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|
SUBROUTINE PSGEBDRV( M, N, A, IA, JA, DESCA, D, E, TAUQ, TAUP,
$ WORK, INFO )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER INFO, IA, JA, M, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * ), D( * ), E( * ), TAUP( * ), TAUQ( * ),
$ WORK( * )
* ..
*
* Purpose
* =======
*
* PSGEBDRV computes sub( A ) = A(IA:IA+M-1,JA:JA+N-1) from sub( A ),
* Q, P returned by PSGEBRD:
*
* sub( A ) := Q * B * P'.
*
* 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, this array contains the local pieces of sub( A )
* as returned by PSGEBRD. On exit, the original distribu-
* ted 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.
*
* D (local input) REAL array, dimension
* LOCc(JA+MIN(M,N)-1) if M >= N; LOCr(IA+MIN(M,N)-1) otherwise.
* The distributed diagonal elements of the bidiagonal matrix
* B: D(i) = A(i,i). D is tied to the distributed matrix A.
*
* E (local input) REAL array, dimension
* LOCr(IA+MIN(M,N)-1) if M >= N; LOCc(JA+MIN(M,N)-2) otherwise.
* The distributed off-diagonal elements of the bidiagonal
* distributed matrix B:
* if m >= n, E(i) = A(i,i+1) for i = 1,2,...,n-1;
* if m < n, E(i) = A(i+1,i) for i = 1,2,...,m-1.
* E is tied to the distributed matrix A.
*
* TAUQ (local input) REAL array dimension
* LOCc(JA+MIN(M,N)-1). The scalar factors of the elementary
* reflectors which represent the orthogonal matrix Q. TAUQ
* is tied to the distributed matrix A. See Further Details.
*
* TAUP (local input) REAL array, dimension
* LOCr(IA+MIN(M,N)-1). The scalar factors of the elementary
* reflectors which represent the orthogonal matrix P. TAUP
* is tied to the distributed matrix A. See Further Details.
*
* WORK (local workspace) REAL array, dimension (LWORK)
* LWORK >= 2*NB*( MP + NQ + NB )
*
* where NB = MB_A = NB_A,
* IROFFA = MOD( IA-1, NB ), ICOFFA = MOD( JA-1, NB ),
* IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
* IACOL = INDXG2P( JA, NB, MYCOL, CSRC_A, NPCOL ),
* MP = NUMROC( M+IROFFA, NB, MYROW, IAROW, NPROW ),
* NQ = NUMROC( N+ICOFFA, NB, MYCOL, IACOL, NPCOL ).
*
* INDXG2P and NUMROC are ScaLAPACK tool functions;
* MYROW, MYCOL, NPROW and NPCOL can be determined by calling
* the subroutine BLACS_GRIDINFO.
*
* INFO (global output) INTEGER
* On exit, if INFO <> 0, a discrepancy has been found between
* the diagonal and off-diagonal elements of A and the copies
* contained in the arrays D and E.
*
* =====================================================================
*
* .. 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 EIGHT, ONE, ZERO
PARAMETER ( EIGHT = 8.0E+0, ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, IACOL, IAROW, ICTXT, IIA, IL, IPTP, IPTQ,
$ IPV, IPW, IPWK, IOFF, IV, J, JB, JJA, JL, JV,
$ K, MN, MP, MYCOL, MYROW, NB, NPCOL, NPROW, NQ
REAL ADDBND, D1, D2, E1, E2
* ..
* .. Local Arrays ..
INTEGER DESCD( DLEN_ ), DESCE( DLEN_ ), DESCV( DLEN_ ),
$ DESCW( DLEN_ )
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, IGSUM2D, INFOG2L,
$ PSLACPY, PSLARFB, PSLARFT, PSLASET,
$ PSELGET
* ..
* .. External Functions ..
