SUBROUTINE PCGELQRV( 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 * ======= * * PCGELQRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from L, Q * computed by PCGELQF. * * 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 L and Q computed * by PCGELQF. 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 * LOCr(IA+MIN(M,N)-1). This array contains the scalar factors * TAU of the elementary reflectors computed by PCGELQF. TAU * is tied to the distributed matrix A. * * WORK (local workspace) COMPLEX array, dimension * LWORK = MB_A * ( Mp0 + 2*Nq0 + MB_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. * * ===================================================================== * * .. 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 I, IACOL, IAROW, IB, ICOFF, ICTXT, IIA, IL, IN, $ IPT, IPV, IPW, J, JJA, JV, K, MYCOL, MYROW, $ NPCOL, NPROW, NQ * .. * .. Local Arrays .. INTEGER DESCV( DLEN_ ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PCLACPY, $ PCLARFB, PCLARFT, PCLASET * .. * .. External Functions .. INTEGER ICEIL, NUMROC EXTERNAL ICEIL, NUMROC * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * K = MIN( M, N ) IN = MIN( ICEIL( IA, DESCA( MB_ ) ) * DESCA( MB_ ), IA+K-1 ) IL = MAX( ( (IA+K-2) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) * ICOFF = MOD( JA-1, DESCA( NB_ ) ) CALL INFOG2L( IL, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL ) IPV = 1 IPT = IPV + NQ * DESCA( MB_ ) IPW = IPT + DESCA( MB_ ) * DESCA( MB_ ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'D-ring' ) * CALL DESCSET( DESCV, DESCA( MB_ ), N + ICOFF, DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) * DO 10 I = IL, IN+1, -DESCA( MB_ ) IB = MIN( IA+K-I, DESCA( MB_ ) ) J = JA + I - IA JV = 1 + I - IA + ICOFF * * Compute upper triangular matrix T * CALL PCLARFT( 'Forward', 'Rowwise', N-J+JA, IB, A, I, J, DESCA, $ TAU, WORK( IPT ), WORK( IPW ) ) * * Copy Householder vectors into workspace * CALL PCLACPY( 'Upper', IB, N-J+JA, A, I, J, DESCA, WORK( IPV ), $ 1, JV, DESCV ) CALL PCLASET( 'Lower', IB, N-J+JA, ZERO, ONE, WORK( IPV ), 1, $ JV, DESCV ) * * Zeroes the strict upper triangular part of sub( A ) to get * block column of L * CALL PCLASET( 'Upper', IB, N-J+JA-1, ZERO, ZERO, A, I, J+1, $ DESCA ) * * Apply block Householder transformation * CALL PCLARFB( 'Right', 'Conjugate transpose', 'Forward', $ 'Rowwise', M-I+IA, N-J+JA, IB, WORK( IPV ), 1, $ JV, DESCV, WORK( IPT ), A, I, J, DESCA, $ WORK( IPW ) ) * DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + NPROW - 1, NPROW ) * 10 CONTINUE * * Handle first block separately * IB = IN - IA + 1 * * Compute upper triangular matrix T * CALL PCLARFT( 'Forward', 'Rowwise', N, IB, A, IA, JA, DESCA, TAU, $ WORK( IPT ), WORK( IPW ) ) * * Copy Householder vectors into workspace * CALL PCLACPY( 'Upper', IB, N, A, IA, JA, DESCA, WORK( IPV ), 1, $ ICOFF+1, DESCV ) CALL PCLASET( 'Lower', IB, N, ZERO, ONE, WORK, 1, ICOFF+1, DESCV ) * * Zeroes the strict upper triangular part of sub( A ) to get * block column of L * CALL PCLASET( 'Upper', IB, N-1, ZERO, ZERO, A, IA, JA+1, DESCA ) * * Apply block Householder transformation * CALL PCLARFB( 'Right', 'Conjugate transpose', 'Forward', $ 'Rowwise', M, N, IB, WORK( IPV ), 1, ICOFF+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 PCGELQRV * END