo data +exchanges. In doing so, the library will need to identify the set of +processes owning the halo indices through the use of the +\verb|desc%fnd_owner()| method; the owning processes are the +topological neighbours of the calling process. If the user has some +background information on the processes that are neighbours of the +current one, it is possible to specify explicitly the list of adjacent +processes with a call to \verb|desc%set_p_adjcncy(list)|; this will +speed up the subsequent call to \verb|psb_cdasb|. % %% psb_cdcpy %% % -\clearpage\subsection*{psb\_cdcpy --- Copies a communication descriptor} -\addcontentsline{toc}{subsection}{psb\_cdcpy} +\clearpage\subsection{psb\_cdcpy --- Copies a communication descriptor} \begin{verbatim} call psb_cdcpy(desc_in, desc_out, info) @@ -376,8 +379,7 @@ An integer value; 0 means no error has been detected. % %% psb_cdfree %% % -\clearpage\subsection*{psb\_cdfree --- Frees a communication descriptor} -\addcontentsline{toc}{subsection}{psb\_cdfree} +\clearpage\subsection{psb\_cdfree --- Frees a communication descriptor} \begin{verbatim} call psb_cdfree(desc_a, info) @@ -407,9 +409,8 @@ An integer value; 0 means no error has been detected. % %% psb_cdcpy %% % -\clearpage\subsection*{psb\_cdbldext --- Build an extended communication +\clearpage\subsection{psb\_cdbldext --- Build an extended communication descriptor} -\addcontentsline{toc}{subsection}{psb\_cdbldext} \begin{verbatim} call psb_cdbldext(a,desc_a,nl,desc_out, info, extype) @@ -477,9 +478,9 @@ An integer value; 0 means no error has been detected. %% % %% %% psb_cdren %% %% % -%% \subsection*{psb\_cdren --- Applies a renumeration to a +%% \subsection{psb\_cdren --- Applies a renumeration to a %% communication descriptor} -%% \addcontentsline{toc}{subsection}{psb\_cdren} +%%% \addcontentsline{toc}{subsection}{psb\_cdren} %% \syntax{call psb\_cdren}{trans, iperm, desc\_a, info} @@ -514,8 +515,7 @@ An integer value; 0 means no error has been detected. % %% psb_descprt %% % -%% \subsection*{psb\_cdprt --- Prints a descriptor} -%%\addcontentsline{toc}{subsection}{psb\_cdprt} +%% \subsection{psb\_cdprt --- Prints a descriptor} %% \syntax{call psb\_cdprt}{iout, desc\_a, glob, short} @@ -544,8 +544,7 @@ An integer value; 0 means no error has been detected. % %% psb_spalloc %% % -\clearpage\subsection*{psb\_spall --- Allocates a sparse matrix} -\addcontentsline{toc}{subsection}{psb\_spall} +\clearpage\subsection{psb\_spall --- Allocates a sparse matrix} \begin{verbatim} call psb_spall(a, desc_a, info, nnz) @@ -596,9 +595,8 @@ An integer value; 0 means no error has been detected. % %% psb_spins %% % -\clearpage\subsection*{psb\_spins --- Insert a set of coefficients into a sparse +\clearpage\subsection{psb\_spins --- Insert a set of coefficients into a sparse matrix} -\addcontentsline{toc}{subsection}{psb\_spins} \begin{verbatim} call psb_spins(nz, ia, ja, val, a, desc_a, info [,local]) @@ -723,8 +721,7 @@ An integer value; 0 means no error has been detected. % %% psb_spasb %% % -\clearpage\subsection*{psb\_spasb --- Sparse matrix assembly routine} -\addcontentsline{toc}{subsection}{psb\_spasb} +\clearpage\subsection{psb\_spasb --- Sparse matrix assembly routine} \begin{verbatim} call psb_spasb(a, desc_a, info, afmt, upd, dupl, mold) @@ -798,9 +795,8 @@ An integer value; 0 means no error has been detected. %% % %% %% psb_spcnv %% %% % -%% \subsection*{psb\_spcnv --- Converts