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|
SUBROUTINE PBCHER2( ICONTXT, UPLO, XYDIST, N, NB, NZ, ALPHA, X,
$ INCX, Y, INCY, A, LDA, IXPOS, IYPOS, IAROW,
$ IACOL, XYCOMM, XWORK, YWORK, AWORK, MULLEN,
$ WORK )
*
* -- PB-BLAS routine (version 2.1) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory.
* April 28, 1996
*
* Jaeyoung Choi, Oak Ridge National Laboratory
* Jack Dongarra, University of Tennessee and Oak Ridge National Lab.
* David Walker, Oak Ridge National Laboratory
*
* .. Scalar Arguments ..
CHARACTER*1 AWORK, UPLO, XWORK, XYCOMM, XYDIST, YWORK
INTEGER IACOL, IAROW, ICONTXT, INCX, INCY, IXPOS,
$ IYPOS, LDA, MULLEN, N, NB, NZ
COMPLEX ALPHA
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), X( * ), Y( * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PBCHER2 is a parallel blocked version of CHER2.
* PBCHER2 performs the Hermitian rank 2 operation
*
* A := alpha*x*y' + alpha'*y*x' + A,
*
* where alpha is a scalar, x and y are N-element vectors distributed on
* columns or rows of the process template, and A is an N-by-N
* Hermitian matrix.
*
* The first elements of the vectors x and y and the matrix A can be
* located in the the middle of the first blocks.
* X and Y can be broadcast if necessary and then transposed.
* The communication scheme can be selected.
*
* Parameters
* ==========
*
* ICONTXT (input) INTEGER
* ICONTXT is the BLACS mechanism for partitioning communication
* space. A defining property of a context is that a message in
* a context cannot be sent or received in another context. The
* BLACS context includes the definition of a grid, and each
* process' coordinates in it.
*
* UPLO (input) CHARACTER*1
* UPLO specifies whether the upper or lower triangular part of
* the array A is to be referenced as follows:
*
* UPLO = 'U', Only the upper triangular part of A
* is to be referenced.
* UPLO = 'L', Only the lower triangular part of A
* is to be referenced.
*
* XYDIST (input) CHARACTER*1
* XYDIST specifies the distribution of the vectors X and Y
* as follows:
*
* XYDIST = 'C', X and Y are distributed columnwise
* or in a column of processes
* XYDIST = 'R', X and Y are distributed rowwise
* or in a row of processes
*
* N (input) INTEGER
* N specifies the order of the matrix C. N >= 0.
*
* NB (input) INTEGER
* NB specifies the row and column block size of the matrix A.
* It also specifies the block size of the vectors X and Y.
* NB >= 1.
*
* NZ (input) INTEGER
* NZ is the row and column offset to specify the row and column
* distance from the beginning of the block to the first element
* of A. And it also specifies the offset to the first elements
* of the vectors X and Y. 0 <= NZ < NB.
*
* ALPHA (input) COMPLEX
* ALPHA specifies the scalar alpha.
*
* X (input) COMPLEX array of DIMENSION at least
* ( 1 + ( Np - 1 ) * abs( INCX ) ) if XYDIST = 'C', or
* ( 1 + ( Nq - 1 ) * abs( INCX ) ) if XYDIST = 'R'.
* The incremented array X must contain the vector X.
*
* INCX (input) INTEGER
* INCX specifies the increment for the elements of X.
* INCX <> 0.
*
* Y (input) COMPLEX array of DIMENSION at least
* ( 1 + ( Np - 1 ) * abs( INCY ) ) if XYDIST = 'C', or
* ( 1 + ( Nq - 1 ) * abs( INCY ) ) if XYDIST = 'R'.
* The incremented array Y must contain the vector Y.
*
* INCY (input) INTEGER
* INCY specifies the increment for the elements of Y.
* INCY <> 0.
*
* A (input/output) COMPLEX array of local DIMENSION ( LDA, Nq ).
