diff --git a/docs/Makefile b/docs/Makefile index b723f0d1..6ac24e64 100644 --- a/docs/Makefile +++ b/docs/Makefile @@ -1,7 +1,7 @@ all: guide guide: - cd src && $(MAKE) + cd src && $(MAKE) clean all doxy: - doxygen doxypsb \ No newline at end of file + doxygen doxypsb diff --git a/docs/html/dia-.png b/docs/html/dia-.png new file mode 100644 index 00000000..de7db919 Binary files /dev/null and b/docs/html/dia-.png differ diff --git a/docs/html/ell-.png b/docs/html/ell-.png new file mode 100644 index 00000000..31911882 Binary files /dev/null and b/docs/html/ell-.png differ diff --git a/docs/html/hdia-.png b/docs/html/hdia-.png new file mode 100644 index 00000000..08bfb5ff Binary files /dev/null and b/docs/html/hdia-.png differ diff --git a/docs/html/hll-.png b/docs/html/hll-.png new file mode 100644 index 00000000..219b751a Binary files /dev/null and b/docs/html/hll-.png differ diff --git a/docs/html/index.html b/docs/html/index.html index 7174fd18..becc711a 100644 --- a/docs/html/index.html +++ b/docs/html/index.html @@ -52,13 +52,13 @@ href="userhtmlse9.html#x14-1280009" id="QQ2-14-158">Utilities
 10 Preconditioner routines
 11 Iterative Methods +href="userhtmlse11.html#x17-14300011" id="QQ2-17-174">Iterative Methods
 12 Extensions +href="userhtmlse12.html#x19-14600012" id="QQ2-19-177">Extensions
 13 CUDA Environment Routines +href="userhtmlse13.html#x20-15500013" id="QQ2-20-192">CUDA Environment Routines
 References +href="userhtmlli2.html#x21-170000" id="QQ2-21-221">References diff --git a/docs/html/mat-.png b/docs/html/mat-.png new file mode 100644 index 00000000..d4f5c6f9 Binary files /dev/null and b/docs/html/mat-.png differ diff --git a/docs/html/userhtml.css b/docs/html/userhtml.css index 55445be8..7e85fe60 100644 --- a/docs/html/userhtml.css +++ b/docs/html/userhtml.css @@ -3,7 +3,6 @@ .pplb7t-x-x-172{font-size:172%;font-weight: bold;} .pplb7t-x-x-172{font-weight: bold;} .pplb7t-x-x-172{font-weight: bold;} -.pplb7t-x-x-172{font-weight: bold;} .pplri7t-{font-style: italic;} .pplri7t-{font-style: italic;} .pplri7t-x-x-120{font-size:120%;font-style: italic;} @@ -11,7 +10,6 @@ .pplb7t-{font-weight: bold;} .pplb7t-{font-weight: bold;} .pplb7t-{font-weight: bold;} -.pplb7t-{font-weight: bold;} .cmtt-10{font-family: monospace,monospace;} .cmtt-10{font-family: monospace,monospace;} .cmtt-10{font-family: monospace,monospace;} @@ -38,7 +36,6 @@ .pplb7t-x-x-120{font-size:120%;font-weight: bold;} .pplb7t-x-x-120{font-weight: bold;} .pplb7t-x-x-120{font-weight: bold;} -.pplb7t-x-x-120{font-weight: bold;} .cmtt-8{font-size:80%;font-family: monospace,monospace;} .cmtt-8{font-family: monospace,monospace;} .cmtt-8{font-family: monospace,monospace;} @@ -59,10 +56,6 @@ .zplmr7m-x-x-80{font-style: italic;} .zplmr7t-x-x-80{font-size:80%;} .pplrc7t-x-x-90{font-size:90%;} -.pplb7t-x-x-90{font-size:90%;font-weight: bold;} -.pplb7t-x-x-90{font-weight: bold;} -.pplb7t-x-x-90{font-weight: bold;} -.pplb7t-x-x-90{font-weight: bold;} .small-caps{font-variant: small-caps; } p{margin-top:0;margin-bottom:0} p.indent{text-indent:0;} @@ -200,11 +193,5 @@ pre.lstinputlisting{ font-family: monospace,monospace; white-space: pre-wrap; } #TBL-24-3{border-right:1px solid black;} #TBL-24-4{border-right:1px solid black;} #TBL-24-5{border-right:1px solid black;} -#TBL-25-1{border-left: 1px solid black;} -#TBL-25-1{border-right:1px solid black;} -#TBL-25-2{border-right:1px solid black;} -#TBL-25-3{border-right:1px solid black;} -#TBL-25-4{border-right:1px solid black;} -#TBL-25-5{border-right:1px solid black;} /* end css.sty */ diff --git a/docs/html/userhtml.html b/docs/html/userhtml.html index 7174fd18..becc711a 100644 --- a/docs/html/userhtml.html +++ b/docs/html/userhtml.html @@ -52,13 +52,13 @@ href="userhtmlse9.html#x14-1280009" id="QQ2-14-158">Utilities
 10 Preconditioner routines
 11 Iterative Methods +href="userhtmlse11.html#x17-14300011" id="QQ2-17-174">Iterative Methods
 12 Extensions +href="userhtmlse12.html#x19-14600012" id="QQ2-19-177">Extensions
 13 CUDA Environment Routines +href="userhtmlse13.html#x20-15500013" id="QQ2-20-192">CUDA Environment Routines
 References +href="userhtmlli2.html#x21-170000" id="QQ2-21-221">References diff --git a/docs/html/userhtmlli1.html b/docs/html/userhtmlli1.html index 1a48b7aa..77486e09 100644 --- a/docs/html/userhtmlli1.html +++ b/docs/html/userhtmlli1.html @@ -299,61 +299,61 @@ href="userhtmlse10.html#x15-13600010.1" id="QQ2-15-166">init — Initialize
  10.2 Set — set preconditioner parameters
  10.3 build — Builds a preconditioner +href="userhtmlse10.html#x15-13800010.3" id="QQ2-15-169">build — Builds a preconditioner
  10.4 apply — Preconditioner application routine +href="userhtmlse10.html#x15-13900010.4" id="QQ2-15-170">apply — Preconditioner application routine
  10.5 descr — Prints a description of current preconditioner +href="userhtmlse10.html#x15-14000010.5" id="QQ2-15-171">descr — Prints a description of current preconditioner
  10.6 clone — clone current preconditioner +href="userhtmlse10.html#x15-14100010.6" id="QQ2-15-172">clone — clone current preconditioner
  10.7 free — Free a preconditioner +href="userhtmlse10.html#x15-14200010.7" id="QQ2-15-173">free — Free a preconditioner
 11 Iterative Methods
  11.1 psb_krylov — Krylov Methods Driver Routine +href="userhtmlse11.html#x17-14400011.1" id="QQ2-17-175">psb_krylov — Krylov Methods Driver Routine
  11.2 psb_richardson — Richardson Iteration Driver Routine +href="userhtmlse11.html#x17-14500011.2" id="QQ2-17-176">psb_richardson — Richardson Iteration Driver Routine
 12 Extensions
  12.1 Using the extensions +href="userhtmlse12.html#x19-14700012.1" id="QQ2-19-178">Using the extensions
  12.2 Extensions’ Data Structures +href="userhtmlse12.html#x19-14800012.2" id="QQ2-19-179">Extensions’ Data Structures
  12.3 CPU-class extensions +href="userhtmlse12.html#x19-14900012.3" id="QQ2-19-182">CPU-class extensions
  12.4 CUDA-class extensions +href="userhtmlse12.html#x19-15400012.4" id="QQ2-19-191">CUDA-class extensions
 13 CUDA Environment Routines
  psb_cuda_init +href="userhtmlse13.html#Q1-20-194">psb_cuda_init
  psb_cuda_exit +href="userhtmlse13.html#Q1-20-196">psb_cuda_exit
  psb_cuda_DeviceSync +href="userhtmlse13.html#Q1-20-198">psb_cuda_DeviceSync
  psb_cuda_getDeviceCount +href="userhtmlse13.html#Q1-20-200">psb_cuda_getDeviceCount
  psb_cuda_getDevice +href="userhtmlse13.html#Q1-20-202">psb_cuda_getDevice
  psb_cuda_setDevice +href="userhtmlse13.html#Q1-20-204">psb_cuda_setDevice
  psb_cuda_DeviceHasUVA +href="userhtmlse13.html#Q1-20-206">psb_cuda_DeviceHasUVA
  psb_cuda_WarpSize +href="userhtmlse13.html#Q1-20-208">psb_cuda_WarpSize
  psb_cuda_MultiProcessors +href="userhtmlse13.html#Q1-20-210">psb_cuda_MultiProcessors
  psb_cuda_MaxThreadsPerMP +href="userhtmlse13.html#Q1-20-212">psb_cuda_MaxThreadsPerMP
  psb_cuda_MaxRegisterPerBlock +href="userhtmlse13.html#Q1-20-214">psb_cuda_MaxRegisterPerBlock
  psb_cuda_MemoryClockRate +href="userhtmlse13.html#Q1-20-216">psb_cuda_MemoryClockRate
  psb_cuda_MemoryBusWidth +href="userhtmlse13.html#Q1-20-218">psb_cuda_MemoryBusWidth
  psb_cuda_MemoryPeakBandwidth +href="userhtmlse13.html#Q1-20-220">psb_cuda_MemoryPeakBandwidth diff --git a/docs/html/userhtmlli2.html b/docs/html/userhtmlli2.html index 08bf60fc..953072ab 100644 --- a/docs/html/userhtmlli2.html +++ b/docs/html/userhtmlli2.html @@ -31,44 +31,52 @@ class="pplri7t-">for Forest Fires, in J. Dongarra, K.&#x

[2]   D. Bertaccini and S. Filippone, Sparse approximate + inverse preconditioners on high performance GPU platforms, Comput. Math. + Appl., 71, (2016), no. 3, 693–711. +

+

+ [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

- [3]      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.

- [4]      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.

- [5]      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. + + +

- [6]      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). - - -

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

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

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

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

- [11]      S. Filippone, P. D’Ambra, M. Colajanni, Using a Parallel Library of Clusters, in G. Joubert, A. Murli, College Press, 2002.

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

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

- [14]      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. - - -

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

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

- [17]      Metcalf, M., Reid, J. and Cohen, M. Modern Fortran explained. Oxford University Press, 2011.

- [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.

- [20]      D. Barbieri, V. Cardellini, S. Filippone and D. Rouson Design Patterns for Scientific Computations @@ -179,7 +187,7 @@ class="pplri7t-">on Sparse Matrices, HPSS 2011, Algorithms and Pro 2011

- [21]       Cardellini, V., Filippone, S., and Rouson, D. 2014, Design patterns for sparse-matrix computations on hybrid CPU/GPU platforms, Scientific @@ -187,11 +195,21 @@ class="pplri7t-">Scientific class="pplri7t-">Programming 22, 1, 1–19.

+ + +

- [22]      D. Barbieri, V. Cardellini, A. Fanfarillo, S. Filippone, Three storage formats for sparse matrices on GPGPUs, Tech. Rep. DICII RR-15.6, Universit di Roma Tor Vergata (February 2015). +

+

+ [24]   S. Filippone, V. Cardellini, D. Barbieri, and A. Fanfarillo. Sparse + matrix-vector multiplication on GPGPUs. ACM Trans. Math. Softw., + 43(4):30:1–30:49, 2017.

diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index 3c051ada..d442f68e 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -28,35 +28,35 @@ 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 [16] +href="userhtmlli2.html#Xmetcalf">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 [10]; other works discussing advanced programming in +href="userhtmlli2.html#XSparse03">11]; other works discussing advanced programming in Fortran 2003 include [2018]; sufficient support for Fortran 2003 is now available +href="userhtmlli2.html#XDesPat:11">21, 19]; 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. [15]. Moreover, the Fortran 95 facilities for dynamic memory +href="userhtmlli2.html#Xmachiels">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 [78], which in its turn is based on the proposal for +href="userhtmlli2.html#Xsblas97">8, 9], which in its turn is based on the proposal for BLAS on dense matrices [1445]. +href="userhtmlli2.html#XBLAS1">15, 56].

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 diff --git a/docs/html/userhtmlse10.html b/docs/html/userhtmlse10.html index 0ba3cd87..6968240e 100644 --- a/docs/html/userhtmlse10.html +++ b/docs/html/userhtmlse10.html @@ -101,7 +101,7 @@ class="pplb7t-">inout.
Specified as: a preconditioner data structure psb_prec_Tprec_type. @@ -144,14 +144,12 @@ class="zplmr7m-">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.

+

Precondition by a factorization or an approximante inverse of the + block-diagonal of matrix A, where block boundaries are determined + by the data allocation boundaries for each process; requires no + communication. See also Table-21. @@ -159,13 +157,13 @@ class="zplmr7t-">) is currently implemented. id="x15-13700010.2">Set — set preconditioner parameters

-

-

call p%set(what,val,info)

-

This method sets the parameters defining the subdomain solver when the +

+

call p%set(what,val,info) +

This method sets the parameters defining the subdomain solver when the preconditioner type is BJAC. More precisely, the parameter identified by what is assigned the value contained in val. -

Arguments

Arguments id="TBL-23-1"> +class="td11">

what

+class="td11">

+class="td11">

info

what

character(len=*).

character(len=*).

The parameter to be set. It can be specified through its name; the string is -case-insensitive. See Tables ??-22.

The parameter to be set. It can be specified through its name; the string is +case-insensitive. See Table 21.

val

integer

val

integer or character(len=*) or real(psb_spk_) or real(psb_dpk_), intent(in).

The value of the parameter to be set. The list of allowed values and the -corresponding data types is given in Tables ??-22. When the value is of type +class="td11">

The value of the parameter to be set. The list of allowed values and the +corresponding data types is given in Table 21. When the value is of type character(len=*), it is also treated as case insensitive.

info

integer, intent(out).

integer, intent(out).

Error code. If no error, 0 is returned. See Section ?? for details.

-

A number of subdomain solvers can be chosen with this method; a list of the +class="td11">

Error code. If no error, 0 is returned. See Section 8 for details. +

A number of subdomain solvers can be chosen with this method; a list of the parameters that can be set, along with their allowed and default values, is given in -Tables ??-22.
21.

-


@@ -225,7 +220,7 @@ class="newline" />
-

+

s +class="pplr7t-x-x-90">.





what

what

da type

val

e

val

dfault

t

cments






SUB_SOLVE

character(len=*)

SUB_SOLVE

character(len=*)

ILU

ILUT

INVT

INVK -

AINV

AINV

The local solver to be used with the smoother +class="pplr7t-x-x-90">The local solver to be used with the smoother or one-level preconditioner ILU(p, t), Approximate Inverses +class="pplr7t-x-x-90">Approximate Inverses INVK(p, q), INVT(), INVT(p1, 1, t2) and AINV() and AINV(t); note that approximate inverses are specifically +class="pplr7t-x-x-90">note that approximate inverses are specifically suited for GPUs since they do not employ +class="pplr7t-x-x-90">suited for GPUs since they do not employ triangular system solve kernels, see [?[2].











-
Table 21: Parameters defining the solver or the details of the one-level -preconditioner.
- - - -

-
-
- - - -


- - - -
-

-

+ + + + +





what

data type

val

default

comments






SUB_FILLIN

integer

SUB_FILLIN

integer

Any integer -

number 0

0

0

0

Fill-in level p of the incomplete LU @@ -410,19 +338,19 @@ class="pplr7t-x-x-90">of the incomplete LU class="pplr7t-x-x-90">factorizations.






SUB_ILUTHRS

real(kind_parameter)

SUB_ILUTHRS

real(kind_parameter)

Any real number 0

0

0

0

Drop tolerance t in the ILU(, t) factorization.











ILU_ALG

character(len=*)

MILU

NONE

ILU algorithmic variant






ILUT_SCALE

character(len=*)

MAXVAL +

DIAG +

ARSWUM +

ARCSUM +

ACLSUM +

NONE

NONE

ILU scaling strategy






INV_FILLIN

integer

Any integer +

number 0

0

Second fill-in level q of the INVK(p, q) +approximate inverse.






INV_ILUTHRS

real(kind_parameter)

Any real +number 0

0

Second drop tolerance s in the INVT(t, s) +approximate inverse.






AINV_ALG

character(len=*)

LLK +

SYM-LLK +

STAB-LLK +

MLK,LMX

LLK

AINV algorithmic strategy.







Table 22: Parameters defining the smoother or the details of the one-level -preconditioner (continued).
+>Table 21: Parameters defining the solver of the BJAC preconditioner.
@@ -455,26 +464,26 @@ preconditioner (continued).
 call prec%build(a, desc_a, info[,amold,vmold,imold])
 
-

-

+

+

-

+

Type:

-

Synchronous. +

Synchronous.

-

+

On Entry

-

+

-

+

a

-

the system sparse matrix. Scope:

the system sparse matrix. Scope: local
Type: required
psb_Tspmat_type.

-

+

prec

-

the preconditioner.

the preconditioner.
Scope: local
Type: Specified as: an already initialized precondtioner psb_prec_Tprec_type

-

+

desc_a

-

the problem communication descriptor. Scope:

the problem communication descriptor. Scope: local
Type: required
psb_desc_type.

-

+

amold

-

The desired dynamic type for the internal matrix storage.

The desired dynamic type for the internal matrix storage.
Scope: local.
Type: _base_sparse_mat.

-

+

vmold

-

The desired dynamic type for the internal vector storage.

The desired dynamic type for the internal vector storage.
Scope: local.
Type: _base_vect_type.

-

+

imold

-

The desired dynamic type for the internal integer vector storage.

The desired dynamic type for the internal integer vector storage.
Scope: local.
Type: _T_base_vect_type.

-

+

-

+

On Return

-

+

-

+

prec

-

the preconditioner.

the preconditioner.
Scope: local
Type: inout.
Specified as: a precondtioner data structure psb_prec_Tprec_type

-

+

info

-

Error code.

Error code.
Scope: local
Type: An integer value; 0 means no error has been detected.

The

The amold, vmold and imold arguments may be employed to interface with special @@ -640,26 +649,26 @@ devices, such as GPUs and other accelerators. call prec%apply(x,y,desc_a,info,trans,work) call prec%apply(x,desc_a,info,trans) -

-

+

+

-

+

Type:

-

Synchronous. +

Synchronous.

