/* --------------------------------------------------------------------- * * -- 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 pzherk_( F_CHAR_T UPLO, F_CHAR_T TRANS, int * N, int * K, double * ALPHA, double * A, int * IA, int * JA, int * DESCA, double * BETA, double * C, int * IC, int * JC, int * DESCC ) #else void pzherk_( UPLO, TRANS, N, K, ALPHA, A, IA, JA, DESCA, BETA, C, IC, JC, DESCC ) /* * .. Scalar Arguments .. */ F_CHAR_T TRANS, UPLO; int * IA, * IC, * JA, * JC, * K, * N; double * ALPHA, * BETA; /* * .. Array Arguments .. */ int * DESCA, * DESCC; double * A, * C; #endif { /* * Purpose * ======= * * PZHERK performs one of the Hermitian rank k operations * * sub( C ) := alpha*sub( A )*conjg( sub( A )' ) + beta*sub( C ), * * or * * sub( C ) := alpha*conjg( sub( A )' )*sub( A ) + beta*sub( C ), * * where * * sub( C ) denotes C(IC:IC+N-1,JC:JC+N-1), and, * * sub( A ) denotes A(IA:IA+N-1,JA:JA+K-1) if TRANS = 'N', * A(IA:IA+K-1,JA:JA+N-1) otherwise. * * Alpha and beta are real scalars, sub( C ) is an n by n Hermitian * submatrix and sub( A ) is an n by k submatrix in the first case and a * k by n submatrix in the second case. * * 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 * ========= * * UPLO (global input) CHARACTER*1 * On entry, UPLO specifies whether the local pieces of * the array C containing the upper or lower triangular part * of the Hermitian submatrix sub( C ) are to be referenced as * follows: * * UPLO = 'U' or 'u' Only the local pieces corresponding to * the upper triangular part of the * Hermitian submatrix sub( C ) are to be * referenced, * * UPLO = 'L' or 'l' Only the local pieces corresponding to * the lower triangular part of the * Hermitian submatrix sub( C ) are to be * referenced. * * TRANS (global input) CHARACTER*1 * On entry, TRANS specifies the operation to be performed as * follows: * * TRANS = 'N' or 'n' * sub( C ) := alpha*sub( A )*conjg( sub( A )' ) + * beta*sub( C ), * * TRANS = 'C' or 'c' * sub( C ) := alpha*conjg( sub( A )' )*sub( A ) + * beta*sub( C ). * * N (global input) INTEGER * On entry, N specifies the order of the submatrix sub( C ). * N must be at least zero. * * K (global input) INTEGER * On entry, with TRANS = 'N' or 'n', K specifies the number of * columns of the submatrix sub( A ), and with TRANS = 'C' or * 'c', K specifies the number of rows of the submatrix * sub( A ). K must be at least zero. * * ALPHA (global input) DOUBLE PRECISION * On entry, ALPHA specifies the scalar alpha. When ALPHA is * supplied as zero then the local entries of the array A * corresponding to the entries of the submatrix sub( A ) need * not be set on input. * * A (local input) COMPLEX*16 array * On entry, A is an array of dimension (LLD_A, Ka), where Ka is * at least Lc( 1, JA+K-1 ) when TRANS = 'N' or 'n', 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 TRANS = 'N' or 'n', this array contains the * local entries corresponding to the entries of the n by k sub- * matrix sub( A ), otherwise the local entries corresponding to * the entries of the k by n submatrix sub( A ). * * 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. * * BETA (global input) DOUBLE PRECISION * On entry, BETA specifies the scalar beta. When BETA is * supplied as zero then the local entries of the array C * corresponding to the entries of the submatrix sub( C ) need * not be set on input. * * C (local input/local output) COMPLEX*16 array * On entry, C is an array of dimension (LLD_C, Kc), where Kc is * at least Lc( 1, JC+N-1 ). Before entry, this array contains * the local entries of the matrix C. * Before entry with UPLO = 'U' or 'u', this array contains * the local entries corresponding to the upper triangular part * of the Hermitian submatrix sub( C ), and the local entries * corresponding to the strictly lower triangular of sub( C ) * are not referenced. On exit, the upper triangular part of * sub( C ) is overwritten by the upper triangular part of the * updated submatrix. * Before entry with UPLO = 'L' or 'l', this array contains * the local entries corresponding to the lower triangular part * of the Hermitian submatrix sub( C ), and the local entries * corresponding to the strictly upper triangular of sub( C ) * are not referenced. On exit, the lower triangular part of * sub( C ) is overwritten by the lower triangular part of the * updated submatrix. * Note that the imaginary parts of the local entries corres- * ponding to the diagonal elements of sub( C ) need not be * set, they are assumed to be zero, and on exit they are set * to zero. * * IC (global input) INTEGER * On entry, IC specifies C's global row index, which points to * the beginning of the submatrix sub( C ). * * JC (global input) INTEGER * On entry, JC specifies C's global column index, which points * to the beginning of the submatrix sub( C ). * * DESCC (global and local input) INTEGER array * On entry, DESCC is an integer array of dimension DLEN_. This * is the array descriptor for the matrix C. * * -- Written on April 1, 1998 by * Antoine Petitet, University of Tennessee, Knoxville 37996, USA. * * --------------------------------------------------------------------- */ /* * .. Local Scalars .. */ char DirA, OpC, OpR, TopC, TopR, TranOp, UploC, ctop, ctopsave, rtop, rtopsave; int Ai, Aj, ChooseAC, Ci, Cj, ForceTop, ctxt, info, mycol, myrow, nb, notran, npcol, nprow, upper; double Aest, ACest, tmp1, tmp2, tmp3, tmp4; cmplx16 Calph; PBTYP_T * type; /* * .. Local Arrays .. */ int Ad[DLEN_], Cd[DLEN_]; /* .. * .. Executable Statements .. * */ upper = ( ( UploC = Mupcase( F2C_CHAR( UPLO )[0] ) ) == CUPPER ); notran = ( ( TranOp = Mupcase( F2C_CHAR( TRANS )[0] ) ) == CNOTRAN ); PB_CargFtoC( *IA, *JA, DESCA, &Ai, &Aj, Ad ); PB_CargFtoC( *IC, *JC, DESCC, &Ci, &Cj, Cd ); #ifndef NO_ARGCHK /* * Test the input parameters */ Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); if( !( info = ( ( nprow == -1 ) ? -( 901 + CTXT_ ) : 0 ) ) ) { if( ( !upper ) && ( UploC != CLOWER ) ) { PB_Cwarn( ctxt, __LINE__, "PZHERK", "Illegal UPLO = %c\n", UploC ); info = -1; } else if( ( !notran ) && ( TranOp != CCOTRAN ) ) { PB_Cwarn( ctxt, __LINE__, "PZHERK", "Illegal TRANS = %c\n", TranOp ); info = -2; } if( notran ) PB_Cchkmat( ctxt, "PZHERK", "A", *N, 3, *K, 4, Ai, Aj, Ad, 9, &info ); else PB_Cchkmat( ctxt, "PZHERK", "A", *K, 4, *N, 3, Ai, Aj, Ad, 9, &info ); PB_Cchkmat( ctxt, "PZHERK", "C", *N, 3, *N, 3, Ci, Cj, Cd, 14, &info ); } if( info ) { PB_Cabort( ctxt, "PZHERK", info ); return; } #endif /* * Quick return if possible */ if( ( *N == 0 ) || ( ( ( ALPHA[REAL_PART] == ZERO ) || ( *K == 0 ) ) && ( BETA[REAL_PART] == ONE ) ) ) return; /* * Get type structure */ type = PB_Cztypeset(); /* * And when alpha or K is zero */ if( ( ALPHA[REAL_PART] == ZERO ) || ( *K == 0 ) ) { if( BETA[REAL_PART] == ZERO ) { PB_Cplapad( type, &UploC, NOCONJG, *N, *N, type->zero, type->zero, ((char *) C), Ci, Cj, Cd ); } else { PB_Cplascal( type, &UploC, CONJG, *N, *N, ((char *) BETA), ((char *) C), Ci, Cj, Cd ); } return; } /* * Start the operations */ #ifdef NO_ARGCHK Cblacs_gridinfo( ( ctxt = Ad[CTXT_] ), &nprow, &npcol, &myrow, &mycol ); #endif Calph[REAL_PART] = ALPHA[REAL_PART]; Calph[IMAG_PART] = ZERO; /* * Algorithm selection is based on approximation of the communication volume * for distributed and aligned operands. * * ACest: both operands sub( A ) and sub( C ) are communicated (K >> N) * Aest : only sub( A ) is communicated (N >> K) */ if( notran ) { tmp1 = DNROC( *N, Cd[MB_], nprow ); tmp3 = DNROC( *K, Ad[NB_], npcol ); ACest = (double)(*N) * ( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp3 ) + ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : CBRATIO * tmp1 / TWO ) ); tmp1 = DNROC( *N, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp4 = DNROC( *N, Ad[MB_], nprow ); Aest = (double)(*K) * ( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp1 ) + ( nprow == 1 ? ZERO : tmp2 ) + MAX( tmp2, tmp4 ) ); } else { tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp4 = DNROC( *K, Ad[MB_], nprow ); ACest = (double)(*N) * ( ( ( ( Ad[CSRC_] == -1 ) || ( npcol == 1 ) ) ? ZERO : tmp4 ) + ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : CBRATIO * tmp2 / TWO ) ); tmp1 = DNROC( *N, Cd[MB_], nprow ); tmp2 = DNROC( *N, Cd[NB_], npcol ); tmp3 = DNROC( *N, Ad[NB_], npcol ); Aest = (double)(*K) * ( ( ( ( Ad[RSRC_] == -1 ) || ( nprow == 1 ) ) ? ZERO : tmp2 ) + ( npcol == 1 ? ZERO : tmp1 ) + MAX( tmp1, tmp3 ) ); } /* * Shift a little the cross-over point between both algorithms. */ ChooseAC = ( ( 1.3 * ACest ) <= Aest ); /* * BLACS topologies are enforced iff N and K 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 = ( ( *N > nb ) && ( *K > nb ) ); if( ChooseAC ) { if( notran ) { OpC = CBCAST; ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { OpR = CCOMBINE; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); rtopsave = rtop; ctopsave = ctop; if( upper ) { TopR = CTOP_IRING; TopC = CTOP_DRING; } else { TopR = CTOP_DRING; TopC = CTOP_IRING; } ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, &TopC ); rtop = *PB_Ctop( &ctxt, &OpR, ROW, &TopR ); /* * Remove the next line when the BLACS combine operations support ring * topologies */ rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_DEFAULT ); } DirA = ( ctop == CTOP_DRING ? CBACKWARD : CFORWARD ); } else { OpR = CBCAST; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); if( ForceTop ) { OpC = CCOMBINE; ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); rtopsave = rtop; ctopsave = ctop; if( upper ) { TopR = CTOP_IRING; TopC = CTOP_DRING; } else { TopR = CTOP_DRING; TopC = CTOP_IRING; } rtop = *PB_Ctop( &ctxt, &OpR, ROW, &TopR ); ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, &TopC ); /* * Remove the next line when the BLACS combine operations support ring * topologies */ ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_DEFAULT ); } DirA = ( rtop == CTOP_DRING ? CBACKWARD : CFORWARD ); } PB_CpsyrkAC( type, &DirA, CONJG, &UploC, ( notran ? NOTRAN : COTRAN ), *N, *K, ((char *)Calph), ((char *)A), Ai, Aj, Ad, ((char *)BETA), ((char *)C), Ci, Cj, Cd ); } else { if( notran ) { OpR = CBCAST; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); if( ForceTop ) { OpC = CBCAST; ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); 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 ); if( ( ctop != CTOP_DRING ) && ( ctop != CTOP_IRING ) && ( ctop != CTOP_SRING ) ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_SRING ); } DirA = ( rtop == CTOP_DRING ? CBACKWARD : CFORWARD ); } else { OpC = CBCAST; ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_GET ); if( ForceTop ) { OpR = CBCAST; rtop = *PB_Ctop( &ctxt, &OpR, ROW, TOP_GET ); 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 ); if( ( ctop != CTOP_DRING ) && ( ctop != CTOP_IRING ) && ( ctop != CTOP_SRING ) ) ctop = *PB_Ctop( &ctxt, &OpC, COLUMN, TOP_SRING ); } DirA = ( ctop == CTOP_DRING ? CBACKWARD : CFORWARD ); } PB_CpsyrkA( type, &DirA, CONJG, &UploC, ( notran ? NOTRAN : COTRAN ), *N, *K, ((char *)Calph), ((char *)A), Ai, Aj, Ad, ((char *)BETA), ((char *)C), Ci, Cj, Cd ); } /* * Restore the BLACS topologies when necessary. */ if( ForceTop ) { rtopsave = *PB_Ctop( &ctxt, &OpR, ROW, &rtopsave ); ctopsave = *PB_Ctop( &ctxt, &OpC, COLUMN, &ctopsave ); } /* * End of PZHERK */ }