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psblas3/prec/impl/psb_z_invt_fact.f90

739 lines
22 KiB
Fortran

!
! Parallel Sparse BLAS version 3.5
! (C) Copyright 2006-2018
! Salvatore Filippone
! 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.
!
! Moved here from AMG4PSBLAS, original copyright below.
!
!
! AMG-AINV: Approximate Inverse plugin for
! AMG4PSBLAS version 1.0
!
! (C) Copyright 2020
!
! Salvatore Filippone University of Rome Tor Vergata
!
! 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 AMG4PSBLAS 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 AMG4PSBLAS 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_z_invt_bld(a,fillin,invfill,thresh,invthresh,&
& lmat,d,umat,desc,info,blck)
use psb_base_mod
use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_bld
use psb_z_ilu_fact_mod
implicit none
! Arguments
type(psb_zspmat_type), intent(in), target :: a
integer(psb_ipk_), intent(in) :: fillin,invfill
real(psb_dpk_), intent(in) :: thresh
real(psb_dpk_), intent(in) :: invthresh
type(psb_zspmat_type), intent(inout) :: lmat, umat
complex(psb_dpk_), allocatable :: d(:)
Type(psb_desc_type), Intent(inout) :: desc
integer(psb_ipk_), intent(out) :: info
type(psb_zspmat_type), intent(in), optional :: blck
!
integer(psb_ipk_) :: i, nztota, err_act, n_row, nrow_a, n_col
type(psb_zspmat_type) :: atmp
complex(psb_dpk_), allocatable :: pq(:), pd(:), w(:)
integer(psb_ipk_) :: debug_level, debug_unit
integer(psb_ipk_) :: ictxt,np,me
integer(psb_ipk_) :: nzrmax
real(psb_dpk_) :: sp_thresh
character(len=20) :: name, ch_err, fname
info = psb_success_
name='psb_zinvt_fact'
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 = psb_cd_get_context(desc)
call psb_info(ictxt, me, np)
if (debug_level >= psb_debug_outer_) &
& write(debug_unit,*) me,' ',trim(name),' start'
!
! Check the memory available to hold the incomplete L and U factors
! and allocate it if needed
!
nrow_a = a%get_nrows()
nztota = a%get_nzeros()
if (present(blck)) then
nztota = nztota + blck%get_nzeros()
end if
if (debug_level >= psb_debug_outer_) &
& write(debug_unit,*) me,' ',trim(name),&
& ': out get_nnzeros',nrow_a,nztota,&
& a%get_nrows(),a%get_ncols(),a%get_nzeros()
n_row = psb_cd_get_local_rows(desc)
n_col = psb_cd_get_local_cols(desc)
allocate(pd(n_row),w(n_row),stat=info)
if (info /= psb_success_) then
call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate')
goto 9999
end if
nzrmax = fillin
sp_thresh = thresh
call lmat%allocate(n_row,n_row,info,nz=nztota)
if (info == psb_success_) call umat%allocate(n_row,n_row,info,nz=nztota)
if (info == 0) call psb_ilut_fact(nzrmax,sp_thresh,&
& a,lmat,umat,pd,info,blck=blck,iscale=psb_ilu_scale_maxval_)
if (info == psb_success_) call atmp%allocate(n_row,n_row,info,nz=nztota)
if(info/=0) then
info=psb_err_from_subroutine_
ch_err='psb_sp_all'
call psb_errpush(info,name,a_err=ch_err)
goto 9999
end if
if (.false.) then
!!$ if (debug_level >= psb_debug_inner_) then
write(fname,'(a,i0,a)') 'invt-lo-',me,'.mtx'
call lmat%print(fname,head="INVTLOW")
write(fname,'(a,i0,a)') 'invt-up-',me,'.mtx'
call umat%print(fname,head="INVTUPP")
end if
!
