/* --------------------------------------------------------------------- * * -- PBLAS 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 pctrmm_( F_CHAR_T SIDE, F_CHAR_T UPLO, F_CHAR_T TRANS, F_CHAR_T DIAG, int * M, int * N, float * ALPHA, float * A, int * IA, int * JA, int * DESCA, float * B, int * IB, int * JB, int * DESCB ) #else void pctrmm_( SIDE, UPLO, TRANS, DIAG, M, N, ALPHA, A, IA, JA, DESCA, B, IB, JB, DESCB ) /* * .. Scalar Arguments .. */ F_CHAR_T DIAG, SIDE, TRANS, UPLO; int * IA, * IB, * JA, * JB, * M, * N; float * ALPHA; /* * .. Array Arguments .. */ int * DESCA, * DESCB; float * A, * B; #endif { /* * Purpose * ======= * * PCTRMM performs one of the matrix-matrix operations * * sub( B ) := alpha * op( sub( A ) ) * sub( B ), * * or * * sub( B ) := alpha * sub( B ) * op( sub( A ) ), * * 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, sub( B ) is an m by n submatrix, sub( A ) is a * unit, or non-unit, upper or lower triangular submatrix and op( X ) is * one of * * op( X ) = X or op( X ) = X' or op( X ) = conjg( X' ). * * 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 * ========= * * SIDE (global input) CHARACTER*1 * On entry, SIDE specifies whether op( sub( A ) ) multiplies * sub( B ) from the left or right as follows: * * SIDE = 'L' or 'l' sub( B ) := alpha*op( sub( A ) )*sub( B ), * * SIDE = 'R' or 'r' sub( B ) := alpha*sub( B )*op( sub( A ) ). * * UPLO (global input) CHARACTER*1 * 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) CHARACTER*1 * 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) CHARACTER*1 * 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) COMPLEX * 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) COMPLEX array * 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) COMPLEX array * 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 transformed 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 DiagA, DirB, OpC, OpR, SideOp, TopC, TopR, TranOp, UploA, Var, ctop, ctopsave, rtop, rtopsave; int Ai, Aj, Bi, Bj, ChooseAB, ForceTop, ctxt, info, lside, mycol, myrow, nb, notran, nounit, npcol, nprow, upper; double ABestL, ABestR, Best, tmp1, tmp2, tmp3, tmp4; PBTYP_T * type; /* * .. Local Arrays .. */ int Ad[DLEN_], Bd[DLEN_]; /* .. * .. Executable Statements .. * */ lside = ( ( SideOp = Mupcase( F2C_CHAR( SIDE )[0] ) ) == CLEFT ); upper = ( ( UploA = Mupcase( F2C_CHAR( UPLO )[0] ) ) == CUPPER ); notran = ( ( TranOp = Mupcase( F2C_CHAR( TRANS )[0] ) ) == CNOTRAN ); nounit = ( ( DiagA = Mupcase( F2C_CHAR( DIAG )[0] ) ) == CNOUNIT ); PB_CargFtoC( *IA, *JA, DESCA, &Ai, &Aj, Ad ); PB_CargFtoC( *IB, *JB, DESCB, &Bi, &Bj, Bd ); #ifndef NO_ARGCHK /* * Test the input parameters */ Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); if( !( info = ( ( nprow == -1 ) ? -( 1101 + CTXT_ ) : 0 ) ) ) { if( ( !lside ) && ( SideOp != CRIGHT ) ) { PB_Cwarn( ctxt, __LINE__, "PCTRMM", "Illegal SIDE = %c\n", SideOp ); info = -1; } else if( ( !upper ) && ( UploA != CLOWER ) ) { PB_Cwarn( ctxt, __LINE__, "PCTRMM", "Illegal UPLO = %c\n", UploA ); info = -2; } else if( ( !notran ) && ( TranOp != CTRAN ) && ( TranOp != CCOTRAN ) ) { PB_Cwarn( ctxt, __LINE__, "PCTRMM", "Illegal TRANS = %c\n", TranOp ); info = -3; } if( ( !nounit ) && ( DiagA != CUNIT ) ) { PB_Cwarn( ctxt, __LINE__, "PCTRMM", "Illegal DIAG = %c\n", DiagA ); info = -4; } if( lside ) PB_Cchkmat( ctxt, "PCTRMM", "A", *M, 5, *M, 5, Ai, Aj, Ad, 11, &info ); else PB_Cchkmat( ctxt, "PCTRMM", "A", *N, 6, *N, 6, Ai, Aj, Ad, 11, &info ); PB_Cchkmat( ctxt, "PCTRMM", "B", *M, 