INTEGER INDXG2P, NUMROC
REAL PSLAMCH
EXTERNAL INDXG2P, NUMROC, PSLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
INFO = 0
NB = DESCA( MB_ )
IOFF = MOD( IA-1, NB )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
MP = NUMROC( M+IOFF, NB, MYROW, IAROW, NPROW )
NQ = NUMROC( N+IOFF, NB, MYCOL, IACOL, NPCOL )
IPV = 1
IPW = IPV + MP*NB
IPTP = IPW + NQ*NB
IPTQ = IPTP + NB*NB
IPWK = IPTQ + NB*NB
*
IV = 1
JV = 1
MN = MIN( M, N )
IL = MAX( ( (IA+MN-2) / NB )*NB + 1, IA )
JL = MAX( ( (JA+MN-2) / NB )*NB + 1, JA )
IAROW = INDXG2P( IL, NB, MYROW, DESCA( RSRC_ ), NPROW )
IACOL = INDXG2P( JL, NB, MYCOL, DESCA( CSRC_ ), NPCOL )
CALL DESCSET( DESCV, IA+M-IL, NB, NB, NB, IAROW, IACOL, ICTXT,
$ MAX( 1, MP ) )
CALL DESCSET( DESCW, NB, JA+N-JL, NB, NB, IAROW, IACOL, ICTXT,
$ NB )
*
ADDBND = EIGHT * PSLAMCH( ICTXT, 'eps' )
*
* When A is an upper bidiagonal form
*
IF( M.GE.N ) THEN
*
CALL DESCSET( DESCD, 1, JA+MN-1, 1, DESCA( NB_ ), MYROW,
$ DESCA( CSRC_ ), DESCA( CTXT_ ), 1 )
CALL DESCSET( DESCE, IA+MN-1, 1, DESCA( MB_ ), 1,
$ DESCA( RSRC_ ), MYCOL, DESCA( CTXT_ ),
$ DESCA( LLD_ ) )
*
DO 10 J = 0, MN-1
D1 = ZERO
E1 = ZERO
D2 = ZERO
E2 = ZERO
CALL PSELGET( ' ', ' ', D2, D, 1, JA+J, DESCD )
CALL PSELGET( 'Columnwise', ' ', D1, A, IA+J, JA+J, DESCA )
IF( J.LT.(MN-1) ) THEN
CALL PSELGET( ' ', ' ', E2, E, IA+J, 1, DESCE )
CALL PSELGET( 'Rowwise', ' ', E1, A, IA+J, JA+J+1,
$ DESCA )
END IF
*
IF( ( ABS( D1 - D2 ).GT.( ABS( D2 ) * ADDBND ) ) .OR.
$ ( ABS( E1 - E2 ).GT.( ABS( E2 ) * ADDBND ) ) )
$ INFO = INFO + 1
10 CONTINUE
*
DO 20 J = JL, JA+NB-IOFF, -NB
JB = MIN( JA+N-J, NB )
I = IA + J - JA
K = I - IA + 1
*
* Compute upper triangular matrix TQ from TAUQ.
*
CALL PSLARFT( 'Forward', 'Columnwise', M-K+1, JB, A, I, J,
$ DESCA, TAUQ, WORK( IPTQ ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Lower', M-K+1, JB, A, I, J, DESCA,
$ WORK( IPV ), IV, JV, DESCV )
CALL PSLASET( 'Upper', M-K+1, JB, ZERO, ONE, WORK( IPV ),
$ IV, JV, DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PSLASET( 'Lower', M-K, JB, ZERO, ZERO, A, I+1, J,
$ DESCA )
*
* Compute upper triangular matrix TP from TAUP.
*
CALL PSLARFT( 'Forward', 'Rowwise', N-K, JB, A, I, J+1,
$ DESCA, TAUP, WORK( IPTP ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Upper', JB, N-K, A, I, J+1, DESCA,
$ WORK( IPW ), IV, JV+1, DESCW )
CALL PSLASET( 'Lower', JB, N-K, ZERO, ONE, WORK( IPW ), IV,
$ JV+1, DESCW )
*
* Zero out the strict+1 upper triangular part of A.
*
CALL PSLASET( 'Upper', JB, N-K-1, ZERO, ZERO, A, I, J+2,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward',
$ 'Columnwise', M-K+1, N-K+1, JB, WORK( IPV ),
$ IV, JV, DESCV, WORK( IPTQ ), A, I, J, DESCA,
$ WORK( IPWK ) )
*
* Apply block Householder transformation from Right.