-

+

On Entry

-

+

-

+

prec

-

the preconditioner. Scope:

the preconditioner. Scope: local
Type: required
in.
Specified as: a preconditioner data structure psb_prec_Tprec_type.

-

+

x

-

the source vector. Scope:

the source vector. Scope: local
Type: required
_T_vect_type.

-

+

desc_a

-

the problem communication descriptor. Scope:

the problem communication descriptor. Scope: local
Type: required
psb_desc_type.

-

+

trans

-

Scope:

Scope:
Type: optional
Intent: Specified as: a character.

-

+

work

-

an optional work space Scope:

an optional work space Scope: local
Type: optional
Intent: inout.
Specified as: a double precision array.

-

+

-

+

On Return

-

+

-

+

y

-

the destination vector. Scope:

the destination vector. Scope: local
Type: required
_T_vect_type.

-

+

info

-

Error code.

Error code.
Scope: local
Type: An integer value; 0 means no error has been detected.

-

-

+

+

-

+

Type:

-

Asynchronous. +

Asynchronous.

-

+

On Entry

-

+

-

+

prec

-

the preconditioner. Scope:

the preconditioner. Scope: local
Type: required
in.
Specified as: a preconditioner data structure psb_prec_Tprec_type.

-

+

iout

-

output unit. Scope:

output unit. Scope: local
Type: optional
Intent: in.
Specified as: an integer number. Default: default output unit.

-

+

root

-

Process from which to print Scope:

Process from which to print Scope: local
Type: optional
- 1, in which case class="zplmr7y-">-1, in which case all processes will print. Default: 0.

-

+

On Return

-

+

-

+

info

-

Error code.

Error code.
Scope: local
Type: An integer value; 0 means no error has been detected.

call  prec%clone(precout,info) -

-

+

+

-

+

Type:

-

Asynchronous. +

Asynchronous.

-

+

On Entry

-

+

-

+

prec

-

the preconditioner.

the preconditioner.
Scope: local.

-

+

-

+

On Return

-

+

-

+

precout

-

A copy of the input object. +

A copy of the input object.

-

+

info

-

Return code.

+

Return code. @@ -924,26 +933,26 @@ class="description">

 call prec%free(info)
 
-

-

+

+

-

+

Type:

-

Asynchronous. +

Asynchronous.

-

+

On Entry

-

+

-

+

prec

-

the preconditioner.

the preconditioner.
Scope: local.
Type: inout.
Specified as: a preconditioner data structure psb_prec_Tprec_type.

-

+

On Exit

-

+

-

+

prec

-

Scope:

Scope: local
Type: required
inout.
Specified as: a preconditioner data structure psb_prec_Tprec_type.

-

+

info

-

Scope:

Scope: global
Type: required
Intent: out.
Error code: if no error, 0 is returned.

-

Notes Releases all internal storage. diff --git a/docs/html/userhtmlse11.html b/docs/html/userhtmlse11.html index 460347a4..bd2de1e4 100644 --- a/docs/html/userhtmlse11.html +++ b/docs/html/userhtmlse11.html @@ -82,7 +82,7 @@ iteration. -

call psb_krylovin.
Specified as: a structured data of type psb_prec_Tprec_type.

@@ -524,7 +524,7 @@ class="zplmr7m-x-x-76">i the corresponding residual at the i-th iteration. -

call psb_richardsonin.
Specified as: a structured data of type psb_prec_Tprec_type.

diff --git a/docs/html/userhtmlse12.html b/docs/html/userhtmlse12.html index d5ab2548..70b3b138 100644 --- a/docs/html/userhtmlse12.html +++ b/docs/html/userhtmlse12.html @@ -42,11 +42,11 @@ class="cmtt-10">http://sourceforge.net/projects/librsb/, for comput multicore parallel machines.

The infrastructure laid out in the base library to allow for these extensions is detailed in the references [202110]; the CUDA-specific data formats are described +href="userhtmlli2.html#XDesPat:11">21, 2211]; the CUDA-specific data formats are described in [22]. +href="userhtmlli2.html#XOurTechRep">23].

12.1 Using the extensions

@@ -149,120 +149,120 @@ the base classes in PSBLAS, through the Fortran 2003 mechanism of type extension [17]. +href="userhtmlli2.html#XMRC:11">18].

The data classes are divided between the general purpose CPU extensions, the GPU interfaces and the RSB interfaces. In the description we will make use of the notation introduced in Table 23. +href="#x19-148001r22">22.



Table 23: Notation for parameters describing a sparse matrix
+>Table 22: Notation for parameters describing a sparse matrix

-



Name Name Description


M M Number of rows in matrix
N N Number of columns in matrix
NZ NZ Number of nonzeros in matrix
AVGNZR AVGNZR Average number of nonzeros per row
MAXNZRMAXNZRMaximum number of nonzeros per row
NDIAG NDIAG Numero of nonzero diagonals
AS AS Coefficients array
IA IA Row indices array
JA JA Column indices array
IRP IRP Row start pointers array
JCP JCP Column start pointers array
NZR NZR Number of nonzeros per row array
OFFSET OFFSET Offset for diagonals


@@ -343,7 +343,7 @@ href="#x19-148002r5">5
-
  up] 

psb_cuda_init — Initializes PSBLAS-CUDA environment

+ id="Q1-20-194">

@@ -70,7 +70,7 @@ class="pplb7t-x-x-120">Notes

psb_cuda_exit — Exit from PSBLAS-CUDA environment

+ id="Q1-20-196">

@@ -108,7 +108,7 @@ class="newline" />Specified as: an integer variable.

psb_cuda_DeviceSync — Synchronize CUDA device

+ id="Q1-20-198"> @@ -125,7 +125,7 @@ CUDA-side code, have completed.

psb_cuda_getDeviceCount

+ id="Q1-20-200">

@@ -138,7 +138,7 @@ ngpus =  psb_cuda_getDeviceCount()

psb_cuda_getDevice

+ id="Q1-20-202">

@@ -154,7 +154,7 @@ ngpus =  psb_cuda_getDevice()

psb_cuda_setDevice

+ id="Q1-20-204">

@@ -167,7 +167,7 @@ info = psb_cuda_setDevice(dev)

psb_cuda_DeviceHasUVA

+ id="Q1-20-206">

@@ -180,7 +180,7 @@ hasUva = psb_cuda_DeviceHasUVA()

psb_cuda_WarpSize

+ id="Q1-20-208">

@@ -196,7 +196,7 @@ nw = psb_cuda_WarpSize()

psb_cuda_MultiProcessors

+ id="Q1-20-210">

@@ -209,7 +209,7 @@ nmp = psb_cuda_MultiProcessors()

psb_cuda_MaxThreadsPerMP

+ id="Q1-20-212">

@@ -222,7 +222,7 @@ nt = psb_cuda_MaxThreadsPerMP()

psb_cuda_MaxRegistersPerBlock

+ id="Q1-20-214">

@@ -238,7 +238,7 @@ nr = psb_cuda_MaxRegistersPerBlock()

psb_cuda_MemoryClockRate

+ id="Q1-20-216">

@@ -251,7 +251,7 @@ cl = psb_cuda_MemoryClockRate()

psb_cuda_MemoryBusWidth

+ id="Q1-20-218">

@@ -264,7 +264,7 @@ nb = psb_cuda_MemoryBusWidth()

psb_cuda_MemoryPeakBandwidth

+ id="Q1-20-220">

@@ -282,6 +282,10 @@ bw = psb_cuda_MemoryPeakBandwidth() +

+ + + diff --git a/docs/html/userhtmlse2.html b/docs/html/userhtmlse2.html index f9fb994e..7ef19577 100644 --- a/docs/html/userhtmlse2.html +++ b/docs/html/userhtmlse2.html @@ -35,7 +35,7 @@ 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 [6]. Usually there is no need to deal +href="userhtmlli2.html#XBLACS">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. 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 [13]. Dense vectors conform to sparse matrices, +href="userhtmlli2.html#XMETIS">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 @@ -164,8 +164,8 @@ class="description">

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 [32]. +href="userhtmlli2.html#X2007c">4, 3].

We denote the sets of internal, boundary and halo points for a given subdomain by _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 [12] as detailed in [10]; the type declaration is shown in figure 13] as detailed in [11]; the type declaration is shown in figure 2 where T is a placeholder for the data type and precision variants

