/* --------------------------------------------------------------------- * * -- PBLAS auxiliary routine (version 2.0) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * April 1, 1998 * * --------------------------------------------------------------------- */ /* * Include files */ #include "../pblas.h" #include "../PBpblas.h" #include "../PBtools.h" #include "../PBblacs.h" #include "../PBblas.h" #ifdef __STDC__ void PB_CptrsmB( PBTYP_T * TYPE, char * DIRECB, char * SIDE, char * UPLO, char * TRANSA, char * DIAG, int M, int N, char * ALPHA, char * A, int IA, int JA, int * DESCA, char * B, int IB, int JB, int * DESCB ) #else void PB_CptrsmB( TYPE, DIRECB, SIDE, UPLO, TRANSA, DIAG, M, N, ALPHA, A, IA, JA, DESCA, B, IB, JB, DESCB ) /* * .. Scalar Arguments .. */ char * DIAG, * DIRECB, * SIDE, * TRANSA, * UPLO; int IA, IB, JA, JB, M, N; char * ALPHA; PBTYP_T * TYPE; /* * .. Array Arguments .. */ int * DESCA, * DESCB; char * A, * B; #endif { /* * Purpose * ======= * * PB_CptrsmB solves one of the matrix equations * * op( sub( A ) )*X = alpha*sub( B ), or * * X*op( sub( A ) ) = alpha*sub( B ), * * where * * sub( A ) denotes A(IA:IA+M-1,JA:JA+M-1) if SIDE = 'L', * A(IA:IA+N-1,JA:JA+N-1) if SIDE = 'R', and, * * sub( B ) denotes B(IB:IB+M-1,JB:JB+N-1). * * Alpha is a scalar, X and sub( B ) are m by n submatrices, sub( A ) is * a unit, or non-unit, upper or lower triangular submatrix and op( Y ) * is one of * * op( Y ) = Y or op( Y ) = Y' or op( Y ) = conjg( Y' ). * * The submatrix X is overwritten on sub( B ). * * This is the inner-product algorithm using the logical LCM hybrid * and static blocking techniques. The submatrix operand sub( A ) stays * in place. * * Notes * ===== * * A description vector is associated with each 2D block-cyclicly dis- * tributed matrix. This vector stores the information required to * establish the mapping between a matrix entry and its corresponding * process and memory location. * * In the following comments, the character _ should be read as * "of the distributed matrix". Let A be a generic term for any 2D * block cyclicly distributed matrix. Its description vector is DESC_A: * * NOTATION STORED IN EXPLANATION * ---------------- --------------- ------------------------------------ * DTYPE_A (global) DESCA[ DTYPE_ ] The descriptor type. * CTXT_A (global) DESCA[ CTXT_ ] The BLACS context handle, indicating * the NPROW x NPCOL BLACS process grid * A is distributed over. The context * itself is global, but the handle * (the integer value) may vary. * M_A (global) DESCA[ M_ ] The number of rows in the distribu- * ted matrix A, M_A >= 0. * N_A (global) DESCA[ N_ ] The number of columns in the distri- * buted matrix A, N_A >= 0. * IMB_A (global) DESCA[ IMB_ ] The number of rows of the upper left * block of the matrix A, IMB_A > 0. * INB_A (global) DESCA[ INB_ ] The number of columns of the upper * left block of the matrix A, * INB_A > 0. * MB_A (global) DESCA[ MB_ ] The blocking factor used to distri- * bute the last M_A-IMB_A rows of A, * MB_A > 0. * NB_A (global) DESCA[ NB_ ] The blocking factor used to distri- * bute the last N_A-INB_A columns of * A, NB_A > 0. * RSRC_A (global) DESCA[ RSRC_ ] The process row over which the first * row of the matrix A is distributed, * NPROW > RSRC_A >= 0. * CSRC_A (global) DESCA[ CSRC_ ] The process column over which the * first column of A is distributed. * NPCOL > CSRC_A >= 0. * LLD_A (local) DESCA[ LLD_ ] The