a sparse matrix storage +%% \subsection{psb\_spcnv --- Converts a sparse matrix storage %% format} -%%\addcontentsline{toc}{subsection}{psb\_spcnv} %% \syntax{call psb\_spcnv}{a, b, desc\_a, info} @@ -833,8 +829,7 @@ An integer value; 0 means no error has been detected. % %% psb_spfree %% % -\clearpage\subsection*{psb\_spfree --- Frees a sparse matrix} -\addcontentsline{toc}{subsection}{psb\_spfree} +\clearpage\subsection{psb\_spfree --- Frees a sparse matrix} \begin{verbatim} call psb_spfree(a, desc_a, info) @@ -870,9 +865,8 @@ An integer value; 0 means no error has been detected. % %% psb_sprn %% % -\clearpage\subsection*{psb\_sprn --- Reinit sparse matrix structure for psblas +\clearpage\subsection{psb\_sprn --- Reinit sparse matrix structure for psblas routines.} -\addcontentsline{toc}{subsection}{psb\_sprn} \begin{verbatim} call psb_sprn(a, decsc_a, info, clear) @@ -914,8 +908,7 @@ An integer value; 0 means no error has been detected. % %% psb_spupdate %% % -%% \subsection*{psb\_spupdate --- Updates a sparse matrix.} -%%\addcontentsline{toc}{subsection}{psb\_spupdate} +%% \subsection{psb\_spupdate --- Updates a sparse matrix.} %% \syntax{call psb\_spupdate}{a, ia, ja, blck, desc\_a, info, ix, jx, updflag} @@ -929,9 +922,8 @@ An integer value; 0 means no error has been detected. %% % %% %% psb_csrp %% %% % -%% \subsection*{psb\_csrp --- Applies a right permutation to a sparse +%% \subsection{psb\_csrp --- Applies a right permutation to a sparse %% matrix} -%%\addcontentsline{toc}{subsection}{psb\_csrp} %% \syntax{call psb\_csrp}{trans, iperm, a, info} @@ -961,8 +953,8 @@ An integer value; 0 means no error has been detected. % %% psb_alloc %% % -\clearpage\subsection*{psb\_geall --- Allocates a dense matrix} -\addcontentsline{toc}{subsection}{psb\_geall} +\clearpage\subsection{psb\_geall --- Allocates a dense matrix} +%\addcontentsline{toc}{subsection}{psb\_geall} \begin{verbatim} call psb_geall(x, desc_a, info, n, lb) @@ -1009,8 +1001,8 @@ An integer value; 0 means no error has been detected. % %% psb_ins %% % -\clearpage\subsection*{psb\_geins --- Dense matrix insertion routine} -\addcontentsline{toc}{subsection}{psb\_geins} +\clearpage\subsection{psb\_geins --- Dense matrix insertion routine} +%\addcontentsline{toc}{subsection}{psb\_geins} \begin{verbatim} call psb_geins(m, irw, val, x, desc_a, info [,dupl,local]) @@ -1082,8 +1074,8 @@ An integer value; 0 means no error has been detected. % %% psb_asb %% % -\clearpage\subsection*{psb\_geasb --- Assembly a dense matrix} -\addcontentsline{toc}{subsection}{psb\_geasb} +\clearpage\subsection{psb\_geasb --- Assembly a dense matrix} +%\addcontentsline{toc}{subsection}{psb\_geasb} \begin{verbatim} call psb_geasb(x, desc_a, info, mold) @@ -1122,8 +1114,8 @@ An integer value; 0 means no error has been detected. % %% psb_free %% % -\clearpage\subsection*{psb\_gefree --- Frees a dense matrix} -\addcontentsline{toc}{subsection}{psb\_gefree} +\clearpage\subsection{psb\_gefree --- Frees a dense matrix} +%\addcontentsline{toc}{subsection}{psb\_gefree} \begin{verbatim} call psb_gefree(x, desc_a, info) @@ -1160,9 +1152,9 @@ An integer value; 0 means no error has been detected. % %% psb_gelp %% % -\clearpage\subsection*{psb\_gelp --- Applies a left permutation to a dense +\clearpage\subsection{psb\_gelp --- Applies a left permutation to a dense matrix} -\addcontentsline{toc}{subsection}{psb\_gelp} +%\addcontentsline{toc}{subsection}{psb\_gelp} \begin{verbatim} call