diff --git a/docs/html/userhtmlse6.html b/docs/html/userhtmlse6.html index 382f28d3..9369ac6f 100644 --- a/docs/html/userhtmlse6.html +++ b/docs/html/userhtmlse6.html @@ -3843,7 +3843,7 @@ class="pplb7t-">in.
Specified as: a preconditioner data structure psb_prec_Tprec_type. diff --git a/docs/html/zplmr7y-42.png b/docs/html/zplmr7y-42.png new file mode 100644 index 00000000..1879254d Binary files /dev/null and b/docs/html/zplmr7y-42.png differ diff --git a/docs/html/zplmr7y-48.png b/docs/html/zplmr7y-48.png new file mode 100644 index 00000000..a3d208c1 Binary files /dev/null and b/docs/html/zplmr7y-48.png differ diff --git a/docs/html/zplmr7y-49.png b/docs/html/zplmr7y-49.png new file mode 100644 index 00000000..230ddcab Binary files /dev/null and b/docs/html/zplmr7y-49.png differ diff --git a/docs/psblas-3.9.pdf b/docs/psblas-3.9.pdf index 3779ddf4..4cb1ebcb 100644 --- a/docs/psblas-3.9.pdf +++ b/docs/psblas-3.9.pdf @@ -3318,40 +3318,40 @@ BT 0 g 0 G [-970(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(155)]TJ + [-1000(154)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(10.4)-550(apply)-250(\227)-250(Pr)18(econditioner)-250(application)-250(r)18(outine)]TJ 0 g 0 G [-421(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(157)]TJ + [-1000(156)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(10.5)-550(descr)-250(\227)-250(Prints)-250(a)-250(description)-250(of)-250(curr)18(ent)-250(pr)18(econditioner)]TJ 0 g 0 G [-350(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(158)]TJ + [-1000(157)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(10.6)-550(clone)-250(\227)-250(clone)-250(curr)18(ent)-250(pr)18(econditioner)]TJ 0 g 0 G [-260(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(159)]TJ + [-1000(158)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.956 Td [(10.7)-550(fr)18(ee)-250(\227)-250(Fr)18(ee)-250(a)-250(pr)18(econditioner)]TJ 0 g 0 G [-341(.)-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 - [-1000(160)]TJ + [-1000(159)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F75 9.9626 Tf -14.944 -21.917 Td [(11)-500(Iterative)-250(Methods)]TJ 0 g 0 G - [-23362(161)]TJ + [-23362(160)]TJ 0 0 1 rg 0 0 1 RG /F84 9.9626 Tf 14.944 -11.956 Td [(11.1)-520(psb)]TJ ET @@ -3364,7 +3364,7 @@ BT 0 g 0 G [-746(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(162)]TJ + [-1000(161)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -41.922 -11.955 Td [(11.2)-520(psb)]TJ @@ -3378,44 +3378,44 @@ BT 0 g 0 G [-839(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(165)]TJ + [-1000(164)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F75 9.9626 Tf -56.866 -21.918 Td [(12)-500(Extensions)]TJ 0 g 0 G - [-26557(168)]TJ + [-26557(167)]TJ 0 0 1 rg 0 0 1 RG /F84 9.9626 Tf 14.944 -11.955 Td [(12.1)-550(Using)-250(the)-250(extensions)]TJ 0 g 0 G [-783(.)-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 - [-1000(168)]TJ + [-1000(167)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(12.2)-550(Extensions')-250(Data)-250(Str)8(uctur)18(es)]TJ 0 g 0 G [-797(.)-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 - [-1000(169)]TJ + [-1000(168)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(12.3)-550(CPU-class)-250(extensions)]TJ 0 g 0 G [-544(.)-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 - [-1000(169)]TJ + [-1000(168)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG 0 -11.955 Td [(12.4)-550(CUDA-class)-250(extensions)]TJ 0 g 0 G [-346(.)-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 - [-1000(176)]TJ + [-1000(175)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG /F75 9.9626 Tf -14.944 -21.918 Td [(13)-500(CUDA)-250(Environment)-250(Routines)]TJ 0 g 0 G - [-17779(177)]TJ + [-17779(176)]TJ 0 0 1 rg 0 0 1 RG /F84 9.9626 Tf 14.944 -11.955 Td [(psb)]TJ ET @@ -3435,7 +3435,7 @@ BT 0 g 0 G [-304(.)-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(.)]TJ 0 g 0 G - [-1000(177)]TJ + [-1000(176)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3456,7 +3456,7 @@ BT 0 g 0 G [-932(.)-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 0 g 0 G - [-1000(177)]TJ + [-1000(176)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.956 Td [(psb)]TJ @@ -3477,7 +3477,7 @@ BT 0 g 0 G [-405(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3498,7 +3498,7 @@ BT 0 g 0 G [-635(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3519,7 +3519,7 @@ BT 0 g 0 G [-401(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3540,7 +3540,7 @@ BT 0 g 0 G [-533(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3561,7 +3561,7 @@ BT 0 g 0 G [-839(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3582,7 +3582,7 @@ BT 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(.)]TJ 0 g 0 G - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.956 Td [(psb)]TJ @@ -3603,7 +3603,7 @@ BT 0 g 0 G [-674(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3624,7 +3624,7 @@ BT 0 g 0 G [-718(.)-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 - [-1000(178)]TJ + [-1000(177)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3645,7 +3645,7 @@ BT 0 g 0 G [-538(.)-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 - [-1000(179)]TJ + [-1000(178)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3666,7 +3666,7 @@ BT 0 g 0 G [-970(.)-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 - [-1000(179)]TJ + [-1000(178)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3687,7 +3687,7 @@ BT 0 g 0 G [-346(.)-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 - [-1000(179)]TJ + [-1000(178)]TJ 0 g 0 G 0 0 1 rg 0 0 1 RG -44.393 -11.955 Td [(psb)]TJ @@ -3708,7 +3708,7 @@ BT 0 g 0 G [-652(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)-500(.)]TJ 0 g 0 G - [-1000(179)]TJ + [-1000(178)]TJ 0 g 0 G 0 g 0 G 108.254 -169.365 Td [(iv)]TJ @@ -4536,43 +4536,43 @@ stream BT /F75 14.3462 Tf 99.895 705.784 Td [(1)-1000(Introduction)]TJ/F84 9.9626 Tf 1.009 0 0 1 99.587 682.871 Tm [(The)-247(PSBLAS)-247(library)110(,)-247(developed)-246(with)-247(the)-247(aim)-247(to)-247(facilitate)-246(the)-247(parallelization)-247(of)]TJ 0.98 0 0 1 99.895 670.916 Tm [(computationally)-246(intensive)-247(scienti\002c)-246(applications,)-248(is)-246(designed)-247(to)-246(addr)18(ess)-246(parallel)]TJ 1.02 0 0 1 99.895 658.961 Tm [(implementation)-250(of)-250(iterative)-251(solvers)-250(for)-250(sparse)-250(linear)-250(systems)-251(thr)18(ough)-250(the)-250(dis-)]TJ 0.98 0 0 1 99.895 647.006 Tm [(tributed)-232(memory)-232(paradigm.)-309(It)-232(includes)-232(r)18(outines)-232(for)-232(multiplying)-232(sparse)-232(matrices)]TJ 1.02 0 0 1 99.895 635.051 Tm [(by)-305(dense)-305(matrices,)-320(solving)-305(block)-305(diagonal)-305(systems)-306(with)-305(triangular)-305(diagonal)]TJ 1.02 0 0 1 99.895 623.095 Tm [(entries,)-366(pr)18(epr)18(ocessing)-342(sparse)-342(matrices,)-365(and)-342(contains)-342(additional)-341(r)17(outines)-341(for)]TJ 1.015 0 0 1 99.895 611.14 Tm [(dense)-245(matrix)-244(operations.)-305(The)-245(curr)18(ent)-245(implementation)-244(of)-245(PSBLAS)-244(addr)17(esses)-244(a)]TJ 1 0 0 1 99.895 599.185 Tm [(distributed)-250(memory)-250(execution)-250(model)-250(operating)-250(with)-250(message)-250(passing.)]TJ 1.013 0 0 1 114.839 587.121 Tm [(The)-247(PSBLAS)-246(library)-247(version)-246(3)-247(is)-247(implemented)-246(in)-247(the)-246(Fortran)-247(2003)-247([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 410.705 587.121 Tm [(16)]TJ + 1 0 0 1 410.705 587.121 Tm [(17)]TJ 0 g 0 G 1.013 0 0 1 420.668 587.121 Tm [(])-247(pr)18(o-)]TJ 1.009 0 0 1 99.895 575.166 Tm [(gramming)-247(language,)-248(with)-247(r)17(e)1(use)-248(and/or)-247(adaptation)-248(of)-247(existing)-248(Fortran)-247(77)-247(and)]TJ 1 0 0 1 99.895 563.211 Tm [(Fortran)-250(95)-250(softwar)18(e,)-250(plus)-250(a)-250(handful)-250(of)-250(C)-250(r)18(outines.)]TJ 1.02 0 0 1 114.839 551.147 Tm [(The)-348(use)-347(of)-348(Fortran)-348(2003)-348(of)18(fers)-347(a)-348(number)-348(of)-348(advant)1(ages)-348(over)-348(Fortran)-348(95,)]TJ 1.02 0 0 1 99.895 539.192 Tm [(mostly)-323(in)-324(the)-323(handling)-324(of)-323(r)17(equir)18(ements)-323(for)-324(evolution)-323(and)-324(adaptation)-323(of)-324(the)]TJ 0.995 0 0 1 99.895 527.237 Tm [(library)-252(to)-252(new)-252(computin)1(g)-252(ar)18(chitectur)18(es)-252(and)-252(integration)-252(of)-251(new)-252(algorithms.)-314(For)]TJ 1.011 0 0 1 99.895 515.281 Tm [(a)-247(detailed)-247(discussion)-247(of)-248(our)-247(design)-247(see)-247([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 276.552 515.281 Tm [(10)]TJ + 1 0 0 1 276.552 515.281 Tm [(11)]TJ 0 g 0 G 1.011 0 0 1 286.514 515.281 Tm [(];)-247(other)-247(works)-248(discussi)1(ng)-248(advanced)]TJ 0.98 0 0 1 99.596 503.326 Tm [(pr)18(ogramming)-202(in)-203(Fortran)-202(2003)-203(include)-202([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 265.469 503.326 Tm [(20)]TJ + 1 0 0 1 265.469 503.326 Tm [(21)]TJ 0 g 0 G 0.98 0 0 1 275.432 503.326 Tm [(,)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 279.85 503.326 Tm [(18)]TJ + 1 0 0 1 279.85 503.326 Tm [(19)]TJ 0 g 0 G 0.98 0 0 1 289.813 503.326 Tm [(];)-220(suf)18(\002cient)-203(suppor)1(t)-203(for)-203(Fortran)-202(2003)]TJ 1.02 0 0 1 99.895 491.371 Tm [(is)-269(now)-268(available)-269(fr)18(om)-269(many)-268(compilers,)-275(including)-269(the)-268(GNU)-269(Fortran)-268(compiler)]TJ 1 0 0 1 99.895 479.416 Tm [(fr)18(om)-250(the)-250(Fr)18(ee)-250(Softwar)18(e)-250(Foundation)-250(\050as)-250(of)-250(version)-250(4.8\051.)]TJ 0.98 0 0 1 114.839 467.352 Tm [(Pr)18(evious)-234(appr)19(oaches)-234(have)-234(been)-234(based)-234(on)-234(mixing)-234(Fortran)-234(95,)-239(with)-234(its)-234(support)]TJ 1.02 0 0 1 99.895 455.397 Tm [(for)-260(object-based)-260(design,)-264(with)-260(other)-260(languages;)-267(these)-260(have)-260(been)-260(advocated)-260(by)]TJ 1.016 0 0 1 99.895 443.442 Tm [(a)-246(number)-246(of)-247(aut)1(hors,)-247(e.g.)-246([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 217.299 443.442 Tm [(15)]TJ + 1 0 0 1 217.299 443.442 Tm [(16)]TJ 0 g 0 G 1.016 0 0 1 227.261 443.442 Tm [(].)-305(Mor)17(eover)73(,)-246(the)-246(Fortran)-246(95)-247(facil)1(ities)-247(for)-246(dynamic)]TJ 1.006 0 0 1 99.895 431.486 Tm [(memory)-248(management)-248(and)-247(interface)-248(overloading)-248(gr)18(eatly)-248(enhance)-247(the)-248(usability)]TJ 1.02 0 0 1 99.895 419.531 Tm [(of)-287(the)-287(PSBLAS)-288(su)1(br)17(outines.)-430(In)-287(this)-287(way)109(,)-298(the)-287(library)-288(can)-287(take)-287(car)18(e)-287(of)-288(r)8(untime)]TJ 1.02 0 0 1 99.895 407.576 Tm [(memory)-248(r)17(equ)1(ir)17(ements)-248(that)-248(ar)18(e)-249(quite)-248(dif)18(\002cult)-248(or)-248(even)-248(impossible)-248(to)-248(pr)17(edict)-248(at)]TJ 1 0 0 1 99.895 395.621 Tm [(implementation)-250(or)-250(compilation)-250(time.)]TJ 14.944 -12.064 Td [(The)-249(pr)18(esentation)-250(of)-249(the)-250(PSBLAS)-249(library)-249(follows)-250(the)-249(general)-249(str)8(uctur)18(e)-250(of)-249(the)]TJ 0.98 0 0 1 99.596 371.602 Tm [(pr)18(oposal)-255(for)-255(serial)-254(Sparse)-255(BLAS)-255([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 242.106 371.602 Tm [(7)]TJ + 1 0 0 1 242.106 371.602 Tm [(8)]TJ 0 g 0 G 0.98 0 0 1 247.087 371.602 Tm [(,)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 252.017 371.602 Tm [(8)]TJ + 1 0 0 1 252.017 371.602 Tm [(9)]TJ 0 g 0 G 0.98 0 0 1 256.998 371.602 Tm [(],)-255(which)-255(in)-255(its)-255(turn)-255(is)-255(based)-255(on)-255(the)-255(pr)19(oposal)]TJ 1 0 0 1 99.895 359.647 Tm [(for)-250(BLAS)-250(on)-250(dense)-250(matrices)-250([)]TJ 1 0 0 rg 1 0 0 RG - [(14)]TJ + [(15)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-250(4)]TJ + [-250(5)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-250(5)]TJ + [-250(6)]TJ 0 g 0 G [(].)]TJ 1.016 0 0 1 114.839 347.583 Tm [(The)-245(applicability)-245(of)-246(sparse)-245(iterative)-245(solvers)-245(to)-245(many)-246(dif)18(fe)1(r)17(ent)-245(ar)18(eas)-245(causes)]TJ 0.98 0 0 1 99.895 335.627 Tm [(some)-251(terminology)-252(pr)19(oblems)-252(because)-251(the)-252(same)-251(concept)-251(may)-252(be)-251(denoted)-252(thr)19(ough)]TJ 1.013 0 0 1 99.895 323.672 Tm [(dif)18(fer)18(ent)-248(names)-247(depending)-247(on)-248(the)-247(application)-248(ar)18(ea.)-308(The)-247(PSBLAS)-247(featur)17(es)-247(pr)18(e-)]TJ 1.02 0 0 1 99.895 311.717 Tm [(sented)-290(in)-289(this)-289(document)-290(will)-289(be)-290(discussed)-289(r)17(eferring)-289(to)-290(a)-289(\002nite)-290(dif)18(fer)18(ence)-289(dis-)]TJ 1.012 0 0 1 99.895 299.762 Tm [(cr)18(etization)-248(of)-248(a)-248(Partial)-248(Dif)18(fer)18(ential)-248(Equation)-248(\050PDE\051.)-248(Howe)1(ver)73(,)-248(the)-248(scope)-248(of)-248(the)]TJ 1.02 0 0 1 99.895 287.807 Tm [(library)-249(is)-249(wider)-249(than)-249(that:)-312(for)-250(example,)-250(it)-249(can)-249(be)-249(applied)-249(to)-249(\002nite)-249(element)-249(dis-)]TJ 0.98 0 0 1 99.895 275.852 Tm [(cr)18(etizations)-240(of)-241(PDEs,)-244(and)-240(even)-241(to)-240(dif)18(fer)18(ent)-241(classes)-240(of)-241(pr)18(oblems)-240(such)-241(as)-241(nonlinear)]TJ 1 0 0 1 99.895 263.896 Tm [(optimization,)-250(for)-250(example)-250(in)-250(optimal)-250(contr)18(ol)-250(pr)18(oblems.)]TJ 1.02 0 0 1 114.839 251.832 Tm [(The)-346(design)-346(of)-346(a)-345(solver)-346(for)-346(sparse)-346(linear)-346(systems)-346(is)-345(driven)-346(by)-346(many)-346(con-)]TJ 1.006 0 0 1 99.895 239.877 Tm [(\003icting)-250(objectives,)-250(such)-249(as)-250(limiting)-249(occupation)-250(of)-250(storage)-249(r)18(esour)17(ces,)-249(exploiting)]TJ 1.013 0 0 1 99.895 227.922 Tm [(r)18(egularities)-247(in)-247(the)-247(input)-247(data,)-247(exploiting)-246(har)17(dwar)18(e)-247(characteristics)-247(of)-246(the)-247(paral-)]TJ 1.02 0 0 1 99.895 215.967 Tm [(lel)-293(platform.)-447(T)90(o)-292(achieve)-293(an)-293(optimal)-293(communication)-292(to)-293(computation)-293(ratio)-293(on)]TJ 1.02 0 0 1 99.895 204.012 Tm [(distributed)-322(memory)-322(machines)-323(it)-322(is)-322(essential)-322(to)-323(keep)-322(the)]TJ/F78 9.9626 Tf 1.02 0 0 1 356.37 204.012 Tm [(data)-322(locality)]TJ/F84 9.9626 Tf 1.02 0 0 1 410.507 204.012 Tm [(as)-322(high)]TJ 1.02 0 0 1 99.895 192.057 Tm [(as)-270(possible;)-283(this)-270(can)-270(be)-270(done)-271(thr)18(ough)-270(an)-270(appr)17(opriate)-270(data)-270(allocation)-270(strategy)109(.)]TJ 1.02 0 0 1 99.587 180.101 Tm [(The)-264(choice)-265(of)-264(the)-265(pr)18(econditioner)-264(is)-265(another)-264(very)-265(important)-264(factor)-265(that)-264(af)18(fects)]TJ 1.02 0 0 1 99.895 168.146 Tm [(ef)18(\002ciency)-248(of)-247(the)-248(implemented)-247(application.)-311(Optimal)-248(data)-247(distribution)-248(r)18(equir)18(e-)]TJ 1.014 0 0 1 99.895 156.191 Tm [(ments)-247(for)-246(a)-247(given)-247(pr)18(econditioner)-247(may)-246(con\003ict)-247(with)-247(distribution)-246(r)17(equir)18(ements)]TJ 1.02 0 0 1 99.895 144.236 Tm [(of)-310(the)-311(r)18(est)-310(of)-311(the)-310(solver)72(.)-499(Finding)-311(the)-310(optimal)-310(trade-of)17(f)-310(may)-310(be)-310(very)-311(dif)18(\002cult)]TJ 1.016 0 0 1 99.895 132.281 Tm [(because)-246(it)-245(is)-246(application)-246(depende)1(nt.)