From 1911fec97b96f75d19ec6807c7f238d179a2d7ee Mon Sep 17 00:00:00 2001 From: Salvatore Filippone Date: Thu, 11 Jul 2024 13:12:17 +0200 Subject: [PATCH] Update docs --- docs/html/cmsy10-42.png | Bin 334 -> 328 bytes docs/html/cmsy10-48.png | Bin 382 -> 366 bytes docs/html/cmsy10-49.png | Bin 296 -> 289 bytes docs/html/dia.png | Bin 0 -> 50686 bytes docs/html/ell.png | Bin 0 -> 52842 bytes docs/html/hdia.png | Bin 0 -> 59145 bytes docs/html/hll.png | Bin 0 -> 62128 bytes docs/html/index.html | 242 +-- docs/html/mat.png | Bin 0 -> 92468 bytes docs/html/userhtml.css | 23 +- docs/html/userhtml.html | 242 +-- docs/html/userhtml0x.png | Bin 1688 -> 1499 bytes docs/html/userhtml10x.png | Bin 2141 -> 1863 bytes docs/html/userhtml11x.png | Bin 1331 -> 1159 bytes docs/html/userhtml12x.png | Bin 2039 -> 1754 bytes docs/html/userhtml13x.png | Bin 1289 -> 1188 bytes docs/html/userhtml14x.png | Bin 1317 -> 1217 bytes docs/html/userhtml15x.png | Bin 1599 -> 1361 bytes docs/html/userhtml16.html | 19 + 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PSBLAS
User’s and Reference Guide
Salvatore Filippone
Alfredo Buttari
Software version: 3.8.0
May 1st, 2022 +class="newline" />Software version: 3.9.0
Aug 1st, 2024 @@ -29,219 +29,39 @@ class="newline" />May 1st, 2022

- Contents -
1  1 Introduction -
2  2 General overview -
 2.1 Basic Nomenclature -
 2.2 Library contents -
 2.3 Application structure -
 2.4 Programming model -
3 Data Structures and Classes -
 3.1 Descriptor data structure -
 3.2 Sparse Matrix class -
 3.3 Dense Vector Data Structure -
 3.4 Preconditioner data structure -
 3.5 Heap data structure -
4 Computational routines -
 4.1 psb_geaxpby — General Dense Matrix Sum -
 4.2 psb_gedot — Dot Product -
 4.3 psb_gedots — Generalized Dot Product -
 4.4 psb_normi — Infinity-Norm of Vector -
 4.5 psb_geamaxs — Generalized Infinity Norm -
 4.6 psb_norm1 — 1-Norm of Vector -
 4.7 psb_geasums — Generalized 1-Norm of Vector -
 4.8 psb_norm2 — 2-Norm of Vector -
 4.9 psb_genrm2s — Generalized 2-Norm of Vector -
 4.10 psb_norm1 — 1-Norm of Sparse Matrix -
 4.11 psb_normi — Infinity Norm of Sparse Matrix -
 4.12 psb_spmm — Sparse Matrix by Dense Matrix Product -
 4.13 psb_spsm — Triangular System Solve -
 4.14 psb_gemlt — Entrywise Product -
 4.15 psb_gediv — Entrywise Division -
 4.16 psb_geinv — Entrywise Inversion -
5 Communication routines -
 5.1 psb_halo — Halo Data Communication -
 5.2 psb_ovrl — Overlap Update -
 5.3 psb_gather — Gather Global Dense Matrix -
 5.4 psb_scatter — Scatter Global Dense Matrix -
6 Data management routines -
 6.1 psb_cdall — Allocates a communication descriptor -
 6.2 psb_cdins — Communication descriptor insert routine -
 6.3 psb_cdasb — Communication descriptor assembly routine -
 6.4 psb_cdcpy — Copies a communication descriptor -
 6.5 psb_cdfree — Frees a communication descriptor -
 6.6 psb_cdbldext — Build an extended communication descriptor -
 6.7 psb_spall — Allocates a sparse matrix -
 6.8 psb_spins — Insert a set of coefficients into a sparse matrix -
 6.9 psb_spasb — Sparse matrix assembly routine -
 6.10 psb_spfree — Frees a sparse matrix -
 6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. -
 6.12 psb_geall — Allocates a dense matrix - +
 3 Data Structures and Classes +
 4 Computational routines +
 5 Communication routines +
 6 Data management routines +
 7 Parallel environment routines +
 8 Error handling +
 9 Utilities +
 10 Preconditioner routines +
 11 Iterative Methods +
 12 Extensions +
 13 CUDA Environment Routines +
 References +
- -
 6.13 psb_geins — Dense matrix insertion routine -
 6.14 psb_geasb — Assembly a dense matrix -
 6.15 psb_gefree — Frees a dense matrix -
 6.16 psb_gelp — Applies a left permutation to a dense matrix -
 6.17 psb_glob_to_loc — Global to local indices convertion -
 6.18 psb_loc_to_glob — Local to global indices conversion -
 6.19 psb_is_owned — -
 6.20 psb_owned_index — -
 6.21 psb_is_local — -
 6.22 psb_local_index — -
 6.23 psb_get_boundary — Extract list of boundary elements -
 6.24 psb_get_overlap — Extract list of overlap elements -
 6.25 psb_sp_getrow — Extract row(s) from a sparse matrix -
 6.26 psb_sizeof — Memory occupation -
 6.27 Sorting utilities — -
7 Parallel environment routines -
 7.1 psb_init — Initializes PSBLAS parallel environment -
 7.2 psb_info — Return information about PSBLAS parallel environment -
 7.3 psb_exit — Exit from PSBLAS parallel environment -
 7.4 psb_get_mpi_comm — Get the MPI communicator -
 7.5 psb_get_mpi_rank — Get the MPI rank -
 7.6 psb_wtime — Wall clock timing -
 7.7 psb_barrier — Sinchronization point parallel environment -
 7.8 psb_abort — Abort a computation -
 7.9 psb_bcast — Broadcast data -
 7.10 psb_sum — Global sum -
 7.11 psb_max — Global maximum -
 7.12 psb_min — Global minimum -
 7.13 psb_amx — Global maximum absolute value -
 7.14 psb_amn — Global minimum absolute value -
 7.15 psb_nrm2 — Global 2-norm reduction -
 7.16 psb_snd — Send data -
 7.17 psb_rcv — Receive data -
8 Error handling -
 8.1 psb_errpush — Pushes an error code onto the error stack -
 8.2 psb_error — Prints the error stack content and aborts execution -
 8.3 psb_set_errverbosity — Sets the verbosity of error messages -
 8.4 psb_set_erraction — Set the type of action to be taken upon error condition -
9 Utilities -
 9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format -
 9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format -
 9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format -
 9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format -
 9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format -
 9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format -
10 Preconditioner routines -
 10.1 init — Initialize a preconditioner -
 10.2 build — Builds a preconditioner -
 10.3 apply — Preconditioner application routine -
 10.4 descr — Prints a description of current preconditioner - - -
 10.5 clone — clone current preconditioner -
 10.6 free — Free a preconditioner -
11 Iterative Methods -
 11.1 psb_krylov — Krylov Methods Driver Routine -
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{visibility:hidden;}} +table.tabular{border-collapse: collapse; border-spacing: 0;} a img { border-top: 0; border-left: 0; border-right: 0; } center { margin-top:1em; margin-bottom:1em; } td center { margin-top:0em; margin-bottom:0em; } .Canvas { position:relative; } img.math{vertical-align:middle;} +div.par-math-display, div.math-display{text-align:center;} li p.indent { text-indent: 0em } li p:first-child{ margin-top:0em; } li p:last-child, li div:last-child { margin-bottom:0.5em; } +li p:first-child{ margin-bottom:0; } li p~ul:last-child, li p~ol:last-child{ margin-bottom:0.5em; } .enumerate1 {list-style-type:decimal;} .enumerate2 {list-style-type:lower-alpha;} .enumerate3 {list-style-type:lower-roman;} .enumerate4 {list-style-type:upper-alpha;} div.newtheorem { margin-bottom: 2em; margin-top: 2em;} +div.newtheorem .head{font-weight: bold;} .obeylines-h,.obeylines-v {white-space: nowrap; } div.obeylines-v p { margin-top:0; margin-bottom:0; } .overline{ text-decoration:overline; } @@ 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      PSBLAS
      User’s and Reference Guide
      Salvatore Filippone
      Alfredo Buttari
      Software version: 3.8.0
      May 1st, 2022 +class="newline" />Software version: 3.9.0
      Aug 1st, 2024 @@ -29,219 +29,39 @@ class="newline" />May 1st, 2022

      - Contents -
      1  1 Introduction -
      2  2 General overview -
       2.1 Basic Nomenclature -
       2.2 Library contents -
       2.3 Application structure -
       2.4 Programming model -
      3 Data Structures and Classes -
       3.1 Descriptor data structure -
       3.2 Sparse Matrix class -
       3.3 Dense Vector Data Structure -
       3.4 Preconditioner data structure -
       3.5 Heap data structure -
      4 Computational routines -
       4.1 psb_geaxpby — General Dense Matrix Sum -
       4.2 psb_gedot — Dot Product -
       4.3 psb_gedots — Generalized Dot Product -
       4.4 psb_normi — Infinity-Norm of Vector -
       4.5 psb_geamaxs — Generalized Infinity Norm -
       4.6 psb_norm1 — 1-Norm of Vector -
       4.7 psb_geasums — Generalized 1-Norm of Vector -
       4.8 psb_norm2 — 2-Norm of Vector -
       4.9 psb_genrm2s — Generalized 2-Norm of Vector -
       4.10 psb_norm1 — 1-Norm of Sparse Matrix -
       4.11 psb_normi — Infinity Norm of Sparse Matrix -
       4.12 psb_spmm — Sparse Matrix by Dense Matrix Product -
       4.13 psb_spsm — Triangular System Solve -
       4.14 psb_gemlt — Entrywise Product -
       4.15 psb_gediv — Entrywise Division -
       4.16 psb_geinv — Entrywise Inversion -
      5 Communication routines -
       5.1 psb_halo — Halo Data Communication -
       5.2 psb_ovrl — Overlap Update -
       5.3 psb_gather — Gather Global Dense Matrix -
       5.4 psb_scatter — Scatter Global Dense Matrix -
      6 Data management routines -
       6.1 psb_cdall — Allocates a communication descriptor -
       6.2 psb_cdins — Communication descriptor insert routine -
       6.3 psb_cdasb — Communication descriptor assembly routine -
       6.4 psb_cdcpy — Copies a communication descriptor -
       6.5 psb_cdfree — Frees a communication descriptor -
       6.6 psb_cdbldext — Build an extended communication descriptor -
       6.7 psb_spall — Allocates a sparse matrix -
       6.8 psb_spins — Insert a set of coefficients into a sparse matrix -
       6.9 psb_spasb — Sparse matrix assembly routine -
       6.10 psb_spfree — Frees a sparse matrix -
       6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. -
       6.12 psb_geall — Allocates a dense matrix - +
       3 Data Structures and Classes +
       4 Computational routines +
       5 Communication routines +
       6 Data management routines +
       7 Parallel environment routines +
       8 Error handling +
       9 Utilities +
       10 Preconditioner routines +
       11 Iterative Methods +
       12 Extensions +
       13 CUDA Environment Routines +
       References +
      - -
       6.13 psb_geins — Dense matrix insertion routine -
       6.14 psb_geasb — Assembly a dense matrix -
       6.15 psb_gefree — Frees a dense matrix -
       6.16 psb_gelp — Applies a left permutation to a dense matrix -
       6.17 psb_glob_to_loc — Global to local indices convertion -
       6.18 psb_loc_to_glob — Local to global indices conversion -
       6.19 psb_is_owned — -
       6.20 psb_owned_index — -
       6.21 psb_is_local — -
       6.22 psb_local_index — -
       6.23 psb_get_boundary — Extract list of boundary elements -
       6.24 psb_get_overlap — Extract list of overlap elements -
       6.25 psb_sp_getrow — Extract row(s) from a sparse matrix -
       6.26 psb_sizeof — Memory occupation -
       6.27 Sorting utilities — -
      7 Parallel environment routines -
       7.1 psb_init — Initializes PSBLAS parallel environment -
       7.2 psb_info — Return information about PSBLAS parallel environment -
       7.3 psb_exit — Exit from PSBLAS parallel environment -
       7.4 psb_get_mpi_comm — Get the MPI communicator -
       7.5 psb_get_mpi_rank — Get the MPI rank -
       7.6 psb_wtime — Wall clock timing -
       7.7 psb_barrier — Sinchronization point parallel environment -
       7.8 psb_abort — Abort a computation -
       7.9 psb_bcast — Broadcast data -
       7.10 psb_sum — Global sum -
       7.11 psb_max — Global maximum -
       7.12 psb_min — Global minimum -
       7.13 psb_amx — Global maximum absolute value -
       7.14 psb_amn — Global minimum absolute value -
       7.15 psb_nrm2 — Global 2-norm reduction -
       7.16 psb_snd — Send data -
       7.17 psb_rcv — Receive data -
      8 Error handling -
       8.1 psb_errpush — Pushes an error code onto the error stack -
       8.2 psb_error — Prints the error stack content and aborts execution -
       8.3 psb_set_errverbosity — Sets the verbosity of error messages -
       8.4 psb_set_erraction — Set the type of action to be taken upon error condition -
      9 Utilities -
       9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format -
       9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format -
       9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format -
       9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format -
       9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format -
       9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format -
      10 Preconditioner routines -
       10.1 init — Initialize a preconditioner -
       10.2 build — Builds a preconditioner -
       10.3 apply — Preconditioner application routine -
       10.4 descr — Prints a description of current preconditioner - - -
       10.5 clone — clone current preconditioner -
       10.6 free — Free a preconditioner -
      11 Iterative Methods -
       11.1 psb_krylov — Krylov Methods Driver Routine -
      References - diff --git a/docs/html/userhtml0x.png b/docs/html/userhtml0x.png index bed5b30411c06478e013e4a446657647971a0591..3e324fc864b1e0d36888ad4e96e38b1bffd729c7 100644 GIT binary patch delta 1461 zcmV;m1xosu4ciNlIDZ9=Nklqmw5_O6h9| z;lnPL4%}zlgb<$JX9Z7*lPAW3??@@VNhv-0{^mf9`^*u00yY|4&qA0+hA$xmmH=1m zLHuQPZbO*r(1vdcn@`~oT_=B=3}Wq_oOxxts7BW&06tY7yH8`k)goJEcrvAJlw zOE%S!zZD-}MtD&jPyQ4X`atQ(n?_CxuGYv*=dBqdCsieHMyl_3>D~ev2S#QQOU)!nX|SHJ9plt*kqr1%@9vT~;a!8ChFS*NoAXx29bE-GV6xjg|t9ddwEn zvcz;&snMxe+L$AYplis~^xw7Jx9d6G^eYAq+JCw>Sw|NfMPS;JDi0LC@3s3;UrNr7 z#OU(raUd2pD87hgi{xkMzI>q95u4M zt+1nD2-mS8!T-J?2YueBl;XlwlMG0pMeMMB4d{ULYCN$QEgesWAGL?UDaOc(VF_J6 z?*RXr%3 zIBk&i-j`1A+4SrW6Vzs8nJ{X*WKz0iQA-ak>xyqSz!Y{lKI>C5f^Y9qijg$?OnSQ| zR_$X>&2nG1`7iWzGLTy=`}D0YdmK@B)ONqDURsvbefOU0&e5bkMamm;7aTYQ$A2>7 z5ujveUf(%my7GF8Eq!ycNsfGKRM)qS7kWaMWY=!zMb*I+(qD<2@%)lMItbTl`hXZRuaX+hUK|gl_POF4!~m?d6(I zqkOJ%w8eIJP&DyOTd&*Jdl{|GvVVSezzI05$a-@O!G$v*hI)|2bD@Z}hd?=dCU2{< 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      +

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

      + diff --git a/docs/html/userhtml18x.png b/docs/html/userhtml18x.png index ebcb935dfd1bd9e40303f5a28b54f8f0086877dc..d33d825c3b43bb1883af57650d877c62074343e0 100644 GIT binary patch delta 1134 zcmV-!1d;og3YZCyIe$t?L_t(&1?`xPjTAW$g{u$&tRRCU10aMY1Go%;3>Faqf(+OU z_{m_&0N4y5gJU;?I(_Dq<>_(vbk7VUVD?F)?s41Yay{3N?Ga(e40k_a{Sk3}Y<9SH zYzyw-tC{`VY5(ov?x*hl+TG9G{e!zdUZV8vC7u5^xcf6R`+vvG?)_WSkQE4*_}VPV>3@eKY$J5uXM+e=)PuLE9*fmV7gNX=cx5 z8NB~cV6HnmPIej*A3HK2ez+k<@k_{OcaP5a8^GNQ*$R&odb^TwFi7{cuGjRmJHGoxtx+WbGu_udoT7?a<$zJJL7`P8N=cA*WYzz))ZoPE{G z$#I*Wl2i5H)PMNB;R+pCd;Y2o7}N9{<&;i%DLI69h{p5lq#S|gk||j$o2Qkv%e%evY(C|2mQwEg< zG)62N0e|5lbImZriPd*)hxPhx+a{x3^~Q_5^ng*XQdFwzlioxs*0?gR^Ph+_xv_e> z4cm4hUz=`a^QU|{ZbtA~oZfD7B{~1P&G%*{r*M{>%%>{wAphFk*@4^OQ+sCZfZhDQ z(+<#&dIkN@dwrAxk#XYgneV|v^(SxELaHsClz;pA{;nsx2X`l|rtB8Txp4QMO`o*$ zb}(gwB9}1@U(=j6JBKhf4EYdAAyNB{y(>!4f5n5w`Y&nMj>kJ|u5QOG|9)%RhVRPP zYhhY7z^H8GD6g(Woo&~-qvv-cPZPCE>dUoju2D|gqaMZ7XGS!jt?Z^vP{hEa*hG6p 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      1 1In our prototype implementation we provide sample scatter/gather routines.

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      +

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

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      -

      2This is the normal situation when the pattern of the sparse matrix is symmetric, which is +

      3The subroutine style psb_precinit and psb_precbl are still supported for backward equivalent to say that the interaction between two variables is reciprocal. If the matrix pattern is - non-symmetric we may have one-way interactions, and these could cause a situation in which a - boundary point is not a halo point for its neighbour.