psb_gelp(trans, iperm, x, info) @@ -1201,9 +1193,9 @@ An integer value; 0 means no error has been detected. % %% psb_glob_to_loc %% % -\clearpage\subsection*{psb\_glob\_to\_loc --- Global to local indices +\clearpage\subsection{psb\_glob\_to\_loc --- Global to local indices convertion} -\addcontentsline{toc}{subsection}{psb\_glob\_to\_loc} +%\addcontentsline{toc}{subsection}{psb\_glob\_to\_loc} \begin{verbatim} call psb_glob_to_loc(x, y, desc_a, info, iact,owned) @@ -1269,9 +1261,9 @@ An integer value; 0 means no error has been detected. \end{enumerate} -\clearpage\subsection*{psb\_loc\_to\_glob --- Local to global indices +\clearpage\subsection{psb\_loc\_to\_glob --- Local to global indices conversion} -\addcontentsline{toc}{subsection}{psb\_loc\_to\_glob} +%\addcontentsline{toc}{subsection}{psb\_loc\_to\_glob} \begin{verbatim} call psb_loc_to_glob(x, y, desc_a, info, iact) @@ -1326,8 +1318,8 @@ An integer value; 0 means no error has been detected. % %% psb_loc_to_glob %% % -\clearpage\subsection*{psb\_is\_owned --- } -\addcontentsline{toc}{subsection}{psb\_is\_owned } +\clearpage\subsection{psb\_is\_owned --- } +%\addcontentsline{toc}{subsection}{psb\_is\_owned } \begin{verbatim} call psb_is_owned(x, desc_a) @@ -1366,8 +1358,8 @@ Intent: {\bf out}.\\ \end{enumerate} -\clearpage\subsection*{psb\_owned\_index --- } -\addcontentsline{toc}{subsection}{psb\_owned\_index } +\clearpage\subsection{psb\_owned\_index --- } +%\addcontentsline{toc}{subsection}{psb\_owned\_index } \begin{verbatim} call psb_owned_index(y, x, desc_a, info) @@ -1418,8 +1410,8 @@ An integer value; 0 means no error has been detected. \end{enumerate} -\clearpage\subsection*{psb\_is\_local --- } -\addcontentsline{toc}{subsection}{psb\_is\_local } +\clearpage\subsection{psb\_is\_local --- } +%\addcontentsline{toc}{subsection}{psb\_is\_local } \begin{verbatim} call psb_is_local(x, desc_a) @@ -1457,8 +1449,8 @@ Intent: {\bf out}.\\ indices \end{enumerate} -\clearpage\subsection*{psb\_local\_index --- } -\addcontentsline{toc}{subsection}{psb\_local\_index } +\clearpage\subsection{psb\_local\_index --- } +%\addcontentsline{toc}{subsection}{psb\_local\_index } \begin{verbatim} call psb_local_index(y, x, desc_a, info) @@ -1513,9 +1505,9 @@ An integer value; 0 means no error has been detected. % %% psb_ins %% % -\clearpage\subsection*{psb\_get\_boundary --- Extract list of boundary +\clearpage\subsection{psb\_get\_boundary --- Extract list of boundary elements} -\addcontentsline{toc}{subsection}{psb\_get\_boundary} +%\addcontentsline{toc}{subsection}{psb\_get\_boundary} \begin{verbatim} call psb_get_boundary(bndel, desc, info) @@ -1556,9 +1548,9 @@ An integer value; 0 means no error has been detected. number of boundary elements. \end{enumerate} -\clearpage\subsection*{psb\_get\_overlap --- Extract list of overlap +\clearpage\subsection{psb\_get\_overlap --- Extract list of overlap elements} -\addcontentsline{toc}{subsection}{psb\_get\_overlap} +%\addcontentsline{toc}{subsection}{psb\_get\_overlap} \begin{verbatim} call psb_get_overlap(ovrel, desc, info) @@ -1600,9 +1592,9 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{psb\_sp\_getrow --- Extract row(s) from a sparse +\clearpage\subsection{psb\_sp\_getrow --- Extract row(s) from a sparse matrix} -\addcontentsline{toc}{subsection}{psb\_sp\_getrow} +%\addcontentsline{toc}{subsection}{psb\_sp\_getrow} \begin{verbatim} call