* On entry with UPLO = 'U', the leading N-by-N upper triangular
* part of the (global) array A must contain the upper triangu-
* lar part of the Hermitian matrix and the strictly lower
* triangular part of A is not referenced. On exit, the upper
* triangular part of the array A is overwritten by the upper
* triangular part of the updated matrix.
* On entry with UPLO = 'L', the leading N-by-N lower triangular
* part of the (global) array A must contain the lower
* triangular part of the Hermitian matrix and the strictly
* upper triangular part of A is not referenced. On exit,
* the lower triangular part of the array A is overwritten by
* the lower triangular part of the updated matrix.
*
* LDA (input) INTEGER
* LDA specifies the leading dimension of the (local) array A.
* LDA >= MAX(1,Np).
*
* IXPOS (input) INTEGER
* If XYDIST = 'C', IXPOS specifies a column of process
* template, which holds the vector X. And if XYDIST = 'R',
* IXPOS specifies a row of the template, which holds the
* vector X. If all columns or rows of processes have their
* own copies of X, then set IXPOS = -1.
*
* IYPOS (input) INTEGER
* If XYDIST = 'C', IYPOS specifies a column of process
* template, which holds the vector Y. And if XYDIST = 'R',
* IYPOS specifies a row of the template, which holds the
* vector Y. If all columns or rows of processes have their
* own copies of Y, then set IYPOS = -1.
*
* IAROW (input) INTEGER
* It specifies a row of process template which has the
* first block of A. It also represents a row of the template
* which holds the first blcok of the vectors X and Y if
* XYDIST = 'C'.
*
* IACOL (input) INTEGER
* It specifies a column of process template which has the
* first block of A. It also represents the column of the
* template which holds the first blcok of the vectors X and Y
* if XYDIST = 'R'.
*
* XYCOMM (input) CHARACTER*1
* XYCOMM specifies the communication scheme of the vectors X
* and Y if communication is necessary. It follows topology
* definition of BLACS.
*
* XWORK (input) CHARACTER*1
* XWORK determines whether X is a workspace or not.
*
* XWORK = 'Y': X is workspace in other processes.
* X is sent to X position in other processes.
* It is assumed that processes have
* sufficient space to store (local) X.
* XWORK = 'N': Data in X will be untouched (unchanged).
*
* YWORK (input) CHARACTER*1
* YWORK determines whether Y is a workspace or not.
*
* YWORK = 'Y': Y is workspace in other processes.
* Y is sent to Y position in other processes.
* It is assumed that processes have
* sufficient space to store (local) Y.
* YWORK = 'N': Data in Y will be untouched (unchanged).
*
* AWORK (input) CHARACTER*1
* AWORK determines whether the other triangular part of A is
* accessed and modified or not.
*
* AWORK = 'N': if UPLO = 'U', only upper triangular portion
* portion of the matrix A is accessed and the
* lower triangular portion is untouched.
* Likewise if UPLO = 'L', only lower triangular
* portion of the matrix A is accessed and the
* upper triangular portion is untouched.
* AWORK = 'Y': if UPLO = 'U', only lower triangular portion
* of the matrix A may be accessed and modified
* for fast computation. And if UPLO = 'L', the
* upper triangular portion of the matrix A may
* be accessed and modified for fast computation.
*
* MULLEN (input) INTEGER
* MULLEN specifies multiplication length of the optimum column
* number of the matrix A for multiplying X with Y'. The value
* depends on machine characteristics.
*
* WORK (workspace) COMPLEX array of DIMENSION SIZE(WORK).
* It will store copy of X and/or X'.
*
* Parameters Details
* ==================
*
* Lx It is a local portion of L owned by a process, (L is
* replaced by M, or N, and x is replaced by either p
* (=NPROW) or q (=NPCOL)). The value is determined by L, LB,
* x, and MI, where LB is a block size and MI is a row or
* column position in a process template. Lx is equal to or
* less than Lx0 = CEIL( L, LB*x ) * LB.