! Compute the approx U^-1 and L^-1
!
nzrmax = invfill
call psb_zsparse_invt(n_row,umat,atmp,nzrmax,invthresh,info)
if (info == psb_success_) call psb_move_alloc(atmp,umat,info)
if (info == psb_success_) call lmat%transp()
if (info == psb_success_) call psb_zsparse_invt(n_row,lmat,atmp,nzrmax,invthresh,info)
if (info == psb_success_) call psb_move_alloc(atmp,lmat,info)
if (info == psb_success_) call lmat%transp()
! Done. Hopefully....
if (info /= psb_success_) then
info = psb_err_internal_error_
call psb_errpush(info,name,a_err='invt')
goto 9999
end if
call psb_move_alloc(pd,d,info)
call lmat%set_asb()
call lmat%trim()
call umat%set_asb()
call umat%trim()
if (debug_level >= psb_debug_outer_) &
& write(debug_unit,*) me,' ',trim(name),' end'
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
end subroutine psb_z_invt_bld
subroutine psb_zsparse_invt(n,a,z,nzrmax,sp_thresh,info)
use psb_base_mod
use psb_z_invt_fact_mod, psb_protect_name => psb_zsparse_invt
implicit none
integer(psb_ipk_), intent(in) :: n
type(psb_zspmat_type), intent(in) :: a
type(psb_zspmat_type), intent(inout) :: z
integer(psb_ipk_), intent(in) :: nzrmax
real(psb_dpk_), intent(in) :: sp_thresh
integer(psb_ipk_), intent(out) :: info
!
integer(psb_ipk_) :: i,j,k, err_act, nz, nzra, nzrz, ipz1,ipz2, nzz, ip1, ip2, l2
integer(psb_ipk_), allocatable :: ia(:), ja(:), iz(:),jz(:)
complex(psb_dpk_), allocatable :: zw(:), val(:), valz(:)
integer(psb_ipk_), allocatable :: uplevs(:), rowlevs(:),idxs(:)
complex(psb_dpk_), allocatable :: row(:)
type(psb_z_coo_sparse_mat) :: trw
type(psb_z_csr_sparse_mat) :: acsr, zcsr
integer(psb_ipk_) :: ktrw, nidx, nlw,nup,jmaxup
type(psb_i_heap) :: heap
real(psb_dpk_) :: alpha, nrmi
character(len=20) :: name='psb_sp_invt'
info = psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
if (.not.(a%is_triangle().and.a%is_unit().and.a%is_upper())) then
write(psb_err_unit,*) 'Wrong A '
info = psb_err_internal_error_
call psb_errpush(psb_err_internal_error_,name,a_err='wrong A')
goto 9999
end if
call a%cp_to(acsr)
call trw%allocate(izero,izero,ione)
if (info == psb_success_) allocate(zw(n),iz(n),valz(n),&
& row(n),rowlevs(n),stat=info)
if (info /= psb_success_) then
call psb_errpush(psb_err_from_subroutine_,name,a_err='Allocate')
goto 9999
end if
call zcsr%allocate(n,n,n*nzrmax)
call zcsr%set_triangle()
call zcsr%set_unit(.false.)
call zcsr%set_upper()
!
!
