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SUBROUTINE PZHETDRV( UPLO, N, A, IA, JA, DESCA, D, E, TAU, 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 ..
CHARACTER UPLO
INTEGER IA, INFO, JA, N
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION D( * ), E( * )
COMPLEX*16 A( * ), TAU( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PZHETDRV computes sub( A ) = A(IA:IA+N-1,JA:JA+N-1) from Q, the
* Hermitian tridiagonal matrix T (or D and E), and TAU, which were
* computed by PZHETRD: sub( A ) := Q * T * Q'.
*
* 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 matrix sub( A ) is 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)).
* This array contains the local pieces of sub( A ). On entry,
* if UPLO='U', the diagonal and first superdiagonal of sub( A )
* have the corresponding elements of the tridiagonal matrix T,
* and the elements above the first superdiagonal, with the
* array TAU, represent the unitary matrix Q as a product of
* elementary reflectors, and the strictly lower triangular part
* of sub( A ) is not referenced. If UPLO='L', the diagonal and
* first subdiagonal of sub( A ) have the corresponding elements
* of the tridiagonal matrix T, and the elements below the first
* subdiagonal, with the array TAU, represent the unitary
* matrix Q as a product of elementary reflectors, and the
* strictly upper triangular part of sub( A ) is not referenced.
* On exit, if UPLO = 'U', the upper triangular part of the
* distributed Hermitian matrix sub( A ) is recovered.
* If UPLO='L', the lower triangular part of the distributed
* Hermitian 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.
*
* D (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
* The diagonal elements of the tridiagonal matrix T:
* D(i) = A(i,i). D is tied to the distributed matrix A.
*
* E (local input) DOUBLE PRECISION array, dimension LOCc(JA+N-1)
* if UPLO = 'U', LOCc(JA+N-2) otherwise. The off-diagonal
* elements of the tridiagonal matrix T: E(i) = A(i,i+1) if
* UPLO = 'U', E(i) = A(i+1,i) if UPLO = 'L'. E is tied to the
* distributed matrix A.
*
* TAU (local input) COMPLEX*16, array, dimension
* LOCc(JA+N-1). This array contains the scalar factors TAU of
* the elementary reflectors. TAU is tied to the distributed
* matrix A.
*
* WORK (local workspace) COMPLEX*16 array, dimension (LWORK)
* LWORK >= 2 * NB *( NB + NP )
*
* where NB = MB_A = NB_A,
* NP = NUMROC( N, NB, MYROW, IAROW, NPROW ),
* IAROW = INDXG2P( IA, NB, MYROW, RSRC_A, NPROW ).
*
* 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 )
DOUBLE PRECISION REIGHT, RONE, RZERO
PARAMETER ( REIGHT = 8.0D+0, RONE = 1.0D+0,
$ RZERO = 0.0D+0 )
COMPLEX*16 HALF, ONE, ZERO
PARAMETER ( HALF = ( 0.5D+0, 0.0D+0 ),
$ ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
LOGICAL UPPER
INTEGER I, IACOL, IAROW, ICTXT, II, IPT, IPV, IPX,
$ IPY, J, JB, JJ, JL, K, MYCOL, MYROW, NB, NP,
$ NPCOL, NPROW
DOUBLE PRECISION ADDBND, D2, E2
COMPLEX*16 D1, E1
* ..
* .. Local Arrays ..
INTEGER DESCD( DLEN_ ), DESCE( DLEN_ ), DESCV( DLEN_ ),
$ DESCT( DLEN_ )
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER INDXG2P, NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL INDXG2P, LSAME, NUMROC, PDLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DESCSET, INFOG2L, IGSUM2D,
$ PDELGET, PZELGET, PZGEMM,
$ PZHEMM, PZHER2K, PZLACPY,
$ PZLARFT, PZLASET, PZTRMM
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DCMPLX, MAX, MIN, MOD
* ..
* .. Executable statements ..
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
INFO = 0
NB = DESCA( MB_ )
UPPER = LSAME( UPLO, 'U' )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, II, JJ,
$ IAROW, IACOL )
NP = NUMROC( N, NB, MYROW, IAROW, NPROW )
*
IPT = 1
IPV = NB * NB + IPT
IPX = NB * NP + IPV
IPY = NB * NP + IPX
*
CALL DESCSET( DESCD, 1, JA+N-1, 1, DESCA( NB_ ), MYROW,
$ DESCA( CSRC_ ), DESCA( CTXT_ ), 1 )
*
ADDBND = REIGHT * PDLAMCH( ICTXT, 'eps' )
*
IF( UPPER ) THEN
*
CALL DESCSET( DESCE, 1, JA+N-1, 1, DESCA( NB_ ), MYROW,
$ DESCA( CSRC_ ), DESCA( CTXT_ ), 1 )
*
DO 10 J = 0, N-1
D1 = ZERO
E1 = ZERO
D2 = RZERO
E2 = RZERO
CALL PDELGET( ' ', ' ', D2, D, 1, JA+J, DESCD )
CALL PZELGET( 'Columnwise', ' ', D1, A, IA+J, JA+J, DESCA )
IF( J.LT.(N-1) ) THEN
CALL PDELGET( ' ', ' ', E2, E, 1, JA+J+1, DESCE )
CALL PZELGET( 'Columnwise', ' ', E1, A, IA+J, JA+J+1,
$ DESCA )
END IF
*
IF( ( ABS( D1-DCMPLX( D2 ) ).GT.( ABS( D2 )*ADDBND ) ) .OR.