-305(Possible)-246(solutions)-246(to)-245(these)-246(pr)18(oblems)-246(and)]TJ 1.02 0 0 1 99.895 120.326 Tm [(other)-274(important)-274(inputs)-275(to)-274(the)-274(development)-274(of)-275(the)-274(PSBLAS)-274(softwar)18(e)-275(package)]TJ 0 g 0 G @@ -4596,7 +4596,7 @@ BT 0 g 0 G [(;)-251(lower)-251(layers)-251(of)-250(the)-251(library)-251(indi)1(cate)-251(an)]TJ 1.005 0 0 1 150.705 524.952 Tm [(encapsulation)-247(r)18(elationship)-247(with)-247(upper)-247(layers.)-308(The)-247(ongoing)-247(discussion)-246(focuses)]TJ 1.018 0 0 1 150.705 512.997 Tm [(on)-244(the)-245(Fortran)-244(2003)-245(layer)-244(immediately)-245(below)-244(the)-245(application)-244(layer)73(.)-305(The)-244(serial)]TJ 0.98 0 0 1 150.406 501.041 Tm [(parts)-246(of)-245(the)-246(computation)-246(on)-245(each)-246(pr)18(ocess)-245(ar)18(e)-246(executed)-245(thr)18(ough)-246(calls)-245(to)-246(the)-246(serial)]TJ 0.98 0 0 1 150.705 489.086 Tm [(sparse)-243(BLAS)-243(subr)18(outines.)-312(In)-243(a)-243(similar)-243(way)113(,)-245(the)-243(inter)18(-pr)19(ocess)-243(message)-243(exchanges)]TJ 1 0 0 1 150.705 477.131 Tm [(ar)18(e)-251(encapsulated)-251(in)-251(an)-251(applicaiton)-251(layer)-251(that)-251(has)-251(been)-251(str)18(ongly)-251(inspir)18(ed)-251(by)-251(the)]TJ 0.987 0 0 1 150.705 465.176 Tm [(Basic)-251(Linear)-252(Algebra)-251(Communication)-251(Subr)18(outines)-251(\050BLACS\051)-252(library)-251([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 447.153 465.176 Tm [(6)]TJ + 1 0 0 1 447.153 465.176 Tm [(7)]TJ 0 g 0 G 0.987 0 0 1 452.135 465.176 Tm [(].)-313(Usually)]TJ 0.98 0 0 1 150.705 453.221 Tm [(ther)18(e)-240(is)-241(no)-241(need)-240(to)-241(deal)-241(dir)19(ectly)-241(with)-240(MPI;)-241(however)75(,)-243(in)-241(some)-240(cases,)-244(MPI)-241(r)19(outines)]TJ 0.98 0 0 1 150.705 441.266 Tm [(ar)18(e)-199(used)-198(dir)18(ectly)-199(to)-199(impr)18(o)1(ve)-199(ef)18(\002ciency)113(.)-298(For)-199(further)-199(det)1(ails)-199(on)-199(our)-199(communication)]TJ 1 0 0 1 150.705 429.31 Tm [(layer)-250(see)-250(Sec.)]TJ 0 0 1 rg 0 0 1 RG @@ -4693,7 +4693,7 @@ stream BT /F84 9.9626 Tf 1.02 0 0 1 99.895 706.129 Tm [(assigned)-295(to)-294(a)-295(pr)17(ocess)-294(that)-295(will)-295(own)-294(the)-295(corr)18(esponding)-295(r)17(ow)-294(in)-295(the)-295(coef)18(\002cient)]TJ 1.02 0 0 1 99.895 694.174 Tm [(matrix)-247(and)-247(will)-246(carry)-247(out)-247(all)-247(r)18(elated)-247(computations.)-309(T)1(his)-247(allocation)-247(strategy)-247(is)]TJ 0.98 0 0 1 99.895 682.219 Tm [(equivalent)-251(to)-251(a)-251(partition)-252(of)-251(the)-251(discr)18(etizati)1(on)-252(mesh)-251(into)]TJ/F78 9.9626 Tf 0.98 0 0 1 339.419 682.219 Tm [(sub-domains)]TJ/F84 9.9626 Tf 0.98 0 0 1 389.504 682.219 Tm [(.)-315(Our)-251(library)]TJ 1.02 0 0 1 99.895 670.263 Tm [(supports)-297(any)-298(distribution)-297(that)-297(keeps)-298(together)-297(the)-297(coef)17(\002)1(cients)-298(of)-297(each)-297(matrix)]TJ 1.02 0 0 1 99.895 658.308 Tm [(r)18(ow;)-366(ther)18(e)-326(ar)18(e)-325(no)-326(other)-325(constraints)-325(on)-326(the)-325(variable)-326(assignment.)-544(This)-326(choice)]TJ 1.02 0 0 1 99.895 646.353 Tm [(is)-276(consistent)-275(with)-276(simple)-276(data)-276(distributi)1(ons)-276(such)-276(as)]TJ/F131 9.9626 Tf 1 0 0 1 332.842 646.353 Tm [(CYCLIC\050N\051)]TJ/F84 9.9626 Tf 1.02 0 0 1 382.717 646.353 Tm [(and)]TJ/F131 9.9626 Tf 1 0 0 1 402.723 646.353 Tm [(BLOCK)]TJ/F84 9.9626 Tf 1.02 0 0 1 428.874 646.353 Tm [(,)-276(as)]TJ 1.02 0 0 1 99.477 634.398 Tm [(well)-256(as)-256(completely)-256(arbitrary)-256(assignments)-256(of)-256(equation)-256(indices)-256(to)-256(pr)18(ocesses.)-337(In)]TJ 1.002 0 0 1 99.596 622.443 Tm [(particular)-250(it)-250(is)-251(consistent)-250(with)-250(the)-250(usage)-250(of)-251(graph)-250(partitioning)-250(tools)-250(commonly)]TJ 1.02 0 0 1 99.895 610.488 Tm [(available)-288(in)-289(the)-288(literatur)18(e,)-299(e.g.)-434(METIS)-288([)]TJ 1 0 0 rg 1 0 0 RG - 1 0 0 1 276.029 610.488 Tm [(13)]TJ + 1 0 0 1 276.029 610.488 Tm [(14)]TJ 0 g 0 G 1.02 0 0 1 285.992 610.488 Tm [(].)-433(Dense)-289(vectors)-288(conform)-288(to)-288(sparse)]TJ 0.98 0 0 1 99.895 598.532 Tm [(matrices,)-228(that)-222(is,)-228(the)-221(entries)-221(of)-222(a)-221(vector)-222(follow)-221(the)-221(same)-222(distribution)-221(of)-221(the)-222(matrix)]TJ 1 0 0 1 99.895 586.577 Tm [(r)18(ows.)]TJ 1.02 0 0 1 114.839 573.93 Tm [(W)90(e)-290(assume)-290(that)-291(the)-290(sparse)-290(matrix)-290(is)-291(built)-290(in)-290(parallel,)-302(wher)18(e)-290(each)-291(pr)18(ocess)]TJ 1.002 0 0 1 99.895 561.974 Tm [(generates)-249(its)-249(own)-250(port)1(ion.)-310(W)92(e)-249(never)-249(r)18(equir)18(e)-250(th)1(at)-250(the)-249(entir)18(e)-249(matrix)-249(be)-249(available)]TJ 0.98 0 0 1 99.895 550.019 Tm [(on)-244(a)-244(single)-244(node.)-313(However)76(,)-247(it)-244(is)-244(possible)-244(to)-244(hold)-244(the)-244(entir)19(e)-244(matrix)-245(in)-244(one)-244(pr)19(ocess)]TJ 0.98 0 0 1 99.895 538.064 Tm [(and)-199(distr)1(ibute)-199(it)-198(explicitly)]TJ 0 0 1 rg 0 0 1 RG @@ -4745,11 +4745,11 @@ BT 0 g 0 G /F84 9.9626 Tf 1.006 0 0 1 194.869 706.129 Tm [(An)-248(overlap)-248(point)-248(is)-248(a)-248(boundary)-248(point)-249(assigned)-248(to)-248(multiple)-248(domains.)]TJ 0.983 0 0 1 175.223 694.174 Tm [(Any)-253(operation)-254(that)-253(involves)-254(an)-253(overlap)-254(point)-253(has)-254(to)-253(be)-254(r)19(eplicated)-254(for)-253(each)]TJ 1 0 0 1 175.611 682.219 Tm [(assignment.)]TJ 0.98 0 0 1 150.705 663.276 Tm [(Overlap)-232(points)-233(do)-232(not)-233(usually)-232(exist)-233(in)-232(the)-233(basic)-232(data)-233(distributions;)-240(however)-232(they)]TJ 0.989 0 0 1 150.705 651.321 Tm [(ar)18(e)-251(a)-252(featur)19(e)-252(of)-251(Domain)-251(Decomposition)-252(Schwarz)-251(pr)18(econditioners)-251(which)-252(ar)19(e)-252(the)]TJ 1 0 0 1 150.705 639.365 Tm [(subject)-250(of)-250(r)18(elated)-250(r)18(esear)18(ch)-250(work)-250([)]TJ 1 0 0 rg 1 0 0 RG - [(3)]TJ + [(4)]TJ 0 g 0 G [(,)]TJ 1 0 0 rg 1 0 0 RG - [-250(2)]TJ + [-250(3)]TJ 0 g 0 G [(].)]TJ 0.995 0 0 1 165.649 627.41 Tm [(W)92(e)-251(denote)-251(the)-251(sets)-251(of)-251(internal,)-251(boundary)-251(and)-251(halo)-251(points)-251(for)-251(a)-251(given)-251(subdo-)]TJ 1.001 0 0 1 150.705 615.455 Tm [(main)-249(by)]TJ/F179 10.3811 Tf 1 0 0 1 189.363 615.455 Tm [(I)]TJ/F84 9.9626 Tf 1.001 0 0 1 195.893 615.455 Tm [(,)]TJ/F179 10.3811 Tf 1 0 0 1 201 615.455 Tm [(B)]TJ/F84 9.9626 Tf 1.001 0 0 1 210.736 615.455 Tm [(and)]TJ/F179 10.3811 Tf 1 0 0 1 230.232 615.455 Tm [(H)]TJ/F84 9.9626 Tf 1.001 0 0 1 239.203 615.455 Tm [(.)-310(Each)-249(subdomain)-250(is)-249(assigned)-249(to)-250(one)-249(pr)18(ocess;)-250(each)-249(pr)17(oc)1(ess)]TJ 1.02 0 0 1 150.705 603.5 Tm [(usually)-286(owns)-285(one)-286(subdomain,)-295(although)-286(the)-285(user)-286(may)-286(choose)-285(to)-286(assign)-285(mor)17(e)]TJ 1.02 0 0 1 150.705 591.545 Tm [(than)-257(one)-257(subdomain)-257(to)-257(a)-257(pr)18(ocess.)-340(If)-257(each)-257(pr)18(ocess)]TJ/F78 9.9626 Tf 1 0 0 1 373.028 591.545 Tm [(i)]TJ/F84 9.9626 Tf 1.02 0 0 1 378.603 591.545 Tm [(owns)-257(one)-257(subdomain,)-260(the)]TJ 0.983 0 0 1 150.705 579.589 Tm [(number)-255(of)-255(r)19(ows)-255(in)-255(the)-255(local)-255(sparse)-255(matrix)-255(is)]TJ/F179 10.3811 Tf 1 0 0 1 343.065 579.589 Tm [(j)-24(I)]TJ/F78 7.5716 Tf 8.943 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F181 10.3811 Tf 5.068 0 Td [(+)]TJ/F179 10.3811 Tf 10.258 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.108 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.876 1.96 Td [(j)]TJ/F84 9.9626 Tf 0.983 0 0 1 386.196 579.589 Tm [(,)-255(and)-255(the)-255(number)-255(of)-254(local)]TJ 0.982 0 0 1 150.705 567.634 Tm [(columns)-254(\050i.e.)-316(those)-254(for)-255(which)-254(ther)18(e)-254(exists)-254(at)-255(least)-254(one)-254(non-zer)18(o)-254(entry)-255(in)-254(the)-255(local)]TJ 1 0 0 1 150.705 555.679 Tm [(r)18(ows\051)-250(is)]TJ/F179 10.3811 Tf 37.275 0 Td [(j)-24(I)]TJ/F78 7.5716 Tf 8.943 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F181 10.3811 Tf 5.066 0 Td [(+)]TJ/F179 10.3811 Tf 10.255 0 Td [(j)-24(B)]TJ/F78 7.5716 Tf 10.109 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F181 10.3811 Tf 5.066 0 Td [(+)]TJ/F179 10.3811 Tf 10.256 0 Td [(j)-24(H)]TJ/F78 7.5716 Tf 12.051 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(j)]TJ/F84 9.9626 Tf 3.004 0 Td [(.)]TJ 0 g 0 G @@ -5072,19 +5072,19 @@ endobj /Type /ObjStm /N 100 /First 911 -/Length 12758 +/Length 12757 >> stream 843 0 844 153 845 306 846 459 847 606 848 758 849 911 850 1058 851 1211 852 1364 853 1517 854 1670 855 1817 856 1965 857 2113 858 2261 859 2408 860 2557 861 2706 862 2855 863 3004 864 3153 865 3302 866 3451 867 3600 868 3749 872 3897 869 3954 887 4034 876 4240 -877 4390 878 4541 879 4693 880 4847 881 4998 882 5148 883 5298 884 5446 885 5594 7 5742 -886 5796 906 5889 909 6039 910 6280 911 6322 912 6708 900 7008 901 7154 902 7301 11 7448 -908 7503 905 7560 918 7681 904 7831 915 7979 916 8127 920 8275 15 8331 924 8386 925 8443 -917 8500 931 8635 935 8777 936 8891 937 8933 927 9002 928 9149 933 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cm +1 0 0 1 658.734 276.891 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q BT -/F84 7.1731 Tf 668.277 175.671 Td [(C)-62(O)-62(M)-61(M)-62(E)-61(N)-62(T)-62(S)]TJ +/F84 7.1731 Tf 664.936 280.179 Td [(C)-62(O)-62(M)-61(M)-62(E)-61(N)-62(T)-62(S)]TJ ET q -1 0 0 1 858.283 172.383 cm +1 0 0 1 860.611 276.891 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q q -1 0 0 1 280.985 172.184 cm -[]0 d 0 J 0.398 w 0 0 m 577.297 0 l S +1 0 0 1 278.657 276.692 cm +[]0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 280.985 95.272 cm +1 0 0 1 278.657 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q 0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 286.963 164.313 Td [(\015SUB_SOLVE\015)]TJ +/F231 8.9664 Tf 284.635 268.821 Td [(\015SUB_SOLVE\015)]TJ 0 g 0 G ET q -1 0 0 1 394.988 95.272 cm +1 0 0 1 381.321 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q 0.56 0.13 0.00 rg 0.56 0.13 0.00 RG BT -/F231 8.9664 Tf 400.965 164.313 Td [(character)]TJ +/F231 8.9664 Tf 387.299 268.821 Td [(character)]TJ 0 g 0 G [(\050)]TJ 0.00 0.44 0.13 rg 0.00 0.44 0.13 RG @@ -26765,12 +26773,12 @@ BT [(\051)]TJ ET q -1 0 0 1 482.26 95.272 cm +1 0 0 1 487.422 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q 0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 488.237 164.313 Td [(\015ILU\015)]TJ +/F231 8.9664 Tf 493.4 268.821 Td [(\015ILU\015)]TJ 0 g 0 G 0.25 0.44 0.63 rg 0.25 0.44 0.63 RG 0 -10.959 Td [(\015ILUT\015)]TJ @@ -26786,234 +26794,446 @@ BT 0 g 0 G ET q -1 0 0 1 548.073 95.272 cm +1 0 0 1 573.078 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q q -1 0 0 1 662.075 95.272 cm +1 0 0 1 658.734 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q BT -/F84 8.9664 Tf 1.02 0 0 1 667.775 164.313 Tm [(The)-899(local)-898(solver)-899(to)-898(be)-899(used)-898(with)-899(the)]TJ 1.02 0 0 1 668.053 153.354 Tm [(smoother)-335(or)-335(one-level)-336(pr)18(econditioner)-335(ILU\050)]TJ/F78 8.9664 Tf 1 0 0 1 843.499 153.354 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 848.094 153.354 Tm [(\051,)]TJ 1.02 0 0 1 668.053 142.395 Tm [(ILU\050)]TJ/F78 8.9664 Tf 1 0 0 1 687.489 142.395 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 692.084 142.395 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 695.977 142.395 Tm [(t)]TJ/F84 8.9664 Tf 1.02 0 0 1 699.075 142.395 Tm [(\051,)-623(Appr)18(oximate)-548(Inverses)-547(INVK\050)]TJ/F78 8.9664 Tf 1 0 0 1 835.342 142.395 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 839.938 142.395 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 843.83 142.395 Tm [(q)]TJ/F84 8.9664 Tf 1.02 0 0 1 848.094 142.395 Tm [(\051,)]TJ 1.02 0 0 1 668.053 131.436 Tm [(INVT\050)]TJ/F78 8.9664 Tf 1 0 0 1 694.595 131.436 Tm [(p)]TJ/F84 6.9738 Tf 4.595 -1.783 Td [(1)]TJ/F84 8.9664 Tf 1.02 0 0 1 703.175 131.436 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 707.561 131.436 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 712.157 131.436 Tm [(2,)]TJ/F78 8.9664 Tf 1 0 0 1 720.622 131.436 Tm [(t)]TJ/F84 6.9738 Tf 3.098 -1.783 Td [(1)]TJ/F84 8.9664 Tf 1.02 0 0 1 727.705 131.436 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 731.598 131.436 Tm [(t)]TJ/F84 6.9738 Tf 3.098 -1.678 Td [(2)]TJ/F84 8.9664 Tf 1.02 0 0 1 738.681 131.436 Tm [(\051)-649(and)-648(AINV\050)]TJ/F78 8.9664 Tf 1 0 0 1 796.631 131.436 Tm [(t)]TJ/F84 8.9664 Tf 1.02 0 0 1 799.729 131.436 Tm [(\051;)-850(note)-649(that)]TJ 1.02 0 0 1 668.053 120.478 Tm [(appr)18(oximate)-468(inverses)-468(ar)18(e)-468(speci\002cally)-467(suited)]TJ 1.02 0 0 1 668.053 109.519 Tm [(for)-251(GPUs)-250(since)-251(they)-250(do)-251(not)-250(employ)-251(triangular)]TJ 1 0 0 1 668.053 98.56 Tm [(system)-250(solve)-250(kernels,)-250(see)-250([)]TJ/F75 8.9664 Tf 103.722 0 Td [(?)]TJ/F84 8.9664 Tf 3.981 0 Td [(].)]TJ +/F84 8.9664 Tf 1.02 0 0 1 664.434 268.821 Tm [(The)-987(local)-987(solver)-987(to)-987(be)-987(used)-987(with)-988(the)]TJ 1.02 0 0 1 664.712 257.862 Tm [(smoother)-490(or)-490(one-level)-491(pr)18(econditioner)-490(ILU\050)]TJ/F78 8.9664 Tf 1 0 0 1 845.827 257.862 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 850.422 257.862 Tm [(\051,)]TJ 1.02 0 0 1 664.712 246.903 Tm [(ILU\050)]TJ/F78 8.9664 Tf 1 0 0 1 684.148 246.903 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 688.743 246.903 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 692.636 246.903 Tm [(t)]TJ/F84 8.9664 Tf 1.02 0 0 1 695.734 246.903 Tm [(\051,)-862(App)1(r)17(oximate)-738(Inverses)-738(INVK\050)]TJ/F78 8.9664 Tf 1 0 0 1 837.67 246.903 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 842.266 246.903 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 846.158 246.903 Tm [(q)]TJ/F84 8.9664 Tf 1.02 0 0 1 850.422 246.903 Tm [(\051,)]TJ 1.02 0 0 1 664.712 235.945 Tm [(INVT\050)]TJ/F78 8.9664 Tf 1 0 0 1 691.254 235.945 Tm [(p)]TJ/F84 6.9738 Tf 4.595 -1.784 Td [(1)]TJ/F84 8.9664 Tf 1.02 0 0 1 699.834 235.945 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 704.22 235.945 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 708.815 235.945 Tm [(2,)]TJ/F78 8.9664 Tf 1 0 0 1 717.281 235.945 Tm [(t)]TJ/F84 6.9738 Tf 3.098 -1.784 Td [(1)]TJ/F84 8.9664 Tf 1.02 0 0 1 724.364 235.945 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 728.257 235.945 Tm [(t)]TJ/F84 6.9738 Tf 3.098 -1.679 Td [(2)]TJ/F84 8.9664 Tf 1.02 0 0 1 735.34 235.945 Tm [(\051)-786(and)-787(AINV\050)]TJ/F78 8.9664 Tf 1 0 0 1 795.809 235.945 Tm [(t)]TJ/F84 8.9664 Tf 1.02 0 0 1 798.907 235.945 Tm [(\051;)-1057(note)-786(that)]TJ 1.02 0 0 1 664.712 224.986 Tm [(appr)18(oximate)-623(inverses)-623(ar)18(e)-623(speci\002)1(cally)-623(suited)]TJ 1.02 0 0 1 664.712 214.027 Tm [(for)-339(GPUs)-339(since)-339(they)-339(do)-340(not)-339(employ)-339(triangular)]TJ 1 0 0 1 664.712 203.068 Tm [(system)-250(solve)-250(kernels,)-250(see)-250([)]TJ +1 0 0 rg 1 0 0 RG + [(2)]TJ +0 g 0 G + [(].)]TJ ET q -1 0 0 1 858.283 95.272 cm +1 0 0 1 860.611 199.78 cm []0 d 0 J 0.398 w 0 0 m 0 76.712 l S Q q -1 0 0 1 280.985 95.073 cm -[]0 d 0 J 0.398 w 0 0 m 577.297 0 l S +1 0 0 1 278.657 199.581 cm +[]0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 280.985 93.08 cm -[]0 d 0 J 0.398 w 0 0 m 577.297 0 l S +1 0 0 1 278.657 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q -0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F84 9.9626 Tf 380.202 64.702 Td [(T)92(able)-250(21:)-310(Parameters)-250(de\002ning)-250(the)-250(solver)-250(or)-250(the)-250(details)-250(of)-250(the)-250(one-level)-250(pr)18(econditioner)74(.)]TJ -0 g 0 G +/F231 8.9664 Tf 284.635 191.71 Td [(\015SUB_FILLIN\015)]TJ 0 g 0 G ET -1 0 0 1 271.751 120.326 cm +q +1 0 0 1 381.321 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q -0 g 0 G -0 g 0 G -1 0 0 1 -271.751 -120.326 cm +0.56 0.13 0.00 rg 0.56 0.13 0.00 RG BT -/F84 9.9626 Tf 264.279 90.438 Td [(153)]TJ +/F231 8.9664 Tf 387.299 191.71 Td [(integer)]TJ 0 g 0 G ET - -endstream -endobj -1991 0 obj -<< -/Length 3855 ->> -stream -0 g 0 G -0 g 0 G -0 g 0 G -1 0 0 1 322.56 716.092 cm q -0 -1 1 0 0 0 cm -0 g 0 G +1 0 0 1 487.422 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 493.05 191.71 Td [(Any)-250(integer)]TJ 0.35 -10.959 Td [(number)]TJ/F179 9.343 Tf 33.69 0 Td [(\025)]TJ/F84 8.9664 Tf 9.866 0 Td [(0)]TJ +ET +q +1 0 0 1 573.078 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 579.056 191.71 Td [(0)]TJ +ET +q +1 0 0 1 658.734 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 0.98 0 0 1 664.712 191.71 Tm [(Fill-in)-207(level)]TJ/F78 8.9664 Tf 1 0 0 1 710.61 191.71 Tm [(p)]TJ/F84 8.9664 Tf 0.98 0 0 1 717.027 191.71 Tm [(of)-207(the)-208(incomplete)-207(LU)-207(factorizations.)]TJ +ET +q +1 0 0 1 860.611 177.464 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +q +1 0 0 1 278.657 177.265 cm +[]0 d 0 J 0.398 w 0 0 m 581.953 0 l S +Q +q +1 0 0 1 278.657 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 284.635 169.394 Td [(\015SUB_ILUTHRS\015)]TJ 0 g 0 G +ET +q +1 0 0 1 381.321 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +0.56 0.13 0.00 rg 0.56 0.13 0.00 RG +BT +/F231 8.9664 Tf 387.299 169.394 Td [(real)]TJ 0 g 0 G + [(\050kind_parameter\051)]TJ +ET q -1 0 0 1 6.907 46.976 cm +1 0 0 1 487.422 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 1.02 0 0 1 493.05 169.394 Tm [(Any)-1148(r)18(eal)-1148(nu)1(m-)]TJ 1 0 0 1 493.4 158.435 Tm [(ber)]TJ/F179 9.343 Tf 15.148 0 Td [(\025)]TJ/F84 8.9664 Tf 9.865 0 Td [(0)]TJ +ET +q +1 0 0 1 573.078 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 579.056 169.394 Td [(0)]TJ +ET +q +1 0 0 1 658.734 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +BT +/F84 8.9664 Tf 664.712 169.394 Td [(Dr)18(op)-250(tolerance)]TJ/F78 8.9664 Tf 61.441 0 Td [(t)]TJ/F84 8.9664 Tf 5.34 0 Td [(in)-250(the)-250(ILU\050)]TJ/F78 8.9664 Tf 43.813 0 Td [(p)]TJ/F84 8.9664 Tf 4.595 0 Td [(,)]TJ/F78 8.9664 Tf 3.848 0 Td [(t)]TJ/F84 8.9664 Tf 3.098 0 Td [(\051)-250(factorization.)]TJ +ET +q +1 0 0 1 860.611 155.147 cm +[]0 d 0 J 0.398 w 0 0 m 0 21.918 l S +Q +q +1 0 0 1 278.657 154.948 cm []0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 6.907 35.818 cm +1 0 0 1 278.657 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q -1 0 0 1 -322.56 -716.092 cm +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 335.209 755.197 Td [(what)]TJ +/F231 8.9664 Tf 284.635 147.078 Td [(\015ILU_ALG\015)]TJ +0 g 0 G ET q -1 0 0 1 432.13 751.91 cm +1 0 0 1 381.321 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q +0.56 0.13 0.00 rg 0.56 0.13 0.00 RG BT -/F84 7.1731 Tf 438.332 755.197 Td [(D)-62(A)11(T)12(A)-374(T)-62(Y)-62(P)-62(E)]TJ +/F231 8.9664 Tf 387.299 147.078 Td [(character)]TJ +0 g 0 G + [(\050)]TJ +0.00 0.44 0.13 rg 0.00 0.44 0.13 RG + [(len)]TJ +0 g 0 G +0.40 0.40 0.40 rg 0.40 0.40 0.40 RG + [(=*)]TJ +0 g 0 G + [(\051)]TJ ET q -1 0 0 1 538.231 751.91 cm +1 0 0 1 487.422 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 543.974 755.197 Td [(val)]TJ +/F231 8.9664 Tf 493.4 147.078 Td [(\015MILU\015)]TJ +0 g 0 G ET q -1 0 0 1 623.888 751.91 cm +1 0 0 1 573.078 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F84 7.1731 Tf 630.089 755.197 Td [(D)-62(E)-62(F)12(A)-62(U)-62(L)13(T)]TJ +/F231 8.9664 Tf 579.056 147.078 Td [(\015NONE\015)]TJ +0 g 0 G ET q -1 0 0 1 709.544 751.91 cm +1 0 0 1 658.734 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q BT -/F84 7.1731 Tf 715.745 755.197 Td [(C)-62(O)-62(M)-61(M)-62(E)-61(N)-62(T)-62(S)]TJ +/F84 8.9664 Tf 664.712 147.078 Td [(ILU)-250(algorithmic)-250(variant)]TJ ET q -1 0 0 1 911.42 751.91 cm +1 0 0 1 860.611 143.79 cm []0 d 0 J 0.398 w 0 0 m 0 10.959 l S Q q -1 0 0 1 329.467 751.71 cm +1 0 0 1 278.657 143.591 cm +[]0 d 0 J 0.398 w 0 0 m 581.953 0 l S +Q +q +1 0 0 1 278.657 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 284.635 135.72 Td [(\015ILUT_SCALE\015)]TJ +0 g 0 G +ET +q +1 0 0 1 381.321 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +0.56 0.13 0.00 rg 0.56 0.13 0.00 RG +BT +/F231 8.9664 Tf 387.299 135.72 Td [(character)]TJ +0 g 0 G + [(\050)]TJ +0.00 0.44 0.13 rg 0.00 0.44 0.13 RG + [(len)]TJ +0 g 0 G +0.40 0.40 0.40 rg 0.40 0.40 0.40 RG + [(=*)]TJ +0 g 0 G + [(\051)]TJ +ET +q +1 0 0 1 487.422 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 493.4 135.72 Td [(\015MAXVAL\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015DIAG\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.958 Td [(\015ARSWUM\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015ARCSUM\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015ACLSUM\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015NONE\015)]TJ +0 g 0 G +ET +q +1 0 0 1 573.078 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 579.056 135.72 Td [(\015NONE\015)]TJ +0 g 0 G +ET +q +1 0 0 1 658.734 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +BT +/F84 8.9664 Tf 664.712 135.72 Td [(ILU)-250(scaling)-250(strategy)]TJ +ET +q +1 0 0 1 860.611 77.638 cm +[]0 d 0 J 0.398 w 0 0 m 0 65.753 l S +Q +q +1 0 0 1 278.657 77.439 cm []0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 329.467 729.593 cm +1 0 0 1 278.657 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q 0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 335.444 743.84 Td [(\015SUB_FILLIN\015)]TJ +/F231 8.9664 Tf 284.635 69.568 Td [(\015INV_FILLIN\015)]TJ 0 g 0 G ET q -1 0 0 1 432.13 729.593 cm +1 0 0 1 381.321 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q 0.56 0.13 0.00 rg 0.56 0.13 0.00 RG BT -/F231 8.9664 Tf 438.108 743.84 Td [(integer)]TJ +/F231 8.9664 Tf 387.299 69.568 Td [(integer)]TJ 0 g 0 G ET q -1 0 0 1 538.231 729.593 cm +1 0 0 1 487.422 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 543.859 743.84 Td [(Any)-250(integer)]TJ 0.35 -10.959 Td [(number)]TJ/F179 9.343 Tf 33.691 0 Td [(\025)]TJ/F84 8.9664 Tf 9.865 0 Td [(0)]TJ +/F84 8.9664 Tf 493.05 69.568 Td [(Any)-250(integer)]TJ 0.35 -10.958 Td [(number)]TJ/F179 9.343 Tf 33.69 0 Td [(\025)]TJ/F84 8.9664 Tf 9.866 0 Td [(0)]TJ ET q -1 0 0 1 623.888 729.593 cm +1 0 0 1 573.078 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 629.865 743.84 Td [(0)]TJ +/F84 8.9664 Tf 579.056 69.568 Td [(0)]TJ ET q -1 0 0 1 709.544 729.593 cm +1 0 0 1 658.734 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 0.98 0 0 1 715.521 743.84 Tm [(Fill-in)-207(level)]TJ/F78 8.9664 Tf 1 0 0 1 761.42 743.84 Tm [(p)]TJ/F84 8.9664 Tf 0.98 0 0 1 767.837 743.84 Tm [(of)-207(the)-208(incomplete)-207(LU)-207(factorizations.)]TJ +/F84 8.9664 Tf 1.02 0 0 1 664.712 69.568 Tm [(Second)-285(\002)1(ll-in)-285(level)]TJ/F78 8.9664 Tf 1 0 0 1 742.915 69.568 Tm [(q)]TJ/F84 8.9664 Tf 1.02 0 0 1 749.781 69.568 Tm [(of)-285(the)-284(INVK\050)]TJ/F78 8.9664 Tf 1 0 0 1 803.286 69.568 Tm [(p)]TJ/F84 8.9664 Tf 1.02 0 0 1 807.881 69.568 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 811.774 69.568 Tm [(q)]TJ/F84 8.9664 Tf 1.02 0 0 1 816.037 69.568 Tm [(\051)-285(appr)18(oxi-)]TJ 1 0 0 1 664.712 58.61 Tm [(mate)-250(inverse.)]TJ ET q -1 0 0 1 911.42 729.593 cm +1 0 0 1 860.611 55.322 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q q -1 0 0 1 329.467 729.394 cm +1 0 0 1 278.657 55.123 cm []0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 329.467 707.277 cm +1 0 0 1 278.657 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q 0.25 0.44 0.63 rg 0.25 0.44 0.63 RG BT -/F231 8.9664 Tf 335.444 721.524 Td [(\015SUB_ILUTHRS\015)]TJ +/F231 8.9664 Tf 284.635 47.252 Td [(\015INV_ILUTHRS\015)]TJ 0 g 0 G ET q -1 0 0 1 432.13 707.277 cm +1 0 0 1 381.321 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q 0.56 0.13 0.00 rg 0.56 0.13 0.00 RG BT -/F231 8.9664 Tf 438.108 721.524 Td [(real)]TJ +/F231 8.9664 Tf 387.299 47.252 Td [(real)]TJ 0 g 0 G [(\050kind_parameter\051)]TJ ET q -1 0 0 1 538.231 707.277 cm +1 0 0 1 487.422 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 1.02 0 0 1 543.859 721.524 Tm [(Any)-1148(r)18(eal)-1148(num-)]TJ 1 0 0 1 544.209 710.565 Tm [(ber)]TJ/F179 9.343 Tf 15.148 0 Td [(\025)]TJ/F84 8.9664 Tf 9.866 0 Td [(0)]TJ +/F84 8.9664 Tf 1.02 0 0 1 493.05 47.252 Tm [(Any)-1148(r)18(eal)-1148(nu)1(m-)]TJ 1 0 0 1 493.4 36.293 Tm [(ber)]TJ/F179 9.343 Tf 15.148 0 Td [(\025)]TJ/F84 8.9664 Tf 9.865 0 Td [(0)]TJ ET q -1 0 0 1 623.888 707.277 cm +1 0 0 1 573.078 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 629.865 721.524 Td [(0)]TJ +/F84 8.9664 Tf 579.056 47.252 Td [(0)]TJ ET q -1 0 0 1 709.544 707.277 cm +1 0 0 1 658.734 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q BT -/F84 8.9664 Tf 715.521 721.524 Td [(Dr)18(op)-250(tolerance)]TJ/F78 8.9664 Tf 61.442 0 Td [(t)]TJ/F84 8.9664 Tf 5.339 0 Td [(in)-250(the)-250(ILU\050)]TJ/F78 8.9664 Tf 43.814 0 Td [(p)]TJ/F84 8.9664 Tf 4.595 0 Td [(,)]TJ/F78 8.9664 Tf 3.848 0 Td [(t)]TJ/F84 8.9664 Tf 3.098 0 Td [(\051)-250(factorization.)]TJ +/F84 8.9664 Tf 0.985 0 0 1 664.712 47.252 Tm [(Second)-255(dr)19(op)-255(tolerance)]TJ/F78 8.9664 Tf 1 0 0 1 754.271 47.252 Tm [(s)]TJ/F84 8.9664 Tf 0.985 0 0 1 760.121 47.252 Tm [(in)-255(the)-254(INVT\050)]TJ/F78 8.9664 Tf 1 0 0 1 809.739 47.252 Tm [(t)]TJ/F84 8.9664 Tf 0.985 0 0 1 812.837 47.252 Tm [(,)]TJ/F78 8.9664 Tf 1 0 0 1 816.652 47.252 Tm [(s)]TJ/F84 8.9664 Tf 0.985 0 0 1 820.252 47.252 Tm [(\051)-255(appr)19(ox-)]TJ 1 0 0 1 664.712 36.293 Tm [(imate)-250(inverse.)]TJ ET q -1 0 0 1 911.42 707.277 cm +1 0 0 1 860.611 33.006 cm []0 d 0 J 0.398 w 0 0 m 0 21.918 l S Q q -1 0 0 1 329.467 707.078 cm +1 0 0 1 278.657 32.806 cm []0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q q -1 0 0 1 329.467 705.085 cm +1 0 0 1 278.657 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 284.635 24.936 Td [(\015AINV_ALG\015)]TJ +0 g 0 G +ET +q +1 0 0 1 381.321 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +0.56 0.13 0.00 rg 0.56 0.13 0.00 RG +BT +/F231 8.9664 Tf 387.299 24.936 Td [(character)]TJ +0 g 0 G + [(\050)]TJ +0.00 0.44 0.13 rg 0.00 0.44 0.13 RG + [(len)]TJ +0 g 0 G +0.40 0.40 0.40 rg 0.40 0.40 0.40 RG + [(=*)]TJ +0 g 0 G + [(\051)]TJ +ET +q +1 0 0 1 487.422 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 493.4 24.936 Td [(\015LLK\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015SYM-LLK\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015STAB-LLK\015)]TJ +0 g 0 G +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG + 0 -10.959 Td [(\015MLK,LMX\015)]TJ +0 g 0 G +ET +q +1 0 0 1 573.078 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +0.25 0.44 0.63 rg 0.25 0.44 0.63 RG +BT +/F231 8.9664 Tf 579.056 24.936 Td [(\015LLK\015)]TJ +0 g 0 G +ET +q +1 0 0 1 658.734 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +BT +/F84 8.9664 Tf 664.362 24.936 Td [(AINV)-250(algorithmic)-250(strategy)111(.)]TJ +ET +q +1 0 0 1 860.611 -11.229 cm +[]0 d 0 J 0.398 w 0 0 m 0 43.836 l S +Q +q +1 0 0 1 278.657 -11.428 cm []0 d 0 J 0.398 w 0 0 m 581.953 0 l S Q 0 g 0 G BT -/F84 9.9626 Tf 398.01 676.707 Td [(T)92(able)-250(22:)-310(Parameters)-250(de\002ning)-250(the)-250(smoother)-250(or)-250(the)-250(details)-250(of)-250(the)-250(one-level)-250(pr)18(econditioner)-250(\050continued\051.)]TJ +/F84 9.9626 Tf 419.673 -39.806 Td [(T)92(able)-250(21:)-310(Parameters)-250(de\002ning)-250(the)-250(solver)-250(of)-250(the)-250(BJAC)-250(pr)18(econditioner)74(.)]TJ 0 g 0 G 0 g 0 G ET -1 0 0 1 322.56 716.092 cm +1 0 0 1 271.751 120.326 cm Q 0 g 0 G 0 g 0 G -1 0 0 1 -322.56 -716.092 cm +1 0 0 1 -271.751 -120.326 cm BT -/F84 9.9626 Tf 315.088 90.438 Td [(154)]TJ +/F84 9.9626 Tf 264.279 90.438 Td [(153)]TJ 0 g 0 G ET endstream endobj -1999 0 obj +1998 0 obj << -/Length 7657 +/Length 7669 >> stream 0 g 0 G 0 g 0 G BT -/F75 11.9552 Tf 99.895 706.129 Td [(10.3)-1000(build)-250(\227)-250(Builds)-250(a)-250(preconditioner)]TJ +/F75 11.9552 Tf 150.705 706.129 Td [(10.3)-1000(build)-250(\227)-250(Builds)-250(a)-250(preconditioner)]TJ 0 g 0 G 0 g 0 G /F131 9.9626 Tf 0 -20.364 Td [(call)-525(prec%build\050a,)-525(desc_a,)-525(info[,amold,vmold,imold]\051)]TJ @@ -27027,230 +27247,230 @@ BT 0 g 0 G 0 -22.816 Td [(a)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(the)-250(system)-250(sparse)-250(matrix.)-310(Scope:)]TJ/F75 9.9626 Tf 146.23 0 Td [(local)]TJ/F84 9.9626 Tf -131.595 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(,)-250(tar)18(get.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(sparse)-250(matrix)-250(data)-250(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 9.963 0 Td [(the)-250(system)-250(sparse)-250(matrix.)-310(Scope:)]TJ/F75 9.9626 Tf 146.229 0 Td [(local)]TJ/F84 9.9626 Tf -131.594 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(,)-250(tar)18(get.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(sparse)-250(matrix)-250(data)-250(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 190.872 0 Td [(psb)]TJ ET q -1 0 0 1 331.993 580.382 cm +1 0 0 1 382.802 580.382 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 335.131 580.183 Td [(Tspmat)]TJ +/F131 9.9626 Tf 385.94 580.183 Td [(Tspmat)]TJ ET q -1 0 0 1 367.141 580.382 cm +1 0 0 1 417.95 580.382 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 370.279 580.183 Td [(type)]TJ +/F131 9.9626 Tf 421.088 580.183 Td [(type)]TJ 0 g 0 G -/F84 9.9626 Tf 20.921 0 Td [(.)]TJ +/F84 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G /F75 9.9626 Tf -291.305 -22.815 Td [(prec)]TJ 0 g 0 G -/F84 9.9626 Tf 24.349 0 Td [(the)-250(pr)18(econditioner)74(.)]TJ 0.558 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(inout)]TJ/F84 9.9626 Tf 24.349 0 Td [(.)]TJ 0.98 0 0 1 124.802 509.547 Tm [(Speci\002ed)-194(as:)-286(an)-193(alr)18(eady)-194(initialized)-194(pr)19(econdtioner)-194(data)-194(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 24.348 0 Td [(the)-250(pr)18(econditioner)74(.)]TJ 0.558 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(inout)]TJ/F84 9.9626 Tf 24.348 0 Td [(.)]TJ 0.98 0 0 1 175.611 509.547 Tm [(Speci\002ed)-194(as:)-286(an)-193(alr)18(eady)-194(initialized)-194(pr)19(econdtioner)-194(data)-194(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG -/F131 9.9626 Tf 1 0 0 1 396.852 509.547 Tm [(psb)]TJ +/F131 9.9626 Tf 1 0 0 1 447.661 509.547 Tm [(psb)]TJ ET q -1 0 0 1 413.17 509.746 cm +1 0 0 1 463.98 509.746 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 416.309 509.547 Td [(prec)]TJ +/F131 9.9626 Tf 467.118 509.547 Td [(Tprec)]TJ ET q -1 0 0 1 437.858 509.746 cm +1 0 0 1 493.897 509.746 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 440.996 509.547 Td [(type)]TJ +/F131 9.9626 Tf 497.036 509.547 Td [(type)]TJ 0 g 0 G 0 g 0 G -/F75 9.9626 Tf -341.101 -34.771 Td [(desc)]TJ +/F75 9.9626 Tf -346.331 -34.771 Td [(desc)]TJ ET q -1 0 0 1 120.408 474.975 cm +1 0 0 1 171.218 474.975 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F75 9.9626 Tf 123.397 474.776 Td [(a)]TJ +/F75 9.9626 Tf 174.207 474.776 Td [(a)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(the)-250(pr)18(oblem)-250(communication)-250(descriptor)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 208.625 0 Td [(local)]TJ/F84 9.9626 Tf -217.492 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(,)-250(tar)18(get.