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SUBROUTINE PZPOTRRV( 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*16 A( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PZPOTRRV recomputes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from L or U
* computed by PZPOTRF. 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*16 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*16 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 )
DOUBLE PRECISION ONE
PARAMETER ( ONE = 1.0D+0 )
COMPLEX*16 CONE, ZERO
PARAMETER ( CONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+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, PB_TOPGET, PB_TOPSET,
$ PZLACPY, PZLASET, PZHERK, PZTRMM
* ..
* .. 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 PZHERK( '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 PZLACPY( 'All', JB, JB, A, IL, J, DESCA, WORK, 1, 1,
$ DESCW )
*
* Zero strict lower triangular part of diagonal block, to make
* it U1.
*
CALL PZLASET( 'Lower', JB-1, JB, ZERO, ZERO, A, IL+1, J,
$ DESCA )
*
* Update the row panel U with the triangular matrix
*
CALL PZTRMM( '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 PZLACPY( '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 PZHERK( '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 PZLACPY( 'All', JB, JB, A, IA, JA, DESCA, WORK, 1, 1,
$ DESCW )
*
* Zero strict lower triangular part of diagonal block, to make
* it U1.
*
CALL PZLASET( 'Lower', JB-1, JB, ZERO, ZERO, A, IA+1, JA,
$ DESCA )
*
* Update the row panel U with the triangular matrix
*
CALL PZTRMM( '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 PZLACPY( '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 PZHERK( '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 PZLACPY( 'All', JB, JB, A, IL, J, DESCA, WORK, 1, 1,
$ DESCW )
*
* Zero strict upper triangular part of diagonal block, to make
* it L1.
*
CALL PZLASET( 'Upper', JB, JB-1, ZERO, ZERO, A, IL, J+1,
$ DESCA )
*
* Update the column panel L with the triangular matrix
*
CALL PZTRMM( '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 PZLACPY( '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 PZHERK( '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 PZLACPY( 'All', JB, JB, A, IA, JA, DESCA, WORK, 1, 1,
$ DESCW )
*
* Zero strict upper triangular part of diagonal block, to make
* it L1.
*
CALL PZLASET( 'Upper', JB, JB-1, ZERO, ZERO, A, IA, JA+1,
$ DESCA )
*
* Update the column panel L with the triangular matrix
*
CALL PZTRMM( '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 PZLACPY( '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 PZPOTRRV
*
END
|