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      Contents

      - 1 1 Introduction -
      2  2 General overview -
       2.1 Basic Nomenclature -
       2.2 Library contents -
       2.3 Application structure -
        2.3.1 User-defined index mappings -
       2.4 Programming model -
      3 Data Structures and Classes -
       3.1 Descriptor data structure -
        3.1.1 Descriptor Methods -
        3.1.2 get_local_rows — Get number of local rows -
        3.1.3 get_local_cols — Get number of local cols -
        3.1.4 get_global_rows — Get number of global rows -
        3.1.5 get_global_cols — Get number of global cols -
        3.1.6 get_global_indices — Get vector of global indices -
        3.1.7 get_context — Get communication context -
        3.1.8 Clone — clone current object -
        3.1.9 CNV — convert internal storage format -
        3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping switch -
        3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping switch -
        3.1.12 get_p_adjcncy — Get process adjacency list -
        3.1.13 set_p_adjcncy — Set process adjacency list -
        3.1.14 fnd_owner — Find the owner process of a set of indices -
        3.1.15 Named Constants -
       3.2 Sparse Matrix class -
        3.2.1 Sparse Matrix Methods -
        3.2.2 get_nrows — Get number of rows in a sparse matrix -
        3.2.3 get_ncols — Get number of columns in a sparse matrix -
        3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix -
        3.2.5 get_size — Get maximum number of nonzero elements in a sparse matrix -
        3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix -
        3.2.7 get_fmt — Short description of the dynamic type -
        3.2.8 is_bld, is_upd, is_asb — Status check -
        3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check -
        3.2.10 cscnv — Convert to a different storage format -
        3.2.11 csclip — Reduce to a submatrix -
        3.2.12 clean_zeros — Eliminate zero coefficients -
        3.2.13 get_diag — Get main diagonal -
        3.2.14 clip_diag — Cut out main diagonal +
        2.1 Basic Nomenclature +
        2.2 Library contents +
        2.3 Application structure +
         2.3.1 User-defined index mappings +
        2.4 Programming model +
       3 Data Structures and Classes +
        3.1 Descriptor data structure +
         3.1.1 Descriptor Methods +
         3.1.2 get_local_rows — Get number of local rows +
         3.1.3 get_local_cols — Get number of local cols +
         3.1.4 get_global_rows — Get number of global rows +
         3.1.5 get_global_cols — Get number of global cols +
         3.1.6 get_global_indices — Get vector of global indices +
         3.1.7 get_context — Get communication context +
         3.1.8 Clone — clone current object +
         3.1.9 CNV — convert internal storage format +
         3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping switch +
         3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping switch +
         3.1.12 get_p_adjcncy — Get process adjacency list +
         3.1.13 set_p_adjcncy — Set process adjacency list +
         3.1.14 fnd_owner — Find the owner process of a set of indices +
         3.1.15 Named Constants +
        3.2 Sparse Matrix class +
         3.2.1 Sparse Matrix Methods +
         3.2.2 get_nrows — Get number of rows in a sparse matrix -
        3.2.15 tril — Return the lower triangle -
        3.2.16 triu — Return the upper triangle -
        3.2.17 psb_set_mat_default — Set default storage format -
        3.2.18 clone — Clone current object -
        3.2.19 Named Constants -
       3.3 Dense Vector Data Structure -
        3.3.1 Vector Methods -
        3.3.2 get_nrows — Get number of rows in a dense vector -
        3.3.3 sizeof — Get memory occupation in bytes of a dense vector -
        3.3.4 set — Set contents of the vector -
        3.3.5 get_vect — Get a copy of the vector contents -
        3.3.6 clone — Clone current object -
       3.4 Preconditioner data structure -
       3.5 Heap data structure -
      4 Computational routines -
       4.1 psb_geaxpby — General Dense Matrix Sum -
       4.2 psb_gedot — Dot Product -
       4.3 psb_gedots — Generalized Dot Product -
       4.4 psb_normi — Infinity-Norm of Vector -
       4.5 psb_geamaxs — Generalized Infinity Norm -
       4.6 psb_norm1 — 1-Norm of Vector -
       4.7 psb_geasums — Generalized 1-Norm of Vector -
       4.8 psb_norm2 — 2-Norm of Vector -
       4.9 psb_genrm2s — Generalized 2-Norm of Vector -
       4.10 psb_norm1 — 1-Norm of Sparse Matrix -
       4.11 psb_normi — Infinity Norm of Sparse Matrix -
       4.12 psb_spmm — Sparse Matrix by Dense Matrix Product -
       4.13 psb_spsm — Triangular System Solve -
       4.14 psb_gemlt — Entrywise Product -
       4.15 psb_gediv — Entrywise Division -
       4.16 psb_geinv — Entrywise Inversion -
      5 Communication routines -
       5.1 psb_halo — Halo Data Communication -
       5.2 psb_ovrl — Overlap Update -
       5.3 psb_gather — Gather Global Dense Matrix -
       5.4 psb_scatter — Scatter Global Dense Matrix -
      6 Data management routines -
       6.1 psb_cdall — Allocates a communication descriptor -
       6.2 psb_cdins — Communication descriptor insert routine -
       6.3 psb_cdasb — Communication descriptor assembly routine -
       6.4 psb_cdcpy — Copies a communication descriptor -
       6.5 psb_cdfree — Frees a communication descriptor -
       6.6 psb_cdbldext — Build an extended communication descriptor -
       6.7 psb_spall — Allocates a sparse matrix -
       6.8 psb_spins — Insert a set of coefficients into a sparse matrix -
       6.9 psb_spasb — Sparse matrix assembly routine -
       6.10 psb_spfree — Frees a sparse matrix -
       6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. -
       6.12 psb_geall — Allocates a dense matrix -
       6.13 psb_geins — Dense matrix insertion routine +
         3.2.3 get_ncols — Get number of columns in a sparse matrix +
         3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix +
         3.2.5 get_size — Get maximum number of nonzero elements in a sparse matrix +
         3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix +
         3.2.7 get_fmt — Short description of the dynamic type +
         3.2.8 is_bld, is_upd, is_asb — Status check +
         3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check +
         3.2.10 cscnv — Convert to a different storage format +
         3.2.11 csclip — Reduce to a submatrix +
         3.2.12 clean_zeros — Eliminate zero coefficients +
         3.2.13 get_diag — Get main diagonal +
         3.2.14 clip_diag — Cut out main diagonal +
         3.2.15 tril — Return the lower triangle +
         3.2.16 triu — Return the upper triangle +
         3.2.17 psb_set_mat_default — Set default storage format +
         3.2.18 clone — Clone current object +
         3.2.19 Named Constants +
        3.3 Dense Vector Data Structure +
         3.3.1 Vector Methods +
         3.3.2 get_nrows — Get number of rows in a dense vector +
         3.3.3 sizeof — Get memory occupation in bytes of a dense vector +
         3.3.4 set — Set contents of the vector +
         3.3.5 get_vect — Get a copy of the vector contents +
         3.3.6 clone — Clone current object +
        3.4 Preconditioner data structure +
        3.5 Heap data structure +
       4 Computational routines +
        4.1 psb_geaxpby — General Dense Matrix Sum +
        4.2 psb_gedot — Dot Product +
        4.3 psb_gedots — Generalized Dot Product +
        4.4 psb_normi — Infinity-Norm of Vector +
        4.5 psb_geamaxs — Generalized Infinity Norm +
        4.6 psb_norm1 — 1-Norm of Vector +
        4.7 psb_geasums — Generalized 1-Norm of Vector +
        4.8 psb_norm2 — 2-Norm of Vector +
        4.9 psb_genrm2s — Generalized 2-Norm of Vector +
        4.10 psb_norm1 — 1-Norm of Sparse Matrix +
        4.11 psb_normi — Infinity Norm of Sparse Matrix +
        4.12 psb_spmm — Sparse Matrix by Dense Matrix Product +
        4.13 psb_spsm — Triangular System Solve +
        4.14 psb_gemlt — Entrywise Product +
        4.15 psb_gediv — Entrywise Division +
        4.16 psb_geinv — Entrywise Inversion +
       5 Communication routines +
        5.1 psb_halo — Halo Data Communication +
        5.2 psb_ovrl — Overlap Update +
        5.3 psb_gather — Gather Global Dense Matrix +
        5.4 psb_scatter — Scatter Global Dense Matrix +
       6 Data management routines +
        6.1 psb_cdall — Allocates a communication descriptor -
       6.14 psb_geasb — Assembly a dense matrix -
       6.15 psb_gefree — Frees a dense matrix -
       6.16 psb_gelp — Applies a left permutation to a dense matrix -
       6.17 psb_glob_to_loc — Global to local indices convertion -
       6.18 psb_loc_to_glob — Local to global indices conversion -
       6.19 psb_is_owned — -
       6.20 psb_owned_index — -
       6.21 psb_is_local — -
       6.22 psb_local_index — -
       6.23 psb_get_boundary — Extract list of boundary elements -
       6.24 psb_get_overlap — Extract list of overlap elements -
       6.25 psb_sp_getrow — Extract row(s) from a sparse matrix -
       6.26 psb_sizeof — Memory occupation -
       6.27 Sorting utilities — -
      7 Parallel environment routines -
       7.1 psb_init — Initializes PSBLAS parallel environment -
       7.2 psb_info — Return information about PSBLAS parallel environment -
       7.3 psb_exit — Exit from PSBLAS parallel environment -
       7.4 psb_get_mpi_comm — Get the MPI communicator -
       7.5 psb_get_mpi_rank — Get the MPI rank -
       7.6 psb_wtime — Wall clock timing -
       7.7 psb_barrier — Sinchronization point parallel environment -
       7.8 psb_abort — Abort a computation -
       7.9 psb_bcast — Broadcast data -
       7.10 psb_sum — Global sum -
       7.11 psb_max — Global maximum -
       7.12 psb_min — Global minimum -
       7.13 psb_amx — Global maximum absolute value -
       7.14 psb_amn — Global minimum absolute value -
       7.15 psb_nrm2 — Global 2-norm reduction -
       7.16 psb_snd — Send data -
       7.17 psb_rcv — Receive data -
      8 Error handling -
       8.1 psb_errpush — Pushes an error code onto the error stack -
       8.2 psb_error — Prints the error stack content and aborts execution -
       8.3 psb_set_errverbosity — Sets the verbosity of error messages -
       8.4 psb_set_erraction — Set the type of action to be taken upon error condition -
      9 Utilities -
       9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format -
       9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format -
       9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format -
       9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format -
       9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format -
       9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format -
      10 Preconditioner routines -
       10.1 init — Initialize a preconditioner -
       10.2 build — Builds a preconditioner -
       10.3 apply — Preconditioner application routine -
       10.4 descr — Prints a description of current preconditioner -
       10.5 clone — clone current preconditioner +
        6.2 psb_cdins — Communication descriptor insert routine +
        6.3 psb_cdasb — Communication descriptor assembly routine +
        6.4 psb_cdcpy — Copies a communication descriptor +
        6.5 psb_cdfree — Frees a communication descriptor +
        6.6 psb_cdbldext — Build an extended communication descriptor +
        6.7 psb_spall — Allocates a sparse matrix +
        6.8 psb_spins — Insert a set of coefficients into a sparse matrix +
        6.9 psb_spasb — Sparse matrix assembly routine +
        6.10 psb_spfree — Frees a sparse matrix +
        6.11 psb_sprn — Reinit sparse matrix structure for psblas routines. +
        6.12 psb_geall — Allocates a dense matrix +
        6.13 psb_geins — Dense matrix insertion routine +
        6.14 psb_geasb — Assembly a dense matrix +
        6.15 psb_gefree — Frees a dense matrix +
        6.16 psb_gelp — Applies a left permutation to a dense matrix +
        6.17 psb_glob_to_loc — Global to local indices convertion +
        6.18 psb_loc_to_glob — Local to global indices conversion +
        6.19 psb_is_owned — +
        6.20 psb_owned_index — +
        6.21 psb_is_local — +
        6.22 psb_local_index — +
        6.23 psb_get_boundary — Extract list of boundary elements +
        6.24 psb_get_overlap — Extract list of overlap elements +
        6.25 psb_sp_getrow — Extract row(s) from a sparse matrix +
        6.26 psb_sizeof — Memory occupation +
        6.27 Sorting utilities — +
       7 Parallel environment routines +
        7.1 psb_init — Initializes PSBLAS parallel environment +
        7.2 psb_info — Return information about PSBLAS parallel environment +
        7.3 psb_exit — Exit from PSBLAS parallel environment +
        7.4 psb_get_mpi_comm — Get the MPI communicator +
        7.5 psb_get_mpi_rank — Get the MPI rank +
        7.6 psb_wtime — Wall clock timing +
        7.7 psb_barrier — Sinchronization point parallel environment +
        7.8 psb_abort — Abort a computation +
        7.9 psb_bcast — Broadcast data +
        7.10 psb_sum — Global sum +
        7.11 psb_max — Global maximum +
        7.12 psb_min — Global minimum +
        7.13 psb_amx — Global maximum absolute value +
        7.14 psb_amn — Global minimum absolute value +
        7.15 psb_nrm2 — Global 2-norm reduction +
        7.16 psb_snd — Send data +
        7.17 psb_rcv — Receive data +
       8 Error handling +
        8.1 psb_errpush — Pushes an error code onto the error stack +
        8.2 psb_error — Prints the error stack content and aborts execution +
        8.3 psb_set_errverbosity — Sets the verbosity of error messages +
        8.4 psb_set_erraction — Set the type of action to be taken upon error condition +
       9 Utilities -
       10.6 free — Free a preconditioner -
      11 Iterative Methods -
       11.1 psb_krylov — Krylov Methods Driver Routine +
        9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing format +
        9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing format +
        9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket format +
        9.4 mm_array_read — Read a dense array from a file in the MatrixMarket format +
        9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket format +
        9.6 mm_array_write — Write a dense array from a file in the MatrixMarket format +
       10 Preconditioner routines +
        10.1 init — Initialize a preconditioner +
        10.2 build — Builds a preconditioner +
        10.3 apply — Preconditioner application routine +
        10.4 descr — Prints a description of current preconditioner +
        10.5 clone — clone current preconditioner +
        10.6 free — Free a preconditioner +
       11 Iterative Methods +
        11.1 psb_krylov — Krylov Methods Driver Routine +
       12 Extensions +
        12.1 Using the extensions +
        12.2 Extensions’ Data Structures +
        12.3 CPU-class extensions +
        12.4 CUDA-class extensions +
       13 CUDA Environment Routines +
        psb_cuda_init +
        psb_cuda_exit +
        psb_cuda_DeviceSync +
        psb_cuda_getDeviceCount +
        psb_cuda_getDevice +
        psb_cuda_setDevice +
        psb_cuda_DeviceHasUVA +
        psb_cuda_WarpSize +
        psb_cuda_MultiProcessors +
        psb_cuda_MaxThreadsPerMP +
        psb_cuda_MaxRegisterPerBlock +
        psb_cuda_MemoryClockRate +
        psb_cuda_MemoryBusWidth +
        psb_cuda_MemoryPeakBandwidth
      diff --git a/docs/html/userhtmlli2.html b/docs/html/userhtmlli2.html index ab983b78..e486077a 100644 --- a/docs/html/userhtmlli2.html +++ b/docs/html/userhtmlli2.html @@ -11,26 +11,16 @@

      [prev] [prev-tail] [tail] [prev] [prev-tail] [tail] [up]

      References

      + id="x21-168000">References

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

      -

      - [2]      G. Bella, S. Filippone, A. De Maio and M. Testa, A Simulation Model for Forest Fires, in J. Dongarra, K. M 2005.

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

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

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

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

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

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

      - [9]      I. Duff, M. Heroux and R. Pozo, An Overview of the Sparse Basic Forum, ACM Transactions on Mathematical Software, 28(2), 2002.

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

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

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

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

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

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

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

      - [17]      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) @@ -172,15 +168,42 @@ class="cmti-10">Fortran 95/2003 explained. Oxford id="XMPI1">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.

      + MIT Press, 1998. +

      +

      + [20]    + D. Barbieri, V. Cardellini, S. Filippone and D. Rouson Design Patterns + for Scientific Computations on Sparse Matrices, HPSS 2011, Algorithms + and Programming Tools for Next-Generation High-Performance Scientific + Software, Bordeaux, Sep. 2011 +

      +

      + [21]    Cardellini, V., Filippone, S., and Rouson, D. 2014, Design patterns + for sparse-matrix computations on hybrid CPU/GPU platforms, Scientific + 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, + Università di Roma Tor Vergata (February 2015). +

      +
      -

      [prev] [prev-tail] [

      [prev] [prev-tail] [front] [up]

      -

      diff --git a/docs/html/userhtmlse1.html b/docs/html/userhtmlse1.html index 3208af54..d25c8a9a 100644 --- a/docs/html/userhtmlse1.html +++ b/docs/html/userhtmlse1.html @@ -27,35 +27,35 @@ preprocessing sparse matrices, and contains additional routines for dense matrix operations. The current implementation of PSBLAS addresses a distributed memory execution model operating with message passing.

      The PSBLAS library version 3 is implemented in the Fortran 2003 [17] +href="userhtmlli2.html#Xmetcalf">16] programming language, with reuse and/or adaptation of existing Fortran 77 and Fortran 95 software, plus a handful of C routines.

      The use of Fortran 2003 offers a number of advantages over Fortran 95, mostly in the handling of requirements for evolution and adaptation of the library to new computing architectures and integration of new algorithms. For a detailed discussion of our design see [11]; other works discussing advanced programming in Fortran 2003 +href="userhtmlli2.html#XSparse03">10]; other works discussing advanced programming in Fortran 2003 include [1, 20, 18]; sufficient support for Fortran 2003 is now available from many compilers, including the GNU Fortran compiler from the Free Software Foundation (as of version 4.8).

      Previous approaches have been based on mixing Fortran 95, with its support for object-based design, with other languages; these have been advocated by a number of authors, e.g. [16]. Moreover, the Fortran 95 facilities for dynamic memory +href="userhtmlli2.html#Xmachiels">15]. Moreover, the Fortran 95 facilities for dynamic memory management and interface overloading greatly enhance the usability of the PSBLAS subroutines. In this way, the library can take care of runtime memory requirements that are quite difficult or even impossible to predict at implementation or compilation time.

      The presentation of the PSBLAS library follows the general structure of the proposal for serial Sparse BLAS [8, 9], which in its turn is based on the proposal for +href="userhtmlli2.html#Xsblas97">7, 8], which in its turn is based on the proposal for BLAS on dense matrices [15, 5, 6]. +href="userhtmlli2.html#XBLAS1">14, 4, 5].

      The applicability of sparse iterative solvers to many different areas causes some terminology problems because the same concept may be denoted through different names depending on the application area. The PSBLAS features presented in this diff --git a/docs/html/userhtmlse10.html b/docs/html/userhtmlse10.html index 83a2b343..e99244c4 100644 --- a/docs/html/userhtmlse10.html +++ b/docs/html/userhtmlse10.html @@ -13,16 +13,18 @@

      [prev] [prev-tail] [tail] [up]

      +href="userhtmlse7.html#tailuserhtmlse10.html">tail] [up]

      10 Preconditioner routines

      + id="x15-13500010">Preconditioner routines

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

        -
      • Diagonal Scaling +
      • +

        Diagonal Scaling

        • -
      • Block Jacobi with ILU(0) factorization
      +
    1. +

      Block Jacobi with ILU(0) factorization

      2. The supporting data type and subroutine interfaces are defined in the module psb_prec_mod. The old interfaces -  10.1 init — Initialize a preconditioner -
       10.2 build — Builds a preconditioner -
       10.3 apply — Preconditioner application routine -
       10.4 descr — Prints a description of current preconditioner -
       10.5 clone — clone current preconditioner -
       10.6 free — Free a preconditioner - +

      10.1 init — Initialize a preconditioner

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +icontxt

      +

      the communication context.
      Scope:global.
      Type:required.
      Intent: in.
      Specified as: an integer value. +

      +

      +ptype

      +

      the type of preconditioner. Scope: global
      Type: required
      Intent: in.
      Specified as: a character string, see usage notes. +

      +

      +On Exit

      +

      +

      +

      +prec

      +

      Scope: local
      Type: required
      Intent: inout.
      Specified as: a preconditioner data structure psb_prec_type. + + + +

      +

      +info

      +

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

      +

      Notes Legal inputs to this subroutine are interpreted depending on the ptype string as +follows4 : +

      +

      +NONE

      +

      No preconditioning, i.e. the preconditioner is just a copy operator. +

      +

      +DIAG

      +

      Diagonal scaling; each entry of the input vector is multiplied by the + reciprocal of the sum of the absolute values of the coefficients in the + corresponding row of matrix A; +

      +

      +BJAC

      +

      Precondition by a factorization of the block-diagonal of matrix A, where + block boundaries are determined by the data allocation boundaries + for each process; requires no communication. Only the incomplete + factorization ILU(0) is currently implemented.

      + + + +

      10.2 build — Builds a preconditioner

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the system sparse matrix. Scope: local
      Type: required
      Intent: in, target.
      Specified as: a sparse matrix data structure psb_Tspmat_type. +

      +

      +prec

      +

      the preconditioner.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an already initialized precondtioner data structure + psb_prec_type
      +

      +

      +desc_a

      +

      the problem communication descriptor. Scope: local
      Type: required
      Intent: in, target.
      Specified as: a communication descriptor data structure psb_desc_type. +

      +

      +amold

      + + + +

      The desired dynamic type for the internal matrix storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from psb_T_base_sparse_mat. +

      +

      +vmold

      +

      The desired dynamic type for the internal vector storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from psb_T_base_vect_type. +

      +

      +imold

      +

      The desired dynamic type for the internal integer vector storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from (integer) + psb_T_base_vect_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +prec

      +

      the preconditioner.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a precondtioner data structure psb_prec_type
      +

      +

      +info

      +

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

      + + + +

      The amold, vmold and imold arguments may be employed to interface with special +devices, such as GPUs and other accelerators. + + + +

      10.3 apply — Preconditioner application routine

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +prec

      +

      the preconditioner. Scope: local
      Type: required
      Intent: in.
      Specified as: a preconditioner data structure psb_prec_type. +

      +

      +x

      +

      the source vector. Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one array or an object of type psb_T_vect_type. +

      +

      +desc_a

      +

      the problem communication descriptor. Scope: local
      Type: required
      Intent: in.
      Specified as: a communication data structure psb_desc_type. +

      +

      +trans

      +

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

      +

      +work

      +

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

      +

      +

      +

      +On Return

      +

      +

      +

      +y

      +

      the destination vector. Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one array or an object of type psb_T_vect_type. +

      +

      +info

      +

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

      + + + +

      10.4 descr — Prints a description of current preconditioner

      + + + + 
      +call prec%descr(info)
+call prec%descr(info,iout, root)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +prec

      +

      the preconditioner. Scope: local
      Type: required
      Intent: in.
      Specified as: a preconditioner data structure psb_prec_type. +

      +

      +iout

      +

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

      +

      +root

      +

      Process from which to print Scope: local
      Type: optional
      Intent: in.
      Specified as: an integer number between 0 and np - 1, in which case + the specified process will print the description, or -1, in which case all + processes will print. Default: 0. +

      +

      +On Return

      +

      + + + +

      +

      +info

      +

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

      + + + +

      10.5 clone — clone current preconditioner

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +prec

      +

      the preconditioner.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +precout

      +

      A copy of the input object. +

      +

      +info

      +

      Return code.

      + + +

      10.6 free — Free a preconditioner

      + + + 
      +call prec%free(info)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +prec

      +

      the preconditioner.
      Scope: local.
      Type: required
      Intent: inout.
      Specified as: a preconditioner data structure psb_prec_type. +

      +

      +On Exit

      +

      +

      +

      +prec

      +

      Scope: local
      Type: required
      Intent: inout.
      Specified as: a preconditioner data structure psb_prec_type. +

      +

      +info

      +

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

      +

      Notes Releases all internal storage. + + + + + + +

      [prev] [prev-tail] [front] [up]

      +href="userhtml.html#userhtmlse13.html" >up]

      + id="tailuserhtmlse10.html"> diff --git a/docs/html/userhtmlse11.html b/docs/html/userhtmlse11.html index a9cc2529..41a4cd65 100644 --- a/docs/html/userhtmlse11.html +++ b/docs/html/userhtmlse11.html @@ -13,10 +13,10 @@

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      11 Iterative Methods

      + id="x17-14200011">Iterative Methods

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

      -  11.1 psb_krylov — Krylov Methods Driver Routine -
      +

      11.1 psb_krylov — Krylov Methods Driver Routine

      +

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

      The stopping criterion can take the following values: +

      +

      +1

      +

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

      + -----∥ri∥------ +err = (∥A∥∥xi∥+ ∥b∥) < eps +
      +

      +

      +

      +2

      +

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

      + ∥ri∥- +err = ∥b∥2 < eps +
      +

      +

      +

      +3

      +

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

      + ∥ri∥ +err = ∥r0∥2 < eps +
      +

      +

      The behaviour is controlled by the istop argument (see later). In the above formulae, xi +is the tentative solution and ri = b - Axi the corresponding residual at the i-th +iteration. + -

      [call psb_krylov(method,a,prec,b,x,eps,desc_a,info,& +    & itmax,iter,err,itrace,irst,istop,cond) + +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +method

      +

      a string that defines the iterative method to be used. Supported values + are: +

      +

      + CG:

      +

      the Conjugate Gradient method; +

      +

      + CGS:

      +

      the Conjugate Gradient Stabilized method; +

      +

      + GCR:

      +

      the Generalized Conjugate Residual method; +

      +

      + FCG:

      +

      the Flexible Conjugate Gradient method5 ; +

      +

      + BICG:

      +

      the Bi-Conjugate Gradient method; +

      +

      + BICGSTAB:

      +

      the Bi-Conjugate Gradient Stabilized method; + + + +

      +

      + BICGSTABL:

      +

      the Bi-Conjugate Gradient Stabilized method with restarting; +

      +

      + RGMRES:

      +

      the Generalized Minimal Residual method with restarting.

      +
      +

      +a

      +

      the local portion of global sparse matrix A.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +prec

      +

      The data structure containing the preconditioner.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_prec_type. +

      +

      +b

      +

      The RHS vector.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one array or an object of type psb_T_vect_type. +

      +

      +x

      +

      The initial guess.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one array or an object of type psb_T_vect_type. +

      +

      +eps

      + + + +

      The stopping tolerance.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a real number. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +itmax

      +

      The maximum number of iterations to perform.
      Scope: global
      Type: optional
      Intent: in.
      Default: itmax = 1000.
      Specified as: an integer variable itmax ≥ 1. +

      +

      +itrace

      +

      If > 0 print out an informational message about convergence every itrace + iterations. If = 0 print a message in case of convergence failure.
      Scope: global
      Type: optional
      Intent: in.
      Default: itrace = -1.
      +

      +

      +irst

      +

      An integer specifying the restart parameter.
      Scope: global
      Type: optional.
      Intent: in.
      Values: irst > 0. This is employed for the BiCGSTABL or RGMRES methods, + otherwise it is ignored. +

      +

      +istop

      + + + +

      An integer specifying the stopping criterion.
      Scope: global
      Type: optional.
      Intent: in.
      Values: 1: use the normwise backward error, 2: use the scaled 2-norm + of the residual, 3: use the residual reduction in the 2-norm. Default: + 2. +

      +

      +On Return

      +

      +

      +

      +x

      +

      The computed solution.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one array or an object of type psb_T_vect_type. +

      +

      +iter

      +

      The number of iterations performed.
      Scope: global
      Type: optional
      Intent: out.
      Returned as: an integer variable. +

      +

      +err

      +

      The convergence estimate on exit.
      Scope: global
      Type: optional
      Intent: out.
      Returned as: a real number. +

      +

      +cond

      +

      An estimate of the condition number of matrix A; only available with the CG + method on real data.
      Scope: global
      Type: optional
      Intent: out.
      Returned as: a real number. A correct result will be greater than or + equal to one; if specified for non-real data, or an error occurred, zero is + returned. +

      +

      +info

      +

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

      + + + + + + + + + + + + +

      [prev] [prev-tail] [front] [up]

      -

      +

      diff --git a/docs/html/userhtmlse12.html b/docs/html/userhtmlse12.html new file mode 100644 index 00000000..e47c099d --- /dev/null +++ b/docs/html/userhtmlse12.html @@ -0,0 +1,921 @@ + + +Extensions + + + + + + + +

      [prev] [prev-tail] [tail] [up]

      +

      12 Extensions

      +

      The EXT, CUDA and RSB subdirectories contains a set of extensions to the base +library. The extensions provide additional storage formats beyond the ones already +contained in the base library, as well as interfaces to: +

      +

      +SPGPU

      +

      a CUDA library originally + published as https://code.google.com/p/spgpu/ and now included + in the cuda subdir, for computations on NVIDIA GPUs; +

      +

      +LIBRSB

      +

      http://sourceforge.net/projects/librsb/, for computations on + multicore parallel machines.

      +

      The infrastructure laid out in the base library to allow for these extensions is detailed in +the references [20, 21, 10]; the CUDA-specific data formats are described +in [22]. +

      +

      12.1 Using the extensions

      +

      A sample application using the PSBLAS extensions will contain the following +steps: +

        +
      • +

        USE the appropriat modules (psb_ext_mod, psb_cuda_mod); +

        • +
      • +

        Declare a mold variable of the necessary type (e.g. + psb_d_ell_sparse_mat, psb_d_hlg_sparse_mat, psb_d_vect_cuda); +

        • +
      • +

        Pass the mold variable to the base library interface where needed to ensure + the appropriate dynamic type.

      + + + +

      Suppose you want to use the CUDA-enabled ELLPACK data structure; you would use a +piece of code like this (and don’t forget, you need CUDA-side vectors along with the +matrices): +

      +

      + + + +

      +program my_cuda_test
+  use psb_base_mod
+  use psb_util_mod
+  use psb_ext_mod
+  use psb_cuda_mod
+  type(psb_dspmat_type) :: a, agpu
+  type(psb_d_vect_type) :: x, xg, bg
+
+  real(psb_dpk_), allocatable :: xtmp(:)
+  type(psb_d_vect_cuda)       :: vmold
+  type(psb_d_elg_sparse_mat) :: aelg
+  type(psb_ctxt_type) :: ctxt
+  integer             :: iam, np
+
+
+  call psb_init(ctxt)
+  call psb_info(ctxt,iam,np)
+  call psb_cuda_init(ctxt, iam)
+
+
+  ! My own home-grown matrix generator
+  call gen_matrix(ctxt,idim,desc_a,a,x,info)
+  if (info /= 0) goto 9999
+
+  call a%cscnv(agpu,info,mold=aelg)
+  if (info /= 0) goto 9999
+  xtmp = x%get_vect()
+  call xg%bld(xtmp,mold=vmold)
+  call bg%bld(size(xtmp),mold=vmold)
+
+  ! Do sparse MV
+  call psb_spmm(done,agpu,xg,dzero,bg,desc_a,info)
+
+
+9999 continue
+  if (info == 0) then
+     write(*,*) ’42’
+  else
+     write(*,*) ’Something went wrong ’,info
+  end if
+
+
+  call psb_cuda_exit()
+  call psb_exit(ctxt)
+  stop
+end program my_cuda_test
+
      +

      + + + +

      A full example of this strategy can be seen in the test/ext/kernel and +test/cuda/kernel subdirectories, where we provide sample programs to test the +speed of the sparse matrix-vector product with the various data structures included +in the library. +

      +

      12.2 Extensions’ Data Structures

      +

      Access to the facilities provided by the EXT library is mainly achieved through +the data types that are provided within. The data classes are derived from +the base classes in PSBLAS, through the Fortran 2003 mechanism of type +extension [17]. +

      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 21. +

      + + + +

      + + + +
      Table 21: Notation for parameters describing a sparse matrix
      +
      +

      +

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

      + + + + + + + +

      PIC +

      Figure 5: Example of sparse matrix
      + + + +

      +

      12.3 CPU-class extensions

      +

      +

      ELLPACK
      +

      The ELLPACK/ITPACK format (shown in Figure 6) comprises two 2-dimensional +arrays AS and JA with M rows and MAXNZR columns, where MAXNZR is the maximum +number of nonzeros in any row [?]. Each row of the arrays AS and JA contains the +coefficients and column indices; rows shorter than MAXNZR are padded with zero +coefficients and appropriate column indices, e.g. the last valid one found in the same +row. +

      + + + + + + + +

      PIC +

      Figure 6: ELLPACK compression of matrix in Figure 5
      + + + +

      + + + + +

      + + + + + 
          do i=1,n 
+      t=0 
+      do j=1,maxnzr 
+        t = t +  as(i,j)*x(ja(i,j)) 
+      end do 
+      y(i) = t 
+    end do
      + + + + Algorithm 1:  Matrix-Vector product in ELL format + + + +
      +

      The matrix-vector product y = Ax can be computed with the code shown in +Alg. 1; it costs one memory write per outer iteration, plus three memory reads and +two floating-point operations per inner iteration. +

      Unless all rows have exactly the same number of nonzeros, some of the coefficients +in the AS array will be zeros; therefore this data structure will have an overhead both +in terms of memory space and redundant operations (multiplications by zero). The +overhead can be acceptable if: +

        +
      1. +

        The maximum number of nonzeros per row is not much larger than the + average; +

        2. +
      2. +

        The regularity of the data structure allows for faster code, e.g. by allowing + vectorization, thereby offsetting the additional storage requirements.