*
* Memory Requirement of WORK
* ==========================
*
* NN = N + NZ
* Npb = CEIL( NN, NB*NPROW )
* Nqb = CEIL( NN, NB*NPCOL )
* Np0 = NUMROC( NN, NB, 0, 0, NPROW ) ~= Npb * NB
* Nq0 = NUMROC( NN, NB, 0, 0, NPCOL ) ~= Nqb * NB
* LCMQ = LCM / NPCOL
* LCMP = LCM / NPROW
* ISZCMP = CEIL(MULLEN, LCMQ*NB)
* SZCMP = ISZCMP * ISZCMP * LCMQ*NB * LCMP*NB
*
* (1) XYDIST = 'Col'
* Size(WORK) = Nq0
* + Np0 ( if IXPOS <> -1 and XWORK <> 'Y' )
* + Np0 ( if IYPOS <> -1 and YWORK <> 'Y' )
* + MAX[ SZCMP ( if AWORK <> 'Y' ),
* CEIL(Nqb,LCMQ)*NB*MIN(LCMQ,CEIL(NN,NB) ]
* (b) XYDIST = 'Row'
* Size(WORK) = Np0
* + Nq0 ( if IXPOS <> -1 and XWORK <> 'Y' )
* + Nq0 ( if IYPOS <> -1 and YWORK <> 'Y' )
* + MAX[ SZCMP ( if AWORK <> 'Y' ),
* CEIL(Npb,LCMP)*NB*MIN(LCMP,CEIL(NN,NB) ]
*
* Notes
* -----
* More precise space can be computed as
*
* CEIL(Nqb,LCMQ)*NB => NUMROC( NUMROC(NN,NB,0,0,NPCOL), NB, 0, 0, LCMQ)
* = NUMROC( Nq0, NB, 0, 0, LCMQ )
* CEIL(Npb,LCMP)*NB => NUMROC( NUMROC(NN,NB,0,0,NPROW), NB, 0, 0, LCMP)
* = NUMROC( Np0, NB, 0, 0, LCMP )
*
* =====================================================================
*
* .. Parameters ..
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
CHARACTER*1 COMMXY, FORM
LOGICAL ASPACE, COLUMN, UPPER, XDATA, YDATA
INTEGER INFO, IPBZ, IPT, IPW, IPY, IQBZ, ISZCMP, IZ,
$ JJ, JNPBZ, JPBZ, JQBZ, JZ, KI, KIZ, KJ, KJZ,
$ KZ, LCM, LCMP, LCMQ, LMW, LNW, LPBZ, LQBZ,
$ MRCOL, MRROW, MYCOL, MYROW, MZCOL, MZROW, NN,
$ NP, NPCOL, NPROW, NQ
COMPLEX DUMMY, TALPHA
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, NUMROC
EXTERNAL ICEIL, ILCM, LSAME, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CGEBR2D, CGEBS2D, CGERC,
$ PBCTRAD1, PBCTRNV, PBCVECADD, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CONJG, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible.
*
IF( N.EQ.0 .OR. ALPHA.EQ.ZERO ) RETURN
*
CALL BLACS_GRIDINFO( ICONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
UPPER = LSAME( UPLO, 'U' )
COLUMN = LSAME( XYDIST, 'C' )
*
* Test the input parameters.
*
INFO = 0
IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
INFO = 2
ELSE IF( ( .NOT.COLUMN ).AND.
$ ( .NOT.LSAME( XYDIST, 'R' ) ) ) THEN
INFO = 3
ELSE IF( N .LT.0 ) THEN
INFO = 4
ELSE IF( NB .LT.1 ) THEN
INFO = 5
ELSE IF( NZ .LT.0 .OR. NZ.GE.NB ) THEN
INFO = 6
ELSE IF( INCX.EQ.0 ) THEN
INFO = 9
ELSE IF( INCY.EQ.0 ) THEN
INFO = 11
ELSE IF( IAROW.LT.0 .OR. IAROW.GE.NPROW ) THEN
INFO = 16
ELSE IF( IACOL.LT.0 .OR. IACOL.GE.NPCOL ) THEN
INFO = 17
END IF
*
10 CONTINUE
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICONTXT, 'PBCHER ', INFO )
RETURN
END IF
*
* Start the operations.