5, *N, 6, Bi, Bj, Bd, 15, &info ); } if( info ) { PB_Cabort( ctxt, "PCTRMM", info ); return; } #endif /* * Quick return if possible */ if( *M == 0 || *N == 0 ) return; /* * Get type structure */ type = PB_Cctypeset(); /* * And when alpha is zero */ if( ( ALPHA[REAL_PART] == ZERO ) && ( ALPHA[IMAG_PART] == ZERO ) ) { PB_Cplapad( type, ALL, NOCONJG, *M, *N, type->zero, type->zero, ((char *) B), Bi, Bj, Bd ); return; } /* * Start the operations */ #ifdef NO_ARGCHK Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); #endif /* * Algorithm selection is based on approximation of the communication volume * for distributed and aligned operands. * * ABestR, ABestL : both operands sub( A ) and sub( B ) are communicated * ( N >> M when SIDE is left and M >> N otherwise ) * Best : only sub( B ) is communicated * ( M >> N when SIDE is left and N >> M otherwise ) */ if( lside ) { if( notran ) { tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp4 = DNROC( *N, Bd[NB_], npcol ); ABestR = (double)(*M) * ( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) + ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) ); tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *M, Ad[NB_], npcol ); tmp4 = DNROC( *M, Bd[MB_], nprow ); Best = (double)(*N) * ( CBRATIO * ( npcol == 1 ? ZERO : tmp1 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ) ); ChooseAB = ( ( 1.1 * ABestR ) <= Best ); } else { tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *M, Ad[NB_], npcol ); tmp4 = DNROC( *N, Bd[NB_], npcol ); ABestL = (double)(*M) * ( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) + CBRATIO * ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) ); ABestR = (double)(*M) * ( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 / TWO ) + ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp4 ) + MAX( tmp2, tmp1 ) / TWO ); tmp1 = DNROC( *M, Ad[MB_], nprow ); tmp2 = DNROC( *M, Ad[NB_], npcol ); tmp4 = DNROC( *M, Bd[MB_], nprow ); Best = (double)(*N) * ( ( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + CBRATIO * ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ) ); ChooseAB = ( ( ( 1.1 * ABestL ) <= Best ) || ( ( 1.1 * ABestR ) <= Best ) ); } } else { if( notran ) { tmp2 = DNROC( *N, Ad[NB_], npcol ); tmp3 = DNROC( *M, Bd[MB_], nprow ); ABestR = (double)(*N) * ( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) + ( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) ); tmp1 = DNROC( *N, Ad[MB_], nprow ); tmp2 = DNROC( *N, Ad[NB_], npcol ); tmp3 = DNROC( *N, Bd[NB_], npcol ); Best = (double)(*M) * ( CBRATIO * ( nprow == 1 ? ZERO : tmp2 ) + ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) ); ChooseAB = ( ( 1.1 * ABestR ) <= Best ); } else { tmp1 = DNROC( *N, Ad[MB_], nprow ); tmp2 = DNROC( *N, Ad[NB_], npcol ); tmp3 = DNROC( *M, Bd[MB_], nprow ); ABestL = (double)(*N) * ( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) + CBRATIO * ( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) ); ABestR = (double)(*N) * ( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 / TWO ) + ( ( ( Bd[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp3 ) + MAX( tmp2, tmp1 ) / TWO ); tmp1 = DNROC( *N, Ad[MB_], nprow ); tmp2 = DNROC( *N, Ad[NB_], npcol ); tmp3 = DNROC( *N, Bd[NB_], npcol ); Best = (double)(*M) * ( ( ( ( Bd[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ) + CBRATIO * ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) ); ChooseAB = ( ( ( 1.1 * ABestL ) <= Best ) || ( ( 1.1 * ABestR ) <= Best ) ); } } /* * BLACS topologies are enforced iff M and N