      +

      In the extreme case where the input matrix has one full row, the ELLPACK +structure would require more memory than the normal 2D array storage. The +ELLPACK storage format was very popular in the vector computing days; in +modern CPUs it is not quite as popular, but it is the basis for many GPU +formats. +

      The relevant data type is psb_T_ell_sparse_mat: +

      +

      +

      +  type, extends(psb_d_base_sparse_mat) :: psb_d_ell_sparse_mat
+    !
+    ! ITPACK/ELL format, extended.
+    !
+
+    integer(psb_ipk_), allocatable :: irn(:), ja(:,:), idiag(:)
+    real(psb_dpk_), allocatable :: val(:,:)
+
+  contains
+    ....
+  end type psb_d_ell_sparse_mat
+
      +

      +
      Hacked ELLPACK
      +

      The hacked ELLPACK (HLL) format alleviates the main problem of the ELLPACK +format, that is, the amount of memory required by padding for sparse matrices in +which the maximum row length is larger than the average. + + + +

      The number of elements allocated to padding is +[(m*maxNR) - (m*avgNR) = m* (maxNR-avgNR)] for both AS and JA arrays, +where m is equal to the number of rows of the matrix, maxNR is the maximum +number of nonzero elements in every row and avgNR is the average number of +nonzeros. Therefore a single densely populated row can seriously affect the total size +of the allocation. +

      To limit this effect, in the HLL format we break the original matrix into equally +sized groups of rows (called hacks), and then store these groups as independent +matrices in ELLPACK format. The groups can be arranged selecting rows in an +arbitrarily manner; indeed, if the rows are sorted by decreasing number of nonzeros +we obtain essentially the JAgged Diagonals format. If the rows are not in the original +order, then an additional vector rIdx is required, storing the actual row index for +each row in the data structure. +

      The multiple ELLPACK-like buffers are stacked together inside a single, one +dimensional array; an additional vector hackOffsets is provided to keep track of the +individual submatrices. All hacks have the same number of rows hackSize; hence, the +hackOffsets vector is an array of (m∕hackSize) + 1 elements, each one pointing to +the first index of a submatrix inside the stacked cM/rP buffers, plus an additional +element pointing past the end of the last block, where the next one would begin. We +thus have the property that the elements of the k-th hack are stored between +hackOffsets[k] and hackOffsets[k+1], similarly to what happens in the CSR +format. +

      + + + + + + + +

      PIC +

      Figure 7: Hacked ELLPACK compression of matrix in Figure 5
      + + + +

      +

      With this data structure a very long row only affects one hack, and therefore the +additional memory is limited to the hack in which the row appears. +

      The relevant data type is psb_T_hll_sparse_mat: +

      +

      +

      +  type, extends(psb_d_base_sparse_mat) :: psb_d_hll_sparse_mat
+    !
+    ! HLL format. (Hacked ELL)
+    !
+    integer(psb_ipk_) :: hksz
+    integer(psb_ipk_), allocatable :: irn(:), ja(:), idiag(:), hkoffs(:)
+    real(psb_dpk_), allocatable :: val(:)
+
+  contains
+   ....
+  end type
+
      +

      +
      Diagonal storage
      +

      The DIAgonal (DIA) format (shown in Figure 8) has a 2-dimensional array AS +containing in each column the coefficients along a diagonal of the matrix, and an +integer array OFFSET that determines where each diagonal starts. The diagonals in AS +are padded with zeros as necessary. +

      The code to compute the matrix-vector product y = Ax is shown in Alg. 2; it +costs one memory read per outer iteration, plus three memory reads, one memory +write and two floating-point operations per inner iteration. The accesses to +AS and x are in strict sequential order, therefore no indirect addressing is +required. +

      + + + + + + + +

      PIC +

      Figure 8: DIA compression of matrix in Figure 5
      + + + +

      + + + + +

      + + + +
      +

      + 

      +    do j=1,ndiag
+      if (offset(j) > 0) then
+        ir1 = 1; ir2 = m - offset(j);
+      else
+        ir1 = 1 - offset(j); ir2 = m;
+      end if
+      do i=ir1,ir2
+        y(i) = y(i) + alpha*as(i,j)*x(i+offset(j))
+      end do
+    end do
+
      +

      + + + Algorithm 2:  Matrix-Vector product in DIA format + + + +
      +

      The relevant data type is psb_T_dia_sparse_mat: +

      +

      +

      +  type, extends(psb_d_base_sparse_mat) :: psb_d_dia_sparse_mat
+    !
+    ! DIA format, extended.
+    !
+
+    integer(psb_ipk_), allocatable :: offset(:)
+    integer(psb_ipk_) :: nzeros
+    real(psb_dpk_), allocatable :: data(:,:)
+
+  end type
+
      +

      +
      Hacked DIA
      +

      Storage by DIAgonals is an attractive option for matrices whose coefficients are +located on a small set of diagonals, since they do away with storing explicitly the +indices and therefore reduce significantly memory traffic. However, having a few +coefficients outside of the main set of diagonals may significantly increase the +amount of needed padding; moreover, while the DIA code is easily vectorized, +it does not necessarily make optimal use of the memory hierarchy. While +processing each diagonal we are updating entries in the output vector y, +which is then accessed multiple times; if the vector y is too large to remain +in the cache memory, the associated cache miss penalty is paid multiple +times. +

      The hacked DIA (HDIA) format was designed to contain the amount of padding, +by breaking the original matrix into equally sized groups of rows (hacks), and then +storing these groups as independent matrices in DIA format. This approach is similar +to that of HLL, and requires using an offset vector for each submatrix. Again, +similarly to HLL, the various submatrices are stacked inside a linear array to +improve memory management. The fact that the matrix is accessed in slices +helps in reducing cache misses, especially regarding accesses to the vector +y. +

      An additional vector hackOffsets is provided to complete the matrix format; given +that hackSize is the number of rows of each hack, the hackOffsets vector is made by +an array of (m∕hackSize) + 1 elements, pointing to the first diagonal offset of a +submatrix inside the stacked offsets buffers, plus an additional element equal to the +number of nonzero diagonals in the whole matrix. We thus have the property that +the number of diagonals of the k-th hack is given by hackOffsets[k+1] - +hackOffsets[k]. +

      + + + + + + + +

      PIC +

      Figure 9: Hacked DIA compression of matrix in Figure 5
      + + + +

      +

      The relevant data type is psb_T_hdia_sparse_mat: +

      +

      +

      +  type pm
+     real(psb_dpk_), allocatable  :: data(:,:)
+  end type pm
+
+  type po
+     integer(psb_ipk_), allocatable  :: off(:)
+  end type po
+
+  type, extends(psb_d_base_sparse_mat) :: psb_d_hdia_sparse_mat
+    !
+    ! HDIA format, extended.
+    !
+
+    type(pm), allocatable :: hdia(:)
+    type(po), allocatable :: offset(:)
+    integer(psb_ipk_) :: nblocks, nzeros
+    integer(psb_ipk_) :: hack = 64
+    integer(psb_long_int_k_) :: dim=0
+
+  contains
+   ....
+  end type
+
      +

      + + + + + + + + + +

      12.4 CUDA-class extensions

      +

      For computing with CUDA we define a dual memorization strategy in which each +variable on the CPU (“host”) side has a GPU (“device”) side. When a GPU-type +variable is initialized, the data contained is (usually) the same on both sides. Each +operator invoked on the variable may change the data so that only the host side or +the device side are up-to-date. +

      Keeping track of the updates to data in the variables is essential: we want to +perform most computations on the GPU, but we cannot afford the time needed to +move data between the host memory and the device memory because the bandwidth +of the interconnection bus would become the main bottleneck of the computation. +Thus, each and every computational routine in the library is built according to the +following principles: +

        +
      • +

        If the data type being handled is GPU-enabled, make sure that its device + copy is up to date, perform any arithmetic operation on the GPU, and + if the data has been altered as a result, mark the main-memory copy as + outdated. +

        • +
      • +

        The main-memory copy is never updated unless this is requested by the user + either +

        +

        + explicitly

        +

        by invoking a synchronization method; +

        +

        + implicitly

        +

        by invoking a method that involves other data items that are not + GPU-enabled, e.g., by assignment ov a vector to a normal array.

        +
      +

      In this way, data items are put on the GPU memory “on demand” and remain there as +long as “normal” computations are carried out. As an example, the following call to a +matrix-vector product +

      +

      +

      +    call psb_spmm(alpha,a,x,beta,y,desc_a,info)
+
      +

      + + + +

      will transparently and automatically be performed on the GPU whenever all three data +inputs a, x and y are GPU-enabled. If a program makes many such calls sequentially, +then +

        +
      • +

        The first kernel invocation will find the data in main memory, and will + copy it to the GPU memory, thus incurring a significant overhead; the + result is however not copied back, and therefore: +

        • +
      • +

        Subsequent kernel invocations involving the same vector will find the data + on the GPU side so that they will run at full speed.

      +

      For all invocations after the first the only data that will have to be transferred to/from +the main memory will be the scalars alpha and beta, and the return code +info. +

      +

      +

      +Vectors:

      +

      The data type psb_T_vect_gpu provides a GPU-enabled extension of + the inner type psb_T_base_vect_type, and must be used together with + the other inner matrix type to make full use of the GPU computational + capabilities; +

      +

      +CSR:

      +

      The data type psb_T_csrg_sparse_mat provides an interface to the GPU + version of CSR available in the NVIDIA CuSPARSE library; +

      +

      +HYB:

      +

      The data type psb_T_hybg_sparse_mat provides an interface to the HYB + GPU storage available in the NVIDIA CuSPARSE library. The internal + structure is opaque, hence the host side is just CSR; the HYB data format + is only available up to CUDA version 10. +

      +

      +ELL:

      +

      The data type psb_T_elg_sparse_mat provides an interface to the + ELLPACK implementation from SPGPU; + + + +

      +

      +HLL:

      +

      The data type psb_T_hlg_sparse_mat provides an interface to the Hacked + ELLPACK implementation from SPGPU; +

      +

      +HDIA:

      +

      The data type psb_T_hdiag_sparse_mat provides an interface to the + Hacked DIAgonals implementation from SPGPU;

      + + + +

      [prev] [prev-tail] [front] [up]

      +

      + diff --git a/docs/html/userhtmlse13.html b/docs/html/userhtmlse13.html new file mode 100644 index 00000000..fa8fed8f --- /dev/null +++ b/docs/html/userhtmlse13.html @@ -0,0 +1,299 @@ + + +CUDA Environment Routines + + + + + + + +

      [prev] [prev-tail] [tail] [up]

      +

      13 CUDA Environment Routines

      +

      +

      psb_cuda_init — Initializes PSBLAS-CUDA environment

      + +
      +

      +

      +call psb_cuda_init(ctxt [, device])
+
      +

      +

      This subroutine initializes the PSBLAS-CUDA environment. +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +device

      +

      ID of CUDA device to attach to.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an integer value.  Default: use mod(iam,ngpu) where iam is + the calling process index and ngpu is the total number of CUDA devices + available on the current node.

      +

      Notes + + + +

        +
      1. +

        A call to this routine must precede any other PSBLAS-CUDA call.

      +

      +

      psb_cuda_exit — Exit from PSBLAS-CUDA environment

      + +
      +

      +

      +call psb_cuda_exit(ctxt)
+
      +

      +

      This subroutine exits from the PSBLAS CUDA context. +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

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

      +

      +

      psb_cuda_DeviceSync — Synchronize CUDA device

      + + + + +
      +

      +

      +call psb_cuda_DeviceSync()
+
      +

      +

      This subroutine ensures that all previosly invoked kernels, i.e. all invocation of +CUDA-side code, have completed. +

      +

      psb_cuda_getDeviceCount

      + +
      +

      +

      +ngpus =  psb_cuda_getDeviceCount()
+
      +

      +

      Get number of devices available on current computing node. +

      +

      psb_cuda_getDevice

      + +
      +

      +

      +ngpus =  psb_cuda_getDevice()
+
      +

      +

      Get device in use by current process. +

      +

      psb_cuda_setDevice

      + + + + +
      +

      +

      +info = psb_cuda_setDevice(dev)
+
      +

      +

      Set device to be used by current process. +

      +

      psb_cuda_DeviceHasUVA

      + +
      +

      +

      +hasUva = psb_cuda_DeviceHasUVA()
+
      +

      +

      Returns true if device currently in use supports UVA (Unified Virtual Addressing). +

      +

      psb_cuda_WarpSize

      + +
      +

      +

      +nw = psb_cuda_WarpSize()
+
      +

      +

      Returns the warp size. +

      +

      psb_cuda_MultiProcessors

      + + + + +
      +

      +

      +nmp = psb_cuda_MultiProcessors()
+
      +

      +

      Returns the number of multiprocessors in the CUDA device. +

      +

      psb_cuda_MaxThreadsPerMP

      + +
      +

      +

      +nt = psb_cuda_MaxThreadsPerMP()
+
      +

      +

      Returns the maximum number of threads per multiprocessor. +

      +

      psb_cuda_MaxRegistersPerBlock

      + +
      +

      +

      +nr = psb_cuda_MaxRegistersPerBlock()
+
      +

      +

      Returns the maximum number of register per thread block. +

      +

      psb_cuda_MemoryClockRate

      + + + + +
      +

      +

      +cl = psb_cuda_MemoryClockRate()
+
      +

      +

      Returns the memory clock rate in KHz, as an integer. +

      +

      psb_cuda_MemoryBusWidth

      + +
      +

      +

      +nb = psb_cuda_MemoryBusWidth()
+
      +

      +

      Returns the memory bus width in bits. +

      +

      psb_cuda_MemoryPeakBandwidth

      + +
      +

      +

      +bw = psb_cuda_MemoryPeakBandwidth()
+
      +

      +

      Returns the peak memory bandwidth in MB/s (real double precision). + + + + + + + + + +

      + + + + + + +

      [prev] [prev-tail] [front] [up]

      +

      + diff --git a/docs/html/userhtmlse2.html b/docs/html/userhtmlse2.html index 81d5b244..b2cab256 100644 --- a/docs/html/userhtmlse2.html +++ b/docs/html/userhtmlse2.html @@ -11,7 +11,7 @@

      [next] [next] [prev] [prev-tail] [tail] [[7]. Usually there is no need to deal +href="userhtmlli2.html#XBLACS">6]. Usually there is no need to deal directly with MPI; however, in some cases, MPI routines are used directly to improve efficiency. For further details on our communication layer see Sec. 7. +href="userhtmlse7.html#x12-1050007">7.

      @@ -85,7 +85,7 @@ class="cmtt-10">BLOCK, as well as completely arbitrary assignments of equation indices to processes. In particular it is consistent with the usage of graph partitioning tools commonly available in the literature, e.g. METIS [14]. Dense vectors conform to sparse matrices, +href="userhtmlli2.html#XMETIS">13]. 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 @@ -96,30 +96,610 @@ href="userhtml5.html#fn1x0">1 , even though the resulting memory bottleneck would make this option unattractive in most cases. -

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

      2.1 Basic Nomenclature

      +

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

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

      +

      +Internal.

      +

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

      +

      +Boundary.

      +

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

      +

      +Halo.

      +

      A halo point for a given domain is a point belonging to another domain + such that there is a boundary point which depends on it. Whenever performing + a computational step, such as a matrix-vector product, the values associated + with halo points are requested from other domains. A boundary point of a + given domain is usually a halo point for some other domain2 ; + therefore the cardinality of the boundary points set denotes the amount + of data sent to other domains. +

      +

      +Overlap.

      +

      An overlap point is a boundary point assigned to multiple domains. Any + operation that involves an overlap point has to be replicated for each + assignment.

      +

      Overlap points do not usually exist in the basic data distributions; however they are a +feature of Domain Decomposition Schwarz preconditioners which are the subject of +related research work [3, 2]. +

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

      + + + + + +
      +

      +

      PIC

      +
      Figure 2: Point classfication.
      + + + +

      +

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

      2.2 Library contents

      +

      The PSBLAS library consists of various classes of subroutines: +

      +

      +Computational routines

      +

      comprising: +

        +
      • +

        Sparse matrix by dense matrix product; +

        • +
      • +

        Sparse triangular systems solution for block diagonal matrices; +

        • +
      • +

        Vector and matrix norms; +

        • +
      • +

        Dense matrix sums; +

        • +
      • +

        Dot products.

      +
      +

      +Communication routines

      +

      handling halo and overlap communications; +

      +

      +Data management and auxiliary routines

      +

      including: +

        +
      • +

        Parallel environment management +

        • +
      • +

        Communication descriptors allocation; + + + +

        • +
      • +

        Dense and sparse matrix allocation; +

        • +
      • +

        Dense and sparse matrix build and update; +

        • +
      • +

        Sparse matrix and data distribution preprocessing.

      +
      +

      +Preconditioner routines

      +

      +

      +

      +Iterative methods

      +

      a subset of Krylov subspace iterative methods

      +

      The following naming scheme has been adopted for all the symbols internally defined in +the PSBLAS software package: +

        +
      • +

        all symbols (i.e. subroutine names, data types...) are prefixed by psb_ +

        • +
      • +

        all data type names are suffixed by _type +

        • +
      • +

        all constants are suffixed by _ +

        • +
      • +

        all top-level subroutine names follow the rule psb_xxname where xx can be + either: +

          +
        • +

          ge: the routine is related to dense data, +

          • +
        • +

          sp: the routine is related to sparse data, +

          • +
        • +

          cd: the routine is related to communication descriptor (see 3).

        + + + +

        For example the psb_geins, psb_spins and psb_cdins perform the same + action (see 6) on dense matrices, sparse matrices and communication + descriptors respectively. Interface overloading allows the usage of the same + subroutine names for both real and complex data.

      +

      In the description of the subroutines, arguments or argument entries are classified +as: +

      +

      +global

      +

      For input arguments, the value must be the same on all processes + participating in the subroutine call; for output arguments the value is + guaranteed to be the same. +

      +

      +local

      +

      Each process has its own value(s) independently.

      +

      To finish our general description, we define a version string with the constant +

      +psb_version_string_ +
      +

      whose current value is 3.8.0 +

      +

      2.3 Application structure

      +

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

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

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

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

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

        +
      1. +

        Initialize parallel environment with psb_init +

        2. +
      2. +

        Initialize index space with psb_cdall +

        3. +
      3. +

        Allocate sparse matrix and dense vectors with psb_spall and psb_geall +

        4. +
      4. +

        Loop over all local rows, generate matrix and vector entries, and insert + them with psb_spins and psb_geins +

        5. +
      5. +

        Assemble the various entities: +

          +
        1. +

          psb_cdasb +

          2. +
        2. +

          psb_spasb + + + +

          3. +
        3. +

          psb_geasb

        +
        6. +
      6. +

        Choose the preconditioner to be used with prec%init and build it with + prec%build3 . +

        7. +
      7. +

        Call the iterative driver psb_krylov with the method of choice, e.g. + bicgstab.

      +

      This is the structure of the sample programs in the directory test/pargen/. +

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

        +
      1. +

        Initialize parallel environment with psb_init +

        2. +
      2. +

        Initialize index space with psb_cdall +

        3. +
      3. +

        Loop over the topology of the discretization mesh and build the descriptor + with psb_cdins +

        4. +
      4. +

        Assemble the descriptor with psb_cdasb +

        5. +
      5. +

        Allocate the sparse matrices and dense vectors with psb_spall and + psb_geall + + + +

        6. +
      6. +

        Loop over the time steps: +

          +
        1. +

          If after first time step, reinitialize the sparse matrix with psb_sprn; + also zero out the dense vectors; +

          2. +
        2. +

          Loop over the mesh, generate the coefficients and insert/update them + with psb_spins and psb_geins +

          3. +
        3. +

          Assemble with psb_spasb and psb_geasb +

          4. +
        4. +

          Choose and build preconditioner with prec%init and prec%build +

          5. +
        5. +

          Call the iterative method of choice, e.g. psb_bicgstab

        +
      +

      The insertion routines will be called as many times as needed; they only need to be +called on the data that is actually allocated to the current process, i.e. each process +generates its own data. +

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

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

      +

      2.3.1 User-defined index mappings
      +

      PSBLAS supports user-defined global to local index mappings, subject to the +constraints outlined in sec. 2.3: +

        +
      1. +

        The set of indices owned locally must be mapped to the set 1…nrowi; +

        2. +
      2. +

        The set of halo points must be mapped to the set nrowi + 1…ncol +i;

      +

      but otherwise the mapping is arbitrary. The user application is responsible to ensure +consistency of this mapping; some errors may be caught by the library, but +this is not guaranteed. The application structure to support this usage is as +follows: +

        +
      1. +

        Initialize index + space with psb_cdall(ictx,desc,info,vl=vl,lidx=lidx) passing the + vectors vl(:) containing the set of global indices owned by the current + process and lidx(:) containing the corresponding local indices; +

        2. +
      2. +

        Add the halo points ja(:) and their associated local indices lidx(:) with + a(some) call(s) to psb_cdins(nz,ja,desc,info,lidx=lidx); +

        3. +
      3. +

        Assemble the descriptor with psb_cdasb; +

        4. +
      4. +

        Build the sparse matrices and vectors, optionally making use in psb_spins + and psb_geins of the local argument specifying that the indices in ia, + ja and irw, respectively, are already local indices.

      + + + +

      +

      2.4 Programming model

      +

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

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

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

      Throughout this user’s guide each subroutine will be clearly indicated +as: +

      +

      +Synchronous:

      +

      must be called simultaneously by all the processes in the relevant + communication context; +

      +

      +Asynchronous:

      +

      may be called in a totally independent manner.

      + + + + + + + + + +

      [next] [next] [prev] [prev-tail] [front] [up]

      + id="tailuserhtmlse2.html"> diff --git a/docs/html/userhtmlse3.html b/docs/html/userhtmlse3.html index 25ad41c7..016e8a9f 100644 --- a/docs/html/userhtmlse3.html +++ b/docs/html/userhtmlse3.html @@ -11,70 +11,78 @@

      [next] [next] [prev] [prev-tail] [tail] [up]

      +href="#tailuserhtmlse3.html">tail] [up]

      3 Data Structures and Classes

      + id="x8-90003">Data Structures and Classes

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

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

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

      +

      psb_spk_

      Kind parameter for short precision real and complex data; - corresponds to a REAL declaration and is normally 4 bytes; +class="description"> +

      Kind parameter for short precision real and complex data; corresponds to + a REAL declaration and is normally 4 bytes;

      +

      psb_dpk_

      Kind parameter for long precision real and complex data; - corresponds to a DOUBLE PRECISION declaration and is normally 8 bytes; +class="description"> +

      Kind parameter for long precision real and complex data; corresponds to + a DOUBLE PRECISION declaration and is normally 8 bytes;

      +

      psb_mpk_

      Kind parameter for 4-bytes integer data, as is always used by MPI; +class="description"> +

      Kind parameter for 4-bytes integer data, as is always used by MPI;

      +

      psb_epk_

      Kind parameter for 8-bytes integer data, as is always used by the - sizeof methods; +class="description"> +

      Kind parameter for 8-bytes integer data, as is always used by the sizeof + methods;

      +

      psb_ipk_

      Kind parameter for “local” integer indices and data; with default - build options this is a 4 bytes integer; +class="description"> +

      Kind parameter for “local” integer indices and data; with default build + options this is a 4 bytes integer; + + +

      +

      psb_lpk_

      Kind parameter for “global” integer indices and data; with default - build options this is an 8 bytes integer;
      +class="description"> +

      Kind parameter for “global” integer indices and data; with default build + options this is an 8 bytes integer;

      The integer kinds for local and global indices can be chosen at configure time to hold 4 or 8 bytes, with the global indices at least as large as the local ones. Together with the classes attributes we also discuss their methods. Most methods detailed here only @@ -83,115 +91,2592 @@ otherwise stated. The list of methods here is not completely exhaustive; many methods, especially those that alter the contents of the various objects, are usually not needed by the end-user, and therefore are described in the developer’s documentation. +

      +

      3.1 Descriptor data structure

      +

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

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

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

      +

      There are many different schemes for storing these data; therefore there are a number of +types extending the base one, and the descriptor structure holds a polymorphic +object whose dynamic type can be any of the extended types. The methods +associated with this data type answer the following queries: +

        +
      • +

        For a given set of local indices, find the corresponding indices in the global + numbering; +

        • +
      • +

        For a given set of global indices, find the corresponding indices in the local + numbering, if any, or return an invalid +

        • +
      • +

        Add a global index to the set of halo indices; +

        • +
      • +

        Find the process owner of each member of a set of global indices.