$ ( ABS( E1-DCMPLX( E2 ) ).GT.( ABS( E2 )*ADDBND ) ) )
$ INFO = INFO + 1
10 CONTINUE
*
* Compute the upper triangle of sub( A ).
*
CALL DESCSET( DESCV, N, NB, NB, NB, IAROW, IACOL, ICTXT,
$ MAX( 1, NP ) )
CALL DESCSET( DESCT, NB, NB, NB, NB, IAROW, IACOL, ICTXT, NB )
*
DO 20 K = 0, N-1, NB
JB = MIN( NB, N-K )
I = IA + K
J = JA + K
*
* Compute the lower triangular matrix T.
*
CALL PZLARFT( 'Backward', 'Columnwise', K+JB-1, JB, A, IA,
$ J, DESCA, TAU, WORK( IPT ), WORK( IPV ) )
*
* Copy Householder vectors into WORK( IPV ).
*
CALL PZLACPY( 'All', K+JB-1, JB, A, IA, J, DESCA,
$ WORK( IPV ), 1, 1, DESCV )
*
IF( K.GT.0 ) THEN
CALL PZLASET( 'Lower', JB+1, JB, ZERO, ONE, WORK( IPV ),
$ K, 1, DESCV )
ELSE
CALL PZLASET( 'Lower', JB, JB-1, ZERO, ONE, WORK( IPV ),
$ 1, 2, DESCV )
CALL PZLASET( 'Ge', JB, 1, ZERO, ZERO, WORK( IPV ), 1,
$ 1, DESCV )
END IF
*
* Zero out the strict upper triangular part of A.
*
IF( K.GT.0 ) THEN
CALL PZLASET( 'Ge', K-1, JB, ZERO, ZERO, A, IA, J,
$ DESCA )
CALL PZLASET( 'Upper', JB-1, JB-1, ZERO, ZERO, A, I-1,
$ J+1, DESCA )
ELSE IF( JB.GT.1 ) THEN
CALL PZLASET( 'Upper', JB-2, JB-2, ZERO, ZERO, A, IA,
$ J+2, DESCA )
END IF
*
* (1) X := A * V * T'
*
CALL PZHEMM( 'Left', 'Upper', K+JB, JB, ONE, A, IA, JA,
$ DESCA, WORK( IPV ), 1, 1, DESCV, ZERO,
$ WORK( IPX ), 1, 1, DESCV )
CALL PZTRMM( 'Right', 'Lower', 'Conjugate transpose',
$ 'Non-Unit', K+JB, JB, ONE, WORK( IPT ), 1, 1,
$ DESCT, WORK( IPX ), 1, 1, DESCV )
*
* (2) X := X - 1/2 * V * (T * V' * X)
*
CALL PZGEMM( 'Conjugate transpose', 'No transpose', JB, JB,
$ K+JB, ONE, WORK( IPV ), 1, 1, DESCV,
$ WORK( IPX ), 1, 1, DESCV, ZERO, WORK( IPY ),
$ 1, 1, DESCT )
CALL PZTRMM( 'Left', 'Lower', 'No transpose', 'Non-Unit',
$ JB, JB, ONE, WORK( IPT ), 1, 1, DESCT,
$ WORK( IPY ), 1, 1, DESCT )
CALL PZGEMM( 'No tranpose', 'No transpose', K+JB, JB, JB,
$ -HALF, WORK( IPV ), 1, 1, DESCV, WORK( IPY ),
$ 1, 1, DESCT, ONE, WORK( IPX ), 1, 1, DESCV )
*
* (3) A := A - X * V' - V * X'
*
CALL PZHER2K( 'Upper', 'No transpose', K+JB, JB, -ONE,
$ WORK( IPV ), 1, 1, DESCV, WORK( IPX ), 1, 1,
$ DESCV, RONE, A, IA, JA, DESCA )
*
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + 1, NPCOL )
DESCT( CSRC_ ) = MOD( DESCT( CSRC_ ) + 1, NPCOL )
*
20 CONTINUE
*
ELSE
*
CALL DESCSET( DESCE, 1, JA+N-2, 1, DESCA( NB_ ), MYROW,
$ DESCA( CSRC_ ), DESCA( CTXT_ ), 1 )
*
DO 30 J = 0, N-1
D1 = ZERO
E1 = ZERO
D2 = RZERO
E2 = RZERO
CALL PDELGET( ' ', ' ', D2, D, 1, JA+J, DESCD )
CALL PZELGET( 'Columnwise', ' ', D1, A, IA+J, JA+J, DESCA )
IF( J.LT.(N-1) ) THEN
CALL PDELGET( ' ', ' ', E2, E, 1, JA+J, DESCE )
CALL PZELGET( 'Columnwise', ' ', E1, A, IA+J+1, JA+J,
$ DESCA )
END IF
*
IF( ( ABS( D1-DCMPLX( D2 ) ).GT.( ABS( D2 )*ADDBND ) ) .OR.