*
IZ = 0
JZ = 0
NN = N + NZ
NP = NUMROC( NN, NB, MYROW, IAROW, NPROW )
IF( MYROW.EQ.IAROW ) THEN
NP = NP - NZ
IZ = NZ
END IF
*
NQ = NUMROC( NN, NB, MYCOL, IACOL, NPCOL )
IF( MYCOL.EQ.IACOL ) THEN
NQ = NQ - NZ
JZ = NZ
END IF
KZ = 0
*
ASPACE = LSAME( AWORK, 'Y' )
XDATA = .FALSE.
IF( IXPOS.EQ.-1 ) XDATA = .TRUE.
YDATA = .FALSE.
IF( IYPOS.EQ.-1 ) YDATA = .TRUE.
COMMXY = XYCOMM
IF( LSAME( COMMXY, ' ' ) ) COMMXY = '1'
*
* LCM : the least common multiple of NPROW and NPCOL
*
LCM = ILCM( NPROW, NPCOL )
LCMP = LCM / NPROW
LCMQ = LCM / NPCOL
LPBZ = LCMP * NB
LQBZ = LCMQ * NB
*
MRROW = MOD( NPROW+MYROW-IAROW, NPROW )
MRCOL = MOD( NPCOL+MYCOL-IACOL, NPCOL )
*
TALPHA = CONJG( ALPHA )
IF( LDA.LT.MAX(1,NP) ) INFO = 13
*
* PART 1: Distribute a column (or row) vector X and its transpose
* ===============================================================
*
IF( COLUMN ) THEN
*
* Form A := alpha*X*Y' + alpha*Y'*X + A.
* _____________ _____________
* |\_ | || || |\_ |
* | \_ | || || | \_ |
* | \_ | || ____________ || ____________ | \_ |
* | A_ |=a*|X*-----Y'-----+a'*|Y*-----X'-----+| A_ |
* | \_ | || || | \_ |
* | \_ | || || | \_ |
* |____________\| || || |____________\|
*
IF( IXPOS.LT.-1 .OR. IXPOS.GE.NPCOL ) THEN
INFO = 14
ELSE IF( IYPOS.LT.-1 .OR. IYPOS.GE.NPCOL ) THEN
INFO = 15
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast X and Y if necessary
*
IPT = 1
IPY = 1
IF( .NOT.XDATA ) THEN
IF( LSAME( XWORK, 'Y' ) ) THEN
IF( MYCOL.EQ.IXPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Row', COMMXY, 1, NP, X, INCX )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMXY, 1, NP, X, INCX,
$ MYROW, IXPOS )
END IF
XDATA = .TRUE.
ELSE
IF( MYCOL.EQ.IXPOS ) THEN
CALL PBCVECADD( ICONTXT, 'V', NP, ONE, X, INCX, ZERO,
$ WORK, 1 )
CALL CGEBS2D( ICONTXT, 'Row', COMMXY, 1, NP, WORK, 1 )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMXY, 1, NP, WORK, 1,
$ MYROW, IXPOS )
END IF
IPT = NP + 1
IPY = IPT
END IF
END IF
*
IF( .NOT.YDATA ) THEN
IF( LSAME( YWORK, 'Y' ) ) THEN
IF( MYCOL.EQ.IYPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Row', COMMXY, 1, NP, Y, INCY )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMXY, 1, NP, Y, INCY,
$ MYROW, IYPOS )
END IF
YDATA = .TRUE.