      +

      All methods but the last are purely local; the last method potentially requires +communication among processes, and thus is a synchronous method. The +choice of a specific dynamic type for the index map is made at the time the +descriptor is initially allocated, according to the mode of initialization (see +also 6). +

      The descriptor contents are as follows: +

      +

      +indxmap

      +

      A polymorphic variable of a type that is any extension of the indx_map + type described above.
      +

      +

      +halo_index

      +

      A list of the halo and boundary elements for the current process to be + exchanged with other processes; for each processes with which it is necessary to + communicate: + + + +

        +
      1. +

        Process identifier; +

        2. +
      2. +

        Number of points to be received; +

        3. +
      3. +

        Indices of points to be received; +

        4. +
      4. +

        Number of points to be sent; +

        5. +
      5. +

        Indices of points to be sent;

      +

      Specified as: a vector of integer type, see 3.3. +

      +

      +ext_index

      +

      A list of element indices to be exchanged to implement the mapping between a + base descriptor and a descriptor with overlap.
      Specified as: a vector of integer type, see 3.3. +

      +

      +ovrlap_index

      +

      A list of the overlap elements for the current process, organized in groups like + the previous vector: +

        +
      1. +

        Process identifier; +

        2. +
      2. +

        Number of points to be received; +

        3. +
      3. +

        Indices of points to be received; + + + +

        4. +
      4. +

        Number of points to be sent; +

        5. +
      5. +

        Indices of points to be sent;

      +

      Specified as: a vector of integer type, see 3.3. +

      +

      +ovr_mst_idx

      +

      A list to retrieve the value of each overlap element from the respective master + process.
      Specified as: a vector of integer type, see 3.3. +

      +

      +ovrlap_elem

      +

      For all overlap points belonging to th ecurrent process: +

        +
      1. +

        Overlap point index; +

        2. +
      2. +

        Number of processes sharing that overlap points; +

        3. +
      3. +

        Index of a “master” process:

      +

      Specified as: an allocatable integer array of rank two. +

      +

      +bnd_elem

      +

      A list of all boundary points, i.e. points that have a connection with other + processes.

      +

      The Fortran 2003 declaration for psb_desc_type structures is as follows: +

      + + + +
      +

      +

      +type psb_desc_type
+    class(psb_indx_map), allocatable :: indxmap
+    type(psb_i_vect_type) :: v_halo_index
+    type(psb_i_vect_type) :: v_ext_index
+    type(psb_i_vect_type) :: v_ovrlap_index
+    type(psb_i_vect_type) :: v_ovr_mst_idx
+    integer, allocatable  :: ovrlap_elem(:,:)
+    integer, allocatable  :: bnd_elem(:)
+end type psb_desc_type
+
      +

      +
      Listing 1: The PSBLAS defined data type that contains the communication +descriptor.
      + + + +
      +

      A communication descriptor associated with a sparse matrix has a state, which +can take the following values: +

      +

      +Build:

      +

      State entered after the first allocation, and before the first assembly; in this + state it is possible to add communication requirements among different + processes. +

      +

      +Assembled:

      +

      State entered after the assembly; computations using the associated sparse + matrix, such as matrix-vector products, are only possible in this state.

      +
      3.1.1 Descriptor Methods
      +

      +

      3.1.2 get_local_rows — Get number of local rows
      + + + + 
      +nr = desc%get_local_rows()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of local rows, i.e. the number of rows owned by the current + process; as explained in 1, it is equal to |Ii| + |Bi|. The returned value is + specific to the calling process.

      +

      +

      3.1.3 get_local_cols — Get number of local cols
      + + + + 
      +nc = desc%get_local_cols()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of local cols, i.e. the number of indices used by the current + process, including both local and halo indices; as explained in 1, it is equal + to |Ii| + |Bi| + |Hi|. The returned value is specific to the calling process.

      +

      +

      3.1.4 get_global_rows — Get number of global rows
      + + + + 
      +nr = desc%get_global_rows()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of global rows, i.e. the size of the global index space.

      +

      +

      3.1.5 get_global_cols — Get number of global cols
      + + + + 
      +nr = desc%get_global_cols()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of global cols; usually this is equal to the number of global + rows.

      +

      +

      3.1.6 get_global_indices — Get vector of global indices
      + + + + 
      +myidx = desc%get_global_indices([owned])
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.
      Type: required.
      +

      +

      +owned

      +

      Choose if you only want owned indices (owned=.true.) or also halo indices + (owned=.false.). Scope: local.
      Type: optional; default: .true..

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The global indices, returned as an allocatable integer array of kind + psb_lpk_ and rank 1.

      +

      +

      3.1.7 get_context — Get communication context
      + + + + 
      +ctxt = desc%get_context()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The communication context.

      +

      +

      3.1.8 Clone — clone current object
      + + + + 
      +call  desc%clone(descout,info)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +descout

      +

      A copy of the input object. +

      +

      +info

      +

      Return code.

      +

      +

      3.1.9 CNV — convert internal storage format
      + + + + 
      +call  desc%cnv(mold)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope: local.
      +

      +

      +mold

      +

      the desired integer storage format.
      Scope: local.
      Specified as: a object of type derived from (integer) + psb_T_base_vect_type.

      +

      The mold arguments may be employed to interface with special devices, such as GPUs +and other accelerators. +

      +

      3.1.10 psb_cd_get_large_threshold — Get threshold for index mapping +switch
      + + + + 
      +ith = psb_cd_get_large_threshold()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The current value for the size threshold. +

      +

      +

      3.1.11 psb_cd_set_large_threshold — Set threshold for index mapping +switch
      + + + + 
      +call psb_cd_set_large_threshold(ith)
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ith

      +

      the new threshold for communication descriptors.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer value greater than zero.

      +

      Note: the threshold value is only queried by the library at the time a call to psb_cdall +is executed, therefore changing the threshold has no effect on communication +descriptors that have already been initialized. Moreover the threshold must have the +same value on all processes. +

      +

      3.1.12 get_p_adjcncy — Get process adjacency list
      + + + + 
      +list =  desc%get_p_adjcncy()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The current list of adjacent processes, i.e. processes with which the current + one has to exchange halo data. +

      +

      +

      3.1.13 set_p_adjcncy — Set process adjacency list
      + + + + 
      +call desc%set_p_adjcncy(list)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +list

      +

      the list of adjacent processes.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: a one-dimensional array of integers of kind psb_ipk_.

      +

      Note: this method can be called after a call to psb_cdall and before a call to +psb_cdasb. The user is specifying here some knowledge about which processes are +topological neighbours of the current process. The availability of this information +may speed up the execution of the assembly call psb_cdasb. +

      +

      3.1.14 fnd_owner — Find the owner process of a set of indices
      + + + + 
      +call desc%fnd_owner(idx,iprc,info)
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +idx

      +

      the list of global indices for which we need the owning processes.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: a one-dimensional array of integers of kind psb_lpk_. +

      +

      +On Return

      +

      +

      +

      +iprc

      +

      the list of processes owning the indices in idx.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: an allocatable one-dimensional array of integers of kind + psb_ipk_.

      +

      Note: this method may or may not actually require communications, depending on the +exact internal data storage; given that the choice of storage may be altered by +runtime parameters, it is necessary for safety that this method is called by all +processes. + + +

      +

      3.1.15 Named Constants
      +

      +

      +

      +psb_none_

      +

      Generic no-op; +

      +

      +psb_root_

      +

      Default root process for broadcast and scatter operations; +

      +

      +psb_nohalo_

      +

      Do not fetch halo elements; +

      +

      +psb_halo_

      +

      Fetch halo elements from neighbouring processes; +

      +

      +psb_sum_

      +

      Sum overlapped elements +

      +

      +psb_avg_

      +

      Average overlapped elements +

      +

      +psb_comm_halo_

      +

      Exchange data based on the halo_index list; +

      +

      +psb_comm_ext_

      +

      Exchange data based on the ext_index list; +

      +

      +psb_comm_ovr_

      +

      Exchange data based on the ovrlap_index list; + + +

      +

      +psb_comm_mov_

      +

      Exchange data based on the ovr_mst_idx list; +

      +

      +

      3.2 Sparse Matrix class

      +

      The psb_Tspmat_type class contains all information about the local portion of the +sparse matrix and its storage mode. Its design is based on the STATE design +pattern [12] as detailed in [10]; the type declaration is shown in figure 2 where T is a +placeholder for the data type and precision variants +

      +

      +S

      +

      Single precision real; +

      +

      +D

      +

      Double precision real; +

      +

      +C

      +

      Single precision complex; +

      +

      +Z

      +

      Double precision complex; +

      +

      +LS,LD,LC,LZ

      +

      Same numeric type as above, but with psb_lpk_ integer indices.

      +

      The actual data is contained in the polymorphic component a%a of type +psb_T_base_sparse_mat; its specific layout can be chosen dynamically among the +predefined types, or an entirely new storage layout can be implemented and passed to +the library at runtime via the psb_spasb routine. +

      + + +
      +

      +

      +  type :: psb_Tspmat_type
+    class(psb_T_base_sparse_mat), allocatable  :: a
+  end type  psb_Tspmat_type
+
      +

      +
      Listing 2: The PSBLAS defined data type that contains a sparse matrix.
      + +
      +

      The following very common formats are precompiled in PSBLAS and thus are +always available: +

      +

      +psb_T_coo_sparse_mat

      +

      Coordinate storage; +

      +

      +psb_T_csr_sparse_mat

      +

      Compressed storage by rows; +

      +

      +psb_T_csc_sparse_mat

      +

      Compressed storage by columns;

      +

      The inner sparse matrix has an associated state, which can take the following +values: +

      +

      +Build:

      +

      State entered after the first allocation, and before the first assembly; in + this state it is possible to add nonzero entries. +

      +

      +Assembled:

      +

      State entered after the assembly; computations using the sparse matrix, + such as matrix-vector products, are only possible in this state; +

      +

      +Update:

      +

      State entered after a reinitalization; this is used to handle applications + in which the same sparsity pattern is used multiple times with different + coefficients. In this state it is only possible to enter coefficients for already + existing nonzero entries.

      +

      The only storage variant supporting the build state is COO; all other variants are +obtained by conversion to/from it. +

      3.2.1 Sparse Matrix Methods
      +

      +

      3.2.2 get_nrows — Get number of rows in a sparse matrix
      + + + + 
      +nr = a%get_nrows()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of rows of sparse matrix a.

      +

      +

      3.2.3 get_ncols — Get number of columns in a sparse matrix
      + + + + 
      +nc = a%get_ncols()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of columns of sparse matrix a.

      +

      +

      3.2.4 get_nnzeros — Get number of nonzero elements in a sparse matrix
      + + + + 
      +nz = a%get_nnzeros()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of nonzero elements stored in sparse matrix a.

      +

      Notes +

        +
      1. +

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

      +

      +

      3.2.5 get_size — Get maximum number of nonzero elements in a sparse +matrix
      + + + + 
      +maxnz = a%get_size()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The maximum number of nonzero elements that can be stored in sparse + matrix a using its current memory allocation.

      +

      +

      3.2.6 sizeof — Get memory occupation in bytes of a sparse matrix
      + + + + 
      +memory_size = a%sizeof()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The memory occupation in bytes.

      +

      +

      3.2.7 get_fmt — Short description of the dynamic type
      +

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

      +

      +

      +Type:

      +

      Asynchronous. + + + +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      A short string describing the dynamic type of the matrix. Predefined values + include NULL, COO, CSR and CSC.

      +

      +

      3.2.8 is_bld, is_upd, is_asb — Status check
      +

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

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      + + + +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      A logical value indicating whether the matrix is in the Build, Update or + Assembled state, respectively.

      +

      +

      3.2.9 is_lower, is_upper, is_triangle, is_unit — Format check
      + + + + 
      +if (a%is_triangle()) then
+if (a%is_upper()) then
+if (a%is_lower()) then
+if (a%is_unit()) then
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

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

      +

      +

      3.2.10 cscnv — Convert to a different storage format
      + + + + 
      +call  a%cscnv(b,info [, type, mold, dupl])
+call  a%cscnv(info [, type, mold, dupl])
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.
      +

      +

      +type

      +

      a string requesting a new format.
      Type: optional. +

      +

      +mold

      +

      a variable of class(psb_T_base_sparse_mat) requesting a new format.
      Type: optional. +

      +

      +dupl

      +

      an integer value specifing how to handle duplicates (see Named Constants + below)

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +b,a

      +

      A copy of a with a new storage format.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      +

      The mold arguments may be employed to interface with special devices, such as GPUs +and other accelerators. +

      +

      3.2.11 csclip — Reduce to a submatrix
      + + + + 
      +    call a%csclip(b,info[,&
+       & imin,imax,jmin,jmax,rscale,cscale])
+
      +

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.
      +

      +

      +imin,imax,jmin,jmax

      +

      Minimum and maximum row and column indices.
      Type: optional. +

      +

      +rscale,cscale

      +

      Whether to rescale row/column indices. Type: optional.

      +

      +

      +

      +On Return

      +

      + + + +

      +

      +b

      +

      A copy of a submatrix of a.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      +

      +

      3.2.12 clean_zeros — Eliminate zero coefficients
      +

      call a%clean_zeros(info) +

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

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.

      +

      +

      +

      +On Return

      +

      + + + +

      +

      +a

      +

      The matrix a without zero coefficients.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      +

      +

      3.2.13 get_diag — Get main diagonal
      +

      call a%get_diag(d,info) +

      Returns a copy of the main diagonal. +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +d

      +

      A copy of the main diagonal.
      A one-dimensional array of the appropriate type. + + + +

      +

      +info

      +

      Return code.

      +

      +

      3.2.14 clip_diag — Cut out main diagonal
      +

      call a%clip_diag(b,info) +

      Returns a copy of a without the main diagonal. +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +b

      +

      A copy of a without the main diagonal.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      + + + +

      +

      3.2.15 tril — Return the lower triangle
      + + + + 
      +    call a%tril(l,info[,&
+       & diag,imin,imax,jmin,jmax,rscale,cscale,u])
+
      +

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.
      +

      +

      +diag

      +

      Include diagonals up to this one; diag=1 means the first superdiagonal, + diag=-1 means the first subdiagonal. Default 0. +

      +

      +imin,imax,jmin,jmax

      +

      Minimum and maximum row and column indices.
      Type: optional. +

      +

      +rscale,cscale

      +

      Whether to rescale row/column indices. Type: optional.

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +l

      +

      A copy of the lower triangle of a.
      A variable of type psb_Tspmat_type. +

      +

      +u

      +

      (optional) A copy of the upper triangle of a.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      +

      +

      3.2.16 triu — Return the upper triangle
      + + + + 
      +    call a%triu(u,info[,&
+       & diag,imin,imax,jmin,jmax,rscale,cscale,l])
+
      +

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      A variable of type psb_Tspmat_type.
      Scope: local.
      +

      +

      +diag

      +

      Include diagonals up to this one; diag=1 means the first superdiagonal, + diag=-1 means the first subdiagonal. Default 0. +

      +

      +imin,imax,jmin,jmax

      +

      Minimum and maximum row and column indices.
      Type: optional. +

      +

      +rscale,cscale

      +

      Whether to rescale row/column indices. Type: optional.

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +u

      +

      A copy of the upper triangle of a.
      A variable of type psb_Tspmat_type. +

      +

      +l

      +

      (optional) A copy of the lower triangle of a.
      A variable of type psb_Tspmat_type. +

      +

      +info

      +

      Return code.

      +

      +

      3.2.17 psb_set_mat_default — Set default storage format
      +

      call psb_set_mat_default(a) +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      a variable of class(psb_T_base_sparse_mat) requesting a new default + storage format.
      Type: required.

      + + + +

      +

      3.2.18 clone — Clone current object
      +

      call a%clone(b,info) +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +b

      +

      A copy of the input object. +

      +

      +info

      +

      Return code.

      +

      +

      3.2.19 Named Constants
      +

      +

      +

      +psb_dupl_ovwrt_

      +

      Duplicate coefficients should be overwritten (i.e. ignore duplications) + + + +

      +

      +psb_dupl_add_

      +

      Duplicate coefficients should be added; +

      +

      +psb_dupl_err_

      +

      Duplicate coefficients should trigger an error conditino +

      +

      +psb_upd_dflt_

      +

      Default update strategy for matrix coefficients; +

      +

      +psb_upd_srch_

      +

      Update strategy based on search into the data structure; +

      +

      +psb_upd_perm_

      +

      Update strategy based on additional permutation data (see tools routine + description).

      +

      +

      3.3 Dense Vector Data Structure

      +

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

      The type declaration is shown in figure 3 where T is a placeholder for the data +type and precision variants +

      +

      +I

      +

      Integer; +

      +

      +S

      +

      Single precision real; + + + +

      +

      +D

      +

      Double precision real; +

      +

      +C

      +

      Single precision complex; +

      +

      +Z

      +

      Double precision complex.

      +

      The actual data is contained in the polymorphic component v%v; the separation between +the application and the actual data is essential for cases where it is necessary to link +to data storage made available elsewhere outside the direct control of the +compiler/application, e.g. data stored in a graphics accelerator’s private +memory. +

      + + + +
      +

      +

      +  type psb_T_base_vect_type
+    TYPE(KIND_), allocatable :: v(:)
+  end type psb_T_base_vect_type
+
+  type psb_T_vect_type
+    class(psb_T_base_vect_type), allocatable :: v
+  end type  psb_T_vect_type
+
+
      +

      +
      Listing 3: The PSBLAS defined data type that contains a dense vector.
      + + + +
      +
      3.3.1 Vector Methods
      +

      +

      3.3.2 get_nrows — Get number of rows in a dense vector
      +

      nr = v%get_nrows() +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +v

      +

      the dense vector
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The number of rows of dense vector v.

      +

      +

      3.3.3 sizeof — Get memory occupation in bytes of a dense vector
      +

      memory_size = v%sizeof() +

      + + + +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +v

      +

      the dense vector
      Scope: local

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The memory occupation in bytes.

      +

      +

      3.3.4 set — Set contents of the vector
      + + + + 
      + call  v%set(alpha[,first,last])
+ call  v%set(vect[,first,last])
+ call  v%zero()
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +v

      +

      the dense vector
      Scope: local
      +

      +

      +alpha

      +

      A scalar value.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 1. +

      +

      +first,last

      +

      Boundaries for setting in the vector.
      Scope: local
      Type: optional
      Intent: in.
      Specified as: integers. +

      +

      +vect

      + + + +

      An array
      Scope: local
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 1.

      +

      Note that a call to v%zero() is provided as a shorthand, but is equivalent to a call +to v%set(zero) with the zero constant having the appropriate type and +kind. +

      +

      +

      +On Return

      +

      +

      +

      +v

      +

      the dense vector, with updated entries
      Scope: local

      +

      +

      3.3.5 get_vect — Get a copy of the vector contents
      + + + + 
      +extv = v%get_vect([n])
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +v

      +

      the dense vector
      Scope: local
      +

      +

      +n

      +

      Size to be returned
      Scope: local.
      Type: optional; default: entire vector.
      +

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

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

      + + + +

      +

      3.3.6 clone — Clone current object
      + + + + 
      +call  x%clone(y,info)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the dense vector.
      Scope: local.

      +

      +

      +

      +On Return

      +

      +

      +

      +y

      +

      A copy of the input object. +

      +

      +info

      +

      Return code.

      + + + +

      +

      3.4 Preconditioner data structure

      +

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

      A preconditioner is held in the psb_prec_type data structure reported in +figure 4. The psb_prec_type data type may contain a simple preconditioning matrix +with the associated communication descriptor.The internal preconditioner is +allocated appropriately with the dynamic type corresponding to the desired +preconditioner. + + + +

      + + + +
      +

      +

      +
+  type psb_Tprec_type
+    class(psb_T_base_prec_type), allocatable :: prec
+  end type psb_Tprec_type
+
+
      +

      +
      Listing 4: The PSBLAS defined data type that contains a preconditioner.
      + + + +
      +

      3.5 Heap data structure

      +

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

      +

      +psb_T_heap

      +

      : a heap containing elements of type T, where T can be i,s,c,d,z for + integer, real and complex data; +

      +

      +psb_T_idx_heap

      +

      : a heap containing elements of type T, as above, together with an integer + index.

      +

      Given a heap object, the following methods are defined on it: +

      +

      +init

      +

      Initialize memory; also choose ascending or descending order; +

      +

      +howmany

      +

      Current heap occupancy; +

      +

      +insert

      +

      Add an item (or an item and its index); +

      +

      +get_first

      +

      Remove and return the first element; +

      +

      +dump

      +

      Print on file; + + + +

      +

      +free

      +

      Release memory.