$ ( ABS( E1-DCMPLX( E2 ) ).GT.( ABS( E2 )*ADDBND ) ) )
$ INFO = INFO + 1
30 CONTINUE
*
* Compute the lower triangle of sub( A ).
*
JL = MAX( ( ( JA+N-2 ) / NB ) * NB + 1, JA )
IACOL = INDXG2P( JL, NB, MYCOL, DESCA( CSRC_ ), NPCOL )
CALL DESCSET( DESCV, N, NB, NB, NB, IAROW, IACOL, ICTXT,
$ MAX( 1, NP ) )
CALL DESCSET( DESCT, NB, NB, NB, NB, INDXG2P( IA+JL-JA+1, NB,
$ MYROW, DESCA( RSRC_ ), NPROW ), IACOL, ICTXT,
$ NB )
*
DO 40 J = JL, JA, -NB
K = J - JA + 1
I = IA + K - 1
JB = MIN( N-K+1, NB )
*
* Compute upper triangular matrix T from TAU.
*
CALL PZLARFT( 'Forward', 'Columnwise', N-K, JB, A, I+1, J,
$ DESCA, TAU, WORK( IPT ), WORK( IPV ) )
*
* Copy Householder vectors into WORK( IPV ).
*
CALL PZLACPY( 'Lower', N-K, JB, A, I+1, J, DESCA,
$ WORK( IPV ), K+1, 1, DESCV )
CALL PZLASET( 'Upper', N-K, JB, ZERO, ONE, WORK( IPV ),
$ K+1, 1, DESCV )
CALL PZLASET( 'Ge', 1, JB, ZERO, ZERO, WORK( IPV ), K, 1,
$ DESCV )
*
* Zero out the strict lower triangular part of A.
*
CALL PZLASET( 'Lower', N-K-1, JB, ZERO, ZERO, A, I+2, J,
$ DESCA )
*
* (1) X := A * V * T'
*
CALL PZHEMM( 'Left', 'Lower', N-K+1, JB, ONE, A, I, J,
$ DESCA, WORK( IPV ), K, 1, DESCV, ZERO,
$ WORK( IPX ), K, 1, DESCV )
CALL PZTRMM( 'Right', 'Upper', 'Conjugate transpose',
$ 'Non-Unit', N-K+1, JB, ONE, WORK( IPT ), 1, 1,
$ DESCT, WORK( IPX ), K, 1, DESCV )
*
* (2) X := X - 1/2 * V * (T * V' * X)
*
CALL PZGEMM( 'Conjugate transpose', 'No transpose', JB, JB,
$ N-K+1, ONE, WORK( IPV ), K, 1, DESCV,
$ WORK( IPX ), K, 1, DESCV, ZERO, WORK( IPY ),
$ 1, 1, DESCT )
CALL PZTRMM( 'Left', 'Upper', 'No transpose', 'Non-Unit',
$ JB, JB, ONE, WORK( IPT ), 1, 1, DESCT,
$ WORK( IPY ), 1, 1, DESCT )
CALL PZGEMM( 'No transpose', 'No transpose', N-K+1, JB, JB,
$ -HALF, WORK( IPV ), K, 1, DESCV, WORK( IPY ),
$ 1, 1, DESCT, ONE, WORK( IPX ), K, 1, DESCV )
*
* (3) A := A - X * V' - V * X'
*
CALL PZHER2K( 'Lower', 'No tranpose', N-K+1, JB, -ONE,
$ WORK( IPV ), K, 1, DESCV, WORK( IPX ), K, 1,
$ DESCV, RONE, A, I, J, DESCA )
*
DESCV( CSRC_ ) = MOD( DESCV( CSRC_ ) + NPCOL - 1, NPCOL )
DESCT( RSRC_ ) = MOD( DESCT( RSRC_ ) + NPROW - 1, NPROW )
DESCT( CSRC_ ) = MOD( DESCT( CSRC_ ) + NPCOL - 1, NPCOL )
*
40 CONTINUE
*
END IF
*
CALL IGSUM2D( ICTXT, 'All', ' ', 1, 1, INFO, 1, -1, 0 )
*
RETURN
*
* End of PZHETDRV
*
END
|
