SUBROUTINE PCPOTRRV( UPLO, N, A, IA, JA, DESCA, WORK ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 28, 2001 * * .. Scalar Arguments .. CHARACTER UPLO INTEGER IA, JA, N * .. * .. Array Arguments .. INTEGER DESCA( * ) COMPLEX A( * ), WORK( * ) * .. * * Purpose * ======= * * PCPOTRRV recomputes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from L or U * computed by PCPOTRF. The routine performs the Cholesky factorization * in reverse. * * 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 * ========= * * UPLO (global input) CHARACTER * Specifies whether the upper or lower triangular part of the * hermitian distributed matrix sub( A ) is stored: * stored: * = 'U': Upper triangular * = 'L': Lower triangular * * N (global input) INTEGER * The number of rows and columns to be operated on, i.e. the * order 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, the local pieces of the factors L or U of the * distributed matrix sub( A ) from the Cholesky factorization. * 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. * * WORK (local workspace) COMPLEX array, dimension (LWORK) * LWORK >= MB_A*NB_A. * * ===================================================================== * * .. 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 PARAMETER ( ONE = 1.0E+0 ) COMPLEX CONE, ZERO PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ), $ ZERO = ( 0.0E+0, 0.0E+0 ) ) * .. * .. Local Scalars .. LOGICAL UPPER CHARACTER COLBTOP, ROWBTOP INTEGER IACOL, IAROW, ICTXT, IL, J, JB, JL, JN, MYCOL, $ MYROW, NPCOL, NPROW * .. Local Arrays .. INTEGER DESCW( DLEN_ ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, PCLACPY, PCLASET, $ PCHERK, PCTRMM, PB_TOPGET, PB_TOPSET * .. * .. External Functions .. LOGICAL LSAME INTEGER ICEIL, INDXG2P EXTERNAL ICEIL, INDXG2P, LSAME * .. * .. Intrinsic Functions .. INTRINSIC MIN, MOD * .. * .. Executable Statements .. * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * CALL PB_TOPGET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPGET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * UPPER = LSAME( UPLO, 'U' ) JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) JL = MAX( ( ( JA+N-2 ) / DESCA( NB_ ) ) * DESCA( NB_ ) + 1, JA ) IL = MAX( ( ( IA+N-2 ) / DESCA( MB_ ) ) * DESCA( MB_ ) + 1, IA ) IAROW = INDXG2P( IL, DESCA( MB_ ), MYROW, DESCA( RSRC_ ), NPROW ) IACOL = INDXG2P( JL, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), NPCOL ) * * Define array descriptor for working array WORK * CALL DESCSET( DESCW, DESCA( MB_ ), DESCA( NB_ ), DESCA( MB_ ), $ DESCA( NB_ ), IAROW, IACOL, ICTXT, DESCA( MB_ ) ) * IF ( UPPER ) THEN * * Compute A from the Cholesky factor U : A = U'*U. * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ' ' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', 'S-ring' ) * DO 10 J = JL, JN+1, -DESCA( NB_ ) * JB = MIN( JA+N-J, DESCA( NB_ ) ) * * Update the trailing matrix, A = A + U'*U * CALL PCHERK( 'Upper', 'Conjugate Transpose', JA+N-J-JB, JB, $ ONE, A, IL, J+JB, DESCA, ONE, A, IL+JB, J+JB, $ DESCA ) * * Copy current diagonal block of A into workspace * CALL PCLACPY( 'All', JB, JB, A, IL, J, DESCA, WORK, 1, 1, $ DESCW ) * * Zero strict lower triangular part of diagonal block, to make * it U1. * CALL PCLASET( 'Lower', JB-1, JB, ZERO, ZERO, A, IL+1, J, $ DESCA ) * * Update the row panel U with the triangular matrix * CALL