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(communication)-250(descriptor)-250(data)-250(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 9.962 0 Td [(the)-250(pr)18(oblem)-250(communication)-250(descriptor)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 208.625 0 Td [(local)]TJ/F84 9.9626 Tf -217.491 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(,)-250(tar)18(get.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(communication)-250(descriptor)-250(data)-250(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG -/F131 9.9626 Tf 247.648 0 Td [(psb)]TJ +/F131 9.9626 Tf 247.649 0 Td [(psb)]TJ ET q -1 0 0 1 388.769 439.11 cm +1 0 0 1 439.579 439.11 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 391.907 438.911 Td [(desc)]TJ +/F131 9.9626 Tf 442.717 438.911 Td [(desc)]TJ ET q -1 0 0 1 413.456 439.11 cm +1 0 0 1 464.266 439.11 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 416.594 438.911 Td [(type)]TJ +/F131 9.9626 Tf 467.404 438.911 Td [(type)]TJ 0 g 0 G -/F84 9.9626 Tf 20.922 0 Td [(.)]TJ +/F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -337.621 -22.816 Td [(amold)]TJ +/F75 9.9626 Tf -337.62 -22.816 Td [(amold)]TJ 0 g 0 G -/F84 9.9626 Tf 33.455 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(matrix)-250(storage.)]TJ -8.548 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.32 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(object)-250(of)-250(a)-250(class)-250(derived)-250(fr)18(om)]TJ/F131 9.9626 Tf 201.393 0 Td [(psb)]TJ +/F84 9.9626 Tf 33.454 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(matrix)-250(storage.)]TJ -8.548 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.319 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(an)-250(object)-250(of)-250(a)-250(class)-250(derived)-250(fr)18(om)]TJ/F131 9.9626 Tf 201.393 0 Td [(psb)]TJ ET q -1 0 0 1 342.513 368.474 cm +1 0 0 1 393.323 368.474 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 345.652 368.275 Td [(T)]TJ +/F131 9.9626 Tf 396.461 368.275 Td [(T)]TJ ET q -1 0 0 1 351.51 368.474 cm +1 0 0 1 402.319 368.474 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 354.648 368.275 Td [(base)]TJ +/F131 9.9626 Tf 405.457 368.275 Td [(base)]TJ ET q -1 0 0 1 376.197 368.474 cm +1 0 0 1 427.006 368.474 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 379.335 368.275 Td [(sparse)]TJ +/F131 9.9626 Tf 430.144 368.275 Td [(sparse)]TJ ET q -1 0 0 1 411.345 368.474 cm +1 0 0 1 462.154 368.474 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 414.483 368.275 Td [(mat)]TJ/F84 9.9626 Tf 15.691 0 Td [(.)]TJ +/F131 9.9626 Tf 465.292 368.275 Td [(mat)]TJ/F84 9.9626 Tf 15.691 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -330.279 -22.816 Td [(vmold)]TJ +/F75 9.9626 Tf -330.278 -22.816 Td [(vmold)]TJ 0 g 0 G -/F84 9.9626 Tf 34.013 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(vector)-250(storage.)]TJ -9.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.32 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(an)-250(object)-250(of)-250(a)-250(class)-250(derived)-250(fr)18(om)]TJ/F131 9.9626 Tf 201.393 0 Td [(psb)]TJ +/F84 9.9626 Tf 34.012 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(vector)-250(storage.)]TJ -9.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.319 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(an)-250(object)-250(of)-250(a)-250(class)-250(derived)-250(fr)18(om)]TJ/F131 9.9626 Tf 201.393 0 Td [(psb)]TJ ET q -1 0 0 1 342.513 297.838 cm +1 0 0 1 393.323 297.838 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 345.652 297.638 Td [(T)]TJ +/F131 9.9626 Tf 396.461 297.638 Td [(T)]TJ ET q -1 0 0 1 351.51 297.838 cm +1 0 0 1 402.319 297.838 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 354.648 297.638 Td [(base)]TJ +/F131 9.9626 Tf 405.457 297.638 Td [(base)]TJ ET q -1 0 0 1 376.197 297.838 cm +1 0 0 1 427.006 297.838 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 379.335 297.638 Td [(vect)]TJ +/F131 9.9626 Tf 430.144 297.638 Td [(vect)]TJ ET q -1 0 0 1 400.884 297.838 cm +1 0 0 1 451.693 297.838 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 404.022 297.638 Td [(type)]TJ/F84 9.9626 Tf 20.922 0 Td [(.)]TJ +/F131 9.9626 Tf 454.832 297.638 Td [(type)]TJ/F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -325.049 -22.815 Td [(imold)]TJ +/F75 9.9626 Tf -325.048 -22.815 Td [(imold)]TJ 0 g 0 G -/F84 9.9626 Tf 31.791 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(integer)-250(vector)-250(storage.)]TJ -6.884 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.32 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.187 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ 0.98 0 0 1 124.802 227.002 Tm [(Speci\002ed)-194(as:)-286(an)-193(object)-194(of)-194(a)-194(class)-194(derived)-194(fr)19(om)-194(\050integer\051)]TJ/F131 9.9626 Tf 1 0 0 1 356.282 227.002 Tm [(psb)]TJ +/F84 9.9626 Tf 31.79 0 Td [(The)-250(desir)18(ed)-250(dynamic)-250(type)-250(for)-250(the)-250(internal)-250(integer)-250(vector)-250(storage.)]TJ -6.884 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf 21.579 0 Td [(.)]TJ -53.319 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ 0.98 0 0 1 175.611 227.002 Tm [(Speci\002ed)-194(as:)-286(an)-193(object)-194(of)-194(a)-194(class)-194(derived)-194(fr)19(om)-194(\050integer\051)]TJ/F131 9.9626 Tf 1 0 0 1 407.092 227.002 Tm [(psb)]TJ ET q -1 0 0 1 372.601 227.202 cm +1 0 0 1 423.41 227.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 375.739 227.002 Td [(T)]TJ +/F131 9.9626 Tf 426.549 227.002 Td [(T)]TJ ET q -1 0 0 1 381.597 227.202 cm +1 0 0 1 432.406 227.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 384.735 227.002 Td [(base)]TJ +/F131 9.9626 Tf 435.545 227.002 Td [(base)]TJ ET q -1 0 0 1 406.284 227.202 cm +1 0 0 1 457.094 227.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 409.422 227.002 Td [(vect)]TJ +/F131 9.9626 Tf 460.232 227.002 Td [(vect)]TJ ET q -1 0 0 1 430.971 227.202 cm +1 0 0 1 481.781 227.202 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 434.11 227.002 Td [(type)]TJ/F84 9.9626 Tf 0.98 0 0 1 455.031 227.002 Tm [(.)]TJ +/F131 9.9626 Tf 484.919 227.002 Td [(type)]TJ/F84 9.9626 Tf 0.98 0 0 1 505.84 227.002 Tm [(.)]TJ 0 g 0 G -/F75 9.9626 Tf 1 0 0 1 99.895 202.917 Tm [(On)-250(Return)]TJ +/F75 9.9626 Tf 1 0 0 1 150.705 202.917 Tm [(On)-250(Return)]TJ 0 g 0 G 0 g 0 G 0 -22.816 Td [(prec)]TJ 0 g 0 G -/F84 9.9626 Tf 24.349 0 Td [(the)-250(pr)18(econditioner)74(.)]TJ 0.558 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(inout)]TJ/F84 9.9626 Tf 24.349 0 Td [(.)]TJ -56.149 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(pr)18(econdtioner)-250(data)-250(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 24.348 0 Td [(the)-250(pr)18(econditioner)74(.)]TJ 0.558 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(inout)]TJ/F84 9.9626 Tf 24.348 0 Td [(.)]TJ -56.149 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(pr)18(econdtioner)-250(data)-250(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 193.612 0 Td [(psb)]TJ ET q -1 0 0 1 334.732 132.48 cm +1 0 0 1 385.542 132.48 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 337.871 132.281 Td [(prec)]TJ +/F131 9.9626 Tf 388.68 132.281 Td [(Tprec)]TJ ET q -1 0 0 1 359.42 132.48 cm +1 0 0 1 415.459 132.48 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 362.558 132.281 Td [(type)]TJ +/F131 9.9626 Tf 418.598 132.281 Td [(type)]TJ 0 g 0 G 0 g 0 G -/F84 9.9626 Tf -98.279 -41.843 Td [(155)]TJ +/F84 9.9626 Tf -103.51 -41.843 Td [(154)]TJ 0 g 0 G ET endstream endobj -2003 0 obj +2002 0 obj << -/Length 1133 +/Length 1131 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F75 9.9626 Tf 150.705 706.129 Td [(info)]TJ +/F75 9.9626 Tf 99.895 706.129 Td [(info)]TJ 0 g 0 G -/F84 9.9626 Tf 23.8 0 Td [(Err)18(or)-250(code.)]TJ 1.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -47.133 -11.955 Td [(An)-250(integer)-250(value;)-250(0)-250(means)-250(no)-250(err)18(or)-250(has)-250(been)-250(detected.)]TJ 1.02 0 0 1 150.396 636.39 Tm [(The)]TJ/F131 9.9626 Tf 1 0 0 1 170.746 636.39 Tm [(amold)]TJ/F84 9.9626 Tf 1.02 0 0 1 196.898 636.39 Tm [(,)]TJ/F131 9.9626 Tf 1 0 0 1 202.989 636.39 Tm [(vmold)]TJ/F84 9.9626 Tf 1.02 0 0 1 232.48 636.39 Tm [(and)]TJ/F131 9.9626 Tf 1 0 0 1 253.023 636.39 Tm [(imold)]TJ/F84 9.9626 Tf 1.02 0 0 1 282.514 636.39 Tm [(ar)18(guments)-329(may)-328(be)-329(employed)-329(to)-328(interface)-329(with)]TJ 1 0 0 1 150.705 624.435 Tm [(special)-250(devices,)-250(such)-250(as)-250(GPUs)-250(and)-250(other)-250(accelerators.)]TJ +/F84 9.9626 Tf 23.801 0 Td [(Err)18(or)-250(code.)]TJ 1.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -47.133 -11.955 Td [(An)-250(integer)-250(value;)-250(0)-250(means)-250(no)-250(err)18(or)-250(has)-250(been)-250(detected.)]TJ 1.02 0 0 1 99.587 636.39 Tm [(The)]TJ/F131 9.9626 Tf 1 0 0 1 119.936 636.39 Tm [(amold)]TJ/F84 9.9626 Tf 1.02 0 0 1 146.088 636.39 Tm [(,)]TJ/F131 9.9626 Tf 1 0 0 1 152.18 636.39 Tm [(vmold)]TJ/F84 9.9626 Tf 1.02 0 0 1 181.67 636.39 Tm [(and)]TJ/F131 9.9626 Tf 1 0 0 1 202.214 636.39 Tm [(imold)]TJ/F84 9.9626 Tf 1.02 0 0 1 231.704 636.39 Tm [(ar)18(guments)-329(may)-329(be)-328(employed)-329(to)-328(interface)-329(with)]TJ 1 0 0 1 99.895 624.435 Tm [(special)-250(devices,)-250(such)-250(as)-250(GPUs)-250(and)-250(other)-250(accelerators.)]TJ 0 g 0 G - 164.383 -533.997 Td [(156)]TJ + 164.384 -533.997 Td [(155)]TJ 0 g 0 G ET endstream endobj -2011 0 obj +2010 0 obj << -/Length 5674 +/Length 5678 >> stream 0 g 0 G 0 g 0 G BT -/F75 11.9552 Tf 99.895 706.129 Td [(10.4)-1000(apply)-250(\227)-250(Preconditioner)-250(application)-250(routine)]TJ +/F75 11.9552 Tf 150.705 706.129 Td [(10.4)-1000(apply)-250(\227)-250(Preconditioner)-250(application)-250(routine)]TJ 0 g 0 G 0 g 0 G /F131 9.9626 Tf 0 -18.964 Td [(call)-525(prec%apply\050x,y,desc_a,info,trans,work\051)]TJ 0 -11.955 Td [(call)-525(prec%apply\050x,desc_a,info,trans\051)]TJ @@ -27264,81 +27484,81 @@ BT 0 g 0 G 0 -19.925 Td [(prec)]TJ 0 g 0 G -/F84 9.9626 Tf 24.349 0 Td [(the)-250(pr)18(econditioner)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 117.836 0 Td [(local)]TJ/F84 9.9626 Tf -117.587 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(pr)18(econditioner)-250(data)-250(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 24.348 0 Td [(the)-250(pr)18(econditioner)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 117.837 0 Td [(local)]TJ/F84 9.9626 Tf -117.587 -11.956 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(pr)18(econditioner)-250(data)-250(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 196.511 0 Td [(psb)]TJ ET q -1 0 0 1 337.631 577.775 cm +1 0 0 1 388.441 577.775 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 340.77 577.576 Td [(prec)]TJ +/F131 9.9626 Tf 391.579 577.576 Td [(Tprec)]TJ ET q -1 0 0 1 362.319 577.775 cm +1 0 0 1 418.358 577.775 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 365.457 577.576 Td [(type)]TJ +/F131 9.9626 Tf 421.497 577.576 Td [(type)]TJ 0 g 0 G /F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -286.483 -19.925 Td [(x)]TJ +/F75 9.9626 Tf -291.713 -19.925 Td [(x)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(the)-250(sour)18(ce)-250(vector)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 111.142 0 Td [(local)]TJ/F84 9.9626 Tf -96.507 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(inout)]TJ/F84 9.9626 Tf 24.349 0 Td [(.)]TJ -56.149 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(rank)-250(one)-250(array)-250(or)-250(an)-250(object)-250(of)-250(type)]TJ +/F84 9.9626 Tf 9.962 0 Td [(the)-250(sour)18(ce)-250(vector)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 111.142 0 Td [(local)]TJ/F84 9.9626 Tf -96.506 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(inout)]TJ/F84 9.9626 Tf 24.348 0 Td [(.)]TJ -56.149 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(rank)-250(one)-250(array)-250(or)-250(an)-250(object)-250(of)-250(type)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 218.688 0 Td [(psb)]TJ ET q -1 0 0 1 359.808 521.985 cm +1 0 0 1 410.618 521.985 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 362.947 521.785 Td [(T)]TJ +/F131 9.9626 Tf 413.756 521.785 Td [(T)]TJ ET q -1 0 0 1 368.804 521.985 cm +1 0 0 1 419.614 521.985 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 371.943 521.785 Td [(vect)]TJ +/F131 9.9626 Tf 422.752 521.785 Td [(vect)]TJ ET q -1 0 0 1 393.492 521.985 cm +1 0 0 1 444.301 521.985 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 396.63 521.785 Td [(type)]TJ +/F131 9.9626 Tf 447.439 521.785 Td [(type)]TJ 0 g 0 G -/F84 9.9626 Tf 20.921 0 Td [(.)]TJ +/F84 9.9626 Tf 20.922 0 Td [(.)]TJ 0 g 0 G /F75 9.9626 Tf -317.656 -19.925 Td [(desc)]TJ ET q -1 0 0 1 120.408 502.059 cm +1 0 0 1 171.218 502.059 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F75 9.9626 Tf 123.397 501.86 Td [(a)]TJ +/F75 9.9626 Tf 174.207 501.86 Td [(a)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(the)-250(pr)18(oblem)-250(communication)-250(descriptor)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 208.625 0 Td [(local)]TJ/F84 9.9626 Tf -217.492 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(a)-250(communication)-250(data)-250(str)8(uctur)18(e)]TJ +/F84 9.9626 Tf 9.962 0 Td [(the)-250(pr)18(oblem)-250(communication)-250(descriptor)74(.)