ELSE
IF( MYCOL.EQ.IYPOS ) THEN
CALL PBCVECADD( ICONTXT, 'V', NP, ONE, Y, INCY, ZERO,
$ WORK(IPY), 1 )
CALL CGEBS2D( ICONTXT, 'Row', COMMXY, 1, NP,
$ WORK(IPY), 1 )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMXY, 1, NP,
$ WORK(IPY), 1, MYROW, IYPOS )
END IF
IPT = NP + IPY
END IF
END IF
*
* Transpose the vector Y to WORK(IPT), where Y is distributed
*
IPW = NQ + IPT
IF( YDATA ) THEN
CALL PBCTRNV( ICONTXT, 'Col', 'T', N, NB, NZ, Y, INCY, ZERO,
$ WORK(IPT), 1, IAROW, -1, -1, IACOL, WORK(IPW) )
ELSE
CALL PBCTRNV( ICONTXT, 'Col', 'T', N, NB, NZ, WORK(IPY), 1,
$ ZERO, WORK(IPT), 1, IAROW, -1, -1, IACOL,
$ WORK(IPW) )
END IF
*
ELSE
*
* Form A := alpha*x'*x + A.
* _____________ _____________
* |\_ | || || |\_ |
* | \_ | || || | \_ |
* | \_ | || ____________ || ____________ | \_ |
* | A_ |=a'*|Y*-----X'-----+a*|X*-----Y'----- +| A_ |
* | \_ | || || | \_ |
* | \_ | || || | \_ |
* |____________\| || || |____________\|
*
IF( IXPOS.LT.-1 .OR. IXPOS.GE.NPROW ) THEN
INFO = 14
ELSE IF( IYPOS.LT.-1 .OR. IYPOS.GE.NPROW ) THEN
INFO = 15
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast X and Y if necessary
*
IPT = 1
IPY = 1
IF( .NOT.XDATA ) THEN
IF( LSAME( XWORK, 'Y' ) ) THEN
IF( MYROW.EQ.IXPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Col', COMMXY, 1, NQ, X, INCX )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMXY, 1, NQ, X, INCX,
$ IXPOS, MYCOL )
END IF
XDATA = .TRUE.
ELSE
IF( MYROW.EQ.IXPOS ) THEN
CALL PBCVECADD( ICONTXT, 'G', NQ, ONE, X, INCX, ZERO,
$ WORK, 1 )
CALL CGEBS2D( ICONTXT, 'Col', COMMXY, 1, NQ, WORK, 1 )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMXY, 1, NQ, WORK, 1,
$ IXPOS, MYCOL )
END IF
IPT = NQ + 1
IPY = IPT
END IF
END IF
*
IF( .NOT.YDATA ) THEN
IF( LSAME( YWORK, 'Y' ) ) THEN
IF( MYROW.EQ.IYPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Col', COMMXY, 1, NQ, Y, INCY )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMXY, 1, NQ, Y, INCY,
$ IYPOS, MYCOL )
END IF
YDATA = .TRUE.