PCTRMM( 'Left', 'Upper', 'Conjugate Transpose', $ 'Non-Unit', JB, N-J+JA, CONE, WORK, 1, 1, $ DESCW, A, IL, J, DESCA ) * * Restore the strict lower triangular part of diagonal block. * CALL PCLACPY( 'Lower', JB-1, JB, WORK, 2, 1, DESCW, A, $ IL+1, J, DESCA ) * IL = IL - DESCA( MB_ ) DESCW( RSRC_ ) = MOD( DESCW( RSRC_ ) + NPROW - 1, NPROW ) DESCW( CSRC_ ) = MOD( DESCW( CSRC_ ) + NPCOL - 1, NPCOL ) * 10 CONTINUE * * Handle first block separately * JB = MIN( JN-JA+1, DESCA( NB_ ) ) * * Update the trailing matrix, A = A + U'*U * CALL PCHERK( 'Upper', 'Conjugate Transpose', N-JB, JB, ONE, A, $ IA, JA+JB, DESCA, ONE, A, IA+JB, JA+JB, DESCA ) * * Copy current diagonal block of A into workspace * CALL PCLACPY( 'All', JB, JB, A, IA, JA, DESCA, WORK, 1, 1, $ DESCW ) * * Zero strict lower triangular part of diagonal block, to make * it U1. * CALL PCLASET( 'Lower', JB-1, JB, ZERO, ZERO, A, IA+1, JA, $ DESCA ) * * Update the row panel U with the triangular matrix * CALL PCTRMM( 'Left', 'Upper', 'Conjugate Transpose', 'Non-Unit', $ JB, N, CONE, WORK, 1, 1, DESCW, A, IA, JA, DESCA ) * * Restore the strict lower triangular part of diagonal block. * CALL PCLACPY( 'Lower', JB-1, JB, WORK, 2, 1, DESCW, A, IA+1, $ JA, DESCA ) * ELSE * * Compute A from the Cholesky factor L : A = L*L'. * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', 'S-ring' ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', ' ' ) * DO 20 J = JL, JN+1, -DESCA( NB_ ) * JB = MIN( JA+N-J, DESCA( NB_ ) ) * * Update the trailing matrix, A = A + L*L' * CALL PCHERK( 'Lower', 'No Transpose', IA+N-IL-JB, JB, ONE, A, $ IL+JB, J, DESCA, ONE, A, IL+JB, J+JB, DESCA ) * * Copy current diagonal block of A into workspace * CALL PCLACPY( 'All', JB, JB, A, IL, J, DESCA, WORK, 1, 1, $ DESCW ) * * Zero strict upper triangular part of diagonal block, to make * it L1. * CALL PCLASET( 'Upper', JB, JB-1, ZERO, ZERO, A, IL, J+1, $ DESCA ) * * Update the column panel L with the triangular matrix * CALL PCTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Non-Unit', IA+N-IL, JB, CONE, WORK, 1, 1, $ DESCW, A, IL, J, DESCA ) * * Restore the strict upper triangular part of diagonal block. * CALL PCLACPY( 'Upper', JB, JB-1, WORK, 1, 2, DESCW, A, $ IL, J+1, DESCA ) * IL = IL - DESCA( MB_ ) DESCW( RSRC_ ) = MOD( DESCW( RSRC_ ) + NPROW - 1, NPROW ) DESCW( CSRC_ ) = MOD( DESCW( CSRC_ ) + NPCOL - 1, NPCOL ) * 20 CONTINUE * * Handle first block separately * JB = MIN( JN-JA+1, DESCA( NB_ ) ) * * Update the trailing matrix, A = A + L*L' * CALL PCHERK( 'Lower', 'No Transpose', N-JB, JB, ONE, A, $ IA+JB, JA, DESCA, ONE, A, IA+JB, JA+JB, DESCA ) * * Copy current diagonal block of A into workspace * CALL PCLACPY( 'All', JB, JB, A, IA, JA, DESCA, WORK, 1, 1, $ DESCW ) * * Zero strict upper triangular part of diagonal block, to make * it L1. * CALL PCLASET( 'Upper', JB, JB-1, ZERO, ZERO, A, IA, JA+1, $ DESCA ) * * Update the column panel L with the triangular matrix * CALL PCTRMM( 'Right', 'Lower', 'Conjugate transpose', $ 'Non-Unit', N, JB, CONE, WORK, 1, 1, DESCW, A, $ IA, JA, DESCA ) * * Restore the strict upper triangular part of diagonal block. * CALL PCLACPY( 'Upper', JB, JB-1, WORK, 1, 2, DESCW, A, IA, $ JA+1, DESCA ) * END IF * CALL PB_TOPSET( ICTXT, 'Broadcast', 'Rowwise', ROWBTOP ) CALL PB_TOPSET( ICTXT, 'Broadcast', 'Columnwise', COLBTOP ) * RETURN * * End of PCPOTRRV * END