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise',
$ M-K+1, N-K, JB, WORK( IPW ), IV, JV+1, DESCW,
$ WORK( IPTP ), A, I, J+1, DESCA, WORK( IPWK ) )
*
DESCV( M_ ) = DESCV( M_ ) + NB
DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + NPROW - 1, NPROW )
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL )
DESCW( N_ ) = DESCW( N_ ) + NB
DESCW( RSRC_ ) = DESCV( RSRC_ )
DESCW( CSRC_ ) = DESCV( CSRC_ )
*
20 CONTINUE
*
* Handle first block separately
*
JB = MIN( N, NB - IOFF )
IV = IOFF + 1
JV = IOFF + 1
*
* Compute upper triangular matrix TQ from TAUQ.
*
CALL PSLARFT( 'Forward', 'Columnwise', M, JB, A, IA, JA, DESCA,
$ TAUQ, WORK( IPTQ ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Lower', M, JB, A, IA, JA, DESCA, WORK( IPV ),
$ IV, JV, DESCV )
CALL PSLASET( 'Upper', M, JB, ZERO, ONE, WORK( IPV ), IV, JV,
$ DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PSLASET( 'Lower', M-1, JB, ZERO, ZERO, A, IA+1, JA,
$ DESCA )
*
* Compute upper triangular matrix TP from TAUP.
*
CALL PSLARFT( 'Forward', 'Rowwise', N-1, JB, A, IA, JA+1,
$ DESCA, TAUP, WORK( IPTP ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Upper', JB, N-1, A, IA, JA+1, DESCA,
$ WORK( IPW ), IV, JV+1, DESCW )
CALL PSLASET( 'Lower', JB, N-1, ZERO, ONE, WORK( IPW ), IV,
$ JV+1, DESCW )
*
* Zero out the strict+1 upper triangular part of A.
*
CALL PSLASET( 'Upper', JB, N-2, ZERO, ZERO, A, IA, JA+2,
$ DESCA )
*
* Apply block Householder transformation from left.
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ M, N, JB, WORK( IPV ), IV, JV, DESCV,
$ WORK( IPTQ ), A, IA, JA, DESCA, WORK( IPWK ) )
*
* Apply block Householder transformation from right.
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise', M,
$ N-1, JB, WORK( IPW ), IV, JV+1, DESCW,
$ WORK( IPTP ), A, IA, JA+1, DESCA, WORK( IPWK ) )
*
ELSE
*
CALL DESCSET( DESCD, IA+MN-1, 1, DESCA( MB_ ), 1,
$ DESCA( RSRC_ ), MYCOL, DESCA( CTXT_ ),
$ DESCA( LLD_ ) )
CALL DESCSET( DESCE, 1, JA+MN-2, 1, DESCA( NB_ ), MYROW,
$ DESCA( CSRC_ ), DESCA( CTXT_ ), 1 )
*
DO 30 J = 0, MN-1
D1 = ZERO
E1 = ZERO
D2 = ZERO
E2 = ZERO
CALL PSELGET( ' ', ' ', D2, D, IA+J, 1, DESCD )
CALL PSELGET( 'Rowwise', ' ', D1, A, IA+J, JA+J, DESCA )
IF( J.LT.(MN-1) ) THEN
CALL PSELGET( ' ', ' ', E2, E, 1, JA+J, DESCE )
CALL PSELGET( 'Columnwise', ' ', E1, A, IA+J+1, JA+J,
$ DESCA )
END IF
*
IF( ( ABS( D1 - D2 ).GT.( ABS( D2 ) * ADDBND ) ) .OR.
$ ( ABS( E1 - E2 ).GT.( ABS( E2 ) * ADDBND ) ) )
$ INFO = INFO + 1
30 CONTINUE
*
DO 40 I = IL, IA+NB-IOFF, -NB
JB = MIN( IA+M-I, NB )
J = JA + I - IA
K = J - JA + 1
*
* Compute upper triangular matrix TQ from TAUQ.
