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SUBROUTINE PCGETRRV( 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( * )
COMPLEX A( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PCGETRRV reforms sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from the
* triangular matrices L and U returned by PCGETRF. 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 PCGETRF
* 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) COMPLEX 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) COMPLEX 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 )
COMPLEX 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, PCGEMM, PCLACPY,
$ PCLAPIV, 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_ ) )
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 PCLACPY( 'Lower', M-IL+IA, JB, A, IL, J, DESCA,
$ WORK( IPL ), 1, 1, DESCL )
CALL PCLASET( 'Upper', M-IL+IA, JB, ZERO, ONE, WORK( IPL ),
$ 1, 1, DESCL )
*
* Copy upper triangular part of sub( A ) into WORK(IPU)
*
CALL PCLACPY( 'Upper', JB, JA+N-J, A, IL, J, DESCA,
$ WORK( IPU ), 1, 1, DESCU )
CALL PCLASET( 'Lower', JB-1, JA+N-J, ZERO, ZERO,
$ WORK( IPU ), 2, 1, DESCU )
*
* Zero the strict lower triangular piece of the current block.
*
CALL PCLASET( 'Lower', IA+M-IL-1, JB, ZERO, ZERO, A, IL+1, J,
$ DESCA )
*
* Zero the upper triangular piece of the current block.
*
CALL PCLASET( 'Upper', JB, JA+N-J, ZERO, ZERO, A, IL, J,
$ DESCA )
*
* Update the matrix sub( A ).
*
CALL PCGEMM( '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 PCLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPL ),
$ 1, 1, DESCL )
CALL PCLASET( 'Upper', M, JB, ZERO, ONE, WORK( IPL ), 1, 1,
$ DESCL )
*
* Copy upper triangular part of sub( A ) into WORK(IPU)
*
CALL PCLACPY( 'Upper', JB, N, A, IA, JA, DESCA, WORK( IPU ), 1,
$ 1, DESCU )
CALL PCLASET( 'Lower', JB-1, N, ZERO, ZERO, WORK( IPU ), 2, 1,
$ DESCU )
*
* Zero the strict lower triangular piece of the current block.
*
CALL PCLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA, DESCA )
*
* Zero the upper triangular piece of the current block.
*
CALL PCLASET( 'Upper', JB, N, ZERO, ZERO, A, IA, JA, DESCA )
*
* Update the matrix sub( A ).
*
CALL PCGEMM( '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 PCLAPIV( '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 PCGETRRV
*
END
|