psb_sp_getrow(row, a, nz, ia, ja, val, info, & @@ -1694,8 +1686,8 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{psb\_sizeof --- Memory occupation} -\addcontentsline{toc}{subsection}{psb\_sizeof} +\clearpage\subsection{psb\_sizeof --- Memory occupation} +%\addcontentsline{toc}{subsection}{psb\_sizeof} This function computes the memory occupation of a PSBLAS object. @@ -1733,8 +1725,8 @@ Returned as: an \verb|integer(psb_long_int_k_)| number. \end{description} -\clearpage\subsection*{Sorting utilities --- } -\addcontentsline{toc}{subsection}{Sorting utilities} +\clearpage\subsection{Sorting utilities --- } +%\addcontentsline{toc}{subsection}{Sorting utilities} {\par\noindent\large\bfseries psb\_msort --- Sorting by the Merge-sort algorithm} diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index a3a9c0bd..c98f7d75 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -25,7 +25,7 @@ \relax \pdfcompresslevel=0 %-- 0 = none, 9 = best \pdfinfo{ %-- Info dictionary of PDF output /Author (Alfredo Buttari) - /Title (Parallel Sparse BLAS V. 3.6.0) + /Title (Parallel Sparse BLAS V. 3.7.0) /Subject (Parallel Sparse Basic Linear Algebra Subroutines) /Keywords (Computer Science Linear Algebra Fluid Dynamics Parallel Linux MPI PSBLAS Iterative Solvers Preconditioners) /Creator (pdfLaTeX) @@ -88,7 +88,7 @@ \begin{document} -\pdfbookmark{PSBLAS-v3.6.0 User's Guide}{title} +\pdfbookmark{PSBLAS-v3.7.0 User's Guide}{title} \lstset{language=Fortran} \newlength{\centeroffset} \setlength{\centeroffset}{-0.5\oddsidemargin} @@ -98,7 +98,7 @@ \vspace*{\stretch{1}} \noindent\hspace*{\centeroffset}\makebox[0pt][l]{\begin{minipage}{\textwidth} \flushright -{\Huge\bfseries PSBLAS 3.6.0 User's guide +{\Huge\bfseries PSBLAS 3.7.0 User's guide } \noindent\rule[-1ex]{\textwidth}{5pt}\\[2.5ex] \hfill\emph{\Large A reference guide for the Parallel Sparse BLAS library} @@ -110,7 +110,7 @@ {\bfseries by Salvatore Filippone\\ and Alfredo Buttari}\\ -Dec 1st, 2018 +Jan 7th, 2020 \end{minipage}} %\addtolength{\textwidth}{\centeroffset} diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index dd21efbe..77f52d6f 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -8,7 +8,6 @@ bookmarksnumbered=true, bookmarksopen=false, plainpages=false, - pdfpagelabels, colorlinks, linkcolor=blue]{hyperref} \usepackage{ifthen} @@ -21,18 +20,6 @@ %\setboolean{mtc}{true} \pdfoutput=0 -% \relax -% \pdfcompresslevel=0 %-- 0 = none, 9 = best -% \pdfinfo{ %-- Info dictionary of PDF output /Author (Alfredo Buttari) -% /Title (Parallel Sparse BLAS V. 3.6.0) -% /Subject (Parallel Sparse Basic Linear Algebra Subroutines) -% /Keywords (Computer Science Linear Algebra Fluid Dynamics Parallel Linux MPI PSBLAS Iterative Solvers Preconditioners) -% /Creator (pdfLaTeX) -% /Producer ($Id: userguide.tex 1978 2007-10-19 14:51:12Z sfilippo $) -% } -% \pdfcatalog{ %-- Catalog dictionary of PDF output. -% /URI (http://ce.uniroma2.it/psblas) -% } \newcounter{subroutine}[subsection] \newcounter{example}[subroutine] @@ -93,9 +80,9 @@ Alfredo Buttari } \\ %\\[10ex] %\today -Software version: 3.6.0\\ +Software version: 3.7.0\\ %\today -Dec 1st, 2018 +Jan 7th, 2020 \cleardoublepage \begingroup \renewcommand*{\thepage}{toc} diff --git a/docs/src/util.tex b/docs/src/util.tex index 4d1ba295..fdd7d01d 100644 --- a/docs/src/util.tex +++ b/docs/src/util.tex @@ -9,9 +9,8 @@ module \verb|psb_util_mod|. %\subroutine{PSB\_HBIO\_MOD}{Input/Output in Harwell-Boeing