nzz = 0
row(:) = zzero
rowlevs(:) = 0
l2 = 0
zcsr%irp(1) = 1
outer: do i = 1, n-1
! ZW = e_i
call psb_z_invt_copyin(i,n,acsr,i,ione,n,nlw,nup,jmaxup,nrmi,row,&
& heap,rowlevs,ktrw,trw,info,sign=-done)
if (info /= 0) exit
row(i) = zone
! Adjust norm
if (nrmi < done) then
nrmi = sqrt(done + nrmi**2)
else
nrmi = nrmi*sqrt(zone+zone/(nrmi**2))
end if
call psb_invt_inv(sp_thresh,i,nrmi,row,heap,rowlevs,&
& acsr%ja,acsr%irp,acsr%val,nidx,idxs,info)
if (info /= 0) exit
!!$ write(0,*) 'Calling copyout ',nzrmax,nlw,nup,nidx,l2
call psb_z_invt_copyout(nzrmax,sp_thresh,i,n,nlw,nup,jmaxup,nrmi,row,&
& nidx,idxs,l2,zcsr%ja,zcsr%irp,zcsr%val,info)
if (info /= 0) exit
nzz = l2
end do outer
if (info /= psb_success_) then
info = psb_err_internal_error_
call psb_errpush(info,name,a_err='mainloop')
goto 9999
end if
ipz1 = nzz+1
call psb_ensure_size(ipz1,zcsr%val,info)
call psb_ensure_size(ipz1,zcsr%ja,info)
zcsr%val(ipz1) = zone
zcsr%ja(ipz1) = n
zcsr%irp(n+1) = ipz1+1
call z%mv_from(zcsr)
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
end subroutine psb_zsparse_invt
subroutine psb_z_invt_copyin(i,m,a,jd,jmin,jmax,nlw,nup,jmaxup,nrmi,row,heap,&
& irwt,ktrw,trw,info,sign)
use psb_base_mod
use psb_d_invt_fact_mod, psb_protect_name => psb_d_invt_copyin
implicit none
type(psb_z_csr_sparse_mat), intent(in) :: a
type(psb_z_coo_sparse_mat), intent(inout) :: trw
integer(psb_ipk_), intent(in) :: i, m,jmin,jmax,jd
integer(psb_ipk_), intent(inout) :: ktrw,nlw,nup,jmaxup,info
integer(psb_ipk_), intent(inout) :: irwt(:)
real(psb_dpk_), intent(inout) :: nrmi
complex(psb_dpk_), intent(inout) :: row(:)
type(psb_i_heap), intent(inout) :: heap
real(psb_dpk_), intent(in), optional :: sign
!
integer(psb_ipk_) :: k,j,irb,kin,nz, err_act
integer(psb_ipk_), parameter :: nrb=16
real(psb_dpk_) :: dmaxup, sign_
real(psb_dpk_), external :: dnrm2
character(len=20), parameter :: name='invt_copyin'
info = psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
call heap%init(info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_init_heap')
goto 9999
end if
sign_ = done
if (present(sign)) sign_ = sign
!
! nrmi is the norm of the current sparse row (for the time being,
! we use the 2-norm).
! NOTE: the 2-norm below includes also elements that are outside
! [jmin:jmax] strictly. Is this really important? TO BE CHECKED.
!
nlw = 0
nup = 0
jmaxup = 0
dmaxup = zzero
nrmi = zzero
do j = a%irp(i), a%irp(i+1) - 1
k = a%ja(j)
if ((jmin<=k).and.(k<=jmax)) then
row(k) = sign_ * a%val(j)
call heap%insert(k,info)
irwt(k) = 1
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end if
if (k<jd) nlw = nlw + 1
if (k>jd) then
nup = nup + 1
if (abs(row(k))>dmaxup) then
jmaxup = k
dmaxup = abs(row(k))
end if
end if
end do
nz = a%irp(i+1) - a%irp(i)
nrmi = dnrm2(nz,a%val(a%irp(i):),ione)
return
9999 call psb_error_handler(err_act)
return
end subroutine psb_z_invt_copyin
subroutine psb_z_invt_copyout(fill_in,thres,i,m,nlw,nup,jmaxup,nrmi,row, &
& nidx,idxs,l2,ja,irp,val,info)
use psb_base_mod
use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_copyout
implicit none
! Arguments
integer(psb_ipk_), intent(in) :: fill_in,i,m,nidx,nlw,nup,jmaxup
integer(psb_ipk_), intent(in) :: idxs(:)
integer(psb_ipk_), intent(inout) :: l2, info
integer(psb_ipk_), allocatable, intent(inout) :: ja(:),irp(:)
real(psb_dpk_), intent(in) :: thres,nrmi
complex(psb_dpk_),allocatable, intent(inout) :: val(:)
complex(psb_dpk_), intent(inout) :: row(:)
! Local variables
real(psb_dpk_),allocatable :: xw(:)
integer(psb_ipk_), allocatable :: xwid(:), indx(:)
real(psb_dpk_) :: witem, wmin
integer(psb_ipk_) :: widx
integer(psb_ipk_) :: k,isz,err_act,int_err(5),idxp, nz
type(psb_d_idx_heap) :: heap
character(len=20), parameter :: name='invt_copyout'
character(len=20) :: ch_err
logical :: fndmaxup
info = psb_success_
call psb_erractionsave(err_act)
if (psb_errstatus_fatal()) then
info = psb_err_internal_error_; goto 9999
end if
!