      +

      These objects are used in AMG4PSBLAS to implement the factorization algorithms. + + + + + + + + + +

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      4 Computational routines

      + id="x9-550004">Computational routines -
      -  4.1 psb_geaxpby — General Dense Matrix Sum -
       4.2 psb_gedot — Dot Product -
       4.3 psb_gedots — Generalized Dot Product -
       4.4 psb_normi — Infinity-Norm of Vector -
       4.5 psb_geamaxs — Generalized Infinity Norm -
       4.6 psb_norm1 — 1-Norm of Vector -
       4.7 psb_geasums — Generalized 1-Norm of Vector -
       4.8 psb_norm2 — 2-Norm of Vector -
       4.9 psb_genrm2s — Generalized 2-Norm of Vector -
       4.10 psb_norm1 — 1-Norm of Sparse Matrix -
       4.11 psb_normi — Infinity Norm of Sparse Matrix -
       4.12 psb_spmm — Sparse Matrix by Dense Matrix Product -
       4.13 psb_spsm — Triangular System Solve -
       4.14 psb_gemlt — Entrywise Product -
       4.15 psb_gediv — Entrywise Division -
       4.16 psb_geinv — Entrywise Inversion +

      4.1 psb_geaxpby — General Dense Matrix Sum

      +

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

      +y ← α x+ βy +
      +

      +

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

      + + + +

      + + + +
      +

      +

      + + + + +
      x, y, α, β Subroutine
      Short Precision Real psb_geaxpby
      Long Precision Real psb_geaxpby
      Short Precision Complexpsb_geaxpby
      Long Precision Complex psb_geaxpby
      +
      Table 1: Data types
      + + + +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +alpha

      +

      the scalar α.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 1. +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 1. The + rank of x must be the same of y. +

      +

      +beta

      +

      the scalar β.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 1. +

      +

      +y

      +

      the local portion of the global dense matrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 1. + The rank of y must be the same of x. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +
      +

      +On Return

      +

      +

      +

      +y

      +

      the local portion of result submatrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 1. +

      +

      +info

      +

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

      + + +

      4.2 psb_gedot — Dot Product

      +

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

      +dot ← xTy +
      +

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

      +dot ← xHy +
      +

      +

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

      + + +

      + + +
      +

      +

      + + + + +
      dot, x, y Function
      Short Precision Real psb_gedot
      Long Precision Real psb_gedot
      Short Precision Complexpsb_gedot
      Long Precision Complex psb_gedot
      +
      Table 2: Data types
      + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 2. The + rank of x must be the same of y. +

      +

      +y

      +

      the local portion of global dense matrix y.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 2. The + rank of y must be the same of x. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +global

      + + +

      Specifies whether the computation should include the global reduction + across all processes.
      Scope: global
      Type: optional.
      Intent: in.
      Specified as: a logical scalar. Default: global=.true.
      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      is the dot product of vectors x and y.
      Scope: global unless the optional variable global=.false. has been + specified
      Specified as: a number of the data type indicated in Table 2. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to + compute multiple dot products at the same time; in this case, it is + possible to improve the runtime efficiency by using the following scheme: + + 

           vres(1) = psb_gedot(x1,y1,desc_a,info,global=.false.) 
+   vres(2) = psb_gedot(x2,y2,desc_a,info,global=.false.) 
+   vres(3) = psb_gedot(x3,y3,desc_a,info,global=.false.) 
+   call psb_sum(ctxt,vres(1:3))
        + +

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

      + + +

      4.3 psb_gedots — Generalized Dot Product

      +

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

      +res(i) ← x(:,i)Ty(:,i) +
      +

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

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

      + + +

      + + +
      +

      +

      + + + + +
      res, x, y Subroutine
      Short Precision Real psb_gedots
      Long Precision Real psb_gedots
      Short Precision Complexpsb_gedots
      Long Precision Complex psb_gedots
      +
      Table 3: Data types
      + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 3. The + rank of x must be the same of y. +

      +

      +y

      +

      the local portion of global dense matrix y.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 3. The + rank of y must be the same of x. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      + + +

      +

      +res

      +

      is the dot product of vectors x and y.
      Scope: global
      Intent: out.
      Specified as: a number or a rank-one array of the data type indicated in + Table 2. +

      +

      +info

      +

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

      + + +

      4.4 psb_normi — Infinity-Norm of Vector

      +

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

      +amax ← max |xi| + i +
      +

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

      +amax ← maxi (|re(xi)|+ |im(xi)|) +
      +

      +

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

      + + +

      + + +
      +

      +

      + + + +
      amax x Function
      Short Precision RealShort Precision Real psb_geamax
      Long Precision Real Long Precision Real psb_geamax
      Short Precision RealShort Precision Complexpsb_geamax
      Long Precision Real Long Precision Complex psb_geamax
      +
      Table 4: Data types
      + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 4. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +global

      +

      Specifies whether the computation should include the global reduction + across all processes.
      Scope: global
      Type: optional.
      Intent: in.
      Specified as: a logical scalar. Default: global=.true.
      +

      +

      +On Return

      +

      + + + +

      +

      +Function value

      +

      is the infinity norm of vector x.
      Scope: global unless the optional variable global=.false. has been + specified
      Specified as: a long precision real number. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: + 

           vres(1) = psb_geamax(x1,desc_a,info,global=.false.) 
+   vres(2) = psb_geamax(x2,desc_a,info,global=.false.) 
+   vres(3) = psb_geamax(x3,desc_a,info,global=.false.) 
+   call psb_amx(ctxt,vres(1:3))
        + +

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

      + + + +

      4.5 psb_geamaxs — Generalized Infinity Norm

      +

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

      +res(i) ← max|x(k,i)| + k +
      +

      +

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

      + + + +

      + + + +
      +

      +

      + + + +
      res x Subroutine
      Short Precision RealShort Precision Real psb_geamaxs
      Long Precision Real Long Precision Real psb_geamaxs
      Short Precision RealShort Precision Complexpsb_geamaxs
      Long Precision Real Long Precision Complex psb_geamaxs
      +
      Table 5: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 5. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      +

      +

      +res

      +

      is the infinity norm of the columns of x.
      Scope: global
      Intent: out.
      Specified as: a number or a rank-one array of long precision real numbers. +

      +

      +info

      + + + +

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

      + + + +

      4.6 psb_norm1 — 1-Norm of Vector

      +

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

      +asum ← ∥xi∥ +
      +

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

      +asum ← ∥re(x)∥1 + ∥im (x)∥1 +
      +

      +

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

      + + + +

      + + + +
      +

      +

      + + + +
      asum x Function
      Short Precision RealShort Precision Real psb_geasum
      Long Precision Real Long Precision Real psb_geasum
      Short Precision RealShort Precision Complexpsb_geasum
      Long Precision Real Long Precision Complex psb_geasum
      +
      Table 6: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 6. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +global

      +

      Specifies whether the computation should include the global reduction + across all processes.
      Scope: global
      Type: optional.
      Intent: in.
      Specified as: a logical scalar. Default: global=.true.
      +

      +

      +On Return

      +

      + + + +

      +

      +Function value

      +

      is the 1-norm of vector x.
      Scope: global unless the optional variable global=.false. has been + specified
      Specified as: a long precision real number. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: + 

           vres(1) = psb_geasum(x1,desc_a,info,global=.false.) 
+   vres(2) = psb_geasum(x2,desc_a,info,global=.false.) 
+   vres(3) = psb_geasum(x3,desc_a,info,global=.false.) 
+   call psb_sum(ctxt,vres(1:3))
        + +

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

      + + + +

      4.7 psb_geasums — Generalized 1-Norm of Vector

      +

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

      +res(i) ← max|x(k,i)| + k +
      +

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

      +res(i) ← ∥xi∥ +
      +

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

      +res(i) ← ∥re(x )∥1 +∥im (x )∥1 +
      +

      +

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

      + + + +

      + + + +
      +

      +

      + + + +
      res x Subroutine
      Short Precision RealShort Precision Real psb_geasums
      Long Precision Real Long Precision Real psb_geasums
      Short Precision RealShort Precision Complexpsb_geasums
      Long Precision Real Long Precision Complex psb_geasums
      +
      Table 7: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 7. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      +

      +

      +res

      +

      contains the 1-norm of (the columns of) x.
      Scope: global
      Intent: out.
      Short as: a long precision real number. Specified as: a long precision real + number. + + + +

      +

      +info

      +

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

      + + + +

      4.8 psb_norm2 — 2-Norm of Vector

      +

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

      +nrm2 ← √xT-x- +
      +

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

      + √---- +nrm2 ← xHx +
      +

      +

      + + + +

      + + + +
      +

      +

      + + + +
      nrm2 x Function
      Short Precision RealShort Precision Real psb_genrm2
      Long Precision Real Long Precision Real psb_genrm2
      Short Precision RealShort Precision Complexpsb_genrm2
      Long Precision Real Long Precision Complex psb_genrm2
      +
      Table 8: Data types
      + + + +
      +
      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 8. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +global

      +

      Specifies whether the computation should include the global reduction + across all processes.
      Scope: global
      Type: optional.
      Intent: in.
      Specified as: a logical scalar. Default: global=.true.
      +

      +

      +On Return

      + + + +

      +

      +

      +Function Value

      +

      is the 2-norm of vector x.
      Scope: global unless the optional variable global=.false. has been + specified
      Type: required
      Specified as: a long precision real number. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        The computation of a global result requires a global communication, which + entails a significant overhead. It may be necessary and/or advisable to compute + multiple norms at the same time; in this case, it is possible to improve the + runtime efficiency by using the following scheme: + 

           vres(1) = psb_genrm2(x1,desc_a,info,global=.false.) 
+   vres(2) = psb_genrm2(x2,desc_a,info,global=.false.) 
+   vres(3) = psb_genrm2(x3,desc_a,info,global=.false.) 
+   call psb_nrm2(ctxt,vres(1:3))
        + +

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

      + + + +

      4.9 psb_genrm2s — Generalized 2-Norm of Vector

      +

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

      +res(i) ← ∥x(:,i)∥2 +
      +

      +

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

      + + + +

      + + + +
      +

      +

      + + + +
      res x Subroutine
      Short Precision RealShort Precision Real psb_genrm2s
      Long Precision Real Long Precision Real psb_genrm2s
      Short Precision RealShort Precision Complexpsb_genrm2s
      Long Precision Real Long Precision Complex psb_genrm2s
      +
      Table 9: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 9. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      +

      +

      +res

      +

      contains the 1-norm of (the columns of) x.
      Scope: global
      Intent: out.
      Specified as: a long precision real number. +

      +

      +info

      + + + +

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

      + + + +

      4.10 psb_norm1 — 1-Norm of Sparse Matrix

      +

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

      +nrm1 ← ∥A ∥1 +
      +

      where: +

      +

      +A

      +

      represents the global matrix A

      +
      + + + +

      + +
      +

      +

      + + + +
      A Function
      Short Precision Real psb_spnrm1
      Long Precision Real psb_spnrm1
      Short Precision Complexpsb_spnrm1
      Long Precision Complex psb_spnrm1
      +
      Table 10: Data types
      + + + +
      +
      + + + + 
      +psb_spnrm1(A, desc_a, info)
+psb_norm1(A, desc_a, info)
+
      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the local portion of the global sparse matrix A.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_Tspmat_type. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      is the 1-norm of sparse submatrix A.
      Scope: global
      Specified as: a long precision real number. + + + +

      +

      +info

      +

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

      + + + +

      4.11 psb_normi — Infinity Norm of Sparse Matrix

      +

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

      +nrmi ← ∥A∥∞ +
      +

      where: +

      +

      +A

      +

      represents the global matrix A

      +
      + + + +

      + + + +
      +

      +

      + + + +
      A Function
      Short Precision Real psb_spnrmi
      Long Precision Real psb_spnrmi
      Short Precision Complexpsb_spnrmi
      Long Precision Complex psb_spnrmi
      +
      Table 11: Data types
      + + + +
      +
      + + + + 
      +psb_spnrmi(A, desc_a, info)
+psb_normi(A, desc_a, info)
+
      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the local portion of the global sparse matrix A.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_Tspmat_type. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      is the infinity-norm of sparse submatrix A.
      Scope: global
      Specified as: a long precision real number. + + + +

      +

      +info

      +

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

      + + + +

      4.12 psb_spmm — Sparse Matrix by Dense Matrix Product

      +

      This subroutine computes the Sparse Matrix by Dense Matrix Product: +
      +
      +y ← αAx + βy +
      +       		(1)
      +

      +
      +
      + T +y ← αA x+ βy +
      +       		(2)
      +

      +
      +
      +y ← αAHx + βy +
      +       		(3)
      +

      +

      where: + + + +

      +

      +x

      +

      is the global dense matrix x:,: +

      +

      +y

      +

      is the global dense matrix y:,: +

      +

      +A

      +

      is the global sparse matrix A

      +
      + + + +

      + + + +
      +

      +

      + + + + +
      A, x, y, α, β Subroutine
      Short Precision Real psb_spmm
      Long Precision Real psb_spmm
      Short Precision Complexpsb_spmm
      Long Precision Complex psb_spmm
      +
      Table 12: Data types
      + + + +
      +
      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +alpha

      +

      the scalar α.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 12. +

      +

      +a

      +

      the local portion of the sparse matrix A.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_Tspmat_type. +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 12. The + rank of x must be the same of y. +

      +

      +beta

      + + + +

      the scalar β.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 12. +

      +

      +y

      +

      the local portion of global dense matrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 12. The + rank of y must be the same of x. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +trans

      +

      indicates what kind of operation to perform. +

      +

      + trans = N

      +

      the operation is specified by equation 1 +

      +

      + trans = T

      +

      the operation is specified by equation 2 +

      +

      + trans = C

      +

      the operation is specified by equation 3

      +

      Scope: global
      Type: optional
      Intent: in.
      Default: trans = N
      Specified as: a character variable. + + + +

      +

      +work

      +

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

      +

      +On Return

      +

      +

      +

      +y

      +

      the local portion of result matrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an array of rank one or two containing numbers of type specified + in Table 12. +

      +

      +info

      +

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

      + + + +

      4.13 psb_spsm — Triangular System Solve

      +

      This subroutine computes the Triangular System Solve: +

      +
      +y ← αT- 1x + βy +y ← αDT -1x +βy + - 1 +y ← αT Dx +βy +y ← αT- Tx+ βy +y ← αDT -Tx + βy +y ← αT- TDx + βy + - H +y ← αT x +βy +y ← αDT -Hx + βy +y ← αT- HDx + βy +
      +
      +

      where: +

      +

      +x

      +

      is the global dense matrix x:,: +

      +

      +y

      +

      is the global dense matrix y:,: +

      +

      +T

      +

      is the global sparse block triangular submatrix T +

      +

      +D

      +

      is the scaling diagonal matrix.

      + + + +

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

      + + + +

      + + + +
      +

      +

      + + + + +
      T, x, y, D, α, β Subroutine
      Short Precision Real psb_spsm
      Long Precision Real psb_spsm
      Short Precision Complexpsb_spsm
      Long Precision Complex psb_spsm
      +
      Table 13: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +alpha

      +

      the scalar α.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 13. +

      +

      +t

      +

      the global portion of the sparse matrix T.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object type specified in § 3. +

      +

      +x

      +

      the local portion of global dense matrix x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 13. The + rank of x must be the same of y. +

      +

      +beta

      +

      the scalar β.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a number of the data type indicated in Table 13. + + + +

      +

      +y

      +

      the local portion of global dense matrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 13. The + rank of y must be the same of x. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +trans

      +

      specify with unitd the operation to perform. +

      +

      + trans = ’N’

      +

      the operation is with no transposed matrix +

      +

      + trans = ’T’

      +

      the operation is with transposed matrix. +

      +

      + trans = ’C’

      +

      the operation is with conjugate transposed matrix.

      +

      Scope: global
      Type: optional
      Intent: in.
      Default: trans = N
      Specified as: a character variable. +

      +

      +unitd

      +

      specify with trans the operation to perform. + + + +

      +

      + unitd = ’U’

      +

      the operation is with no scaling +

      +

      + unitd = ’L’

      +

      the operation is with left scaling +

      +

      + unitd = ’R’

      +

      the operation is with right scaling.

      +

      Scope: global
      Type: optional
      Intent: in.
      Default: unitd = U
      Specified as: a character variable. +

      +

      +choice

      +

      specifies the update of overlap elements to be performed on exit: +

      +

      +

      +

      psb_none_ +

      +

      +

      +

      psb_sum_ +

      +

      +

      +

      psb_avg_ +

      +

      +

      +

      psb_square_root_

      +

      Scope: global
      Type: optional
      Intent: in.
      Default: psb_avg_
      Specified as: an integer variable. + + + +

      +

      +diag

      +

      the diagonal scaling matrix.
      Scope: local
      Type: optional
      Intent: in.
      Default: diag(1) = 1(noscaling)
      Specified as: a rank one array containing numbers of the type indicated in + Table 13. +

      +

      +work

      +

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

      +

      +On Return

      +

      +

      +

      +y

      +

      the local portion of global dense matrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an array of rank one or two containing numbers of type specified + in Table 13. +

      +

      +info

      +

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

      + + + +

      4.14 psb_gemlt — Entrywise Product

      +

      This function computes the entrywise product between two vectors x and +y +

      +dot ← x(i)y(i). +
      +

      +

      psb_gemlt(x, y, desc_a, info) +

      + + + +

      + + + +
      +

      +

      + + + + +
      dot, x, y Function
      Short Precision Real psb_gemlt
      Long Precision Real psb_gemlt
      Short Precision Complexpsb_gemlt
      Long Precision Complex psb_gemlt
      +
      Table 14: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense vector x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +

      +

      +y

      +

      the local portion of global dense vector y.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +On Return

      +

      + + + +

      +

      +y

      +

      the local portion of result submatrix y.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 14. +

      +

      +info

      +

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

      + + + +

      4.15 psb_gediv — Entrywise Division

      +

      This function computes the entrywise division between two vectors x and +y +

      +∕ ← x(i)∕y(i). +
      +

      +

      psb_gediv(x, y, desc_a, info, [flag) +

      + + + +

      + + + +
      +

      +

      + + + + +
      ∕, x, y Function
      Short Precision Real psb_gediv
      Long Precision Real psb_gediv
      Short Precision Complexpsb_gediv
      Long Precision Complex psb_gediv
      +
      Table 15: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense vector x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +

      +

      +y

      +

      the local portion of global dense vector y.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +flag

      +

      check if any of the y(i) = 0, and in case returns error halting the + computation.
      Scope: local
      Type: optional Intent: in.
      Specified as: the logical value flag=.true. + + + +

      +

      +On Return

      +

      +

      +

      +x

      +

      the local portion of result submatrix x.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 14. +

      +

      +info

      +

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

      + + + +

      4.16 psb_geinv — Entrywise Inversion

      +

      This function computes the entrywise inverse of a vector x and puts it into +y +

      +∕ ← 1∕x(i). +
      +

      +

      psb_geinv(x, y, desc_a, info, [flag) +

      + + + +

      + + + +
      +

      +

      + + + + +
      ∕, x, y Function
      Short Precision Real psb_geinv
      Long Precision Real psb_geinv
      Short Precision Complexpsb_geinv
      Long Precision Complex psb_geinv
      +
      Table 16: Data types
      + + + +
      +
      +
      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      the local portion of global dense vector x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_T_vect_type containing numbers of + type specified in Table 2. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an object of type psb_desc_type. +

      +

      +flag

      +

      check if any of the x(i) = 0, and in case returns error halting the + computation.
      Scope: local
      Type: optional Intent: in.
      Specified as: the logical value flag=.true. +

      +

      +On Return

      +

      + + + +

      +

      +y

      +

      the local portion of result submatrix x.
      Scope: local
      Type: required
      Intent: out.
      Specified as: an object of type psb_T_vect_type containing numbers of + the type indicated in Table 16. +

      +

      +info

      +

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

      + + + + + + + + + +

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      5 Communication routines

      + id="x10-720005">Communication routines

      The routines in this chapter implement various global communication operators on vectors associated with a discretization mesh. For auxiliary communication routines not tied to a discretization space see 6. +href="userhtmlse6.html#x11-770006">6. -

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

      5.1 psb_halo — Halo Data Communication

      +

      These subroutines gathers the values of the halo elements: +

      +x ← x +
      +

      where: +

      +

      +x

      +

      is a global dense submatrix.

      +
      + + + +

      + + + +
      +

      +

      + + + + + +
      α, x Subroutine
      Integer psb_halo
      Short Precision Real psb_halo
      Long Precision Real psb_halo
      Short Precision Complexpsb_halo
      Long Precision Complex psb_halo
      +
      Table 17: Data types
      + + + +
      +

      call psb_halo(x, desc_a, info)
      call psb_halo(x, desc_a, info, work, data) +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      global dense matrix x.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 17. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +work

      +

      the work array.
      Scope: local
      Type: optional
      Intent: inout.
      Specified as: a rank one array of the same type of x. +

      +

      +data

      + + +

      index list selector.
      Scope: global
      Type: optional
      Specified + as: an integer. Values:psb_comm_halo_,psb_comm_mov_, psb_comm_ext_, + default: psb_comm_halo_. Chooses the index list on which to base the data + exchange. +

      +

      +On Return

      +

      +

      +

      +x

      +

      global dense result matrix x.
      Scope: local
      Type: required
      Intent: inout.
      Returned as: a rank one or two array containing numbers of type specified + in Table 17. +

      +

      +info

      +

      the local portion of result submatrix y.
      Scope: local
      Type: required
      Intent: out.
      An integer value that contains an error code.

      +

      +
      +

      +

      PIC

      +
      Figure 3: Sample discretization mesh.
      +

      +

      Usage Example Consider the discretization mesh depicted in fig. 3, partitioned +among two processes as shown by the dashed line; the data distribution is such that +each process will own 32 entries in the index space, with a halo made of 8 entries +placed at local indices 33 through 40. If process 0 assigns an initial value of 1 to +its entries in the x vector, and process 1 assigns a value of 2, then after +a call to psb_halo the contents of the local vectors will be the following: +

      + + +

      + + + +
      +

      +

      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      Process 0
      Process 1
      +
      IGLOB(I)X(I) IGLOB(I)X(I)
      1 1 1.0 1 33 2.0
      2 2 1.0 2 34 2.0
      3 3 1.0 3 35 2.0
      4 4 1.0 4 36 2.0
      5 5 1.0 5 37 2.0
      6 6 1.0 6 38 2.0
      7 7 1.0 7 39 2.0
      8 8 1.0 8 40 2.0
      9 9 1.0 9 41 2.0
      10 10 1.010 42 2.0
      11 11 1.011 43 2.0
      12 12 1.012 44 2.0
      13 13 1.013 45 2.0
      14 14 1.014 46 2.0
      15 15 1.015 47 2.0
      16 16 1.016 48 2.0
      17 17 1.017 49 2.0
      18 18 1.018 50 2.0
      19 19 1.019 51 2.0
      20 20 1.020 52 2.0
      21 21 1.021 53 2.0
      22 22 1.022 54 2.0
      23 23 1.023 55 2.0
      24 24 1.024 56 2.0
      25 25 1.025 57 2.0
      26 26 1.026 58 2.0
      27 27 1.027 59 2.0
      28 28 1.028 60 2.0
      29 29 1.029 61 2.0
      30 30 1.030 62 2.0
      31 31 1.031 63 2.0
      32 32 1.032 64 2.0
      33 33 2.033 25 1.0
      34 34 2.034 26 1.0
      35 35 2.035 27 1.0
      36 36 2.036 28 1.0
      37 37 2.037 29 1.0
      38 38 2.038 30 1.0
      39 39 2.039 31 1.0
      40 40 2.040 32 1.0
      + + + +
      +
      + + + +

      5.2 psb_ovrl — Overlap Update

      +

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

      +x ← Qx +
      +

      where: +

      +

      +x

      +

      is the global dense submatrix x +

      +

      +Q

      +

      is the overlap operator; it is the composition of two operators Pa and PT.

      +
      + +

      + + + +
      +

      +

      + + + +
      x Subroutine
      Short Precision Real psb_ovrl
      Long Precision Real psb_ovrl
      Short Precision Complexpsb_ovrl
      Long Precision Complex psb_ovrl
      +
      Table 18: Data types
      + + + +
      +
      +

      call psb_ovrl(x, desc_a, info)
      call psb_ovrl(x, desc_a, info, update=update_type, work=work) +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      global dense matrix x.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type containing numbers of type specified in Table 18. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +update

      +

      Update operator.
      +

      +

      + update = psb_none_

      +

      Do nothing; +

      +

      + update = psb_add_

      +

      Sum overlap entries, i.e. apply PT; + + + +

      +

      + update = psb_avg_

      +

      Average overlap entries, i.e. apply PaPT;

      +

      Scope: global
      Intent: in.
      Default: update_type = psb_avg_
      Scope: global
      Specified as: a integer variable. +

      +

      +work

      +

      the work array.
      Scope: local
      Type: optional
      Intent: inout.
      Specified as: a one dimensional array of the same type of x. +

      +

      +On Return

      +

      +

      +

      +x

      +

      global dense result matrix x.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: an array of rank one or two containing numbers of type specified + in Table 18. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. + + + +

        If there is no overlap in the data distribution associated with the + descriptor, no operations are performed; +

        2. +
      2. +

        The operator PT performs the reduction sum of overlap elements; it is a + “prolongation” operator PT that replicates overlap elements, accounting + for the physical replication of data; +

        3. +
      3. +

        The operator Pa performs a scaling on the overlap elements by the + amount of replication; thus, when combined with the reduction operator, + it implements the average of replicated elements over all of their instances.

      +

      + + + + + + + +
      +

      +

      PIC

      +
      Figure 4: Sample discretization mesh.
      + + + +

      +

      Example of use Consider the discretization mesh depicted in fig. 4, partitioned +among two processes as shown by the dashed lines, with an overlap of 1 extra layer +with respect to the partition of fig. 3; the data distribution is such that +each process will own 40 entries in the index space, with an overlap of 16 +entries placed at local indices 25 through 40; the halo will run from local +index 41 through local index 48.. If process 0 assigns an initial value of 1 to +its entries in the x vector, and process 1 assigns a value of 2, then after a +call to psb_ovrl with psb_avg_ and a call to psb_halo_ the contents of +the local vectors will be the following (showing a transition among the two +subdomains) +

      + + + +

      + + + +
      +

      +

      + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +
      Process 0
      Process 1
      +
      IGLOB(I)X(I) IGLOB(I)X(I)
      1 1 1.0 1 33 1.5
      2 2 1.0 2 34 1.5
      3 3 1.0 3 35 1.5
      4 4 1.0 4 36 1.5
      5 5 1.0 5 37 1.5
      6 6 1.0 6 38 1.5
      7 7 1.0 7 39 1.5
      8 8 1.0 8 40 1.5
      9 9 1.0 9 41 2.0
      10 10 1.010 42 2.0
      11 11 1.011 43 2.0
      12 12 1.012 44 2.0
      13 13 1.013 45 2.0
      14 14 1.014 46 2.0
      15 15 1.015 47 2.0
      16 16 1.016 48 2.0
      17 17 1.017 49 2.0
      18 18 1.018 50 2.0
      19 19 1.019 51 2.0
      20 20 1.020 52 2.0
      21 21 1.021 53 2.0
      22 22 1.022 54 2.0
      23 23 1.023 55 2.0
      24 24 1.024 56 2.0
      25 25 1.525 57 2.0
      26 26 1.526 58 2.0
      27 27 1.527 59 2.0
      28 28 1.528 60 2.0
      29 29 1.529 61 2.0
      30 30 1.530 62 2.0
      31 31 1.531 63 2.0
      32 32 1.532 64 2.0
      33 33 1.533 25 1.5
      34 34 1.534 26 1.5
      35 35 1.535 27 1.5
      36 36 1.536 28 1.5
      37 37 1.537 29 1.5
      38 38 1.538 30 1.5
      39 39 1.539 31 1.5
      40 40 1.540 32 1.5
      41 41 2.041 17 1.0
      42 42 2.042 18 1.0
      43 43 2.043 19 1.0
      44 44 2.044 20 1.0
      45 45 2.045 21 1.0
      46 46 2.046 22 1.0
      47 47 2.047 23 1.0
      48 48 2.048 24 1.0
      + + + +
      +
      + + + +

      5.3 psb_gather — Gather Global Dense Matrix

      +

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

      +glob-x ← collect(loc-xi) +
      +

      where: +

      +

      +glob_x

      +

      is the global submatrix glob_x1:m,1:n +

      +

      +loc_xi

      +

      is the local portion of global dense matrix on process i. +

      +

      +collect

      +

      is the collect function.