leading dimension of the local * array storing the local blocks of * the distributed matrix A, * IF( Lc( 1, N_A ) > 0 ) * LLD_A >= MAX( 1, Lr( 1, M_A ) ) * ELSE * LLD_A >= 1. * * Let K be the number of rows of a matrix A starting at the global in- * dex IA,i.e, A( IA:IA+K-1, : ). Lr( IA, K ) denotes the number of rows * that the process of row coordinate MYROW ( 0 <= MYROW < NPROW ) would * receive if these K rows were distributed over NPROW processes. If K * is the number of columns of a matrix A starting at the global index * JA, i.e, A( :, JA:JA+K-1, : ), Lc( JA, K ) denotes the number of co- * lumns that the process MYCOL ( 0 <= MYCOL < NPCOL ) would receive if * these K columns were distributed over NPCOL processes. * * The values of Lr() and Lc() may be determined via a call to the func- * tion PB_Cnumroc: * Lr( IA, K ) = PB_Cnumroc( K, IA, IMB_A, MB_A, MYROW, RSRC_A, NPROW ) * Lc( JA, K ) = PB_Cnumroc( K, JA, INB_A, NB_A, MYCOL, CSRC_A, NPCOL ) * * Arguments * ========= * * TYPE (local input) pointer to a PBTYP_T structure * On entry, TYPE is a pointer to a structure of type PBTYP_T, * that contains type information (See pblas.h). * * DIRECB (global input) pointer to CHAR * On entry, DIRECB specifies the direction in which the rows * or columns of sub( B ) should be looped over as follows: * DIRECB = 'F' or 'f' forward or increasing, * DIRECB = 'B' or 'b' backward or decreasing. * * SIDE (global input) pointer to CHAR * On entry, SIDE specifies whether op( sub( A ) ) appears on * the left or right of X as follows: * * SIDE = 'L' or 'l' op( sub( A ) )*X = alpha*sub( B ), * * SIDE = 'R' or 'r' X*op( sub( A ) ) = alpha*sub( B ). * * UPLO (global input) pointer to CHAR * On entry, UPLO specifies whether the submatrix sub( A ) is * an upper or lower triangular submatrix as follows: * * UPLO = 'U' or 'u' sub( A ) is an upper triangular * submatrix, * * UPLO = 'L' or 'l' sub( A ) is a lower triangular * submatrix. * * TRANSA (global input) pointer to CHAR * On entry, TRANSA specifies the form of op( sub( A ) ) to be * used in the matrix multiplication as follows: * * TRANSA = 'N' or 'n' op( sub( A ) ) = sub( A ), * * TRANSA = 'T' or 't' op( sub( A ) ) = sub( A )', * * TRANSA = 'C' or 'c' op( sub( A ) ) = conjg( sub( A )' ). * * DIAG (global input) pointer to CHAR * On entry, DIAG specifies whether or not sub( A ) is unit * triangular as follows: * * DIAG = 'U' or 'u' sub( A ) is assumed to be unit trian- * gular, * * DIAG = 'N' or 'n' sub( A ) is not assumed to be unit tri- * angular. * * M (global input) INTEGER * On entry, M specifies the number of rows of the submatrix * sub( B ). M must be at least zero. * * N (global input) INTEGER * On entry, N specifies the number of columns of the submatrix * sub( B ). N must be at least zero. * * ALPHA (global input) pointer to CHAR * On entry, ALPHA specifies the scalar alpha. When ALPHA is * supplied as zero then the local entries of the array B * corresponding to the entries of the submatrix sub( B ) need * not be set on input. * * A (local input) pointer to CHAR * On entry, A is an array of dimension (LLD_A, Ka), where Ka is * at least Lc( 1, JA+M-1 ) when SIDE = 'L' or 'l' and is at * least Lc( 1, JA+N-1 ) otherwise. Before entry, this array * contains the local entries of the matrix A. * Before entry with UPLO = 'U' or 'u', this array contains the * local entries corresponding to the entries of the upper tri- * angular