! Here we need to apply also the dropping rule base on the fill-in.
! We do it by putting into a heap the elements that are not dropped
! by using the 2-norm rule, and then copying them out.
!
! The heap goes down on the entry absolute value, so the first item
! is the largest absolute value.
!
!!$ write(0,*) 'invt_copyout ',nidx,nup+fill_in
call heap%init(info,dir=psb_asort_down_)
if (info == psb_success_) allocate(xwid(nidx),xw(nidx),indx(nidx),stat=info)
if (info /= psb_success_) then
info=psb_err_alloc_request_
call psb_errpush(info,name,i_err=(/3*nidx/),&
& a_err='real(psb_dpk_)')
goto 9999
end if
!
! First the lower part
!
nz = 0
idxp = 0
do
idxp = idxp + 1
if (idxp > nidx) exit
if (idxs(idxp) >= i) exit
widx = idxs(idxp)
witem = row(widx)
!
! Dropping rule based on the 2-norm
!
if (abs(witem) < thres*nrmi) cycle
nz = nz + 1
xw(nz) = witem
xwid(nz) = widx
call heap%insert(witem,widx,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end do
if (nz > 1) then
write(psb_err_unit,*) 'Warning: lower triangle from invt???? '
end if
if (idxp <= size(idxs)) then
if (idxs(idxp) < i) then
do
idxp = idxp + 1
if (idxp > nidx) exit
if (idxs(idxp) >= i) exit
end do
end if
end if
idxp = idxp - 1
nz = 0
wmin=HUGE(wmin)
if (.false.) then
do
idxp = idxp + 1
if (idxp > nidx) exit
widx = idxs(idxp)
if (widx < i) then
write(psb_err_unit,*) 'Warning: lower triangle in upper copy',widx,i,idxp,idxs(idxp)
cycle
end if
if (widx > m) then
cycle
end if
witem = row(widx)
!
! Dropping rule based on the 2-norm. But keep the jmaxup-th entry anyway.
!
if ((widx /= jmaxup) .and. (widx /= i) .and. (abs(witem) < thres*nrmi)) then
cycle
end if
if ((widx/=jmaxup).and.(nz > nup+fill_in)) then
if (abs(witem) < wmin) cycle
endif
wmin = min(abs(witem),wmin)
nz = nz + 1
xw(nz) = witem
xwid(nz) = widx
call heap%insert(witem,widx,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end do
!
! Now we have to take out the first nup-fill_in entries. But make sure
! we include entry jmaxup.
!
if (nz <= nup+fill_in) then
!
! Just copy everything from xw
!
fndmaxup=.true.
else
fndmaxup = .false.
nz = nup+fill_in
do k=1,nz
call heap%get_first(witem,widx,info)
xw(k) = witem
xwid(k) = widx
if (widx == jmaxup) fndmaxup=.true.
end do
end if
if ((i<jmaxup).and.(jmaxup<=m)) then
if (.not.fndmaxup) then
!
! Include entry jmaxup, if it is not already there.
! Put it in the place of the smallest coefficient.
!
xw(nz) = row(jmaxup)
xwid(nz) = jmaxup
endif
end if
else if (.true.) then
do
idxp = idxp + 1
if (idxp > nidx) exit
widx = idxs(idxp)
if (widx < i) then
write(psb_err_unit,*) 'Warning: lower triangle in upper copy',widx,i,idxp,idxs(idxp)
cycle
end if
if (widx > m) then
cycle
end if
witem = row(widx)
!
! Dropping rule based on the 2-norm. But keep the jmaxup-th entry anyway.
!
if ((widx /= i) .and. (abs(witem) < thres*nrmi)) then
cycle
end if
if (nz > nup+fill_in) then
if (abs(witem) < wmin) cycle
endif
wmin = min(abs(witem),wmin)
nz = nz + 1
xw(nz) = witem
xwid(nz) = widx
call heap%insert(witem,widx,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='psb_insert_heap')
goto 9999
end if
end do
!