format} -\clearpage\subsection*{ hb\_read --- Read a sparse matrix from a file in the +\clearpage\subsection{ hb\_read --- Read a sparse matrix from a file in the Harwell--Boeing format} -\addcontentsline{toc}{subsection}{hb\_read} \begin{lstlisting} @@ -53,9 +52,8 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{hb\_write --- Write a sparse matrix to a file +\clearpage\subsection{hb\_write --- Write a sparse matrix to a file in the Harwell--Boeing format} -\addcontentsline{toc}{subsection}{hb\_write} \begin{lstlisting} @@ -107,9 +105,8 @@ An integer value; 0 means no error has been detected. %\subroutine{PSB\_MMIO\_MOD}{Input/Output in MatrixMarket format} -\clearpage\subsection*{mm\_mat\_read --- Read a sparse matrix from a +\clearpage\subsection{mm\_mat\_read --- Read a sparse matrix from a file in the MatrixMarket format} -\addcontentsline{toc}{subsection}{mm\_mat\_read} \begin{lstlisting} call mm_mat_read(a, iret, iunit, filename) @@ -139,9 +136,8 @@ An integer value; 0 means no error has been detected. \end{description} -\clearpage\subsection*{mm\_array\_read --- Read a dense array from a +\clearpage\subsection{mm\_array\_read --- Read a dense array from a file in the MatrixMarket format} -\addcontentsline{toc}{subsection}{mm\_array\_read} \begin{lstlisting} call mm_array_read(b, iret, iunit, filename) @@ -174,9 +170,8 @@ An integer value; 0 means no error has been detected. -\clearpage\subsection*{mm\_mat\_write --- Write a sparse matrix to a +\clearpage\subsection{mm\_mat\_write --- Write a sparse matrix to a file in the MatrixMarket format} -\addcontentsline{toc}{subsection}{mm\_mat\_write} \begin{lstlisting} @@ -210,9 +205,8 @@ An integer value; 0 means no error has been detected. \end{description} -\clearpage\subsection*{mm\_array\_write --- Write a dense array from a +\clearpage\subsection{mm\_array\_write --- Write a dense array from a file in the MatrixMarket format} -\addcontentsline{toc}{subsection}{mm\_array\_write} \begin{lstlisting} call mm_array_write(b, iret, iunit, filename) diff --git a/krylov/psb_ccgstabl.f90 b/krylov/psb_ccgstabl.f90 index cbad3d91..4c6dc896 100644 --- a/krylov/psb_ccgstabl.f90 +++ b/krylov/psb_ccgstabl.f90 @@ -198,7 +198,7 @@ Subroutine psb_ccgstabl_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_ckrylov.f90 b/krylov/psb_ckrylov.f90 index 2aae7913..e9f12ea1 100644 --- a/krylov/psb_ckrylov.f90 +++ b/krylov/psb_ckrylov.f90 @@ -211,7 +211,8 @@ Subroutine psb_ckrylov_vect(method,a,prec,b,x,eps,desc_a,info,& if ((info==psb_success_).and.do_alloc_wrk) call prec%free_wrk(info) if(info /= psb_success_) then - call psb_errpush(info,name) + info = psb_err_from_subroutine_ + call psb_errpush(info,name,a_err=trim(method)) goto 9999 end if diff --git a/krylov/psb_crgmres.f90 b/krylov/psb_crgmres.f90 index 4f44b4db..9e20350f 100644 --- a/krylov/psb_crgmres.f90 +++ b/krylov/psb_crgmres.f90 @@ -209,7 +209,7 @@ subroutine psb_crgmres_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_dcgstabl.f90 b/krylov/psb_dcgstabl.f90 index ef57df92..ca8a6fe0 100644 --- a/krylov/psb_dcgstabl.f90 +++ b/krylov/psb_dcgstabl.f90 @@ -198,7 +198,7 @@ Subroutine psb_dcgstabl_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_dkrylov.f90 b/krylov/psb_dkrylov.f90 index 1f887299..a1fe405a 100644 --- a/krylov/psb_dkrylov.f90 +++ b/krylov/psb_dkrylov.f90 @@ -211,7 +211,8 @@ Subroutine psb_dkrylov_vect(method,a,prec,b,x,eps,desc_a,info,& if ((info==psb_success_).and.do_alloc_wrk) call prec%free_wrk(info) if(info /= psb_success_) then - call psb_errpush(info,name) + info = psb_err_from_subroutine_ + call psb_errpush(info,name,a_err=trim(method)) goto 9999 end if diff --git a/krylov/psb_drgmres.f90 b/krylov/psb_drgmres.f90 index 7bf72c6b..f30b3391 100644 --- a/krylov/psb_drgmres.f90 +++ b/krylov/psb_drgmres.f90 @@ -209,7 +209,7 @@ subroutine psb_drgmres_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_scgstabl.f90 b/krylov/psb_scgstabl.f90 index 82cbadc7..5c53781d 100644 --- a/krylov/psb_scgstabl.f90 +++ b/krylov/psb_scgstabl.f90 @@ -198,7 +198,7 @@ Subroutine psb_scgstabl_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_skrylov.f90 b/krylov/psb_skrylov.f90 index 2dc20812..e2c02732 100644 --- a/krylov/psb_skrylov.f90 +++ b/krylov/psb_skrylov.f90 @@ -211,7 +211,8 @@ Subroutine psb_skrylov_vect(method,a,prec,b,x,eps,desc_a,info,& if ((info==psb_success_).and.do_alloc_wrk) call prec%free_wrk(info) if(info /= psb_success_) then - call psb_errpush(info,name) + info = psb_err_from_subroutine_ + call psb_errpush(info,name,a_err=trim(method)) goto 9999 end if diff --git a/krylov/psb_srgmres.f90 b/krylov/psb_srgmres.f90 index 88443d3f..f6443c30 100644 --- a/krylov/psb_srgmres.f90 +++ b/krylov/psb_srgmres.f90 @@ -209,7 +209,7 @@ subroutine psb_srgmres_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_zcgstabl.f90 b/krylov/psb_zcgstabl.f90 index e2519fea..bcb4b652 100644 --- a/krylov/psb_zcgstabl.f90 +++ b/krylov/psb_zcgstabl.f90 @@ -198,7 +198,7 @@ Subroutine psb_zcgstabl_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/krylov/psb_zkrylov.f90 b/krylov/psb_zkrylov.f90 index 626499df..48371920 100644 --- a/krylov/psb_zkrylov.f90 +++ b/krylov/psb_zkrylov.f90 @@ -211,7 +211,8 @@ Subroutine psb_zkrylov_vect(method,a,prec,b,x,eps,desc_a,info,& if ((info==psb_success_).and.do_alloc_wrk) call prec%free_wrk(info) if(info /= psb_success_) then - call psb_errpush(info,name) + info = psb_err_from_subroutine_ + call psb_errpush(info,name,a_err=trim(method)) goto 9999 end if diff --git a/krylov/psb_zrgmres.f90 b/krylov/psb_zrgmres.f90 index 0d065c0a..73d7f08b 100644 --- a/krylov/psb_zrgmres.f90 +++ b/krylov/psb_zrgmres.f90 @@ -209,7 +209,7 @@ subroutine psb_zrgmres_vect(a,prec,b,x,eps,desc_a,info,& & ' not present: irst: ',irst,nl endif if (nl <=0 ) then - info=psb_err_invalid_istop_ + info=psb_err_invalid_irst_ err=info call psb_errpush(info,name,i_err=(/nl/)) goto 9999 diff --git a/prec/impl/psb_cprecinit.f90 b/prec/impl/psb_cprecinit.f90 index 7f6da35f..9f0b4d68 100644 --- a/prec/impl/psb_cprecinit.f90 +++ b/prec/impl/psb_cprecinit.f90 @@ -65,7 +65,7 @@ subroutine psb_cprecinit(ictxt,p,ptype,info) case default write(psb_err_unit,*) 'Unknown preconditioner type request "',ptype,'"' - info = psb_err_pivot_too_small_ + info = psb_err_invalid_preca_ end select if (info == psb_success_) call p%prec%precinit(info) diff --git a/prec/impl/psb_dprecinit.f90 b/prec/impl/psb_dprecinit.f90 index 70f7c05a..f28bd446 100644 --- a/prec/impl/psb_dprecinit.f90 +++ b/prec/impl/psb_dprecinit.f90 @@ -65,7 +65,7 @@ subroutine psb_dprecinit(ictxt,p,ptype,info) case default write(psb_err_unit,*) 'Unknown preconditioner type request "',ptype,'"' - info = psb_err_pivot_too_small_ + info = psb_err_invalid_preca_ end select if (info == psb_success_) call p%prec%precinit(info) diff --git a/prec/impl/psb_sprecinit.f90 b/prec/impl/psb_sprecinit.f90 