submatrix sub( A ), and the local entries correspon- * ding to the entries of the strictly lower triangular part of * the submatrix sub( A ) are not referenced. * Before entry with UPLO = 'L' or 'l', this array contains the * local entries corresponding to the entries of the lower tri- * angular submatrix sub( A ), and the local entries correspon- * ding to the entries of the strictly upper triangular part of * the submatrix sub( A ) are not referenced. * Note that when DIAG = 'U' or 'u', the local entries corres- * ponding to the diagonal elements of the submatrix sub( A ) * are not referenced either, but are assumed to be unity. * * IA (global input) INTEGER * On entry, IA specifies A's global row index, which points to * the beginning of the submatrix sub( A ). * * JA (global input) INTEGER * On entry, JA specifies A's global column index, which points * to the beginning of the submatrix sub( A ). * * DESCA (global and local input) INTEGER array * On entry, DESCA is an integer array of dimension DLEN_. This * is the array descriptor for the matrix A. * * B (local input/local output) pointer to CHAR * On entry, B is an array of dimension (LLD_B, Kb), where Kb is * at least Lc( 1, JB+N-1 ). Before entry, this array contains * the local entries of the matrix B. * On exit, the local entries of this array corresponding to the * to the entries of the submatrix sub( B ) are overwritten by * the local entries of the m by n solution submatrix. * * IB (global input) INTEGER * On entry, IB specifies B's global row index, which points to * the beginning of the submatrix sub( B ). * * JB (global input) INTEGER * On entry, JB specifies B's global column index, which points * to the beginning of the submatrix sub( B ). * * DESCB (global and local input) INTEGER array * On entry, DESCB is an integer array of dimension DLEN_. This * is the array descriptor for the matrix B. * * -- Written on April 1, 1998 by * Antoine Petitet, University of Tennessee, Knoxville 37996, USA. * * --------------------------------------------------------------------- */ /* * .. Local Scalars .. */ char Broc, TranOp, conjg, * negone, * one, * talpha, * talph0, top, * zero; int Acol, Aii, Aimb1, Ainb1, Ajj, Akp, Akq, Alcmb, Ald, Amb, An, Anb, Anp, Anp0, Anq, Anq0, Arow, Asrc, Astart, BcurrocR, Bfwd, BiiD, BiiR, Binb1D, Binb1R, BisR, Bld, BmyprocD, BmyprocR, BnD, BnR, BnbD, BnbR, BnpR, BnprocsD, BnprocsR, BrocD, BrocR, BsrcR, LNorRT, WBCfr, WBCld, WBCapbX, WBCsum, WBRfr, WBRld, WBRapbX, WBRsum, ctxt, izero=0, k, kb, kbnext, kbprev, ktmp, lside, mycol, myrow, n, nb, nbb, notran, npcol, nprow, p=0, size, tmp, upper; TZPAD_T pad; GEMM_T gemm; GSUM2D_T gsum2d; /* * .. Local Arrays .. */ int Ad0[DLEN_], DBUFB[DLEN_], WBCd[DLEN_], WBRd[DLEN_]; char * Aptr = NULL, * Bptr = NULL, * WBC = NULL, * WBR = NULL; /* .. * .. Executable Statements .. * */ /* * Retrieve process grid information */ Cblacs_gridinfo( ( ctxt = DESCA[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); Bfwd = ( Mupcase( DIRECB[0] ) == CFORWARD ); lside = ( Mupcase( SIDE [0] ) == CLEFT ); upper = ( Mupcase( UPLO [0] ) == CUPPER ); notran = ( ( TranOp = Mupcase( TRANSA[0] ) ) == CNOTRAN ); LNorRT = ( lside && notran ) || ( !( lside ) && !