*
CALL PSLARFT( 'Forward', 'Columnwise', M-K, JB, A, I+1, J,
$ DESCA, TAUQ, WORK( IPTQ ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Lower', M-K, JB, A, I+1, J, DESCA,
$ WORK( IPV ), IV+1, JV, DESCV )
CALL PSLASET( 'Upper', M-K, JB, ZERO, ONE, WORK( IPV ),
$ IV+1, JV, DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PSLASET( 'Lower', M-K-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* Compute upper triangular matrix TP from TAUP.
*
CALL PSLARFT( 'Forward', 'Rowwise', N-K+1, JB, A, I, J,
$ DESCA, TAUP, WORK( IPTP ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Upper', JB, N-K+1, A, I, J, DESCA,
$ WORK( IPW ), IV, JV, DESCW )
CALL PSLASET( 'Lower', JB, N-K+1, ZERO, ONE, WORK( IPW ),
$ IV, JV, DESCW )
*
* Zero out the strict+1 upper triangular part of A.
*
CALL PSLASET( 'Upper', JB, N-K, ZERO, ZERO, A, I, J+1,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward',
$ 'Columnwise', M-K, N-K+1, JB, WORK( IPV ),
$ IV+1, JV, DESCV, WORK( IPTQ ), A, I+1, J,
$ DESCA, WORK( IPWK ) )
*
* Apply block Householder transformation from Right.
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise',
$ M-K+1, N-K+1, JB, WORK( IPW ), IV, JV, DESCW,
$ WORK( IPTP ), A, I, J, DESCA, WORK( IPWK ) )
*
DESCV( M_ ) = DESCV( M_ ) + NB
DESCV( RSRC_ ) = MOD( DESCV( RSRC_ ) + NPROW - 1, NPROW )
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL )
DESCW( N_ ) = DESCW( N_ ) + NB
DESCW( RSRC_ ) = DESCV( RSRC_ )
DESCW( CSRC_ ) = DESCV( CSRC_ )
*
40 CONTINUE
*
* Handle first block separately
*
JB = MIN( M, NB - IOFF )
IV = IOFF + 1
JV = IOFF + 1
*
* Compute upper triangular matrix TQ from TAUQ.
*
CALL PSLARFT( 'Forward', 'Columnwise', M-1, JB, A, IA+1, JA,
$ DESCA, TAUQ, WORK( IPTQ ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Lower', M-1, JB, A, IA+1, JA, DESCA,
$ WORK( IPV ), IV+1, JV, DESCV )
CALL PSLASET( 'Upper', M-1, JB, ZERO, ONE, WORK( IPV ), IV+1,
$ JV, DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PSLASET( 'Lower', M-2, JB, ZERO, ZERO, A, IA+2, JA,
$ DESCA )
*
* Compute upper triangular matrix TP from TAUP.
*
CALL PSLARFT( 'Forward', 'Rowwise', N, JB, A, IA, JA, DESCA,
$ TAUP, WORK( IPTP ), WORK( IPWK ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'Upper', JB, N, A, IA, JA, DESCA, WORK( IPW ),
$ IV, JV, DESCW )
CALL PSLASET( 'Lower', JB, N, ZERO, ONE, WORK( IPW ), IV, JV,
$ DESCW )
*
* Zero out the strict+1 upper triangular part of A.
*
CALL PSLASET( 'Upper', JB, N-1, ZERO, ZERO, A, IA, JA+1,
$ DESCA )
*
* Apply block Householder transformation from left
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ M-1, N, JB, WORK( IPV ), IV+1, JV, DESCV,
$ WORK( IPTQ ), A, IA+1, JA, DESCA, WORK( IPWK ) )
*
* Apply block Householder transformation from right
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Rowwise', M, N,
$ JB, WORK( IPW ), IV, JV, DESCW, WORK( IPTP ),
$ A, IA, JA, DESCA, WORK( IPWK ) )
END IF
*
CALL IGSUM2D( ICTXT, 'All', ' ', 1, 1, INFO, 1, -1, 0 )
*
RETURN
*
* End of PSGEBDRV
*
END
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