-310(Scope:)]TJ/F75 9.9626 Tf 208.625 0 Td [(local)]TJ/F84 9.9626 Tf -217.491 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.956 Td [(Speci\002ed)-250(as:)-310(a)-250(communication)-250(data)-250(str)8(uctur)18(e)]TJ 0 0 1 rg 0 0 1 RG -/F131 9.9626 Tf 200.207 0 Td [(psb)]TJ +/F131 9.9626 Tf 200.208 0 Td [(psb)]TJ ET q -1 0 0 1 341.328 466.194 cm +1 0 0 1 392.137 466.194 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 344.466 465.994 Td [(desc)]TJ +/F131 9.9626 Tf 395.275 465.994 Td [(desc)]TJ ET q -1 0 0 1 366.015 466.194 cm +1 0 0 1 416.824 466.194 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT 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[(11)-1000(Iterative)-250(Methods)]TJ/F84 9.9626 Tf 1.006 0 0 1 99.895 683.082 Tm [(In)-249(this)-250(chapter)-249(we)-250(pr)18(ovide)-249(r)18(outines)-250(for)-249(pr)18(econditioners)-250(and)-249(iterative)-249(methods.)]TJ 0.98 0 0 1 99.587 671.127 Tm [(The)-194(interfaces)-194(for)-194(it)1(erative)-194(methods)-194(ar)18(e)-194(available)-194(in)-193(the)-194(module)]TJ/F131 9.9626 Tf 1 0 0 1 369.457 671.127 Tm [(psb_linsolve_mod)]TJ/F84 9.9626 Tf 0.98 0 0 1 453.142 671.127 Tm [(.)]TJ +/F75 14.3462 Tf 150.705 705.784 Td [(11)-1000(Iterative)-250(Methods)]TJ/F84 9.9626 Tf 1.006 0 0 1 150.705 683.082 Tm [(In)-249(this)-250(chapter)-249(we)-250(pr)18(ovide)-249(r)18(outines)-250(for)-249(pr)18(econditioners)-250(and)-249(iterative)-249(methods.)]TJ 0.98 0 0 1 150.396 671.127 Tm [(The)-194(interfaces)-194(for)-194(iterative)-193(methods)-194(ar)18(e)-194(available)-194(in)-193(the)-194(module)]TJ/F131 9.9626 Tf 1 0 0 1 420.266 671.127 Tm [(psb_linsolve_mod)]TJ/F84 9.9626 Tf 0.98 0 0 1 503.952 671.127 Tm [(.)]TJ 0 g 0 G - 1 0 0 1 264.279 90.438 Tm [(161)]TJ + 1 0 0 1 315.088 90.438 Tm [(160)]TJ 0 g 0 G ET endstream endobj -2038 0 obj +2037 0 obj << -/Length 8466 +/Length 8455 >> stream 0 g 0 G 0 g 0 G BT -/F75 11.9552 Tf 150.705 706.129 Td [(11.1)-1000(psb)]TJ +/F75 11.9552 Tf 99.895 706.129 Td [(11.1)-1000(psb)]TJ ET q -1 0 0 1 204.216 706.328 cm +1 0 0 1 153.407 706.328 cm []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 207.803 706.129 Td [(krylov)-250(\227)-250(Krylov)-250(Methods)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf 1.013 0 0 1 150.396 687.165 Tm [(This)-247(subr)18(outine)-247(is)-248(a)-247(driver)-247(that)-247(pr)18(ovides)-247(a)-247(general)-247(interface)-248(for)-247(all)-247(the)-247(Krylov-)]TJ 1 0 0 1 150.705 675.21 Tm [(Subspace)-250(family)-250(methods)-250(implemented)-250(in)-250(PSBLAS)-250(version)-250(2.)]TJ 14.944 -11.955 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ +/F75 11.9552 Tf 156.993 706.129 Td [(krylov)-250(\227)-250(Krylov)-250(Methods)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf 1.013 0 0 1 99.587 687.165 Tm [(This)-247(subr)18(outine)-247(is)-247(a)-248(driver)-247(that)-247(pr)18(ovides)-247(a)-247(general)-247(interface)-248(fo)1(r)-248(all)-247(the)-247(Krylov-)]TJ 1 0 0 1 99.895 675.21 Tm [(Subspace)-250(family)-250(methods)-250(implemented)-250(in)-250(PSBLAS)-250(version)-250(2.)]TJ 14.944 -11.955 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ 0 g 0 G /F75 9.9626 Tf -14.944 -18.774 Td [(1)]TJ 0 g 0 G -/F84 9.9626 Tf 0.99 0 0 1 160.667 644.481 Tm [(normwise)-253(backwar)19(d)-253(err)18(or)-252(in)-253(the)-252(in\002nity)-253(norm;)-252(the)-253(iteration)-252(is)-253(stopped)-252(when)]TJ/F78 9.9626 Tf 1 0 0 1 269.703 617.617 Tm [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 40.619 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td 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6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 136.209 -26.865 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 13.446 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q -1 0 0 1 324.174 563.335 cm +1 0 0 1 273.365 563.335 cm []0 d 0 J 0.398 w 0 0 m 20.025 0 l S Q BT -/F179 10.3811 Tf 324.299 554.01 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F179 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ +/F179 10.3811 Tf 273.49 554.01 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F179 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ 0 g 0 G -/F75 9.9626 Tf -208.667 -29.848 Td [(3)]TJ +/F75 9.9626 Tf -208.668 -29.848 Td [(3)]TJ 0 g 0 G -/F84 9.9626 Tf 9.962 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -26.865 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 15.169 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -26.865 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.14 0 Td [(=)]TJ/F179 10.3811 Tf 15.17 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q -1 0 0 1 322.451 506.622 cm +1 0 0 1 271.641 506.622 cm []0 d 0 J 0.398 w 0 0 m 23.472 0 l S Q BT -/F179 10.3811 Tf 322.575 497.297 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F179 10.3811 Tf 4.409 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 150.396 474.283 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 150.705 462.327 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 194.836 462.327 Tm [(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 204.675 462.327 Tm [(is)-199(the)-199(tentative)-198(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 324.514 462.327 Tm [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F181 10.3811 Tf 5.642 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F179 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.759 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 379.269 462.327 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 150.705 450.372 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.306 -17.357 Td [(c)-175(a)-175(l)-174(l)-880(p)-105(s)-105(b)]TJ +/F179 10.3811 Tf 271.766 497.297 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F179 10.3811 Tf 4.408 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.587 474.283 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 99.895 462.327 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 144.027 462.327 Tm [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 153.866 462.327 Tm [(is)-199(the)-199(tentat)1(ive)-199(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 273.705 462.327 Tm [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F181 10.3811 Tf 5.643 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F179 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.758 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 328.46 462.327 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 99.895 450.372 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.305 -17.357 Td [(c)-175(a)-175(l)-174(l)-880(p)-105(s)-105(b)]TJ ET q -1 0 0 1 201.089 433.215 cm +1 0 0 1 150.28 433.215 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F84 9.9626 Tf 205.122 433.015 Td [(k)-105(r)-105(y)-105(l)-104(o)-105(v)-238(\050)-156(m)-21(e)-22(t)-22(h)-21(o)-22(d)-218(,)-208(a)-242(,)-255(p)-80(r)-81(e)-80(c)-335(,)-191(b)-206(,)-203(x)-231(,)-234(e)-60(p)-59(s)-293(,)-273(d)-98(e)-97(s)-98(c)]TJ +/F84 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-11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf 38.186 0 Td [(.)]TJ -64.966 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ 1.02 0 0 1 175.253 132.281 Tm [(V)90(alues:)]TJ/F78 9.9626 Tf 1 0 0 1 213.338 132.281 Tm [(i)-22(r)-35(s)-25(t)]TJ/F134 10.3811 Tf 20.115 0 Td [(>)]TJ/F84 9.9626 Tf 1.02 0 0 1 246.858 132.281 Tm [(0.)-694(This)-375(i)1(s)-375(employed)-375(for)-375(the)-375(BiCGST)72(ABL)-375(or)-375(RG)1(MRES)]TJ 1 0 0 1 175.611 120.326 Tm [(methods,)-250(otherwise)-250(it)-250(is)-250(ignor)18(ed.)]TJ 0 g 0 G - 139.477 -29.888 Td [(163)]TJ + 139.477 -29.888 Td [(162)]TJ 0 g 0 G ET endstream endobj -2056 0 obj +2054 0 obj << -/Length 4580 +/Length 4581 >> stream 0 g 0 G 0 g 0 G 0 g 0 G BT -/F75 9.9626 Tf 150.705 706.129 Td [(istop)]TJ +/F75 9.9626 Tf 99.895 706.129 Td [(istop)]TJ 0 g 0 G -/F84 9.9626 Tf 27.277 0 Td [(An)-250(integer)-250(specifying)-250(the)-250(stopping)-250(criterion.)]TJ -2.371 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371.943 558.682 Td [(vect)]TJ ET q -1 0 0 1 444.301 558.881 cm +1 0 0 1 393.492 558.881 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 447.439 558.682 Td [(type)]TJ +/F131 9.9626 Tf 396.63 558.682 Td [(type)]TJ 0 g 0 G -/F84 9.9626 Tf 20.922 0 Td [(.)]TJ +/F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G /F75 9.9626 Tf -317.656 -19.925 Td [(iter)]TJ 0 g 0 G -/F84 9.9626 Tf 20.164 0 Td [(The)-250(number)-250(of)-250(iterations)-250(performed.)]TJ 4.742 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.745 -11.955 Td [(Returned)-250(as:)-310(an)-250(integer)-250(variable.)]TJ +/F84 9.9626 Tf 20.165 0 Td [(The)-250(number)-250(of)-250(iterations)-250(performed.)]TJ 4.742 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.744 -11.955 Td [(Returned)-250(as:)-310(an)-250(integer)-250(variable.)]TJ 0 g 0 G -/F75 9.9626 Tf -24.906 -19.925 Td [(err)]TJ +/F75 9.9626 Tf -24.907 -19.925 Td [(err)]TJ 0 g 0 G -/F84 9.9626 Tf 17.404 0 Td [(The)-250(conver)18(gence)-250(estimate)-250(on)-250(exit.)]TJ 7.502 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.744 -11.955 Td [(Returned)-250(as:)-310(a)-250(r)18(eal)-250(number)74(.)]TJ +/F84 9.9626 Tf 17.405 0 Td [(The)-250(conver)18(gence)-250(estimate)-250(on)-250(exit.)]TJ 7.502 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.744 -11.955 Td [(Returned)-250(as:)-310(a)-250(r)18(eal)-250(number)74(.)]TJ 0 g 0 G /F75 9.9626 Tf -24.907 -19.925 Td [(cond)]TJ 0 g 0 G -/F84 9.9626 Tf 0.985 0 0 1 177.434 403.265 Tm [(An)-253(estimate)-254(of)-253(the)-253(condition)-253(number)-254(of)-253(matrix)]TJ/F78 9.9626 Tf 1 0 0 1 382.801 403.265 Tm [(A)]TJ/F84 9.9626 Tf 0.985 0 0 1 390.119 403.265 Tm [(;)-253(only)-254(available)-253(with)-253(the)]TJ/F78 9.9626 Tf 1 0 0 1 175.696 391.309 Tm [(C)-45(G)]TJ/F84 9.9626 Tf 17.001 0 Td [(method)-250(on)-250(r)18(eal)-250(data.)]TJ -17.086 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(global)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(optional)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ 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[(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -46.744 -11.955 Td [(Returned)-249(as:)-310(a)-249(r)18(eal)-249(number)74(.)-310(A)-249(corr)18(ect)-250(r)18(esult)-249(will)-249(be)-249(gr)18(eater)-250(than)-249(or)-249(equal)]TJ 0.98 0 0 1 124.802 331.534 Tm [(to)-255(one;)-255(if)-255(s)1(peci\002ed)-255(for)-255(non-r)18(eal)-254(data,)-255(or)-255(an)-255(err)18(or)-254(occurr)18(ed,)-255(zer)18(o)-254(is)-255(r)18(eturned.)]TJ 0 g 0 G -/F75 9.9626 Tf 1 0 0 1 150.705 311.608 Tm [(info)]TJ +/F75 9.9626 Tf 1 0 0 1 99.895 311.608 Tm [(info)]TJ 0 g 0 G -/F84 9.9626 Tf 23.8 0 Td [(Err)18(or)-250(code.)]TJ 1.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -47.133 -11.955 Td [(An)-250(integer)-250(value;)-250(0)-250(means)-250(no)-250(err)18(or)-250(has)-250(been)-250(detected.)]TJ +/F84 9.9626 Tf 23.801 0 Td [(Err)18(or)-250(code.)]TJ 1.106 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(out)]TJ/F84 9.9626 Tf 14.944 0 Td [(.)]TJ -47.133 -11.955 Td [(An)-250(integer)-250(value;)-250(0)-250(means)-250(no)-250(err)18(or)-250(has)-250(been)-250(detected.)]TJ 0 g 0 G - 139.865 -173.35 Td [(164)]TJ + 139.866 -173.35 Td [(163)]TJ 0 g 0 G ET endstream endobj -2064 0 obj +2063 0 obj << -/Length 8758 +/Length 8762 >> stream 0 g 0 G 0 g 0 G BT -/F75 11.9552 Tf 99.895 706.129 Td [(11.2)-1000(psb)]TJ +/F75 11.9552 Tf 150.705 706.129 Td [(11.2)-1000(psb)]TJ ET q -1 0 0 1 153.407 706.328 cm +1 0 0 1 204.216 706.328 cm []0 d 0 J 0.398 w 0 0 m 3.587 0 l S Q BT -/F75 11.9552 Tf 156.993 706.129 Td [(richardson)-250(\227)-250(Richardson)-250(Iteration)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf -57.406 -19.209 Td [(This)-250(subr)18(outine)-250(is)-250(a)-250(driver)-250(implementig)-250(a)-250(Richar)18(dson)-250(iteration)]TJ/F78 9.9626 Tf 111.157 -22.171 Td [(x)]TJ/F78 7.5716 Tf 5.2 -2.085 Td [(k)]TJ/F181 7.8896 Tf 3.589 0 Td [(+)]TJ/F84 7.5716 Tf 6.228 0 Td [(1)]TJ/F181 10.3811 Tf 7.176 2.085 Td [(=)]TJ/F78 9.9626 Tf 11.534 0 Td [(M)]TJ/F179 7.8896 Tf 9.674 4.115 Td [(\000)]TJ/F84 9.9626 Tf 6.726 -4.115 Td [(1)]TJ/F181 10.3811 Tf 5.105 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(b)]TJ/F179 10.3811 Tf 6.799 0 Td [(\000)]TJ/F78 9.9626 Tf 10.754 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.812 -2.085 Td [(k)]TJ/F181 10.3811 Tf 4.117 2.085 Td [(\051)-209(+)]TJ/F78 9.9626 Tf 16.636 0 Td [(x)]TJ/F78 7.5716 Tf 5.201 -2.085 Td [(k)]TJ/F84 9.9626 Tf 3.992 2.085 Td [(,)]TJ -231.084 -22.17 Td [(with)-250(the)-250(pr)18(econditioner)-250(operator)]TJ/F78 9.9626 Tf 147.599 0 Td [(M)]TJ/F84 9.9626 Tf 12.07 0 Td [(de\002ned)-250(in)-250(the)-250(pr)18(evious)-250(section.)]TJ -144.307 -12.082 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ +/F75 11.9552 Tf 207.803 706.129 Td [(richardson)-250(\227)-250(Richardson)-250(Iteration)-250(Driver)-250(Routine)]TJ/F84 9.9626 Tf -57.407 -19.209 Td [(This)-250(subr)18(outine)-250(is)-250(a)-250(driver)-250(implementig)-250(a)-250(Richar)18(dson)-250(iteration)]TJ/F78 9.9626 Tf 111.158 -22.171 Td [(x)]TJ/F78 7.5716 Tf 5.2 -2.085 Td [(k)]TJ/F181 7.8896 Tf 3.589 0 Td [(+)]TJ/F84 7.5716 Tf 6.227 0 Td [(1)]TJ/F181 10.3811 Tf 7.176 2.085 Td [(=)]TJ/F78 9.9626 Tf 11.535 0 Td [(M)]TJ/F179 7.8896 Tf 9.673 4.115 Td [(\000)]TJ/F84 9.9626 Tf 6.726 -4.115 Td [(1)]TJ/F181 10.3811 Tf 5.106 0 Td [(\050)]TJ/F78 9.9626 Tf 4.274 0 Td [(b)]TJ/F179 10.3811 Tf 6.799 0 Td [(\000)]TJ/F78 9.9626 Tf 10.754 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.811 -2.085 Td [(k)]TJ/F181 10.3811 Tf 4.117 2.085 Td [(\051)-209(+)]TJ/F78 9.9626 Tf 16.637 0 Td [(x)]TJ/F78 7.5716 Tf 5.2 -2.085 Td [(k)]TJ/F84 9.9626 Tf 3.992 2.085 Td [(,)]TJ -231.084 -22.17 Td [(with)-250(the)-250(pr)18(econditioner)-250(operator)]TJ/F78 9.9626 Tf 147.6 0 Td [(M)]TJ/F84 9.9626 Tf 12.07 0 Td [(de\002ned)-250(in)-250(the)-250(pr)18(evious)-250(section.)]TJ -144.307 -12.082 Td [(The)-250(stopping)-250(criterion)-250(can)-250(take)-250(the)-250(following)-250(values:)]TJ 0 g 0 G /F75 9.9626 Tf -14.944 -20.304 Td [(1)]TJ 0 g 0 G -/F84 9.9626 Tf 0.99 0 0 1 109.858 610.193 Tm [(normwise)-252(backwar)18(d)-253(err)18(or)-252(in)-253(the)-252(in\002nity)-253(norm;)-252(the)-253(iteration)-252(is)-253(stopped)-252(when)]TJ/F78 9.9626 Tf 1 0 0 1 218.894 581.636 Tm [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.14 0 Td [(=)]TJ/F179 10.3811 Tf 40.62 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 0.99 0 0 1 160.667 610.193 Tm [(normwise)-253(backwar)19(d)-253(err)18(or)-252(in)-253(the)-252(in\002nity)-253(norm;)-252(the)-253(iteration)-252(is)-253(stopped)-252(when)]TJ/F78 9.9626 Tf 1 0 0 1 269.703 581.636 Tm [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 40.619 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q -1 0 0 1 246.191 584.127 cm +1 0 0 1 297.001 584.127 cm []0 d 0 J 0.398 w 0 0 m 74.372 0 l S Q BT -/F181 10.3811 Tf 246.316 574.802 Td [(\050)]TJ/F179 10.3811 Tf 4.274 0 Td [(k)]TJ/F78 9.9626 Tf 5.938 0 Td [(A)]TJ/F179 10.3811 Tf 7.442 0 Td [(k)-24(k)]TJ/F78 9.9626 Tf 11.048 0 Td [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.876 1.96 Td [(k)]TJ/F181 10.3811 Tf 7.376 0 Td [(+)]TJ/F179 10.3811 Tf 10.256 0 Td [(k)]TJ/F78 9.9626 Tf 5.44 0 Td [(b)]TJ/F179 10.3811 Tf 4.861 0 Td [(k)]TJ/F181 10.3811 Tf 5.44 0 Td [(\051)]TJ/F134 10.3811 Tf 8.236 6.834 Td [(<)]TJ/F78 9.9626 Tf 11.087 0 Td [(e)-80(p)-25(s)]TJ +/F181 10.3811 Tf 297.125 574.802 Td [(\050)]TJ/F179 10.3811 Tf 4.274 0 Td [(k)]TJ/F78 9.9626 Tf 5.938 0 Td [(A)]TJ/F179 10.3811 Tf 7.442 0 Td [(k)-24(k)]TJ/F78 9.9626 Tf 11.048 0 Td [(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ/F181 10.3811 Tf 7.377 0 Td [(+)]TJ/F179 10.3811 Tf 10.255 0 Td [(k)]TJ/F78 9.9626 Tf 5.44 0 Td [(b)]TJ/F179 10.3811 Tf 4.862 0 Td [(k)]TJ/F181 10.3811 Tf 5.439 0 Td [(\051)]TJ/F134 10.3811 Tf 8.237 6.834 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ 0 g 0 G -/F75 9.9626 Tf -235.842 -32.142 Td [(2)]TJ +/F75 9.9626 Tf -235.841 -32.142 Td [(2)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 136.209 -28.557 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 13.446 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 136.209 -28.557 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.14 0 Td [(=)]TJ/F179 10.3811 Tf 13.446 6.745 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q -1 0 0 1 273.365 523.428 cm +1 0 0 1 324.174 523.428 cm []0 d 0 J 0.398 w 0 0 m 20.025 0 l S Q BT -/F179 10.3811 Tf 273.49 514.103 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F179 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ +/F179 10.3811 Tf 324.299 514.103 Td [(k)]TJ/F78 9.9626 Tf 5.439 0 Td [(b)]TJ/F179 10.3811 Tf 4.862 0 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.578 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ 0 g 0 G -/F75 9.9626 Tf -208.668 -32.082 Td [(3)]TJ +/F75 9.9626 Tf -208.667 -32.082 Td [(3)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -28.556 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.14 0 Td [(=)]TJ/F179 10.3811 Tf 15.17 6.744 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ +/F84 9.9626 Tf 9.962 0 Td [(Relative)-250(r)18(esidual)-250(r)18(eduction)-250(in)-250(the)-250(2-norm;)-250(the)-250(iteration)-250(is)-250(stopped)-250(when)]TJ/F78 9.9626 Tf 134.486 -28.556 Td [(e)-15(r)-25(r)]TJ/F181 10.3811 Tf 15.141 0 Td [(=)]TJ/F179 10.3811 Tf 15.169 6.744 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F179 10.3811 Tf 2.875 1.96 Td [(k)]TJ ET q -1 0 0 1 271.641 462.789 cm +1 0 0 1 322.451 462.789 cm []0 d 0 J 0.398 w 0 0 m 23.472 0 l S Q BT -/F179 10.3811 Tf 271.766 453.464 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F179 10.3811 Tf 4.408 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.579 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 99.587 428.217 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 99.895 416.261 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 144.027 416.261 Tm [(x)]TJ/F78 7.5716 Tf 5.147 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 153.866 416.261 Tm [(is)-199(the)-199(tentat)1(ive)-199(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 273.705 416.261 Tm [(r)]TJ/F78 7.5716 Tf 4.041 -1.96 Td [(i)]TJ/F181 10.3811 Tf 5.643 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F179 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.758 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 328.46 416.261 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 99.895 404.306 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.305 -18.185 Td [(c)-175(a)-175(l)-174(l)-888(p)-113(s)-113(b)]TJ +/F179 10.3811 Tf 322.575 453.464 Td [(k)]TJ/F78 9.9626 Tf 5.34 0 Td [(r)]TJ/F84 7.5716 Tf 4 -1.744 Td [(0)]TJ/F179 10.3811 Tf 4.409 1.744 Td [(k)]TJ/F84 7.5716 Tf 5.315 -1.744 Td [(2)]TJ/F134 10.3811 Tf 8.371 8.579 Td [(<)]TJ/F78 9.9626 Tf 11.086 0 Td [(e)-80(p)-25(s)]TJ/F84 9.9626 Tf 1.02 0 0 1 150.396 428.217 Tm [(The)-333(behaviour)-333(is)-333(contr)18(olled)-333(by)-333(the)-333(istop)-333(ar)18(gument)-333(\050see)-333(later\051.)