SUBROUTINE PCGEQRRV( M, N, A, IA, JA, DESCA, TAU, WORK ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 28, 2001 * * .. Scalar Arguments .. INTEGER IA, JA, M, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX A( * ), TAU( * ), WORK( * ) * .. * * Purpose * ======= * * PCGEQRRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from Q, R * computed by PCGEQRF. * * Notes * ===== * * Each global data object is described by an associated description * vector. This vector stores the information required to establish * the mapping between an object element and its corresponding process * and memory location. * * Let A be a generic term for any 2D block cyclicly distributed array. * Such a global array has an associated description vector DESCA. * In the following comments, the character _ should be read as * "of the global array". * * NOTATION STORED IN EXPLANATION * --------------- -------------- -------------------------------------- * DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case, * DTYPE_A = 1. * CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating * the BLACS process grid A is distribu- * ted over. The context itself is glo- * bal, but the handle (the integer * value) may vary. * M_A (global) DESCA( M_ ) The number of rows in the global * array A. * N_A (global) DESCA( N_ ) The number of columns in the global * array A. * MB_A (global) DESCA( MB_ ) The blocking factor used to distribute * the rows of the array. * NB_A (global) DESCA( NB_ ) The blocking factor used to distribute * the columns of the array. * RSRC_A (global) DESCA( RSRC_ ) The process row over which the first * row of the array A is distributed. * CSRC_A (global) DESCA( CSRC_ ) The process column over which the * first column of the array A is * distributed. * LLD_A (local) DESCA( LLD_ ) The leading dimension of the local * array. LLD_A >= MAX(1,LOCr(M_A)). * * Let K be the number of rows or columns of a distributed matrix, * and assume that its process grid has dimension p x q. * LOCr( K ) denotes the number of elements of K that a process * would receive if K were distributed over the p processes of its * process column. * Similarly, LOCc( K ) denotes the number of elements of K that a * process would receive if K were distributed over the q processes of * its process row. * The values of LOCr() and LOCc() may be determined via a call to the * ScaLAPACK tool function, NUMROC: * LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ), * LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ). * An upper bound for these quantities may be computed by: * LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A * LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A * * Arguments * ========= * * M (global input) INTEGER * The number of rows to be operated on, i.e. the number of rows * of the distributed submatrix sub( A ). M >= 0. * * N (global input) INTEGER * The number of columns to be operated on, i.e. the number of * columns of the distributed submatrix sub( A ). N >= 0. * * A (local input/local output) COMPLEX pointer into the * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). * On entry, sub( A ) contains the the factors Q and R computed * by PCGEQRF. On exit, the original matrix is restored. * * IA (global input) INTEGER * The row index in the global array A indicating the first * row of sub( A ). * * JA (global input) INTEGER * The column index in the global array A indicating the * first column of sub( A ). * * DESCA (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix A. * * TAU (local input) COMPLEX, array, dimension * LOCc(JA+MIN(M,N)-1). This array contains the scalar factors * TAU of the elementary reflectors computed by PCGEQRF. TAU * is tied to the distributed matrix A. * * WORK (local workspace) COMPLEX array, dimension (LWORK) * LWORK = NB_A * ( 2*Mp0 + Nq0 + NB_A ), where * Mp0 = NUMROC( M+IROFF, MB_A, MYROW, IAROW, NPROW ) * NB_A, * Nq0 = NUMROC( N+ICOFF, NB_A, MYCOL, IACOL, NPCOL ) * MB_A, * IROFF = MOD( IA-1, MB_A ), ICOFF = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), * NPROW ), * IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), * NPCOL ), * and NUMROC, INDXG2P are ScaLAPACK tool functions; * MYROW, MYCOL, NPROW and NPCOL can be determined by calling * the subroutine BLACS_GRIDINFO. * * ===================================================================== * * .. Parameters .. INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_, $ LLD_, MB_, M_, NB_, N_, RSRC_ PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1, $ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6, $ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 ) COMPLEX ONE, ZERO PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ), $ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. CHARACTER COLBTOP, ROWBTOP INTEGER IACOL, IAROW, I, ICTXT, IIA, IPT, IPV, IPW, $ IROFF, IV, J, JB, JJA, JL, JN, K, MP, MYCOL, $ MYROW, NPCOL, NPROW * .. * .. Local Arrays .. INTEGER DESCV( DLEN_ ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCLACPY, $ PCLARFB, PCLARFT, PCLASET, PB_TOPGET, $ PB_TOPSET * .. * .. External Functions .. INTEGER ICEIL, INDXG2P, NUMROC EXTERNAL ICEIL, INDXG2P, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * IROFF = MOD( IA-1, DESCA( MB_ ) ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) IPV = 1 IPT = IPV + MP * DESCA( NB_ ) IPW = IPT + DESCA( NB_ ) * DESCA( NB_ ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'D-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) * K = MIN( M, N ) JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+K-1 ) JL = MAX( ( (JA+K-2) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1, JA ) * CALL DESCSET( DESCV, M+IROFF, DESCA( NB_ ), DESCA( MB_ ), $ DESCA( NB_ ), IAROW, INDXG2P( JL, DESCA( NB_ ), $ MYCOL, DESCA( CSRC_ ), NPCOL ), ICTXT, $ MAX( 1, MP ) ) * DO 10 J = JL, JN+1, -DESCA( NB_ ) JB = MIN( JA+K-J, DESCA( NB_ ) ) I = IA + J - JA IV = 1 + J - JA + IROFF * * Compute upper triangular matrix T * CALL PCLARFT( 'Forward', 'Columnwise', M-I+IA, JB, A, I, J, $ DESCA, TAU, WORK( IPT ), WORK( IPW ) ) * * Copy Householder vectors into workspace * CALL PCLACPY( 'Lower', M-I+IA, JB, A, I, J, DESCA, WORK( IPV ), $ IV, 1, DESCV ) CALL PCLASET( 'Upper', M-I+IA, JB, ZERO, ONE, WORK( IPV ), IV, $ 1, DESCV ) * * Zeroes the strict lower triangular part of sub( A ) to get * block column of R * CALL PCLASET( 'Lower', M-I+IA-1, JB, ZERO, ZERO, A, I+1, J, $ DESCA ) * * Apply block Householder transformation * CALL PCLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise', $ M-I+IA, N-J+JA, JB, WORK( IPV ), IV, 1, DESCV, $ WORK( IPT ), A, I, J, DESCA, WORK( IPW ) ) * DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL ) * 10 CONTINUE * * Handle first block separately * JB = JN - JA + 1 * * Compute upper triangular matrix T * CALL PCLARFT( 'Forward', 'Columnwise', M, JB, A, IA, JA, DESCA, $ TAU, WORK( IPT ), WORK( IPW ) ) * * Copy Householder vectors into workspace * CALL PCLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPV ), $ IROFF+1, 1, DESCV ) CALL PCLASET( 'Upper', M, JB, ZERO, ONE, WORK, IROFF+1, 1, DESCV ) * * Zeroes the strict lower triangular part of sub( A ) to get block * column of R * CALL PCLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA ) * * Apply block Householder transformation * CALL PCLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise', M, $ N, JB, WORK( IPV ), IROFF+1, 1, DESCV, WORK( IPT ), $ A, IA, JA, DESCA, WORK( IPW ) ) * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * RETURN * * End of PCGEQRRV * END