index 46ab547a..fa5b83c2 100644 --- a/prec/impl/psb_sprecinit.f90 +++ b/prec/impl/psb_sprecinit.f90 @@ -65,7 +65,7 @@ subroutine psb_sprecinit(ictxt,p,ptype,info) case default write(psb_err_unit,*) 'Unknown preconditioner type request "',ptype,'"' - info = psb_err_pivot_too_small_ + info = psb_err_invalid_preca_ end select if (info == psb_success_) call p%prec%precinit(info) diff --git a/prec/impl/psb_zprecinit.f90 b/prec/impl/psb_zprecinit.f90 index 200e36dd..d9f5aa01 100644 --- a/prec/impl/psb_zprecinit.f90 +++ b/prec/impl/psb_zprecinit.f90 @@ -65,7 +65,7 @@ subroutine psb_zprecinit(ictxt,p,ptype,info) case default write(psb_err_unit,*) 'Unknown preconditioner type request "',ptype,'"' - info = psb_err_pivot_too_small_ + info = psb_err_invalid_preca_ end select if (info == psb_success_) call p%prec%precinit(info) diff --git a/test/pargen/psb_d_pde3d.f90 b/test/pargen/psb_d_pde3d.f90 index 60cb9e9e..429e9a0e 100644 --- a/test/pargen/psb_d_pde3d.f90 +++ b/test/pargen/psb_d_pde3d.f90 @@ -214,8 +214,7 @@ contains ! Note: integer control variables going directly into an MPI call ! must be 4 bytes, i.e. psb_mpk_ integer(psb_mpk_) :: npdims(3), npp, minfo - integer(psb_mpk_) :: npx,npy,npz, iamx,iamy,iamz - integer(psb_ipk_) :: mynx,myny,mynz + integer(psb_ipk_) :: npx,npy,npz, iamx,iamy,iamz,mynx,myny,mynz integer(psb_ipk_), allocatable :: bndx(:),bndy(:),bndz(:) ! Process grid integer(psb_ipk_) :: np, iam @@ -236,9 +235,8 @@ contains call psb_erractionsave(err_act) call psb_info(ictxt, iam, np) - call psb_cd_set_large_threshold(1000) - call psb_cd_set_maxspace(-1) - + + if (present(f)) then f_ => f else @@ -373,49 +371,7 @@ contains ! the set of global indices it owns. ! call psb_cdall(ictxt,desc_a,info,vl=myidx) - - block - ! - ! Test adjcncy methods - ! - integer(psb_mpk_), allocatable :: neighbours(:) - integer(psb_mpk_) :: cnt - logical, parameter :: debug_adj=.false. - if (debug_adj.and.(np > 1)) then - cnt = 0 - allocate(neighbours(np)) - if (iamx < npx-1) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx+1,iamy,iamz,npx,npy,npz,base=0) - end if - if (iamy < npy-1) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx,iamy+1,iamz,npx,npy,npz,base=0) - end if - if (iamz < npz-1) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx,iamy,iamz+1,npx,npy,npz,base=0) - end if - if (iamx >0) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx-1,iamy,iamz,npx,npy,npz,base=0) - end if - if (iamy >0) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx,iamy-1,iamz,npx,npy,npz,base=0) - end if - if (iamz >0) then - cnt = cnt + 1 - call ijk2idx(neighbours(cnt),iamx,iamy,iamz-1,npx,npy,npz,base=0) - end if - call psb_realloc(cnt, neighbours,info) - call desc_a%set_p_adjcncy(neighbours) - write(0,*) iam,' Check on neighbours: ',desc_a%get_p_adjcncy() - end if - end block - - case default write(psb_err_unit,*) iam, 'Initialization error: should not get here' info = -1 diff --git a/test/pargen/runs/ppde.inp b/test/pargen/runs/ppde.inp index 82f0bce6..a0f28e99 100644 --- a/test/pargen/runs/ppde.inp +++ b/test/pargen/runs/ppde.inp @@ -2,7 +2,7 @@ BICGSTAB Iterative method BICGSTAB CGS BICG BICGSTABL RGMRES FCG CGR BJAC Preconditioner NONE DIAG BJAC CSR Storage format for matrix A: CSR COO -040 Domain size (acutal system is this**3 (pde3d) or **2 (pde2d) ) +080 Domain size (acutal system is this**3 (pde3d) or **2 (pde2d) ) 3 Partition: 1 BLOCK 3 3D 2 Stopping criterion 1 2 0100 MAXIT