SUBROUTINE PSGETRRV( M, N, A, IA, JA, DESCA, IPIV, 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( * ), IPIV( * ) REAL A( * ), WORK( * ) * .. * * Purpose * ======= * * PSGETRRV reforms sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from the * triangular matrices L and U returned by PSGETRF. It multiplies * an upper triangular matrix stored in the upper triangle of sub( A ) * times the unit lower triangular matrix stored in the lower triangle. * To accomplish this, the routine basically performs the PSGETRF * routine in reverse. * * It computes L*U first, and then apply P: P*L*U => sub( A ). In the * J-th loop, the block column (or column panel), which has the lower * triangular unit matrix L is multiplied with the block row (or row * panel), which contains the upper triangular matrix U. * * ( L1 ) ( 0 0 ) ( L1*U1 L1*U2 ) * A` = L * U + A` = ( ) * (U1 U2) + ( ) = ( ) * ( L2 ) ( 0 A`) ( L2*U1 L2*U2+A` ) * * where L1 is a lower unit triangular matrix and U1 is an upper * triangular matrix. * * 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) REAL pointer into the * local memory to an array of dimension (LLD_A, LOCc(JA+N-1)). * On entry, the local pieces of the distributed matrix sub( A ) * contains the the factors L and U from the factorization * sub( A ) = P*L*U; the unit diagonal elements of L are not * stored. On exit, the original distributed matrix sub( A ) * 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. * * IPIV (local input) INTEGER array, dimension ( LOCr(M_A)+MB_A ) * This array contains the pivoting information. * IPIV(i) -> The global row local row i was swapped with. * This array is tied to the distributed matrix A. * * WORK (local workspace) REAL array of dimension (LWORK) * LWORK >= MpA0 * NB_A + NqA0 * MB_A, where * * IROFFA = MOD( IA-1, MB_A ), ICOFFA = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), * NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * * WORK is used to store a block of columns of L, and a block of * rows of U. INDXG2P and NUMROC 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 ) REAL ONE, ZERO PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 ) * .. * .. Local Scalars .. CHARACTER COLBTOP, ROWBTOP INTEGER IACOL, IAROW, ICTXT, IL, IPL, IPU, IROFF, J, $ JB, JL, JN, MN, MP, MYCOL, MYROW, NPCOL, NPROW * .. Local Arrays .. INTEGER DESCIP( DLEN_ ), DESCL( DLEN_ ), $ DESCU( DLEN_ ), IDUM( 1 ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, PSGEMM, PSLACPY, $ PSLAPIV, PSLASET, 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_ ) ) IAROW = INDXG2P( IA, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) IPL = 1 IPU = IPL + MP * DESCA( NB_ ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) * * Define array descriptors for L and U * MN = MIN( M, N ) IL = MAX( ( ( IA+MN-2 ) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) JL = MAX( ( ( JA+MN-2 ) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1, JA ) JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+MN-1 ) IAROW = INDXG2P( IL, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) IACOL = INDXG2P( JL, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL ) * CALL DESCSET( DESCL, IA+M-IL, DESCA( NB_ ), DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, MAX( 1, MP ) ) * CALL DESCSET( DESCU, DESCA( MB_ ), JA+N-JL, DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) * CALL DESCSET( DESCIP, DESCA( M_ ) + DESCA( MB_ )*NPROW, 1, $ DESCA( MB_ ), 1, DESCA( RSRC_ ), MYCOL, ICTXT, $ NUMROC( DESCA( M_ ), DESCA( MB_ ), MYROW, $ DESCA( RSRC_ ), NPROW ) + DESCA( MB_ ) ) * * DO 10 J = JL, JN+1, -DESCA( NB_ ) * JB = MIN( JA+MN-J, DESCA( NB_ ) ) * * Copy unit lower triangular part of sub( A ) into WORK * CALL PSLACPY( 'Lower', M-IL+IA, JB, A, IL, J, DESCA, $ WORK( IPL ), 1, 1, DESCL ) CALL PSLASET( 'Upper', M-IL+IA, JB, ZERO, ONE, WORK( IPL ), $ 1, 1, DESCL ) * * Copy upper triangular part of sub( A ) into WORK(IPU) * CALL PSLACPY( 'Upper', JB, JA+N-J, A, IL, J, DESCA, $ WORK( IPU ), 1, 1, DESCU ) CALL PSLASET( 'Lower', JB-1, JA+N-J, ZERO, ZERO, $ WORK( IPU ), 2, 1, DESCU ) * * Zero the strict lower triangular piece of the current block. * CALL PSLASET( 'Lower', IA+M-IL-1, JB, ZERO, ZERO, A, IL+1, J, $ DESCA ) * * Zero the upper triangular piece of the current block. * CALL PSLASET( 'Upper', JB, JA+N-J, ZERO, ZERO, A, IL, J, $ DESCA ) * * Update the matrix sub( A ). * CALL PSGEMM( 'No transpose', 'No transpose', IA+M-IL, $ JA+N-J, JB, ONE, WORK( IPL ), 1, 1, DESCL, $ WORK( IPU ), 1, 1, DESCU, ONE, A, IL, J, DESCA ) * IL = IL - DESCA( MB_ ) DESCL( M_ ) = DESCL( M_ ) + DESCL( MB_ ) DESCL( RSRC_ ) = MOD( DESCL( RSRC_ ) + NPROW - 1, NPROW ) DESCL( CSRC_ ) = MOD( DESCL( CSRC_ ) + NPCOL - 1, NPCOL ) DESCU( N_ ) = DESCU( N_ ) + DESCU( NB_ ) DESCU( RSRC_ ) = DESCL( RSRC_ ) DESCU( CSRC_ ) = DESCL( CSRC_ ) * 10 CONTINUE * * Handle first block separately * JB = MIN( JN-JA+1, DESCA( NB_ ) ) * * Copy unit lower triangular part of sub( A ) into WORK * CALL PSLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPL ), $ 1, 1, DESCL ) CALL PSLASET( 'Upper', M, JB, ZERO, ONE, WORK( IPL ), 1, 1, $ DESCL ) * * Copy upper triangular part of sub( A ) into WORK(IPU) * CALL PSLACPY( 'Upper', JB, N, A, IA, JA, DESCA, WORK( IPU ), 1, $ 1, DESCU ) CALL PSLASET( 'Lower', JB-1, N, ZERO, ZERO, WORK( IPU ), 2, 1, $ DESCU ) * * Zero the strict lower triangular piece of the current block. * CALL PSLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA ) * * Zero the upper triangular piece of the current block. * CALL PSLASET( 'Upper', JB, N, ZERO, ZERO, A, IA, JA, DESCA ) * * Update the matrix sub( A ). * CALL PSGEMM( 'No transpose', 'No transpose', M, N, JB, ONE, $ WORK( IPL ), 1, 1, DESCL, WORK( IPU ), 1, 1, $ DESCU, ONE, A, IA, JA, DESCA ) * * Apply pivots so that sub( A ) = P*L*U * CALL PSLAPIV( 'Backward', 'Row', 'Col', MIN( M, N ), N, A, IA, JA, $ DESCA, IPIV, IA, 1, DESCIP, IDUM ) * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * RETURN * * End of PSGETRRV * END