are strictly greater than the * logical block size returned by pilaenv_. Otherwise, it is assumed that the * routine calling this routine has already selected an adequate topology. */ nb = pilaenv_( &ctxt, C2F_CHAR( &type->type ) ); ForceTop = ( ( *M > nb ) && ( *N > nb ) ); if( ChooseAB ) { if( lside ) { if( notran ) { OpR = CBCAST; OpC = CBCAST; Var = CRIGHT; if( upper ) { TopR = TopC = CTOP_IRING; } else { TopR = TopC = CTOP_DRING; } } else { if( ABestL <= ABestR ) { OpR = CBCAST; OpC = CCOMBINE; Var = CLEFT; if( upper ) { TopR = CTOP_DRING; TopC = CTOP_IRING; } else { TopR = CTOP_IRING; TopC = CTOP_DRING; } } else { OpR = CBCAST; OpC = CBCAST; Var = CRIGHT; if( upper ) { TopR = TopC = CTOP_DRING; } else { TopR = TopC = CTOP_IRING; } } } } else { if( notran ) { OpR = CBCAST; OpC = CBCAST; Var = CRIGHT; if( upper ) { TopR = TopC = CTOP_DRING; } else { TopR = TopC = CTOP_IRING; } } else { if( ABestL <= ABestR ) { OpR = CCOMBINE; OpC = CBCAST; Var = CLEFT; if( upper ) { TopR = CTOP_DRING; TopC = CTOP_IRING; } else { TopR = CTOP_IRING; TopC = CTOP_DRING; } } else { OpR = CBCAST; OpC = CBCAST; Var = CRIGHT; if( upper ) { TopR = TopC = CTOP_IRING; } else { TopR = TopC = CTOP_DRING; } } } } rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { if( ( rtopsave = rtop ) != TopR ) rtop = *PB_Ctop( &ctxt, &OpR, ROW, &TopR ); if( ( ctopsave = ctop ) != TopC ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, &TopC ); /* * Remove the next 4 lines when the BLACS combine operations support ring * topologies */ if( OpR == CCOMBINE ) rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT ); if( OpC == CCOMBINE ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT ); } PB_CptrmmAB( type, &Var, &SideOp, &UploA, &TranOp, &DiagA, *M, *N, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad, ((char *)B), Bi, Bj, Bd ); } else { if( ( lside && notran ) || ( !( lside ) && !( notran ) ) ) { OpR = CCOMBINE; OpC = CBCAST; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { rtopsave = rtop; ctopsave = ctop; /* * No clear winner for the ring topologies, so that if a ring topology is * already selected, keep it. */ if( ( rtop != CTOP_DRING ) && ( rtop != CTOP_IRING ) && ( rtop != CTOP_SRING ) ) rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_SRING ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT ); /* * Remove the next line when the BLACS combine operations support ring * topologies */ rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT ); } } else { OpR = CBCAST; OpC = CCOMBINE; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { rtopsave = rtop; ctopsave = ctop; /* * No clear winner for the ring topologies, so that if a ring topology is * already selected, keep it. */ if( ( ctop != CTOP_DRING ) && ( ctop != CTOP_IRING ) && ( ctop != CTOP_SRING ) ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_SRING ); rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT ); /* * Remove the next line when the BLACS combine operations support ring * topologies */ ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT ); } } if( lside ) DirB = ( rtop == CTOP_DRING ? CBACKWARD : CFORWARD ); else DirB = ( ctop == CTOP_DRING ? CBACKWARD : CFORWARD ); PB_CptrmmB( type, &DirB, &SideOp, &UploA, &TranOp, &DiagA, *M, *N, ((char *)ALPHA), ((char *)A), Ai, Aj, Ad, ((char *)B), Bi, Bj, Bd ); } /* * Restore the BLACS topologies when necessary. */ if( ForceTop ) { rtopsave = *PB_Ctop( &ctxt, &OpR, ROW, &rtopsave ); ctopsave = *PB_Ctop( &ctxt, &OpC, COLUMN, &ctopsave ); } /* * End of PCTRMM */ }