! Now we have to take out the first nup-fill_in entries. But make sure
! we include entry jmaxup.
!
if (nz > nup+fill_in) then
nz = nup+fill_in
do k=1,nz
call heap%get_first(witem,widx,info)
xw(k) = witem
xwid(k) = widx
end do
end if
end if
!
! Now we put things back into ascending column order
!
call psb_msort(xwid(1:nz),indx(1:nz),dir=psb_sort_up_)
!
! Copy out the upper part of the row
!
do k=1,nz
l2 = l2 + 1
if (size(val) < l2) then
!
! Figure out a good reallocation size!
!
isz = max(int(1.2*l2),l2+100)
call psb_realloc(isz,val,info)
if (info == psb_success_) call psb_realloc(isz,ja,info)
if (info /= psb_success_) then
info=psb_err_from_subroutine_
call psb_errpush(info,name,a_err='Allocate')
goto 9999
end if
end if
ja(l2) = xwid(k)
val(l2) = xw(indx(k))
end do
!
! Set row to zero
!
do idxp=1,nidx
row(idxs(idxp)) = zzero
end do
irp(i+1) = l2 + 1
call psb_erractionrestore(err_act)
return
9999 call psb_error_handler(err_act)
return
end subroutine psb_z_invt_copyout
subroutine psb_z_invt_inv(thres,i,nrmi,row,heap,irwt,ja,irp,val,nidx,idxs,info)
use psb_base_mod
use psb_z_invt_fact_mod, psb_protect_name => psb_z_invt_inv
implicit none
! Arguments
type(psb_i_heap), intent(inout) :: heap
integer(psb_ipk_), intent(in) :: i
integer(psb_ipk_), intent(inout) :: nidx,info
integer(psb_ipk_), intent(inout) :: irwt(:)
real(psb_dpk_), intent(in) :: thres,nrmi
integer(psb_ipk_), allocatable, intent(inout) :: idxs(:)
integer(psb_ipk_), intent(in) :: ja(:),irp(:)
complex(psb_dpk_), intent(in) :: val(:)
complex(psb_dpk_), intent(inout) :: row(:)
! Local Variables
integer(psb_ipk_) :: k,j,jj,lastk,iret
real(psb_dpk_) :: rwk, alpha
info = psb_success_
call psb_ensure_size(200, idxs, info)
if (info /= psb_success_) return
nidx = 1
idxs(1) = i
lastk = i
irwt(i) = 1
!!$ write(0,*) 'Drop Threshold ',thres*nrmi
!
! Do while there are indices to be processed
!
do
call heap%get_first(k,iret)
if (iret < 0) exit
!
! An index may have been put on the heap more than once.
! Should not happen, but just in case.
!
if (k == lastk) cycle
lastk = k
!
! Dropping rule based on the threshold: compare the absolute
! value of each updated entry of row with thres * 2-norm of row.
!
rwk = row(k)
if (abs(rwk) < thres*nrmi) then
!
! Drop the entry.
!
row(k) = dzero
irwt(k) = 0
cycle
else
!
! Note: since U is scaled while copying it out (see ilut_copyout),
! we can use rwk in the update below.
!
do jj=irp(k),irp(k+1)-1
j = ja(jj)
if (j<=k) then
info = -i
return
endif
!
! Update row(j) and, if it is not to be discarded, insert
! its index into the heap for further processing.
!
row(j) = row(j) - rwk * val(jj)
if (irwt(j) == 0) then
if (abs(row(j)) < thres*nrmi) then
!
! Drop the entry.
!
row(j) = dzero
else
!
! Do the insertion.
!
call heap%insert(j,info)
if (info /= psb_success_) return
irwt(j) = 1
end if
end if
end do
end if
!
! If we get here it is an index we need to keep on copyout.
!
nidx = nidx + 1
call psb_ensure_size(nidx,idxs,info,addsz=psb_heap_resize)
if (info /= psb_success_) return
idxs(nidx) = k
irwt(k) = 0
end do
irwt(i) = 0
end subroutine psb_z_invt_inv