      +
      + + + +

      + + + +
      +

      +

      + + + + + +
      xi,y Subroutine
      Integer psb_gather
      Short Precision Real psb_gather
      Long Precision Real psb_gather
      Short Precision Complexpsb_gather
      Long Precision Complex psb_gather
      +
      Table 19: Data types
      + + + +
      +
      +

      call psb_gather(glob_x, loc_x, desc_a, info, root) +call psb_gather(glob_x, loc_x, desc_a, info, root) +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +loc_x

      +

      the local portion of global dense matrix glob_x.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type indicated in Table 19. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +root

      +

      The process that holds the global copy. If root = -1 all the processes will + have a copy of the global vector.
      Scope: global
      Type: optional
      Intent: in.
      Specified as: an integer variable -1 ≤ root ≤ np - 1, default -1. +

      +

      +On Return

      +

      + + + +

      +

      +glob_x

      +

      The array where the local parts must be gathered.
      Scope: global
      Type: required
      Intent: out.
      Specified as: a rank one or two array with the ALLOCATABLE attribute. +

      +

      +info

      +

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

      + + + +

      5.4 psb_scatter — Scatter Global Dense Matrix

      +

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

      +loc-xi ← scatter(glob-x) +
      +

      where: +

      +

      +glob_x

      +

      is the global matrix glob_x1:m,1:n +

      +

      +loc_xi

      +

      is the local portion of global dense matrix on process i. +

      +

      +scatter

      +

      is the scatter function.

      +
      + + + +

      + + + +
      +

      +

      + + + + + +
      xi,y Subroutine
      Integer psb_scatter
      Short Precision Real psb_scatter
      Long Precision Real psb_scatter
      Short Precision Complexpsb_scatter
      Long Precision Complex psb_scatter
      +
      Table 20: Data types
      + + + +
      +
      +

      call psb_scatter(glob_x, loc_x, desc_a, info, root, mold) +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +glob_x

      +

      The array that must be scattered into local pieces.
      Scope: global
      Type: required
      Intent: in.
      Specified as: a rank one or two array. +

      +

      +desc_a

      +

      contains data structures for communications.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +root

      +

      The process that holds the global copy. If root = -1 all the processes have + a copy of the global vector.
      Scope: global
      Type: optional
      Intent: in.
      Specified as: an integer variable -1 ≤ root ≤ np - 1, default psb_root_, + i.e. process 0. +

      +

      +mold

      + + + +

      The desired dynamic type for the internal vector storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from psb_T_base_vect_type; + this is only allowed when loc_x is of type psb_T_vect_type. +

      +

      +On Return

      +

      +

      +

      +loc_x

      +

      the local portion of global dense matrix glob_x.
      Scope: local
      Type: required
      Intent: out.
      Specified as: a rank one or two ALLOCATABLE array or an object of type + psb_T_vect_type containing numbers of the type indicated in Table 20. +

      +

      +info

      +

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

      + + + + + + + + + +

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      6 Data management routines

      + id="x11-770006">Data management routines

      -

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

      6.1 psb_cdall — Allocates a communication descriptor

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

      +

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

      +

      +On Entry

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +icontxt

      +

      the communication context.
      Scope:global.
      Type:required.
      Intent: in.
      Specified as: an integer value. +

      +

      +vg

      +

      Data allocation: each index i ∈{1…mg} is allocated to process vg(i).
      Scope:global.
      Type:optional.
      Intent: in.
      Specified as: an integer array. +

      +

      +flag

      +

      Specifies whether entries in vg are zero- or one-based.
      Scope:global.
      Type:optional.
      Intent: in.
      Specified as: an integer value 0,1, default 0. + + + +

      +

      +mg

      +

      the (global) number of rows of the problem.
      Scope:global.
      Type:optional.
      Intent: in.
      Specified as: an integer value. It is required if parts or repl is specified, + it is optional if vg is specified. +

      +

      +parts

      +

      the subroutine that defines the partitioning scheme.
      Scope:global.
      Type:required.
      Specified as: a subroutine. +

      +

      +vl

      +

      Data allocation: the set of global indices vl(1 : nl) belonging to the calling + process.
      Scope:local.
      Type:optional.
      Intent: in.
      Specified as: an integer array. +

      +

      +nl

      +

      Data allocation: in a generalized block-row distribution the number of + indices belonging to the current process.
      Scope:local.
      Type:optional.
      Intent: in.
      Specified as: an integer value. May be specified together with vl. +

      +

      +repl

      +

      Data allocation: build a replicated index space (i.e. all processes own all + indices).
      Scope:global.
      Type:optional.
      Intent: in.
      Specified as: the logical value .true. + + + +

      +

      +globalcheck

      +

      Data allocation: do global checks on the local index lists vl
      Scope:global.
      Type:optional.
      Intent: in.
      Specified as: a logical value, default: .false. +

      +

      +lidx

      +

      Data allocation: the set of local indices lidx(1 : nl) to be assigned to the + global indices vl.
      Scope:local.
      Type:optional.
      Intent: in.
      Specified as: an integer array.

      +

      +

      +

      +On Return

      +

      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: out.
      Specified as: a structured data of type psb_desc_type. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. + + + +

        One of the optional arguments parts, vg, vl, nl or repl must be specified, + thereby choosing the initialization strategy as follows: +

        +

        + parts

        +

        In this case we have a subroutine specifying the mapping between global + indices and process/local index pairs. If this optional argument is + specified, then it is mandatory to specify the argument mg as well. The + subroutine must conform to the following interface: + + + + 

        +           interface
+              subroutine psb_parts(glob_index,mg,np,pv,nv)
+                integer, intent (in)  :: glob_index,np,mg
+                integer, intent (out) :: nv, pv(*)
+              end subroutine psb_parts
+           end interface
+
        +

        The input arguments are: +

        +

        + glob_index

        +

        The global index to be mapped; +

        +

        + np

        +

        The number of processes in the mapping; +

        +

        + mg

        +

        The total number of global rows in the mapping;

        +

        The output arguments are: +

        +

        + nv

        +

        The number of entries in pv; +

        +

        + pv

        +

        A vector containing the indices of the processes to which the + global index should be assigend; each entry must satisfy 0 ≤ + pv(i) < np; if nv > 1 we have an index assigned to multiple + processes, i.e. we have an overlap among the subdomains.

        +
        +

        + vg

        +

        In this case the association between an index and a process is specified via + an integer vector vg(1:mg); each index i ∈{1…mg} is assigned to process + vg(i). The vector vg must be identical on all calling processes; its + entries may have the ranges (0…np - 1) or (1…np) according to the + value of flag. The size mg may be specified via the optional + argument mg; the default is to use the entire vector vg, thus having + mg=size(vg). +

        +

        + vl

        + + + +

        In this case we are specifying the list of indices vl(1:nl) assigned to the + current process; thus, the global problem size mg is given by the range of + the aggregate of the individual vectors vl specified in the calling + processes. The size may be specified via the optional argument nl; the + default is to use the entire vector vl, thus having nl=size(vl). If + globalcheck=.true. the subroutine will check how many times each + entry in the global index space (1…mg) is specified in the input lists vl, + thus allowing for the presence of overlap in the input, and checking for + “orphan” indices. If globalcheck=.false., the subroutine will not + check for overlap, and may be significantly faster, but the user is + implicitly guaranteeing that there are neither orphan nor overlap + indices. +

        +

        + lidx

        +

        The optional argument lidx is available for those cases in which the user + has already established a global-to-local mapping; if it is specified, each + index in vl(i) will be mapped to the corresponding local index lidx(i). + When specifying the argument lidx the user would also likely employ + lidx in calls to psb_cdins and local in calls to psb_spins and + psb_geins; see also sec. 2.3.1. +

        +

        + nl

        +

        If this argument is specified alone (i.e. without vl) the result is a + generalized row-block distribution in which each process I gets assigned a + consecutive chunk of NI = nl global indices. +

        +

        + repl

        +

        This arguments specifies to replicate all indices on all processes. This is a + special purpose data allocation that is useful in the construction of some + multilevel preconditioners.

        +
        2. +
      2. +

        On exit from this routine the descriptor is in the build state. +

        3. +
      3. +

        Calling the routine with vg or parts implies that every process will scan the + entire index space to figure out the local indices. +

        4. +
      4. +

        Overlapped indices are possible with both parts and vl invocations. + + + +

        5. +
      5. +

        When the subroutine is invoked with vl in conjunction with globalcheck=.true., + it will perform a scan of the index space to search for overlap or orphan + indices. +

        6. +
      6. +

        When the subroutine is invoked with vl in conjunction with globalcheck=.false., + no index space scan will take place. Thus it is the responsibility of the user to + make sure that the indices specified in vl have neither orphans nor overlaps; if + this assumption fails, results will be unpredictable. +

        7. +
      7. +

        Orphan and overlap indices are impossible by construction when the subroutine + is invoked with nl (alone), or vg.

      + + + +

      6.2 psb_cdins — Communication descriptor insert routine

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

      +

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

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +nz

      +

      the number of points being inserted.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: an integer value. +

      +

      +ia

      +

      the indices of the starting vertex of the edges being inserted.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: an integer array of length nz. +

      +

      +ja

      + + + +

      the indices of the end vertex of the edges being inserted.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: an integer array of length nz. +

      +

      +mask

      +

      Mask entries in ja, they are inserted only when the corresponding mask + entries are .true.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: a logical array of length nz, default .true.. +

      +

      +lidx

      +

      User defined local indices for ja.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an integer array of length nz.

      +

      +

      +

      +On Return

      +

      +

      +

      +desc_a

      +

      the updated communication descriptor.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a structured data of type psb_desc_type. +

      +

      +info

      +

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

      +

      +ila

      +

      the local indices of the starting vertex of the edges being inserted.
      Scope: local.
      Type: optional.
      Intent: out.
      Specified as: an integer array of length nz. +

      +

      +jla

      +

      the local indices of the end vertex of the edges being inserted.
      Scope: local.
      Type: optional.
      Intent: out.
      Specified as: an integer array of length nz. +

      +

      Notes +

        +
      1. +

        This routine may only be called if the descriptor is in the build state; +

        2. +
      2. +

        This routine automatically ignores edges that do not insist on the current + process, i.e. edges for which neither the starting nor the end vertex belong + to the current process. +

        3. +
      3. +

        The second form of this routine will be useful when dealing with + user-specified index mappings; see also 2.3.1.

      + + + +

      6.3 psb_cdasb — Communication descriptor assembly routine

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a structured data of type psb_desc_type. +

      +

      +mold

      +

      The desired dynamic type for the internal index storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: a object of type derived from (integer) + psb_T_base_vect_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +desc_a

      + + + +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a structured data of type psb_desc_type. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        On exit from this routine the descriptor is in the assembled state.

      +

      This call will set up all the necessary information for the halo data exchanges. In doing +so, the library will need to identify the set of processes owning the halo indices +through the use of the desc%fnd_owner() method; the owning processes +are the topological neighbours of the calling process. If the user has some +background information on the processes that are neighbours of the current one, +it is possible to specify explicitly the list of adjacent processes with a call +to desc%set_p_adjcncy(list); this will speed up the subsequent call to +psb_cdasb. + + + +

      6.4 psb_cdcpy — Copies a communication descriptor

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_in

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +

      +

      +On Return

      +

      +

      +

      +desc_out

      +

      the communication descriptor copy.
      Scope:local.
      Type:required.
      Intent: out.
      Specified as: a structured data of type psb_desc_type. +

      +

      +info

      + + + +

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

      + + + +

      6.5 psb_cdfree — Frees a communication descriptor

      + + + + 
      +call psb_cdfree(desc_a, info)
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      the communication descriptor to be freed.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +info

      +

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

      + + + +

      6.6 psb_cdbldext — Build an extended communication descriptor

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

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      A sparse matrix Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data type. +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +nl

      +

      the number of additional layers desired.
      Scope:global.
      Type:required.
      Intent: in.
      Specified as: an integer value nl ≥ 0. + + + +

      +

      +extype

      +

      the kind of estension required.
      Scope:global.
      Type:optional .
      Intent: in.
      Specified as: an integer value psb_ovt_xhal_, psb_ovt_asov_, default: + psb_ovt_xhal_ +

      +

      +

      +

      +On Return

      +

      +

      +

      +desc_out

      +

      the extended communication descriptor.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a structured data of type psb_desc_type. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        Specifying psb_ovt_xhal_ for the extype argument the user will obtain a + descriptor for a domain partition in which the additional layers are fetched + as part of an (extended) halo; however the index-to-process mapping is + identical to that of the base descriptor; +

        2. +
      2. + + + +

        Specifying psb_ovt_asov_ for the extype argument the user will obtain + a descriptor with an overlapped decomposition: the additional layer is + aggregated to the local subdomain (and thus is an overlap), and a new + halo extending beyond the last additional layer is formed.

      + + + +

      6.7 psb_spall — Allocates a sparse matrix

      + + + + 
      +call psb_spall(a, desc_a, info [, nnz, dupl, bldmode])
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +nnz

      +

      An estimate of the number of nonzeroes in the local part of the assembled + matrix.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. +

      +

      +dupl

      +

      How to handle duplicate coefficients.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: integer, possible values: psb_dupl_ovwrt_, psb_dupl_add_, + psb_dupl_err_. + + + +

      +

      +bldmode

      +

      Whether to keep track of matrix entries that do not belong to the current + process.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: + an integer value psb_matbld_noremote_, psb_matbld_remote_. Default: + psb_matbld_noremote_.

      +

      +

      +

      +On Return

      +

      +

      +

      +a

      +

      the matrix to be allocated.
      Scope:local
      Type:required
      Intent: out.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        On exit from this routine the sparse matrix is in the build state. +

        2. +
      2. +

        The descriptor may be in either the build or assembled state. + + + +

        3. +
      3. +

        Providing a good estimate for the number of nonzeroes nnz in the + assembled matrix may substantially improve performance in the matrix + build phase, as it will reduce or eliminate the need for (potentially + multiple) data reallocations; +

        4. +
      4. +

        Using psb_matbld_remote_ is likely to cause a runtime overhead at + assembly time;

      + + + +

      6.8 psb_spins — Insert a set of coefficients into a sparse matrix

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +nz

      +

      the number of coefficients to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer scalar. +

      +

      +nr

      +

      the number of rows to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer scalar. +

      +

      +irw

      +

      the first row to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer scalar. + + + +

      +

      +ia

      +

      the row indices of the coefficients to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer array of size nz. +

      +

      +irp

      +

      the row pointers of the coefficients to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer array of size nr + 1. +

      +

      +ja

      +

      the column indices of the coefficients to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer array of size nz. +

      +

      +val

      +

      the coefficients to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an array of size nz. Must be of the same type and kind of + the coefficients of the sparse matrix a. +

      +

      +desc_a

      +

      The communication descriptor.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: a variable of type psb_desc_type.
      + + + +

      +

      +local

      +

      Whether the entries in the indices vectors ia, ja are already in local + numbering.
      Scope:local.
      Type:optional.
      Specified as: a logical value; default: .false.. +

      +

      +

      +

      +On Return

      +

      +

      +

      +a

      +

      the matrix into which coefficients will be inserted.
      Scope:local
      Type:required
      Intent: inout.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +desc_a

      +

      The communication descriptor.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: a variable of type psb_desc_type.
      +

      +

      +info

      +

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

      +

      Notes + + + +

        +
      1. +

        On entry to this routine the descriptor may be in either the build or + assembled state. +

        2. +
      2. +

        On entry to this routine the sparse matrix may be in either the build or + update state. +

        3. +
      3. +

        If the descriptor is in the build state, then the sparse matrix must also be + in the build state; the action of the routine is to (implicitly) call psb_cdins + to add entries to the sparsity pattern; each sparse matrix entry implicitly + defines a graph edge, that is passed to the descriptor routine for the + appropriate processing; +

        4. +
      4. +

        The input data can be passed in either COO or CSR formats; +

        5. +
      5. +

        In COO format the coefficients to be inserted are represented by the + ordered triples ia(i),ja(i),val(i), for i = 1,…,nz; these triples are + arbitrary; +

        6. +
      6. +

        In CSR format the coefficients to be inserted for each input row i = 1,nr + are represented by the ordered triples (i + irw - 1),ja(j),val(j), for + j = irp(i),…,irp(i + 1) - 1; these triples should belong to the current + process, i.e. i+irw-1 should be one of the local indices, but are otherwise + arbitrary; +

        7. +
      7. +

        There is no requirement that a given row must be passed in its entirety + to a single call to this routine: the buildup of a row may be split into as + many calls as desired (even in the CSR format); + + + +

        8. +
      8. +

        Coefficients from different rows may also be mixed up freely in a single + call, according to the application needs; +

        9. +
      9. +

        Coefficients from matrix rows not owned by the calling process are treated + according to the value of bldmode specified at allocation time; if bldmode + was chosen as psb_matbld_remote_ the library will keep track of them, + otherwise they are silently ignored; +

        10. +
      10. +

        If the descriptor is in the assembled state, then any entries in the sparse + matrix that would generate additional communication requirements are + ignored; +

        11. +
      11. +

        If the matrix is in the update state, any entries in positions that were not + present in the original matrix are ignored.

      + + + +

      6.9 psb_spasb — Sparse matrix assembly routine

      + + + + 
      +call psb_spasb(a, desc_a, info [, afmt, upd,  mold])
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in/out.
      Specified as: a structured data of type psb_desc_type. +

      +

      +afmt

      +

      the storage format for the sparse matrix.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an array of characters. Defalt: ’CSR’. +

      +

      +upd

      +

      Provide for updates to the matrix coefficients.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: integer, possible values: psb_upd_srch_, psb_upd_perm_ +

      +

      +mold

      + + + +

      The desired dynamic type for the internal matrix storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from psb_T_base_sparse_mat.

      +

      +

      +

      +On Return

      +

      +

      +

      +a

      +

      the matrix to be assembled.
      Scope:local
      Type:required
      Intent: inout.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in/out.
      Specified as: a structured data of type psb_desc_type. If the matrix was + allocated with bldmode=psb_matbld_remote_, then the descriptor will be + reassembled. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        On entry to this routine the descriptor must be in the assembled state, + i.e. psb_cdasb must already have been called. + + + +

        2. +
      2. +

        The sparse matrix may be in either the build or update state; +

        3. +
      3. +

        Duplicate entries are detected and handled in both build and update state, + with the exception of the error action that is only taken in the build state, + i.e. on the first assembly; +

        4. +
      4. +

        If the update choice is psb_upd_perm_, then subsequent calls to psb_spins + to update the matrix must be arranged in such a way as to produce exactly + the same sequence of coefficient values as encountered at the first assembly; +

        5. +
      5. +

        The output storage format need not be the same on all processes; +

        6. +
      6. +

        On exit from this routine the matrix is in the assembled state, and thus + is suitable for the computational routines; +

        7. +
      7. +

        If the bldmode=psb_matbld_remote_ value was specified at allocation + time, contributions defined on the current process but belonging to a + remote process will be handled accordingly. This is most likely to occur in + finite element applications, with dupl=psb_dupl_add_; it is necessary to + check for possible updates needed in the descriptor, hence there will be a + runtime overhead.

      + + + +

      6.10 psb_spfree — Frees a sparse matrix

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the matrix to be freed.
      Scope:local
      Type:required
      Intent: inout.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +info

      + + + +

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

      + + + +

      6.11 psb_sprn — Reinit sparse matrix structure for psblas routines.

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the matrix to be reinitialized.
      Scope:local
      Type:required
      Intent: inout.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +clear

      +

      Choose whether to zero out matrix coefficients
      Scope:local.
      Type:optional.
      Intent: in.
      Default: true.

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        On exit from this routine the sparse matrix is in the update state.

      + + + +

      6.12 psb_geall — Allocates a dense matrix

      + + + + 
      +call psb_geall(x, desc_a, info[, dupl, bldmode, n, lb])
+
      +

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      The communication descriptor.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a variable of type psb_desc_type.
      +

      +

      +n

      +

      The number of columns of the dense matrix to be allocated.
      Scope: local
      Type: optional
      Intent: in.
      Specified as: Integer scalar, default 1. It is not a valid argument if x is a + rank-1 array. +

      +

      +lb

      +

      The lower bound for the column index range of the dense matrix to be + allocated.
      Scope: local
      Type: optional
      Intent: in.
      Specified as: Integer scalar, default 1. It is not a valid argument if x is a + rank-1 array. + + + +

      +

      +dupl

      +

      How to handle duplicate coefficients.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: integer, possible values: psb_dupl_ovwrt_, psb_dupl_add_; + psb_dupl_err_ has no effect. +

      +

      +bldmode

      +

      Whether to keep track of matrix entries that do not belong to the current + process.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: + an integer value psb_matbld_noremote_, psb_matbld_remote_. Default: + psb_matbld_noremote_.

      +

      +

      +

      +On Return

      +

      +

      +

      +x

      +

      The dense matrix to be allocated.
      Scope: local
      Type: required
      Intent: out.
      Specified as: a rank one or two array with the ALLOCATABLE attribute + or an object of type psb_T_vect_type, of type real, complex or integer.
      +

      +

      +info

      +

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

      + + +

      Notes +

        +
      1. +

        Using psb_matbld_remote_ is likely to cause a runtime overhead at + assembly time;

      + + +

      6.13 psb_geins — Dense matrix insertion routine

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +m

      +

      Number of rows in val to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer value. +

      +

      +irw

      +

      Indices of the rows to be inserted. Specifically, row i of val will be + inserted into the local row corresponding to the global row index irw(i). + Scope:local.
      Type:required.
      Intent: in.
      Specified as: an integer array. +

      +

      +val

      +

      the dense submatrix to be inserted.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a rank 1 or 2 array. Specified as: an integer value. + + +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +local

      +

      Whether the entries in the index vector irw, are already in local + numbering.
      Scope:local.
      Type:optional.
      Specified as: a logical value; default: .false.. +

      +

      +

      +

      +On Return

      +

      +

      +

      +x

      +

      the output dense matrix.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array or an object of type + psb_T_vect_type, of type real, complex or integer.
      +

      +

      +info

      +

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

      +

      Notes + + +

        +
      1. +

        Dense vectors/matrices do not have an associated state; +

        2. +
      2. +

        Duplicate entries are either overwritten or added, there is no provision for + raising an error condition.

      + + +

      6.14 psb_geasb — Assembly a dense matrix

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +desc_a

      +

      The communication descriptor.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a variable of type psb_desc_type.
      +

      +

      +mold

      +

      The desired dynamic type for the internal vector storage.
      Scope: local.
      Type: optional.
      Intent: in.
      Specified as: an object of a class derived from psb_T_base_vect_type; + this is only allowed when x is of type psb_T_vect_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +x

      + + +

      The dense matrix to be assembled.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a rank one or two array with the ALLOCATABLE or an + object of type psb_T_vect_type, of type real, complex or integer.
      +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        On entry to this routine the descriptor must be in the assembled state, + i.e. psb_cdasb must already have been called. +

        2. +
      2. +

        If the bldmode=psb_matbld_remote_ value was specified at allocation + time, contributions defined on the current process but belonging to a + remote process will be handled accordingly. This is most likely to occur in + finite element applications, with dupl=psb_dupl_add_.

      + + +

      6.15 psb_gefree — Frees a dense matrix

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

      +

      +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

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

      +

      +desc_a

      +

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

      +

      +

      +

      +On Return

      +

      + + +

      +

      +info

      +

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

      + + +

      6.16 psb_gelp — Applies a left permutation to a dense matrix

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +trans

      +

      A character that specifies whether to permute A or AT.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a single character with value ’N’ for A or ’T’ for AT.
      +

      +

      +iperm

      +

      An integer array containing permutation information.
      Scope: local
      Type: required
      Intent: in.
      Specified as: an integer one-dimensional array.
      +

      +

      +x

      +

      The dense matrix to be permuted.
      Scope: local
      Type: required
      Intent: inout.
      Specified as: a one or two dimensional array.

      +

      + + +

      +

      +On Return

      +

      +

      +

      +info

      +

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

      + + +

      6.17 psb_glob_to_loc — Global to local indices convertion

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      An integer vector of indices to be converted.
      Scope: local
      Type: required
      Intent: in, inout.
      Specified as: a rank one integer array.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +iact

      +

      specifies action to be taken in case of range errors. Scope: global
      Type: optional
      Intent: in.
      Specified as: a character variable Ignore, Warning or Abort, default Ignore. + + +

      +

      +owned

      +

      Specfies valid range of input Scope: global
      Type: optional
      Intent: in.
      If true, then only indices strictly owned by the current process are + considered valid, if false then halo indices are also accepted. Default: false.