-567(In)-333(the)-333(above)]TJ 0.98 0 0 1 150.705 416.261 Tm [(formulae,)]TJ/F78 9.9626 Tf 1 0 0 1 194.836 416.261 Tm [(x)]TJ/F78 7.5716 Tf 5.148 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 204.675 416.261 Tm [(is)-199(the)-199(tentative)-198(solution)-199(and)]TJ/F78 9.9626 Tf 1 0 0 1 324.514 416.261 Tm [(r)]TJ/F78 7.5716 Tf 4.042 -1.96 Td [(i)]TJ/F181 10.3811 Tf 5.642 1.96 Td [(=)]TJ/F78 9.9626 Tf 11.086 0 Td [(b)]TJ/F179 10.3811 Tf 6.29 0 Td [(\000)]TJ/F78 9.9626 Tf 10.245 0 Td [(A)-42(x)]TJ/F78 7.5716 Tf 12.759 -1.96 Td [(i)]TJ/F84 9.9626 Tf 0.98 0 0 1 379.269 416.261 Tm [(the)-199(corr)19(esponding)-199(r)18(esidual)]TJ 1 0 0 1 150.705 404.306 Tm [(at)-250(the)]TJ/F78 9.9626 Tf 27.083 0 Td [(i)]TJ/F84 9.9626 Tf 2.964 0 Td [(-th)-250(iteration.)]TJ -28.306 -18.185 Td [(c)-175(a)-175(l)-174(l)-888(p)-113(s)-113(b)]TJ ET q -1 0 0 1 150.598 386.32 cm +1 0 0 1 201.407 386.32 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F84 9.9626 Tf 154.71 386.121 Td [(r)-113(i)-113(c)-112(h)-113(a)-113(r)-113(d)-113(s)-113(o)-112(n)-247(\050)-166(a)-242(,)-255(p)-80(r)-81(e)-80(c)-335(,)-191(b)-206(,)-203(x)-231(,)-234(e)-60(p)-59(s)-293(,)-273(d)-98(e)-98(s)-97(c)]TJ +/F84 9.9626 Tf 205.52 386.121 Td [(r)-113(i)-113(c)-112(h)-113(a)-113(r)-113(d)-113(s)-112(o)-113(n)-247(\050)-166(a)-242(,)-255(p)-80(r)-81(e)-80(c)-335(,)-191(b)-206(,)-203(x)-231(,)-234(e)-60(p)-59(s)-293(,)-273(d)-98(e)-97(s)-98(c)]TJ ET q -1 0 0 1 334.087 386.32 cm +1 0 0 1 384.896 386.32 cm []0 d 0 J 0.398 w 0 0 m 2.989 0 l S Q BT -/F84 9.9626 Tf 338.05 386.121 Td [(a)-370(,)-283(i)-108(n)-109(f)-108(o)-273(,)-57(&)]TJ -209.153 -11.956 Td [(&)-580(i)-69(t)-69(m)-70(a)-69(x)-313(,)-327(i)-151(t)-152(e)-151(r)-478(,)-281(e)-107(r)-106(r)-387(,)-321(i)-145(t)-146(r)-146(a)-145(c)-146(e)-466(,)-311(i)-135(s)-135(t)-136(o)-135(p)-269(\051)]TJ +/F84 9.9626 Tf 388.859 386.121 Td [(a)-371(,)-283(i)-108(n)-108(f)-108(o)-273(,)-57(&)]TJ -209.153 -11.956 Td [(&)-580(i)-69(t)-69(m)-70(a)-69(x)-313(,)-327(i)-151(t)-152(e)-151(r)-478(,)-281(e)-107(r)-106(r)-387(,)-321(i)-145(t)-146(r)-146(a)-145(c)-146(e)-466(,)-311(i)-135(s)-135(t)-136(o)-135(p)-269(\051)]TJ 0 g 0 G 0 g 0 G 0 g 0 G -/F75 9.9626 Tf -29.002 -28.653 Td [(T)90(ype:)]TJ +/F75 9.9626 Tf -29.001 -28.653 Td [(T)90(ype:)]TJ 0 g 0 G /F84 9.9626 Tf 29.828 0 Td [(Synchr)18(onous.)]TJ 0 g 0 G @@ -28630,301 +28858,301 @@ BT 0 g 0 G 0 -20.431 Td [(a)]TJ 0 g 0 G -/F84 9.9626 Tf 9.963 0 Td [(the)-250(local)-250(portion)-250(of)-250(global)-250(sparse)-250(matrix)]TJ/F78 9.9626 Tf 178.414 0 Td [(A)]TJ/F84 9.9626 Tf 7.317 0 Td [(.)]TJ -170.787 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(str)8(uctur)18(ed)-250(data)-250(of)-250(type)]TJ +/F84 9.9626 Tf 9.962 0 Td [(the)-250(local)-250(portion)-250(of)-250(global)-250(sparse)-250(matrix)]TJ/F78 9.9626 Tf 178.414 0 Td [(A)]TJ/F84 9.9626 Tf 7.318 0 Td [(.)]TJ -170.788 -11.956 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(str)8(uctur)18(ed)-250(data)-250(of)-250(type)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 168.138 0 Td [(psb)]TJ ET q -1 0 0 1 309.258 257.028 cm +1 0 0 1 360.068 257.028 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 312.397 256.829 Td [(Tspmat)]TJ +/F131 9.9626 Tf 363.206 256.829 Td [(Tspmat)]TJ ET q -1 0 0 1 344.406 257.028 cm +1 0 0 1 395.216 257.028 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 347.544 256.829 Td [(type)]TJ +/F131 9.9626 Tf 398.354 256.829 Td [(type)]TJ 0 g 0 G -/F84 9.9626 Tf 20.922 0 Td [(.)]TJ +/F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -268.571 -20.431 Td [(prec)]TJ +/F75 9.9626 Tf -268.57 -20.431 Td [(prec)]TJ 0 g 0 G -/F84 9.9626 Tf 24.04 0 Td [(The)-250(data)-250(str)8(uctur)18(e)-250(containing)-250(the)-250(pr)18(econditioner)74(.)]TJ 0.867 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(str)8(uctur)18(ed)-250(data)-250(of)-250(type)]TJ +/F84 9.9626 Tf 24.04 0 Td [(The)-250(data)-250(str)8(uctur)18(e)-250(containing)-250(the)-250(pr)18(econditioner)74(.)]TJ 0.866 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.78 -11.956 Td [(Intent:)]TJ/F75 9.9626 Tf 31.801 0 Td [(in)]TJ/F84 9.9626 Tf 9.404 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(str)8(uctur)18(ed)-250(data)-250(of)-250(type)]TJ 0 0 1 rg 0 0 1 RG /F131 9.9626 Tf 168.138 0 Td [(psb)]TJ ET q -1 0 0 1 309.258 188.777 cm +1 0 0 1 360.068 188.777 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 312.397 188.577 Td [(prec)]TJ +/F131 9.9626 Tf 363.206 188.577 Td [(Tprec)]TJ ET q -1 0 0 1 333.945 188.777 cm +1 0 0 1 389.985 188.777 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 337.084 188.577 Td [(type)]TJ +/F131 9.9626 Tf 393.124 188.577 Td [(type)]TJ 0 g 0 G /F84 9.9626 Tf 20.921 0 Td [(.)]TJ 0 g 0 G -/F75 9.9626 Tf -258.11 -20.431 Td [(b)]TJ +/F75 9.9626 Tf -263.34 -20.431 Td [(b)]TJ 0 g 0 G -/F84 9.9626 Tf 10.76 0 Td [(The)-250(RHS)-250(vector)74(.)]TJ 14.147 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.432 0 Td [(local)]TJ/F84 9.9626 Tf -31.741 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(rank)-250(one)-250(array)-250(or)-250(an)-250(object)-250(of)-250(type)]TJ +/F84 9.9626 Tf 10.76 0 Td [(The)-250(RHS)-250(vector)74(.)]TJ 14.147 -11.955 Td [(Scope:)]TJ/F75 9.9626 Tf 31.431 0 Td [(local)]TJ/F84 9.9626 Tf -31.74 -11.955 Td [(T)90(ype:)]TJ/F75 9.9626 Tf 27.088 0 Td [(required)]TJ/F84 9.9626 Tf -26.779 -11.955 Td [(Intent:)]TJ/F75 9.9626 Tf 31.8 0 Td [(in)]TJ/F84 9.9626 Tf 9.405 0 Td [(.)]TJ -41.205 -11.955 Td [(Speci\002ed)-250(as:)-310(a)-250(rank)-250(one)-250(array)-250(or)-250(an)-250(object)-250(of)-250(type)]TJ 0 0 1 rg 0 0 1 RG -/F131 9.9626 Tf 218.688 0 Td [(psb)]TJ +/F131 9.9626 Tf 218.687 0 Td [(psb)]TJ ET q -1 0 0 1 359.808 120.525 cm +1 0 0 1 410.618 120.525 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 362.947 120.326 Td [(T)]TJ +/F131 9.9626 Tf 413.756 120.326 Td [(T)]TJ ET q -1 0 0 1 368.804 120.525 cm +1 0 0 1 419.614 120.525 cm []0 d 0 J 0.398 w 0 0 m 3.138 0 l S Q BT -/F131 9.9626 Tf 371.943 120.326 Td 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B" B# B$ B% B& B' B( B) B* B+ B, B- B. B/ B0 B1 B2 B3 B4 B5 B6 B7 B8 B9 B: B; B< B= B> B?+, endstream endobj startxref -2882598 +2889113 %%EOF diff --git a/docs/src/biblio.tex b/docs/src/biblio.tex index 5ba3605c..41fa7ddd 100644 --- a/docs/src/biblio.tex +++ b/docs/src/biblio.tex @@ -8,6 +8,11 @@ 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. +\bibitem{BERTACCINIFILIPPONE} +D. Bertaccini\ and\ S. Filippone, +{\em Sparse approximate inverse preconditioners on high performance GPU platforms}, +Comput. Math. Appl., 71, (2016), no.~3, 693--711. +% \bibitem{2007d} A. Buttari, D. di Serafino, P. D'Ambra, S. Filippone,\newblock 2LEV-D2P4: a package of high-performance preconditioners,\newblock Applicable Algebra in Engineering, Communications and Computing, @@ -183,7 +188,14 @@ MIT Press, 1998. {\em Scientific Programming\/}~{\em 22,\/}~1, 1--19. \bibitem{OurTechRep} D.~Barbieri, V.~Cardellini, A.~Fanfarillo, S.~Filippone, Three storage formats - for sparse matrices on {GPGPUs}, Tech. Rep. DICII RR-15.6, Universit\`a di + for sparse matrices on {GPGPUs}, Tech. Rep. DICII RR-15.6, + Universit\`a di Roma Tor Vergata (February 2015). +\bibitem{Filippone:2017:SMM:3034774.3017994} +S.~Filippone, V.~Cardellini, D.~Barbieri, and A.~Fanfarillo. + Sparse matrix-vector multiplication on {GPGPUs}. + {\em ACM Trans. Math. Softw.}, 43(4):30:1--30:49, 2017. + + \end{thebibliography} diff --git a/docs/src/error.tex b/docs/src/error.tex index e6bb0d2d..07d009d8 100644 --- a/docs/src/error.tex +++ b/docs/src/error.tex @@ -1,6 +1,6 @@ -\section{Error handling} +\section{Error handling\label{sec:errors}} The PSBLAS library error handling policy has been completely rewritten in version 2.0. The idea behind the design of this new error handling diff --git a/docs/src/precs.tex b/docs/src/precs.tex index 9211f594..30243827 100644 --- a/docs/src/precs.tex +++ b/docs/src/precs.tex @@ -76,11 +76,10 @@ $ptype$ string as follows\footnote{The string is case-insensitive}: \item[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 $A$; -\item[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. +\item[BJAC] Precondition by a factorization or an approximante inverse + of the block-diagonal of matrix $A$, where block boundaries are + determined by the data allocation boundaries for each process; + requires no communication. See also Table-\ref{tab:p_subsolve_1}. \end{description} @@ -105,13 +104,13 @@ contained in \fortinline|val|. \fortinline|what| & \fortinline|character(len=*)|. \\ & The parameter to be set. It can be specified through its name; the string is case-insensitive. See - Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ + Table~\ref{tab:p_subsolve_1}.\\ \fortinline|val | & \fortinline|integer| \emph{or} \fortinline|character(len=*)| \emph{or} \fortinline|real(psb_spk_)| \emph{or} \fortinline|real(psb_dpk_)|, \fortinline|intent(in)|.\\ & The value of the parameter to be set. The list of allowed values and the corresponding data types is given in - Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}. + Table~\ref{tab:p_subsolve_1}. When the value is of type \fortinline|character(len=*)|, it is also treated as case insensitive.\\ \fortinline|info| & \fortinline|integer, intent(out)|.\\ @@ -123,13 +122,14 @@ contained in \fortinline|val|. \noindent A number of subdomain solvers can be chosen with this method; a list of the parameters that can be set, along with their allowed and -default values, is given in Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ +default values, is given in Table-\ref{tab:p_subsolve_1}.\\ \bsideways \begin{center} \small -\begin{tabular}{|p{3.6cm}|l|p{1.9cm}|p{3.6cm}|p{6.5cm}|} +% \begin{tabular}{|p{3.6cm}|l|p{1.9cm}|p{3.6cm}|p{6.5cm}|} +\begin{tabular}{|p{3.2cm}|l|p{2.6cm}|p{2.6cm}|p{6.7cm}|} \hline \fortinline|what| & \textsc{data type} & \fortinline|val| & \textsc{default} & \textsc{comments} \\ \hline @@ -148,20 +148,6 @@ default values, is given in Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ do not employ triangular system solve kernels, see~\cite{BERTACCINIFILIPPONE}.\\ \hline -\hline -\end{tabular} -\end{center} -\caption{Parameters defining the solver or the details of the one-level preconditioner. -\label{tab:p_smoother}} -\esideways - -\bsideways -\begin{center} -\small -\begin{tabular}{|p{3.2cm}|l|p{2.6cm}|p{2.6cm}|p{6.7cm}|} -\hline -\fortinline|what| & \textsc{data type} & \fortinline|val| & \textsc{default} & -\textsc{comments} \\ \hline \fortinline|'SUB_FILLIN'| & \fortinline|integer| & Any integer \par number~$\ge 0$ & 0 @@ -170,12 +156,41 @@ default values, is given in Tables~\ref{tab:p_cycle}-\ref{tab:p_smoother_1}.\\ & Any real number~$\ge 0$ & 0 & Drop tolerance $t$ in the ILU($p,t$) factorization. \\ \hline -\hline +\fortinline|'ILU_ALG'| & \fortinline|character(len=*)| + & \fortinline|'MILU'| + & \fortinline|'NONE'| + & ILU algorithmic variant \\ \hline +\fortinline|'ILUT_SCALE'| & \fortinline|character(len=*)| + & \fortinline|'MAXVAL'| \par + \fortinline|'DIAG'| \par + \fortinline|'ARSWUM'| \par + \fortinline|'ARCSUM'| \par + \fortinline|'ACLSUM'| \par + \fortinline|'NONE'| + & \fortinline|'NONE'| + & ILU scaling strategy \\ \hline +\fortinline|'INV_FILLIN'| & \fortinline|integer| + & Any integer \par number~$\ge 0$ + & 0 + & Second fill-in level $q$ of the INVK($p,q$) + approximate inverse. \\ \hline +\fortinline|'INV_ILUTHRS'| & \fortinline|real(kind_parameter)| + & Any real number~$\ge 0$ + & 0 + & Second drop tolerance $s$ in the + INVT($t,s$) approximate inverse. \\ \hline +\fortinline|'AINV_ALG'| & \fortinline|character(len=*)| + & \fortinline|'LLK'| \par + \fortinline|'SYM-LLK'| \par + \fortinline|'STAB-LLK'| \par + \fortinline|'MLK,LMX'| + & \fortinline|'LLK'| + & AINV algorithmic strategy. \\ \hline \end{tabular} \end{center} -\caption{Parameters defining the smoother or the details of the one-level preconditioner -(continued).\label{tab:p_smoother_1}} -\esideways +\caption{Parameters defining the solver of the BJAC + preconditioner.\label{tab:p_subsolve_1}} + \esideways diff --git a/docs/src/userguide.tex b/docs/src/userguide.tex index f2925f49..0c18c5dd 100644 --- a/docs/src/userguide.tex +++ b/docs/src/userguide.tex @@ -93,7 +93,7 @@ \newcommand{\example}{\stepcounter{example}% \section*{\examplename~\theexample}} -\newcommand{\precdata}{\hyperlink{precdata}{{\tt psb\_prec\_type}}} +\newcommand{\precdata}{\hyperlink{precdata}{{\tt psb\_Tprec\_type}}} \newcommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}} \newcommand{\spdata}{\hyperlink{spdata}{{\tt psb\_Tspmat\_type}}} \newcommand{\vdata}{\hyperlink{vdata}{{\tt psb\_T\_vect\_type}}} diff --git a/docs/src/userhtml.tex b/docs/src/userhtml.tex index aa142adf..525fb895 100644 --- a/docs/src/userhtml.tex +++ b/docs/src/userhtml.tex @@ -84,7 +84,7 @@ \newcommand{\example}{\stepcounter{example}% \section*{\examplename~\theexample}} -\newcommand{\precdata}{\hyperlink{precdata}{{\tt psb\_prec\_type}}} +\newcommand{\precdata}{\hyperlink{precdata}{{\tt psb\_Tprec\_type}}} \newcommand{\descdata}{\hyperlink{descdata}{{\tt psb\_desc\_type}}} \newcommand{\spdata}{\hyperlink{spdata}{{\tt psb\_Tspmat\_type}}} \newcommand{\vdata}{\hyperlink{vdata}{{\tt psb\_T\_vect\_type}}}