( notran ) ); size = TYPE->size; one = TYPE->one; zero = TYPE->zero; negone = TYPE->negone; pad = TYPE->Ftzpad; gemm = TYPE->Fgemm; gsum2d = TYPE->Cgsum2d; nb = pilaenv_( &ctxt, C2F_CHAR( &TYPE->type ) ); /* * Compute local information for sub( A ) and sub( B ) */ if( lside ) { BnD = An = M; BnR = N; Broc = CCOLUMN; BmyprocD = myrow; BnprocsD = nprow; BmyprocR = mycol; BnprocsR = npcol; BnbD = DESCB[MB_ ]; BnbR = DESCB[NB_ ]; BsrcR = DESCB[CSRC_]; Bld = DESCB[LLD_]; PB_Cinfog2l( IB, JB, DESCB, BnprocsD, BnprocsR, BmyprocD, BmyprocR, &BiiD, &BiiR, &BrocD, &BrocR ); Binb1D = PB_Cfirstnb( BnD, IB, DESCB[IMB_], BnbD ); Binb1R = PB_Cfirstnb( BnR, JB, DESCB[INB_], BnbR ); } else { BnD = An = N; BnR = M; Broc = CROW; BmyprocD = mycol; BnprocsD = npcol; BmyprocR = myrow; BnprocsR = nprow; BnbR = DESCB[MB_ ]; BnbD = DESCB[NB_ ]; BsrcR = DESCB[RSRC_]; Bld = DESCB[LLD_]; PB_Cinfog2l( IB, JB, DESCB, BnprocsR, BnprocsD, BmyprocR, BmyprocD, &BiiR, &BiiD, &BrocR, &BrocD ); Binb1D = PB_Cfirstnb( BnD, JB, DESCB[INB_], BnbD ); Binb1R = PB_Cfirstnb( BnR, IB, DESCB[IMB_], BnbR ); } /* * Compute descriptor Ad0 for sub( A ) */ PB_Cdescribe( An, An, IA, JA, DESCA, nprow, npcol, myrow, mycol, &Aii, &Ajj, &Ald, &Aimb1, &Ainb1, &Amb, &Anb, &Arow, &Acol, Ad0 ); /* * Compute conjugate of alpha for the conjugate transpose cases */ if( TranOp == CCOTRAN ) { conjg = CCONJG; talpha = PB_Cmalloc( size ); PB_Cconjg( TYPE, ALPHA, talpha ); } else { conjg = CNOCONJG; talpha = ALPHA; } /* * Retrieve BLACS combine topology, select backward ot forward substitution. */ if( LNorRT ) { top = *PB_Ctop( &ctxt, COMBINE, ROW, TOP_GET ); Astart = ( upper ? An - 1 : 0 ); } else { top = *PB_Ctop( &ctxt, COMBINE, COLUMN, TOP_GET ); Astart = ( upper ? 0 : An - 1 ); } /* * Computational partitioning size is computed as the product of the logical * value returned by pilaenv_ and 2 * lcm( nprow, npcol ). */ Alcmb = 2 * nb * PB_Clcm( ( Arow >= 0 ? nprow : 1 ), ( Acol >= 0 ? npcol : 1 ) ); /* * When sub( B ) is not replicated and backward pass on sub( B ), find the * virtual process p owning the last row or column of sub( B ). */ if( !( BisR = ( ( BsrcR < 0 ) || ( BnprocsR == 1 ) ) ) && !( Bfwd ) ) { tmp = PB_Cindxg2p( BnR - 1, Binb1R, BnbR, BrocR, BrocR, BnprocsR ); p = MModSub( tmp, BrocR, BnprocsR ); } /* * Loop over the processes rows or columns owning the BnR rows or columns of * sub( B ) to be processed. */ n = BnR; while( n > 0 ) { /* * Find out who is the active process row or column as well as the number of * rows or columns of sub( B ) it owns. */ BcurrocR = ( BisR ? -1 : MModAdd( BrocR, p, BnprocsR ) ); BnpR = PB_Cnumroc( BnR, 0, Binb1R, BnbR, BcurrocR, BrocR, BnprocsR ); n -= BnpR; /* * Re-adjust the number of rows or columns to be handled at each step, in order * to average the message sizes and the computational granularity. */ if( BnpR ) nbb = BnpR / ( ( BnpR - 1 ) / nb + 1 ); while( BnpR ) { nbb = MIN( nbb, BnpR ); /* * Describe the local contiguous panel of sub( B ) */ if( lside ) { PB_Cdescset( DBUFB, BnD, nbb, Binb1D, nbb, BnbD, BnbR, BrocD, BcurrocR, ctxt, Bld ); if( BisR || ( BmyprocR == BcurrocR ) ) Bptr = Mptr( B, BiiD, BiiR, Bld, size ); } else { PB_Cdescset( DBUFB, nbb, BnD, nbb, Binb1D, BnbR, BnbD, BcurrocR, BrocD, ctxt, Bld ); if( BisR || ( BmyprocR == BcurrocR ) ) Bptr = Mptr( B, BiiR, BiiD, Bld, size ); } talph0 = talpha; if( LNorRT ) { /* * Reuse sub( B ) and/or create vector WBC in process column owning the first * or last column of sub( A ) */ PB_CInOutV2( TYPE, &conjg, COLUMN, An, An, Astart, Ad0, nbb, Bptr, 0, 0, DBUFB, &Broc, &WBC, WBCd, &WBCfr, &WBCsum, &WBCapbX ); /* * Create WBR in process rows