      +

      +

      +

      +On Return

      +

      +

      +

      +x

      +

      If y is not present, then x is overwritten with the translated integer indices. + Scope: global
      Type: required
      Intent: inout.
      Specified as: a rank one integer array. +

      +

      +y

      +

      If y is present, then y is overwritten with the translated integer indices, + and x is left unchanged. Scope: global
      Type: optional
      Intent: out.
      Specified as: a rank one integer array. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        If an input index is out of range, then the corresponding output index is + set to a negative number; + + +

        2. +
      2. +

        The default Ignore means that the negative output is the only action + taken on an out-of-range input.

      + + + +

      6.18 psb_loc_to_glob — Local to global indices conversion

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      An integer vector of indices to be converted.
      Scope: local
      Type: required
      Intent: in, inout.
      Specified as: a rank one integer array.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +iact

      +

      specifies action to be taken in case of range errors. Scope: global
      Type: optional
      Intent: in.
      Specified as: a character variable Ignore, Warning or Abort, default Ignore.

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +x

      +

      If y is not present, then x is overwritten with the translated integer indices. + Scope: global
      Type: required
      Intent: inout.
      Specified as: a rank one integer array. +

      +

      +y

      +

      If y is not present, then y is overwritten with the translated integer indices, + and x is left unchanged. Scope: global
      Type: optional
      Intent: out.
      Specified as: a rank one integer array. +

      +

      +info

      +

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

      + + + +

      6.19 psb_is_owned —

      + + + + 
      +call psb_is_owned(x, desc_a)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      Integer index.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a scalar integer.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      + + +

      A logical mask which is true if x is owned by the current process Scope: + local
      Type: required
      Intent: out.

      +

      Notes +

        +
      1. +

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

      + + +

      6.20 psb_owned_index —

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      Integer indices.
      Scope: local
      Type: required
      Intent: in, inout.
      Specified as: a scalar or a rank one integer array.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +iact

      +

      specifies action to be taken in case of range errors. Scope: global
      Type: optional
      Intent: in.
      Specified as: a character variable Ignore, Warning or Abort, default Ignore.

      +

      + + +

      +

      +On Return

      +

      +

      +

      +y

      +

      A logical mask which is true for all corresponding entries of x that are + owned by the current process Scope: local
      Type: required
      Intent: out.
      Specified as: a scalar or rank one logical array. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

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

      + + +

      6.21 psb_is_local —

      + + + 
      +call psb_is_local(x, desc_a)
+
      +

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      Integer index.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a scalar integer.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      + + +

      A logical mask which is true if x is local to the current process Scope: + local
      Type: required
      Intent: out.

      +

      Notes +

        +
      1. +

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

      + +

      6.22 psb_local_index —

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      Integer indices.
      Scope: local
      Type: required
      Intent: in, inout.
      Specified as: a scalar or a rank one integer array.
      +

      +

      +desc_a

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +iact

      +

      specifies action to be taken in case of range errors. Scope: global
      Type: optional
      Intent: in.
      Specified as: a character variable Ignore, Warning or Abort, default Ignore.

      +

      + + + +

      +

      +On Return

      +

      +

      +

      +y

      +

      A logical mask which is true for all corresponding entries of x that are + local to the current process Scope: local
      Type: required
      Intent: out.
      Specified as: a scalar or rank one logical array. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

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

      + + + +

      6.23 psb_get_boundary — Extract list of boundary elements

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +bndel

      +

      The list of boundary elements on the calling process, in local numbering.
      Scope: local
      Type: required
      Intent: out.
      Specified as: a rank one array with the ALLOCATABLE attribute, of type + integer.
      +

      +

      +info

      + + + +

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

      +

      Notes +

        +
      1. +

        If there are no boundary elements (i.e., if the local part of the connectivity + graph is self-contained) the output vector is set to the “not allocated” + state. +

        2. +
      2. +

        Otherwise the size of bndel will be exactly equal to the number of + boundary elements.

      + + + +

      6.24 psb_get_overlap — Extract list of overlap elements

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +desc

      +

      the communication descriptor.
      Scope:local.
      Type:required.
      Intent: in.
      Specified as: a structured data of type psb_desc_type.

      +

      +

      +

      +On Return

      +

      +

      +

      +ovrel

      +

      The list of overlap elements on the calling process, in local numbering.
      Scope: local
      Type: required
      Intent: out.
      Specified as: a rank one array with the ALLOCATABLE attribute, of type + integer.
      +

      +

      +info

      + + + +

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

      +

      Notes +

        +
      1. +

        If there are no overlap elements the output vector is set to the “not + allocated” state. +

        2. +
      2. +

        Otherwise the size of ovrel will be exactly equal to the number of overlap + elements.

      + + + +

      6.25 psb_sp_getrow — Extract row(s) from a sparse matrix

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +row

      +

      The (first) row to be extracted.
      Scope:local
      Type:required
      Intent: in.
      Specified as: an integer > 0. +

      +

      +a

      +

      the matrix from which to get rows.
      Scope:local
      Type:required
      Intent: in.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +append

      +

      Whether to append or overwrite existing output.
      Scope:local
      Type:optional
      Intent: in.
      Specified as: a logical value default: false (overwrite). + + + +

      +

      +nzin

      +

      Input size to be appended to.
      Scope:local
      Type:optional
      Intent: in.
      Specified as: an integer > 0. When append is true, specifies how many + entries in the output vectors are already filled. +

      +

      +lrw

      +

      The last row to be extracted.
      Scope:local
      Type:optional
      Intent: in.
      Specified as: an integer > 0, default: row. +

      +

      +

      +

      +On Return

      +

      +

      +

      +nz

      +

      the number of elements returned by this call.
      Scope:local.
      Type:required.
      Intent: out.
      Returned as: an integer scalar. +

      +

      +ia

      +

      the row indices.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: an integer array with the ALLOCATABLE attribute. +

      +

      +ja

      + + + +

      the column indices of the elements to be inserted.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: an integer array with the ALLOCATABLE attribute. +

      +

      +val

      +

      the elements to be inserted.
      Scope:local.
      Type:required.
      Intent: inout.
      Specified as: a real array with the ALLOCATABLE attribute. +

      +

      +info

      +

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

      +

      Notes +

        +
      1. +

        The output nz is always the size of the output generated by the current + call; thus, if append=.true., the total output size will be nzin + nz, with + the newly extracted coefficients stored in entries nzin+1:nzin+nz of the + array arguments; +

        2. +
      2. +

        When append=.true. the output arrays are reallocated as necessary; +

        3. +
      3. +

        The row and column indices are returned in the local numbering + scheme; if the global numbering is desired, the user may employ the + psb_loc_to_glob routine on the output.

      + + + +

      6.26 psb_sizeof — Memory occupation

      +

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

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

      +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      A sparse matrix A.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +desc_a

      +

      Communication descriptor.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a structured data of type psb_desc_type. +

      +

      +prec

      +

      Scope: local
      Type: required
      Intent: in.
      Specified as: a preconditioner data structure psb_prec_type. + + + +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The memory occupation of the object specified in the calling sequence, in + bytes.
      Scope: local
      Returned as: an integer(psb_long_int_k_) number.

      + + + +

      6.27 Sorting utilities —

      +

      psb_msort — Sorting by the Merge-sort algorithm +

      psb_qsort — Sorting by the Quicksort algorithm +

      psb_hsort — Sorting by the Heapsort algorithm + + + + 

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

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +x

      +

      The sequence to be sorted.
      Type:required.
      Specified as: an integer, real or complex array of rank 1. +

      +

      +ix

      +

      A vector of indices.
      Type:optional.
      Specified as: an integer array of (at least) the same size as X. +

      +

      +dir

      +

      The desired ordering.
      Type:optional.
      Specified as: an integer value: +

      +

      + Integer and real data:

      +

      psb_sort_up_, psb_sort_down_, psb_asort_up_, + psb_asort_down_; default psb_sort_up_. + + + +

      +

      + Complex data:

      +

      psb_lsort_up_, psb_lsort_down_, psb_asort_up_, + psb_asort_down_; default psb_lsort_up_.

      +
      +

      +flag

      +

      Whether to keep the original values in IX.
      Type:optional.
      Specified as: an integer value psb_sort_ovw_idx_ or psb_sort_keep_idx_; + default psb_sort_ovw_idx_. +

      +

      +

      +

      +On Return

      +

      +

      +

      +x

      +

      The sequence of values, in the chosen ordering.
      Type:required.
      Specified as: an integer, real or complex array of rank 1. +

      +

      +ix

      +

      A vector of indices.
      Type: Optional
      An integer array of rank 1, whose entries are moved to the same position + as the corresponding entries in x.

      +

      Notes +

        +
      1. +

        For integer or real data the sorting can be performed in the up/down + direction, on the natural or absolute values; +

        2. +
      2. +

        For complex data the sorting can be done in a lexicographic order (i.e.: + sort on the real part with ties broken according to the imaginary part) or + on the absolute values; + + + +

        3. +
      3. +

        The routines return the items in the chosen ordering; the output difference + is the handling of ties (i.e. items with an equal value) in the original input. + With the merge-sort algorithm ties are preserved in the same relative + order as they had in the original sequence, while this is not guaranteed for + quicksort or heapsort; +

        4. +
      4. +

        If flag = psb_sort_ovw_idx_ then the entries in ix(1 : n) where n is the size + of x are initialized to ix(i) ← i; thus, upon return from the subroutine, + for each index i we have in ix(i) the position that the item x(i) occupied + in the original data sequence; +

        5. +
      5. +

        If flag = psb_sort_keep_idx_ the routine will assume that the entries in + ix(:) have already been initialized by the user; +

        6. +
      6. +

        The three sorting algorithms have a similar O(nlog n) expected running time; + in the average case quicksort will be the fastest and merge-sort the slowest. + However note that: +

          +
        1. +

          The worst case running time for quicksort is O(n2); the algorithm + implemented here follows the well-known median-of-three heuristics, + but the worst case may still apply; +

          2. +
        2. +

          The worst case running time for merge-sort and heap-sort is + O(nlog n) as the average case; +

          3. +
        3. +

          The merge-sort algorithm is implemented to take advantage of + subsequences that may be already in the desired ordering prior to + the subroutine call; this situation is relatively common when dealing + with groups of indices of sparse matrix entries, thus merge-sort is the + preferred choice when a sorting is needed by other routines in the + library.

        + + + +
      + + + + + + + + + +

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      7 Parallel environment routines

      + id="x12-1050007">Parallel environment routines -
      -  7.1 psb_init — Initializes PSBLAS parallel environment -
       7.2 psb_info — Return information about PSBLAS parallel environment -
       7.3 psb_exit — Exit from PSBLAS parallel environment -
       7.4 psb_get_mpi_comm — Get the MPI communicator -
       7.5 psb_get_mpi_rank — Get the MPI rank -
       7.6 psb_wtime — Wall clock timing -
       7.7 psb_barrier — Sinchronization point parallel environment -
       7.8 psb_abort — Abort a computation -
       7.9 psb_bcast — Broadcast data -
       7.10 psb_sum — Global sum -
       7.11 psb_max — Global maximum -
       7.12 psb_min — Global minimum -
       7.13 psb_amx — Global maximum absolute value -
       7.14 psb_amn — Global minimum absolute value -
       7.15 psb_nrm2 — Global 2-norm reduction -
       7.16 psb_snd — Send data -
       7.17 psb_rcv — Receive data -
      +

      7.1 psb_init — Initializes PSBLAS parallel environment

      + + + + 
      +call psb_init(ctxt, np, basectxt, ids)
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +np

      +

      Number of processes in the PSBLAS virtual parallel machine.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value.  Default: use all available processes. +

      +

      +basectxt

      +

      the initial communication context. The new context will be defined from + the processes participating in the initial one.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value.  Default: use MPI_COMM_WORLD. +

      +

      +ids

      +

      Identities of the processes to use for the new context; the argument is + ignored when np is not specified. This allows the processes in the new + environment to be in an order different from the original one.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer array.  Default: use the indices (0…np - 1).

      + + + +

      +

      +

      +On Return

      +

      +

      +

      +ctxt

      +

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

      +

      Notes +

        +
      1. +

        A call to this routine must precede any other PSBLAS call. +

        2. +
      2. +

        It is an error to specify a value for np greater than the number of processes + available in the underlying base parallel environment.

      + + + +

      7.2 psb_info — Return information about PSBLAS parallel environment

      + + + + 
      +call psb_info(ctxt, iam, np)
+
      +

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

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

      +

      +

      +

      +On Return

      +

      +

      +

      +iam

      +

      Identifier of current process in the PSBLAS virtual parallel machine.
      Scope: local.
      Type: required.
      Intent: out.
      Specified as: an integer value. -1 ≤ iam ≤ np - 1  +

      +

      +np

      + + + +

      Number of processes in the PSBLAS virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: out.
      Specified as: an integer variable.  

      +

      Notes +

        +
      1. +

        For processes in the virtual parallel machine the identifier will satisfy + 0 ≤ iam ≤ np - 1; +

        2. +
      2. +

        If the user has requested on psb_init a number of processes less than + the total available in the parallel execution environment, the remaining + processes will have on return iam = -1; the only call involving ctxt that + any such process may execute is to psb_exit.

      + + + +

      7.3 psb_exit — Exit from PSBLAS parallel environment

      + + + + 
      +call psb_exit(ctxt)
+call psb_exit(ctxt,close)
+
      +

      +

      This subroutine exits from the PSBLAS parallel virtual machine. +

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +close

      +

      Whether to close all data structures related to the virtual parallel machine, + besides those associated with ctxt.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: a logical variable, default value: true.

      +

      Notes +

        +
      1. +

        This routine may be called even if a previous call to psb_info has returned + with iam = -1; indeed, it it is the only routine that may be called with + argument ctxt in this situation. + + + +

        2. +
      2. +

        A call to this routine with close=.true. implies a call to MPI_Finalize, + after which no parallel routine may be called. +

        3. +
      3. +

        If the user whishes to use multiple communication contexts in the + same program, or to enter and exit multiple times into the parallel + environment, this routine may be called to selectively close the contexts + with close=.false., while on the last call it should be called with + close=.true. to shutdown in a clean way the entire parallel environment.

      + + + +

      7.4 psb_get_mpi_comm — Get the MPI communicator

      + + + + 
      +icomm = psb_get_mpi_comm(ctxt)
+
      +

      +

      This function returns the MPI communicator associated with a PSBLAS +context +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

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

      +

      +

      +

      +On Return

      +

      +

      +

      +Function value

      +

      The MPI communicator associated with the PSBLAS virtual parallel + machine.
      Scope: global.
      Type: required.
      Intent: out.

      +

      Notes The subroutine version psb_get_mpicomm is still available but is +deprecated. + + + +

      7.5 psb_get_mpi_rank — Get the MPI rank

      + + + + 
      +rank = psb_get_mpi_rank(ctxt, id)
+
      +

      +

      This function returns the MPI rank of the PSBLAS process id +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +id

      +

      Identifier of a process in the PSBLAS virtual parallel machine.
      Scope: local.
      Type: required.
      Intent: in.
      Specified as: an integer value. 0 ≤ id ≤ np - 1 

      +

      +

      +

      +On Return

      +

      +

      +

      +Funciton value

      + + + +

      The MPI rank associated with the PSBLAS process id.
      Scope: local.
      Type: required.
      Intent: out.

      +

      Notes The subroutine version psb_get_rank is still available but is deprecated. + + +

      7.6 psb_wtime — Wall clock timing

      + + + 
      +time = psb_wtime()
+
      +

      +

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

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Exit

      +

      +

      +

      +Function value

      +

      the elapsed time in seconds.
      Returned as: a real(psb_dpk_) variable.

      + + +

      7.7 psb_barrier — Sinchronization point parallel environment

      + + + 
      +call psb_barrier(ctxt)
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

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

      + + +

      7.8 psb_abort — Abort a computation

      + + + 
      +call psb_abort(ctxt)
+
      +

      +

      This subroutine aborts computation on the parallel virtual machine. +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

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

      + + +

      7.9 psb_bcast — Broadcast data

      + + + 
      +call psb_bcast(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

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

      +

      +root

      +

      Root process holding data to be broadcast.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value 0 <= root <= np - 1, default 0   + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_bcast(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_bcast(ctxt,dat,mode=psb_collective_start_,request=bcast_request)
+  ....... ! Do not access dat
+  call psb_bcast(ctxt,dat,mode=psb_collective_end_, request=bcast_request)
+
        +

        +
      + + +

      7.10 psb_sum — Global sum

      + + + 
      +call psb_sum(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global sum.
      Scope: global.
      Type: required.
      Intent: inout.
      Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final sum, or -1 to make it available on all processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.   + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_sum(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_sum(ctxt,dat,mode=psb_collective_start_,request=sum_request)
+  ....... ! Do not access dat
+  call psb_sum(ctxt,dat,mode=psb_collective_end_,request=sum_request)
+
        +

        +
      + + +

      7.11 psb_max — Global maximum

      + + + 
      +call psb_max(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global maximum.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.  Type, kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final maximum, or -1 to make it available on all + processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.
      + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      + +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_max(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_max(ctxt,dat,mode=psb_collective_start_,request=max_request)
+  ....... ! Do not access dat
+  call psb_max(ctxt,dat,mode=psb_collective_end_,request=max_request)
+
        +

        +
      + + + +

      7.12 psb_min — Global minimum

      + + + + 
      +call psb_min(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global minimum.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: an integer or real variable, which may be a scalar, or a rank + 1 or 2 array.  Type, kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final value, or -1 to make it available on all processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.
      + + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_min(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_min(ctxt,dat,mode=psb_collective_start_,request=min_request)
+  ....... ! Do not access dat
+  call psb_min(ctxt,dat,mode=psb_collective_end_,request=min_request)
+
        +

        +
      + + + +

      7.13 psb_amx — Global maximum absolute value

      + + + + 
      +call psb_amx(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global maximum.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final value, or -1 to make it available on all processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.
      + + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      + + + +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_amx(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_amx(ctxt,dat,mode=psb_collective_start_,request=amx_request)
+  ....... ! Do not access dat
+  call psb_amx(ctxt,dat,mode=psb_collective_end_,request=amx_request)
+
        +

        +
      + + + +

      7.14 psb_amn — Global minimum absolute value

      + + + + 
      +call psb_amn(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global minimum.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: an integer, real or complex variable, which may be a scalar, or + a rank 1 or 2 array.  Type, kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final value, or -1 to make it available on all processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.
      + + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      Notes +

        +
      1. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        2. +
      2. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_amn(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        3. +
      3. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: +

        +

        +

        +  call psb_amn(ctxt,dat,mode=psb_collective_start_,request=amn_request)
+  ....... ! Do not access dat
+  call psb_amn(ctxt,dat,mode=psb_collective_end_,request=amn_request)
+
        +

        +
      + + + +

      7.15 psb_nrm2 — Global 2-norm reduction

      + + + + 
      +call psb_nrm2(ctxt, dat [, root, mode, request])
+
      +

      +

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

      +

      +Type:

      +

      Synchronous. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

      The local contribution to the global minimum.
      Scope: local.
      Type: required.
      Intent: inout.
      Specified as: a real variable, which may be a scalar, or a rank 1 array. +  Kind, rank and size must agree on all processes. +

      +

      +root

      +

      Process to hold the final value, or -1 to make it available on all processes.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value -1 <= root <= np - 1, default -1.
      + + + +

      +

      +mode

      +

      Whether the call is started in non-blocking mode and completed later, or + is executed synchronously.
      Scope: global.
      Type: optional.
      Intent: in.
      Specified as: an integer value. The action to be taken is determined by + its bit fields, which can be set with bitwise OR. Basic action values are + psb_collective_start_, psb_collective_end_. Default: both fields are + selected (i.e. require synchronous completion).
      +

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      +request

      +

      A request variable to check for operation completion.
      Scope: local.
      Type: optional.
      Intent: inout.
      If mode does not specify synchronous completion, then this variable must + be present.

      + + + +

      Notes +

        +
      1. +

        This reduction is appropriate to compute the results of multiple (local) + NRM2 operations at the same time. +

        2. +
      2. +

        Denoting by dati the value of the variable dat on process i, the output res + is equivalent to the computation of +

        + ∘ ∑------ +res = dat2i, + i +
        +

        with care taken to avoid unnecessary overflow. +

        3. +
      3. +

        The dat argument is both input and output, and its value may be changed + even on processes different from the final result destination. +

        4. +
      4. +

        The mode argument can be built with the bitwise IOR() operator; in the + following example, the argument is forcing immediate completion, hence the + request argument needs not be specified: +

        +

        +

        +  call psb_nrm2(ctxt,dat,mode=ior(psb_collective_start_,psb_collective_end_))
+
        +

        +
        5. +
      5. +

        When splitting the operation in two calls, the dat argument must not be + accessed between calls: + + + +

        +

        +

        +  call psb_nrm2(ctxt,dat,mode=psb_collective_start_,request=nrm2_request)
+  ....... ! Do not access dat
+  call psb_nrm2(ctxt,dat,mode=psb_collective_end_,request=nrm2_request)
+
        +

        +
      + + + +

      7.16 psb_snd — Send data

      + + + + 
      +call psb_snd(ctxt, dat, dst, m)
+
      +

      +

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

      +

      +Type:

      +

      Synchronous: see usage notes. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +dat

      +

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

      +

      +dst

      +

      Destination process.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer value 0 <= dst <= np - 1.
      + + + +

      +

      +m

      +

      Number of rows.
      Scope: global.
      Type: Optional.
      Intent: in.
      Specified as: an integer value 0 <= m <= size(dat,1).
      When dat is a rank 2 array, specifies the number of rows to be sent + independently of the leading dimension size(dat,1); must have the same + value on sending and receiving processes.

      +

      +

      +

      +On Return

      +

      +

      Notes +

        +
      1. +

        This subroutine implies a synchronization, but only between the calling + process and the destination process dst.

      + + + +

      7.17 psb_rcv — Receive data

      + + + + 
      +call psb_rcv(ctxt, dat, src, m)
+
      +

      +

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

      +

      +Type:

      +

      Synchronous: see usage notes. +

      +

      +On Entry

      +

      +

      +

      +ctxt

      +

      the communication context identifying the virtual parallel machine.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer variable. +

      +

      +src

      +

      Source process.
      Scope: global.
      Type: required.
      Intent: in.
      Specified as: an integer value 0 <= src <= np - 1.
      +

      +

      +m

      +

      Number of rows.
      Scope: global.
      Type: Optional.
      Intent: in.
      Specified as: an integer value 0 <= m <= size(dat,1).
      When dat is a rank 2 array, specifies the number of rows to be sent + independently of the leading dimension size(dat,1); must have the same + value on sending and receiving processes.

      + + + +

      +

      +

      +On Return

      +

      +

      +

      +dat

      +

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

      +

      Notes +

        +
      1. +

        This subroutine implies a synchronization, but only between the calling + process and the source process src.

      + + + +

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      8 Error handling

      + id="x13-1230008">Error handling

      The PSBLAS library error handling policy has been completely rewritten in version 2.0. The idea behind the design of this new error handling strategy is to keep error messages on a stack allowing the user to trace back up to the point where the first @@ -36,7 +36,7 @@ zero, an error condition is raised. This process continues on all the levels of nested calls until the level where the user decides to abort the program execution.

      Figure 5 shows the layout of a generic 5 shows the layout of a generic psb_foo routine with respect to the PSBLAS-2.0 error handling policy. It is possible to see how, whenever an error condition is detected, the

      @@ -67,270 +67,241 @@ explicitly. >

      -
      subroutinesubroutine psb_foo(some args, info) + psb_foo(some args, ... + info) 
        if(error detected) then +  ... 
         if(error info=errcode1 + detected) then 
          call psb_errpush(’psb_foo’, errcode1) +   info=errcode1 
         goto 9999 +   end if +  call ... + psb_errpush(’psb_foo’, errcode1) 
       call psb_bar(some args, info) +   if(info .ne. zero) then +    goto 9999 
       info=errcode2 +   end if 
        call psb_errpush(’psb_foo’, errcode2) +  ... 
         call goto 9999 + psb_bar(some args, end if + info) 
        ... +9999 continue +  if(info if (err_act .eq. act_abort) then + .ne. zero) then 
        call psb_error(icontxt) +     return + info=errcode2 
        else +     return + call psb_errpush(’psb_foo’, errcode2) 
            goto 9999 
         end if 
         ... 
      9999 continue 
         if (err_act .eq. act_abort) then 
           call psb_error(icontxt) 
           return 
         else 
           return 
         end if 
       
      end subroutine psb_foo -
      +class="cmtt-9"> end if + +end subroutine psb_foo

      Listing 5: The layout of a generic psb_foo routine with respect to PSBLAS-2.0 -error handling policy.
      +error handling policy.

      Figure 6 reports a sample error message generated by the PSBLAS-2.0 +href="#x13-123026r6">6 reports a sample error message generated by the PSBLAS-2.0 library. This error has been generated by the fact that the user has chosen the invalid “FOO” storage format to represent the sparse matrix. From this error message it is possible to see that the error has been detected inside @@ -342,7 +313,7 @@ process).

