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SUBROUTINE PSGEHDRV( N, ILO, IHI, A, IA, JA, DESCA, TAU, 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, IHI, ILO, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PSGEHDRV computes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from the
* orthogonal matrix Q, the Hessenberg matrix, and the array TAU
* returned by PSGEHRD:
* sub( A ) := Q * H * Q'
*
* Arguments
* =========
*
* 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.
*
* ILO (global input) INTEGER
* IHI (global input) INTEGER
* It is assumed that sub( A ) is already upper triangular in
* rows and columns 1:ILO-1 and IHI+1:N. If N > 0,
* 1 <= ILO <= IHI <= N; otherwise set ILO = 1, IHI = N.
*
* 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 the N-by-N
* general distributed matrix sub( A ) reduced to Hessenberg
* form by PSGEHRD. The upper triangle and the first sub-
* diagonal of sub( A ) contain the upper Hessenberg matrix H,
* and the elements below the first subdiagonal, with the array
* TAU, represent the orthogonal matrix Q as a product of
* elementary reflectors. On exit, the original distributed
* N-by-N matrix sub( A ) is recovered.
*
* 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.
*
* TAU (local input) REAL array, dimension LOCc(JA+N-2)
* The scalar factors of the elementary reflectors returned by
* PSGEHRD. TAU is tied to the distributed matrix A.
*
* WORK (local workspace) REAL array, dimension (LWORK).
* LWORK >= NB*NB + NB*IHLP + MAX[ NB*( IHLP+INLQ ),
* NB*( IHLQ + MAX[ IHIP,
* IHLP+NUMROC( NUMROC( IHI-ILO+LOFF+1, NB, 0, 0,
* NPCOL ), NB, 0, 0, LCMQ ) ] ) ]
*
* where NB = MB_A = NB_A,
* LCM is the least common multiple of NPROW and NPCOL,
* LCM = ILCM( NPROW, NPCOL ), LCMQ = LCM / NPCOL,
*
* IROFFA = MOD( IA-1, NB ),
* IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ),
* IHIP = NUMROC( IHI+IROFFA, NB, MYROW, IAROW, NPROW ),
*
* ILROW = INDXG2P( IA+ILO-1, NB, MYROW, RSRC_A, NPROW ),
* ILCOL = INDXG2P( JA+ILO-1, NB, MYCOL, CSRC_A, NPCOL ),
* IHLP = NUMROC( IHI-ILO+IROFFA+1, NB, MYROW, ILROW, NPROW ),
* IHLQ = NUMROC( IHI-ILO+IROFFA+1, NB, MYCOL, ILCOL, NPCOL ),
* INLQ = NUMROC( N-ILO+IROFFA+1, NB, MYCOL, ILCOL, NPCOL ).
*
* ILCM, 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 ZERO
PARAMETER ( ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
INTEGER I, IACOL, IAROW, ICTXT, IHLP, II, IOFF, IPT,
$ IPV, IPW, IV, J, JB, JJ, JL, K, MYCOL, MYROW,
$ NB, NPCOL, NPROW
* ..
* .. Local Arrays ..
INTEGER DESCV( DLEN_ )
* ..
* .. External Functions ..
INTEGER INDXG2P, NUMROC
EXTERNAL INDXG2P, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, PSLARFB,
$ PSLARFT, PSLACPY, PSLASET
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Quick return if possible
*
IF( IHI-ILO.LE.0 )
$ RETURN
*
NB = DESCA( MB_ )
IOFF = MOD( IA+ILO-2, NB )
CALL INFOG2L( IA+ILO-1, JA+ILO-1, DESCA, NPROW, NPCOL, MYROW,
$ MYCOL, II, JJ, IAROW, IACOL )
IHLP = NUMROC( IHI-ILO+IOFF+1, NB, MYROW, IAROW, NPROW )
*
IPT = 1
IPV = IPT + NB * NB
IPW = IPV + IHLP * NB
JL = MAX( ( ( JA+IHI-2 ) / NB ) * NB + 1, JA + ILO - 1 )
CALL DESCSET( DESCV, IHI-ILO+IOFF+1, NB, NB, NB, IAROW,
$ INDXG2P( JL, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ),
$ NPCOL ), ICTXT, MAX( 1, IHLP ) )
*
DO 10 J = JL, ILO+JA+NB-IOFF-1, -NB
JB = MIN( JA+IHI-J, NB )
I = IA + J - JA
K = I - IA + 1
IV = K - ILO + IOFF + 1
*
* Compute upper triangular matrix T from TAU.
*
CALL PSLARFT( 'Forward', 'Columnwise', IHI-K, JB, A, I+1, J,
$ DESCA, TAU, WORK( IPT ), WORK( IPW ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'All', IHI-K, JB, A, I+1, J, DESCA, WORK( IPV ),
$ IV+1, 1, DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PSLASET( 'Lower', IHI-K-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ IHI-K, N-K+1, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, I+1, J, DESCA, WORK( IPW ) )
*
* Apply block Householder transformation from Right.
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Columnwise',
$ IHI, IHI-K, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, IA, J+1, DESCA, WORK( IPW ) )
*
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL )
*
10 CONTINUE
*
* Handle the first block separately
*
IV = IOFF + 1
I = IA + ILO - 1
J = JA + ILO - 1
JB = MIN( NB-IOFF, JA+IHI-J )
*
* Compute upper triangular matrix T from TAU.
*
CALL PSLARFT( 'Forward', 'Columnwise', IHI-ILO, JB, A, I+1, J,
$ DESCA, TAU, WORK( IPT ), WORK( IPW ) )
*
* Copy Householder vectors into workspace.
*
CALL PSLACPY( 'All', IHI-ILO, JB, A, I+1, J, DESCA, WORK( IPV ),
$ IV+1, 1, DESCV )
*
* Zero out the strict lower triangular part of A.
*
IF( IHI-ILO.GT.0 )
$ CALL PSLASET( 'Lower', IHI-ILO-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* Apply block Householder transformation from Left.
*
CALL PSLARFB( 'Left', 'No transpose', 'Forward', 'Columnwise',
$ IHI-ILO, N-ILO+1, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, I+1, J, DESCA, WORK( IPW ) )
*
* Apply block Householder transformation from Right.
*
CALL PSLARFB( 'Right', 'Transpose', 'Forward', 'Columnwise', IHI,
$ IHI-ILO, JB, WORK( IPV ), IV+1, 1, DESCV,
$ WORK( IPT ), A, IA, J+1, DESCA, WORK( IPW ) )
*
RETURN
*
* End of PSGEHDRV
*
END
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