spanned by sub( A ) */ PB_COutV( TYPE, ROW, INIT, An, An, Ad0, nbb, &WBR, WBRd, &WBRfr, &WBRsum ); /* * Retrieve local quantities related to sub( A ) -> Ad0 */ Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ]; Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ]; Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_]; Anp = PB_Cnumroc( An, 0, Aimb1, Amb, myrow, Arow, nprow ); Anq = PB_Cnumroc( An, 0, Ainb1, Anb, mycol, Acol, npcol ); if( ( Anp > 0 ) && ( Anq > 0 ) ) Aptr = Mptr( A, Aii, Ajj, Ald, size ); WBCld = WBCd[LLD_]; WBRld = WBRd[LLD_]; if( upper ) { /* * sub( A ) is upper triangular */ for( k = ( Astart / Alcmb ) * Alcmb; k >= 0; k -= Alcmb ) { ktmp = An - k; kb = MIN( ktmp, Alcmb ); /* * Solve logical diagonal block, WBC contains the solution scattered in multiple * process columns and WBR contains the solution replicated in the process rows. */ Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow ); Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol ); PB_Cptrsm( TYPE, WBRsum, SIDE, UPLO, TRANSA, DIAG, kb, nbb, talph0, Aptr, k, k, Ad0, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, Mptr( WBR, 0, Akq, WBRld, size ), WBRld ); /* * Update: only the part of sub( B ) to be solved at the next step is locally * updated and combined, the remaining part of the matrix to be solved later * is only locally updated. */ if( Akp > 0 ) { Anq0 = PB_Cnumroc( kb, k, Ainb1, Anb, mycol, Acol, npcol ); if( WBCsum ) { kbprev = MIN( k, Alcmb ); ktmp = PB_Cnumroc( kbprev, k-kbprev, Aimb1, Amb, myrow, Arow, nprow ); Akp -= ktmp; if( ktmp > 0 ) { if( Anq0 > 0 ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &ktmp, &nbb, &Anq0, negone, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld ); Asrc = PB_Cindxg2p( k-1, Ainb1, Anb, Acol, Acol, npcol ); gsum2d( ctxt, ROW, &top, ktmp, nbb, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, myrow, Asrc ); if( mycol != Asrc ) pad( C2F_CHAR( ALL ), C2F_CHAR( NOCONJG ), &ktmp, &nbb, &izero, zero, zero, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld ); } if( ( Akp > 0 ) && ( Anq0 > 0 ) ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &Akp, &nbb, &Anq0, negone, Mptr( Aptr, 0, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, WBC, &WBCld ); } else { if( Anq0 > 0 ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &Akp, &nbb, &Anq0, negone, Mptr( Aptr, 0, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, WBC, &WBCld ); } } talph0 = one; } } else { /* * sub( A ) is lower triangular */ for( k = 0; k < An; k += Alcmb ) { ktmp = An - k; kb = MIN( ktmp, Alcmb ); /* * Solve logical diagonal block, WBC contains the solution scattered in multiple * process columns and WBR contains the solution replicated in the process rows. */ Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow ); Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol ); PB_Cptrsm( TYPE, WBRsum, SIDE, UPLO, TRANSA, DIAG, kb, nbb, talph0, Aptr, k, k, Ad0, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, Mptr( WBR, 0, Akq, WBRld, size ), WBRld ); /* * Update: only the part of sub( B ) to be solved at the next step is locally * updated and combined, the remaining part of the matrix to be solved later is * only locally updated. */ Akp = PB_Cnumroc( k+kb, 0, Aimb1, Amb, myrow, Arow, nprow ); if( ( Anp0 = Anp - Akp ) > 0 ) { Anq0 = PB_Cnumroc( kb, k, Ainb1, Anb, mycol, Acol, npcol ); if( WBCsum ) { kbnext = ktmp - kb; kbnext = MIN( kbnext, Alcmb ); ktmp = PB_Cnumroc( kbnext, k+kb, Aimb1, Amb, myrow, Arow, nprow ); Anp0 -= ktmp; if( ktmp > 0 ) { if( Anq0 > 0 ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &ktmp, &nbb, &Anq0, negone, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld ); Asrc = PB_Cindxg2p( k+kb, Ainb1, Anb, Acol, Acol, npcol ); gsum2d( ctxt, ROW, &top, ktmp, nbb, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, myrow, Asrc ); if( mycol != Asrc ) pad( C2F_CHAR( ALL ), C2F_CHAR( NOCONJG ), &ktmp, &nbb, &izero, zero, zero, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld ); } if( ( Anp0 > 0 ) && ( Anq0 > 0 ) ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &Anp0, &nbb, &Anq0, negone, Mptr( Aptr, Akp+ktmp, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, Mptr( WBC, Akp+ktmp, 0, WBCld, size ), &WBCld ); } else { if( Anq0 > 0 ) gemm( C2F_CHAR( NOTRAN ), C2F_CHAR( TRAN ), &Anp0, &nbb, &Anq0, negone, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld, talph0, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld ); } } talph0 = one; } } /* * Combine the scattered resulting matrix WBC */ if( WBCsum && ( Anp > 0 ) ) gsum2d( ctxt, ROW, &top, Anp, nbb, WBC, WBCld, myrow, WBCd[CSRC_] ); /* * sub( B ) := WBC (if necessary) */ if( WBCapbX ) PB_Cpaxpby( TYPE, &conjg, An, nbb, one, WBC, 0, 0, WBCd, COLUMN, zero, Bptr, 0, 0, DBUFB, &Broc ); } else { /* * Reuse sub( B ) and/or create vector WBR in process row owning the first or * last row of sub( A ) */ PB_CInOutV2( TYPE, &conjg, ROW, An, An, Astart, Ad0, nbb, Bptr, 0, 0, DBUFB, &Broc, &WBR, WBRd, &WBRfr, &WBRsum, &WBRapbX ); /* * Create WBC in process columns spanned by sub( A ) */ PB_COutV( TYPE, COLUMN, INIT, An, An, Ad0, nbb, &WBC, WBCd, &WBCfr, &WBCsum ); /* * Retrieve local quantities related to Ad0 -> sub( A ) */ Aimb1 = Ad0[IMB_ ]; Ainb1 = Ad0[INB_ ]; Amb = Ad0[MB_ ]; Anb = Ad0[NB_ ]; Arow = Ad0[RSRC_]; Acol = Ad0[CSRC_]; Ald = Ad0[LLD_]; Anp = PB_Cnumroc( An, 0, Aimb1, Amb, myrow, Arow, nprow ); Anq = PB_Cnumroc( An, 0, Ainb1, Anb, mycol, Acol, npcol ); if( ( Anp > 0 ) && ( Anq > 0 ) ) Aptr = Mptr( A, Aii, Ajj, Ald, size ); WBCld = WBCd[LLD_]; WBRld = WBRd[LLD_]; if( upper ) { /* * sub( A ) is upper triangular */ for( k = 0; k < An; k += Alcmb ) { ktmp = An - k; kb = MIN( ktmp, Alcmb ); /* * Solve logical diagonal block, WBR contains the solution scattered in multiple * process rows and WBC contains the solution replicated in the process columns. */ Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow ); Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol ); PB_Cptrsm( TYPE, WBCsum, SIDE, UPLO, TRANSA, DIAG, nbb, kb, talph0, Aptr, k, k, Ad0, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, Mptr( WBR, 0, Akq, WBRld, size ), WBRld ); /* * Update: only the part of sub( B ) to be solved at the next step is locally * updated and combined, the remaining part of the matrix to be solved later is * only locally updated. */ Akq = PB_Cnumroc( k+kb, 0, Ainb1, Anb, mycol, Acol, npcol ); if( ( Anq0 = Anq - Akq ) > 0 ) { Anp0 = PB_Cnumroc( kb, k, Aimb1, Amb, myrow, Arow, nprow ); if( WBRsum ) { kbnext = ktmp - kb; kbnext = MIN( kbnext, Alcmb ); ktmp = PB_Cnumroc( kbnext, k+kb, Ainb1, Anb, mycol, Acol, npcol ); Anq0 -= ktmp; if( ktmp > 0 ) { if( Anp0 > 0 ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &ktmp, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, talph0, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld ); Asrc = PB_Cindxg2p( k+kb, Aimb1, Amb, Arow, Arow, nprow ); gsum2d( ctxt, COLUMN, &top, nbb, ktmp, Mptr( WBR, 0, Akq, WBRld, size ), WBRld, Asrc, mycol ); if( myrow != Asrc ) pad( C2F_CHAR( ALL ), C2F_CHAR( NOCONJG ), &nbb, &ktmp, &izero, zero, zero, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld ); } if( ( Anp0 > 0 ) && ( Anq0 > 0 ) ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &Anq0, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, Akq+ktmp, Ald, size ), &Ald, talph0, Mptr( WBR, 0, Akq+ktmp, WBRld, size ), &WBRld ); } else { if( Anp0 > 0 ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &Anq0, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, talph0, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld ); } } talph0 = one; } } else { /* * sub( A ) is lower triangular */ for( k = ( Astart / Alcmb ) * Alcmb; k >= 0; k -= Alcmb ) { ktmp = An - k; kb = MIN( ktmp, Alcmb ); /* * Solve logical diagonal block, WBR contains the solution scattered in multiple * process rows and WBC contains the solution replicated in the process columns. */ Akp = PB_Cnumroc( k, 0, Aimb1, Amb, myrow, Arow, nprow ); Akq = PB_Cnumroc( k, 0, Ainb1, Anb, mycol, Acol, npcol ); PB_Cptrsm( TYPE, WBCsum, SIDE, UPLO, TRANSA, DIAG, nbb, kb, talph0, Aptr, k, k, Ad0, Mptr( WBC, Akp, 0, WBCld, size ), WBCld, Mptr( WBR, 0, Akq, WBRld, size ), WBRld ); /* * Update: only the part of sub( B ) to be solved at the next step is locally * updated and combined, the remaining part of the matrix to be solved later * is only locally updated. */ if( Akq > 0 ) { Anp0 = PB_Cnumroc( kb, k, Aimb1, Amb, myrow, Arow, nprow ); if( WBRsum ) { kbprev = MIN( k, Alcmb ); ktmp = PB_Cnumroc( kbprev, k-kbprev, Ainb1, Anb, mycol, Acol, npcol ); Akq -= ktmp; if( ktmp > 0 ) { if( Anp0 > 0 ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &ktmp, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, Akq, Ald, size ), &Ald, talph0, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld ); Asrc = PB_Cindxg2p( k-1, Aimb1, Amb, Arow, Arow, nprow ); gsum2d( ctxt, COLUMN, &top, nbb, ktmp, Mptr( WBR, 0, Akq, WBRld, size ), WBRld, Asrc, mycol ); if( myrow != Asrc ) pad( C2F_CHAR( ALL ), C2F_CHAR( NOCONJG ), &nbb, &ktmp, &izero, zero, zero, Mptr( WBR, 0, Akq, WBRld, size ), &WBRld ); } if( ( Anp0 > 0 ) && ( Akq > 0 ) ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &Akq, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, 0, Ald, size ), &Ald, talph0, WBR, &WBRld ); } else { if( Anp0 > 0 ) gemm( C2F_CHAR( TRAN ), C2F_CHAR( NOTRAN ), &nbb, &Akq, &Anp0, negone, Mptr( WBC, Akp, 0, WBCld, size ), &WBCld, Mptr( Aptr, Akp, 0, Ald, size ), &Ald, talph0, WBR, &WBRld ); } } talph0 = one; } } /* * Combine the scattered resulting matrix WBR */ if( WBRsum && ( Anq > 0 ) ) gsum2d( ctxt, COLUMN, &top, nbb, Anq, WBR, WBRld, WBRd[RSRC_], mycol ); /* * sub( B ) := WBR (if necessary) */ if( WBRapbX ) PB_Cpaxpby( TYPE, &conjg, nbb, An, one, WBR, 0, 0, WBRd, ROW, zero, Bptr, 0, 0, DBUFB, &Broc ); } if( WBCfr ) free( WBC ); if( WBRfr ) free( WBR ); /* * Go to the next contiguous panel if any residing in this process row or column */ BnpR -= nbb; if( BisR || ( BmyprocR == BcurrocR ) ) BiiR += nbb; } /* * Go to next or previous process row or column owning some of sub( B ) */ if( !( BisR ) ) p = ( Bfwd ? MModAdd1( p, BnprocsR ) : MModSub1( p, BnprocsR ) ); } if( TranOp == CCOTRAN ) free( talpha ); /* * End of PB_CptrsmB */ }