      @@ -371,7 +342,7 @@ Aborting...
      Listing 6: A sample PSBLAS-3.0 error message. Process 0 detected an error -condition inside the psb_cest subroutine
      +condition inside the psb_cest subroutine
      @@ -379,28 +350,236 @@ condition inside the psb_cest subroutine
      + 
      call psb_errpush(err_c, r_name, i_err, a_err)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +err_c

      +

      the error code
      Scope: local
      Type: required
      Intent: in.
      Specified as: an integer. +

      +

      +r_name

      +

      the soutine where the error has been caught.
      Scope: local
      Type: required
      Intent: in.
      Specified as: a string.
      +

      +

      +i_err

      +

      addional info for error code
      Scope: local
      Type: optional
      Specified as: an integer array
      +

      +

      +a_err

      + + +

      addional info for error code
      Scope: local
      Type: optional
      Specified as: a string.

      + + + +

      8.2 psb_error — Prints the error stack content and aborts execution

      + + 
      call psb_error(icontxt)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +icontxt

      +

      the communication context.
      Scope: global
      Type: optional
      Intent: in.
      Specified as: an integer.

      + + + +

      8.3 psb_set_errverbosity — Sets the verbosity of error messages

      + + 
      call psb_set_errverbosity(v)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +v

      +

      the verbosity level
      Scope: global
      Type: required
      Intent: in.
      Specified as: an integer.

      + + + +

      8.4 psb_set_erraction — Set the type of action to be taken upon error +condition

      + + 
      call psb_set_erraction(err_act)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +err_act

      +

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

      + + + + + + +

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      9 Utilities

      + id="x14-1280009">Utilities

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

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

      9.1 hb_read — Read a sparse matrix from a file in the Harwell–Boeing +format

      + + 
      call hb_read(a, iret, iunit, filename, b, mtitle)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +filename

      +

      The name of the file to be read.
      Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +

      +

      +iunit

      +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -.

      +

      +

      +

      +On Return

      +

      +

      +

      +a

      +

      the sparse matrix read from file.
      Type:required.
      Specified as: a structured data of type psb_Tspmat_type. + + + +

      +

      +b

      +

      Rigth hand side(s).
      Type: Optional
      An array of type real or complex, rank 2 and having the ALLOCATABLE + attribute; will be allocated and filled in if the input file contains a right + hand side, otherwise will be left in the UNALLOCATED state. +

      +

      +mtitle

      +

      Matrix title.
      Type: Optional
      A charachter variable of length 72 holding a copy of the matrix title as + specified by the Harwell-Boeing format and contained in the input file. +

      +

      +iret

      +

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

      + + + +

      9.2 hb_write — Write a sparse matrix to a file in the Harwell–Boeing +format

      + + 
      call hb_write(a, iret, iunit, filename, key, rhs, mtitle)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix to be written.
      Type:required.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +b

      +

      Rigth hand side.
      Type: Optional
      An array of type real or complex, rank 1 and having the ALLOCATABLE + attribute; will be allocated and filled in if the input file contains a right + hand side. +

      +

      +filename

      +

      The name of the file to be written to.
      Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default output unit 6 (i.e. standard output in Unix jargon) + is used. Default: -. +

      +

      +iunit

      +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -. + + + +

      +

      +key

      +

      Matrix key.
      Type: Optional
      A charachter variable of length 8 holding the matrix key as specified by + the Harwell-Boeing format and to be written to file. +

      +

      +mtitle

      +

      Matrix title.
      Type: Optional
      A charachter variable of length 72 holding the matrix title as specified by + the Harwell-Boeing format and to be written to file.

      +

      +

      +

      +On Return

      +

      +

      +

      +iret

      +

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

      + + + +

      9.3 mm_mat_read — Read a sparse matrix from a file in the MatrixMarket +format

      + + 
      call mm_mat_read(a, iret, iunit, filename)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +filename

      +

      The name of the file to be read.
      Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +

      +

      +iunit

      +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -.

      +

      +

      +

      +On Return

      +

      +

      +

      +a

      +

      the sparse matrix read from file.
      Type:required.
      Specified as: a structured data of type psb_Tspmat_type. + + +

      +

      +iret

      +

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

      + + +

      9.4 mm_array_read — Read a dense array from a file in the MatrixMarket +format

      + + 
      call mm_array_read(b, iret, iunit, filename)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +filename

      +

      The name of the file to be read.
      Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +

      +

      +iunit

      +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -.

      +

      +

      +

      +On Return

      +

      +

      +

      +b

      +

      Rigth hand side(s).
      Type: required
      An array of type real or complex, rank 1 or 2 and having the + + + ALLOCATABLE attribute, or an object of type psb_T_vect_type, of + type real or complex.
      Will be allocated and filled in if the input file contains a right hand side, + otherwise will be left in the UNALLOCATED state.
      +

      +

      +iret

      +

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

      + + +

      9.5 mm_mat_write — Write a sparse matrix to a file in the MatrixMarket +format

      + + 
      call mm_mat_write(a, mtitle, iret, iunit, filename)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +a

      +

      the sparse matrix to be written.
      Type:required.
      Specified as: a structured data of type psb_Tspmat_type. +

      +

      +mtitle

      +

      Matrix title.
      Type: required
      A charachter variable holding a descriptive title for the matrix to be + written to file. +

      +

      +filename

      +

      The name of the file to be written to.
      Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default output unit 6 (i.e. standard output in Unix jargon) + is used. Default: -. +

      +

      +iunit

      +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -.

      + +

      +

      +

      +On Return

      +

      +

      +

      +iret

      +

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

      +

      Notes +

      If this function is called on a matrix a on a distributed communicator only the +local part is written in output. To get a single MatrixMarket file with the whole +matrix when appropriate, e.g. for debugging purposes, one could gather the whole +matrix on a single rank and then write it. Consider the following example for a +double precision matrix +

      +

      +

      +type(psb_ldspmat_type) :: aglobal
+
+call psb_gather(aglobal,a,desc_a,info)
+if (iam == psb_root_) then
+call mm_mat_write(aglobal,mtitle,info,filename)
+end if
+call psb_spfree(aglobal, desc_a, info)
+
      +

      +

      To simplify this procedure in C, there is a utility function +

      +

      +

      +psb_i_t psb_c_<s,d,c,z>global_mat_write(ah,cdh);
+
      +

      +

      that produces exactly this result. + + + +

      9.6 mm_array_write — Write a dense array from a file in the MatrixMarket +format

      + + 
      call mm_array_write(b, vtitle, iret, iunit, filename)
      + +

      +

      +

      +Type:

      +

      Asynchronous. +

      +

      +On Entry

      +

      +

      +

      +b

      +

      Rigth hand side(s).
      Type: required
      An array of type real or complex, rank 1 or 2, or an object of type + psb_T_vect_type, of type real or complex; its contents will be written to + disk.
      +

      +

      +filename

      +

      The name of the file to be written.
      +

      +

      +vtitle

      +

      Matrix title.
      Type: required
      A charachter variable holding a descriptive title for the vector to be written + to file. Type:optional.
      Specified as: a character variable containing a valid file name, or -, in + which case the default input unit 5 (i.e. standard input in Unix jargon) is + used. Default: -. +

      +

      +iunit

      + + + +

      The Fortran file unit number.
      Type:optional.
      Specified as: an integer value. Only meaningful if filename is not -.

      +

      +

      +

      +On Return

      +

      +

      +

      +iret

      +

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

      +

      Notes +

      If this function is called on a vector v on a distributed communicator only the +local part is written in output. To get a single MatrixMarket file with the whole +vector when appropriate, e.g. for debugging purposes, one could gather the whole +vector on a single rank and then write it. Consider the following example for a double +precision vector +

      +

      +

      +real(psb_dpk_), allocatable :: vglobal(:)
+
+call psb_gather(vglobal,v,desc,info)
+if (iam == psb_root_) then
+call mm_array_write(vglobal,vtitle,info,filename)
+end if
+call deallocate(vglobal, stat=info)
+
      +

      +

      To simplify this procedure in C, there is a utility function +

      +

      +

      +psb_i_t psb_c_<s,d,c,z>global_vec_write(vh,cdh);
+
      +

      +

      that produces exactly this result. + + + + + + + + + +

      [next] [next] [prev] [prev-tail] [front] [up]

      +href="userhtml.html#userhtmlse12.html" >up]

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a/docs/src/cuda.tex +++ b/docs/src/cuda.tex @@ -31,9 +31,19 @@ routine in the library is built according to the following principles: In this way, data items are put on the {GPU} memory ``on demand'' and remain there as long as ``normal'' computations are carried out. As an example, the following call to a matrix-vector product +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} call psb_spmm(alpha,a,x,beta,y,desc_a,info) \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + call psb_spmm(alpha,a,x,beta,y,desc_a,info) +\end{verbatim} + \end{minipage} + \end{center} +\fi will transparently and automatically be performed on the {GPU} whenever all three data inputs \fortinline|a|, \fortinline|x| and \fortinline|y| are {GPU}-enabled. If a program makes many such calls @@ -81,9 +91,19 @@ and \fortinline|beta|, and the return code \fortinline|info|. environment} \addcontentsline{toc}{subsection}{psb\_cuda\_init} +\ifpdf \begin{minted}[breaklines=true]{fortran} call psb_cuda_init(ctxt [, device]) \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +call psb_cuda_init(ctxt [, device]) +\end{verbatim} + \end{minipage} + \end{center} +\fi This subroutine initializes the PSBLAS-CUDA environment. \begin{description} @@ -109,9 +129,19 @@ available on the current node. environment} \addcontentsline{toc}{subsection}{psb\_cuda\_exit} +\ifpdf \begin{minted}[breaklines=true]{fortran} call psb_cuda_exit(ctxt) \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +call psb_cuda_exit(ctxt) +\end{verbatim} + \end{minipage} + \end{center} +\fi This subroutine exits from the PSBLAS CUDA context. \begin{description} @@ -131,9 +161,19 @@ Specified as: an integer variable. \subsection*{psb\_cuda\_DeviceSync --- Synchronize CUDA device} \addcontentsline{toc}{subsection}{psb\_cuda\_DeviceSync} +\ifpdf \begin{minted}[breaklines=true]{fortran} call psb_cuda_DeviceSync() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +call psb_cuda_DeviceSync() +\end{verbatim} + \end{minipage} + \end{center} +\fi This subroutine ensures that all previosly invoked kernels, i.e. all invocation of CUDA-side code, have completed. @@ -142,45 +182,96 @@ invocation of CUDA-side code, have completed. \subsection*{psb\_cuda\_getDeviceCount } \addcontentsline{toc}{subsection}{psb\_cuda\_getDeviceCount} +\ifpdf \begin{minted}[breaklines=true]{fortran} ngpus = psb_cuda_getDeviceCount() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +ngpus = psb_cuda_getDeviceCount() +\end{verbatim} + \end{minipage} + \end{center} +\fi Get number of devices available on current computing node. \subsection*{psb\_cuda\_getDevice } \addcontentsline{toc}{subsection}{psb\_cuda\_getDevice} +\ifpdf \begin{minted}[breaklines=true]{fortran} ngpus = psb_cuda_getDevice() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +ngpus = psb_cuda_getDevice() +\end{verbatim} + \end{minipage} + \end{center} +\fi Get device in use by current process. \subsection*{psb\_cuda\_setDevice } \addcontentsline{toc}{subsection}{psb\_cuda\_setDevice} +\ifpdf \begin{minted}[breaklines=true]{fortran} info = psb_cuda_setDevice(dev) \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +info = psb_cuda_setDevice(dev) +\end{verbatim} + \end{minipage} + \end{center} +\fi Set device to be used by current process. \subsection*{psb\_cuda\_DeviceHasUVA } \addcontentsline{toc}{subsection}{psb\_cuda\_DeviceHasUVA} +\ifpdf \begin{minted}[breaklines=true]{fortran} hasUva = psb_cuda_DeviceHasUVA() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +hasUva = psb_cuda_DeviceHasUVA() +\end{verbatim} + \end{minipage} + \end{center} +\fi -Returns true if device currently in use supports UVA (Unified Virtual Addressing). +Returns true if device currently in use supports UVA +(Unified Virtual Addressing). \subsection*{psb\_cuda\_WarpSize } \addcontentsline{toc}{subsection}{psb\_cuda\_WarpSize} +\ifpdf \begin{minted}[breaklines=true]{fortran} nw = psb_cuda_WarpSize() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +nw = psb_cuda_WarpSize() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the warp size. @@ -188,18 +279,38 @@ Returns the warp size. \subsection*{psb\_cuda\_MultiProcessors } \addcontentsline{toc}{subsection}{psb\_cuda\_MultiProcessors} +\ifpdf \begin{minted}[breaklines=true]{fortran} nmp = psb_cuda_MultiProcessors() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +nmp = psb_cuda_MultiProcessors() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the number of multiprocessors in the CUDA device. \subsection*{psb\_cuda\_MaxThreadsPerMP } \addcontentsline{toc}{subsection}{psb\_cuda\_MaxThreadsPerMP} +\ifpdf \begin{minted}[breaklines=true]{fortran} nt = psb_cuda_MaxThreadsPerMP() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +nt = psb_cuda_MaxThreadsPerMP() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the maximum number of threads per multiprocessor. @@ -207,9 +318,19 @@ Returns the maximum number of threads per multiprocessor. \subsection*{psb\_cuda\_MaxRegistersPerBlock } \addcontentsline{toc}{subsection}{psb\_cuda\_MaxRegisterPerBlock} +\ifpdf \begin{minted}[breaklines=true]{fortran} nr = psb_cuda_MaxRegistersPerBlock() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +nr = psb_cuda_MaxRegistersPerBlock() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the maximum number of register per thread block. @@ -217,27 +338,57 @@ Returns the maximum number of register per thread block. \subsection*{psb\_cuda\_MemoryClockRate } \addcontentsline{toc}{subsection}{psb\_cuda\_MemoryClockRate} +\ifpdf \begin{minted}[breaklines=true]{fortran} cl = psb_cuda_MemoryClockRate() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +cl = psb_cuda_MemoryClockRate() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the memory clock rate in KHz, as an integer. \subsection*{psb\_cuda\_MemoryBusWidth } \addcontentsline{toc}{subsection}{psb\_cuda\_MemoryBusWidth} +\ifpdf \begin{minted}[breaklines=true]{fortran} nb = psb_cuda_MemoryBusWidth() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +nb = psb_cuda_MemoryBusWidth() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the memory bus width in bits. \subsection*{psb\_cuda\_MemoryPeakBandwidth } \addcontentsline{toc}{subsection}{psb\_cuda\_MemoryPeakBandwidth} +\ifpdf \begin{minted}[breaklines=true]{fortran} bw = psb_cuda_MemoryPeakBandwidth() \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +bw = psb_cuda_MemoryPeakBandwidth() +\end{verbatim} + \end{minipage} + \end{center} +\fi Returns the peak memory bandwidth in MB/s (real double precision). diff --git a/docs/src/ext-intro.tex b/docs/src/ext-intro.tex index ef9b882d..44e9915c 100644 --- a/docs/src/ext-intro.tex +++ b/docs/src/ext-intro.tex @@ -32,6 +32,7 @@ following steps: Suppose you want to use the CUDA-enabled ELLPACK data structure; you would use a piece of code like this (and don't forget, you need CUDA-side vectors along with the matrices): +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} program my_cuda_test use psb_base_mod @@ -80,6 +81,61 @@ program my_cuda_test stop end program my_cuda_test \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} +program my_cuda_test + use psb_base_mod + use psb_util_mod + use psb_ext_mod + use psb_cuda_mod + type(psb_dspmat_type) :: a, agpu + type(psb_d_vect_type) :: x, xg, bg + + real(psb_dpk_), allocatable :: xtmp(:) + type(psb_d_vect_cuda) :: vmold + type(psb_d_elg_sparse_mat) :: aelg + type(psb_ctxt_type) :: ctxt + integer :: iam, np + + + call psb_init(ctxt) + call psb_info(ctxt,iam,np) + call psb_cuda_init(ctxt, iam) + + + ! My own home-grown matrix generator + call gen_matrix(ctxt,idim,desc_a,a,x,info) + if (info /= 0) goto 9999 + + call a%cscnv(agpu,info,mold=aelg) + if (info /= 0) goto 9999 + xtmp = x%get_vect() + call xg%bld(xtmp,mold=vmold) + call bg%bld(size(xtmp),mold=vmold) + + ! Do sparse MV + call psb_spmm(done,agpu,xg,dzero,bg,desc_a,info) + + +9999 continue + if (info == 0) then + write(*,*) '42' + else + write(*,*) 'Something went wrong ',info + end if + + + call psb_cuda_exit() + call psb_exit(ctxt) + stop +end program my_cuda_test +\end{verbatim} + \end{minipage} + \end{center} +\fi + A full example of this strategy can be seen in the \texttt{test/ext/kernel} and \texttt{test/\-cuda/\-kernel} subdirectories, where we provide sample programs @@ -132,7 +188,11 @@ OFFSET & Offset for diagonals \\ \begin{figure}[ht] \centering % \includegraphics[width=5.2cm]{figures/mat.eps} - \includegraphics[width=5.2cm]{figures/mat.pdf} +\ifcase\pdfoutput + \includegraphics[width=5.2cm]{mat.png} +\or + \includegraphics[width=5.2cm]{figures/mat.pdf} +\fi \caption{Example of sparse matrix} \label{fig:dense} \end{figure} @@ -155,7 +215,11 @@ indices, e.g. the last valid one found in the same row. \begin{figure}[ht] \centering % \includegraphics[width=8.2cm]{figures/ell.eps} - \includegraphics[width=8.2cm]{figures/ell.pdf} +\ifcase\pdfoutput + \includegraphics[width=8.2cm]{ell.png} +\or + \includegraphics[width=8.2cm]{figures/ell.pdf} +\fi \caption{ELLPACK compression of matrix in Figure~\ref{fig:dense}} \label{fig:ell} \end{figure} @@ -199,6 +263,7 @@ computing days; in modern CPUs it is not quite as popular, but it is the basis for many GPU formats. The relevant data type is \verb|psb_T_ell_sparse_mat|: +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} type, extends(psb_d_base_sparse_mat) :: psb_d_ell_sparse_mat ! @@ -212,6 +277,25 @@ The relevant data type is \verb|psb_T_ell_sparse_mat|: .... end type psb_d_ell_sparse_mat \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + type, extends(psb_d_base_sparse_mat) :: psb_d_ell_sparse_mat + ! + ! ITPACK/ELL format, extended. + ! + + integer(psb_ipk_), allocatable :: irn(:), ja(:,:), idiag(:) + real(psb_dpk_), allocatable :: val(:,:) + + contains + .... + end type psb_d_ell_sparse_mat +\end{verbatim} + \end{minipage} + \end{center} +\fi \subsubsection*{Hacked ELLPACK} @@ -251,13 +335,18 @@ submatrix inside the stacked \textit{cM}/\textit{rP} buffers, plus an additional element pointing past the end of the last block, where the next one would begin. We thus have the property that -the elements of the $k$-th \textit{hack} are stored between \verb|hackOffsets[k]| and +the elements of the $k$-th \textit{hack} are stored between +\verb|hackOffsets[k]| and \verb|hackOffsets[k+1]|, similarly to what happens in the CSR format. \begin{figure}[ht] \centering % \includegraphics[width=8.2cm]{../figures/hll.eps} - \includegraphics[width=.72\textwidth]{../figures/hll.pdf} +\ifcase\pdfoutput + \includegraphics[width=.72\textwidth]{hll.png} +\or + \includegraphics[width=.72\textwidth]{../figures/hll.pdf} +\fi \caption{Hacked ELLPACK compression of matrix in Figure~\ref{fig:dense}} \label{fig:hll} \end{figure} @@ -267,6 +356,7 @@ therefore the additional memory is limited to the hack in which the row appears. The relevant data type is \verb|psb_T_hll_sparse_mat|: +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} type, extends(psb_d_base_sparse_mat) :: psb_d_hll_sparse_mat ! @@ -280,6 +370,25 @@ The relevant data type is \verb|psb_T_hll_sparse_mat|: .... end type \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + type, extends(psb_d_base_sparse_mat) :: psb_d_hll_sparse_mat + ! + ! HLL format. (Hacked ELL) + ! + integer(psb_ipk_) :: hksz + integer(psb_ipk_), allocatable :: irn(:), ja(:), idiag(:), hkoffs(:) + real(psb_dpk_), allocatable :: val(:) + + contains + .... + end type +\end{verbatim} + \end{minipage} + \end{center} +\fi \subsubsection*{Diagonal storage} @@ -300,13 +409,18 @@ addressing is required. \begin{figure}[ht] \centering % \includegraphics[width=8.2cm]{figures/dia.eps} - \includegraphics[width=.72\textwidth]{figures/dia.pdf} +\ifcase\pdfoutput + \includegraphics[width=.72\textwidth]{dia.png} +\or + \includegraphics[width=.72\textwidth]{figures/dia.pdf} +\fi \caption{DIA compression of matrix in Figure~\ref{fig:dense}} \label{fig:dia} \end{figure} \begin{algorithm} +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} do j=1,ndiag if (offset(j) > 0) then @@ -319,11 +433,30 @@ addressing is required. end do end do \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + do j=1,ndiag + if (offset(j) > 0) then + ir1 = 1; ir2 = m - offset(j); + else + ir1 = 1 - offset(j); ir2 = m; + end if + do i=ir1,ir2 + y(i) = y(i) + alpha*as(i,j)*x(i+offset(j)) + end do + end do +\end{verbatim} + \end{minipage} + \end{center} +\fi \caption{\label{alg:dia} Matrix-Vector product in DIA format} \end{algorithm} The relevant data type is \verb|psb_T_dia_sparse_mat|: +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} type, extends(psb_d_base_sparse_mat) :: psb_d_dia_sparse_mat ! @@ -336,6 +469,24 @@ The relevant data type is \verb|psb_T_dia_sparse_mat|: end type \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + type, extends(psb_d_base_sparse_mat) :: psb_d_dia_sparse_mat + ! + ! DIA format, extended. + ! + + integer(psb_ipk_), allocatable :: offset(:) + integer(psb_ipk_) :: nzeros + real(psb_dpk_), allocatable :: data(:,:) + + end type +\end{verbatim} + \end{minipage} + \end{center} +\fi @@ -378,12 +529,17 @@ the number of diagonals of the $k$-th \textit{hack} is given by \begin{figure}[ht] \centering % \includegraphics[width=8.2cm]{../figures/hdia.eps} - \includegraphics[width=.72\textwidth]{../figures/hdia.pdf} +\ifcase\pdfoutput + \includegraphics[width=.72\textwidth]{hdia.png} +\or + \includegraphics[width=.72\textwidth]{../figures/hdia.pdf} +\fi \caption{Hacked DIA compression of matrix in Figure~\ref{fig:dense}} \label{fig:hdia} \end{figure} The relevant data type is \verb|psb_T_hdia_sparse_mat|: +\ifpdf \begin{minted}[breaklines=true,bgcolor=bg,fontsize=\small]{fortran} type pm real(psb_dpk_), allocatable :: data(:,:) @@ -408,5 +564,35 @@ The relevant data type is \verb|psb_T_hdia_sparse_mat|: .... end type \end{minted} +\else +\begin{center} + \begin{minipage}[tl]{0.9\textwidth} +\begin{verbatim} + type pm + real(psb_dpk_), allocatable :: data(:,:) + end type pm + + type po + integer(psb_ipk_), allocatable :: off(:) + end type po + + type, extends(psb_d_base_sparse_mat) :: psb_d_hdia_sparse_mat + ! + ! HDIA format, extended. + ! + + type(pm), allocatable :: hdia(:) + type(po), allocatable :: offset(:) + integer(psb_ipk_) :: nblocks, nzeros + integer(psb_ipk_) :: hack = 64 + integer(psb_long_int_k_) :: dim=0 + + contains + .... + end type +\end{verbatim} + \end{minipage} + \end{center} +\fi diff --git a/docs/src/figures/dia.png b/docs/src/figures/dia.png new file mode 100644 index 0000000000000000000000000000000000000000..de7db9197139e8b592815942792d983f23f3f93e GIT binary patch literal 50686 zcmc%wWmr`27e0y)As`Y0(v2`mcejYbNW;)wDlqgAl7fmf(t?B{HFOP~3L_x{DBU@9 zcb<)(@A?1Vob%%M>TIsLnAp$W&$HrQYu)SF;aVEci3#ZlK_C#Zs>)Lx5Qu;o1j2D4 zzyrR?%AaEa{$Y9OJb!{U-pvyPe897Q@%$<1=JqeUIX?mT=B}%Xkp~FG_we?G<&!J# z1$@cksch(}>tgTeZRKtUdak9$^8A&Hho^^)`)gNE7C`|%0UjgALSD)hQ5Hy_9BVG@VXoVhNaWXjKdA)HqaFuM=RWG8o%4fb}Z z7&D(?J_MS5rrsj^cbRPSynQSiD#fd+#G#jvHIxim{z5J7SkN^Ml#Iy$ z^8iYk`OUqsc}xDB6iTjTsIPBRj=qVdpG=ac-Iz- zms#{pUfjB}Wyr&6rYau4kGP-mNCHjiTN0{&2ate3mRy99kO(MVR^%cEZ>PeTeK#I+ 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