ELSE
IF( MYROW.EQ.IYPOS ) THEN
CALL PBCVECADD( ICONTXT, 'G', NQ, ONE, Y, INCY, ZERO,
$ WORK(IPY), 1 )
CALL CGEBS2D( ICONTXT, 'Col', COMMXY, 1, NQ,
$ WORK(IPY), 1 )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMXY, 1, NQ,
$ WORK(IPY), 1, IYPOS, MYCOL )
END IF
IPT = NQ + IPY
END IF
END IF
*
* Transpose the vector X to WORK(IPT), where X is distributed
*
IPW = NP + IPT
IF( YDATA ) THEN
CALL PBCTRNV( ICONTXT, 'Row', 'T', N, NB, NZ, Y, INCY, ZERO,
$ WORK(IPT), 1, -1, IACOL, IAROW, -1, WORK(IPW) )
ELSE
CALL PBCTRNV( ICONTXT, 'Row', 'T', N, NB, NZ, WORK(IPY), 1,
$ ZERO, WORK(IPT), 1, -1, IACOL, IAROW, -1,
$ WORK(IPW) )
END IF
END IF
*
* PART 2: Update A with X and Y'
* ==============================
*
IF( NP.EQ.0 .OR. NQ.EQ.0 ) GO TO 80
*
* If A is a Hermitian upper triangular matrix,
*
IF( UPPER ) THEN
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 40 JJ = 1, ICEIL(NQ+JZ, IQBZ)
LMW = MIN( IPBZ-IZ, NP-JPBZ )
LNW = MIN( IQBZ-JZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the lower triangular part
*
IF( ASPACE ) THEN
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( XDATA ) THEN
CALL CGERC( JNPBZ, LNW, ALPHA, X, INCX, WORK(JQBZ+IPT),
$ 1, A(1,JQBZ+1), LDA )
ELSE
CALL CGERC( JNPBZ, LNW, ALPHA, WORK, 1, WORK(JQBZ+IPT),
$ 1, A(1,JQBZ+1), LDA )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( XDATA ) THEN
CALL CGERC( JNPBZ, LNW, TALPHA, WORK(IPT), 1,
$ X(JQBZ*INCX+1), INCX, A(1,JQBZ+1), LDA )
ELSE
CALL CGERC( JNPBZ, LNW, TALPHA, WORK(IPT), 1,
$ WORK(JQBZ+1), 1, A(1,JQBZ+1), LDA )
END IF
END IF
*
* Update data in the upper triangular matrix
* and save data in the lower triangular matrix
*
ELSE
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( XDATA ) THEN
CALL CGERC( JPBZ, LNW, ALPHA, X, INCX,
$ WORK(JQBZ+IPT), 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, X(JPBZ*INCX+1), INCX,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGERC( JPBZ, LNW, ALPHA, WORK, 1, WORK(JQBZ+IPT),
$ 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+1), 1,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( XDATA ) THEN
CALL CGERC( JPBZ, LNW, TALPHA, WORK(IPT), 1,
$ X(JQBZ*INCX+1), INCX, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ X(JQBZ*INCX+1), INCX, WORK(IPW), MAX(1,LMW))
ELSE
CALL CGERC( JPBZ, LNW, TALPHA, WORK(IPT), 1,
$ WORK(JQBZ+1), 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+1), 1, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
IF( MYCOL.EQ.IACOL ) KZ = JZ
*
DO 30 KJ = 0, LCMQ-1
20 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 20
END IF
KIZ = MAX( 0, KI*NB-IZ )
KJZ = MAX( 0, KJ*NB-JZ )
IF( KJZ.GE.LNW )
$ GO TO 40
FORM = 'G'
IF( MZROW.EQ.MZCOL )
$ FORM = 'H'
MZCOL = MZCOL + NPCOL
CALL PBCTRAD1( ICONTXT, 'Upper', FORM, KIZ, NB, KZ, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, ONE,
$ A( JPBZ+1, JQBZ+KJZ+1 ), LDA,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
KZ = 0
30 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
IZ = 0
JZ = 0
40 CONTINUE
*
* If A is a Hermitian lower triangular matrix,
*
ELSE
*
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 70 JJ = 1, ICEIL(NQ+JZ, IQBZ)
LMW = MIN( IPBZ-IZ, NP-JPBZ )
LNW = MIN( IQBZ-JZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the upper triangular part
*
IF( ASPACE ) THEN
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( XDATA ) THEN
CALL CGERC( NP-JPBZ, LNW, ALPHA, X(JPBZ*INCX+1), INCX,
$ WORK(JQBZ+IPT), 1, A(JPBZ+1,JQBZ+1), LDA )
ELSE
CALL CGERC( NP-JPBZ, LNW, ALPHA, WORK(JPBZ+1), 1,
$ WORK(JQBZ+IPT), 1, A(JPBZ+1,JQBZ+1), LDA )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( XDATA ) THEN
CALL CGERC( NP-JPBZ, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ X(JQBZ*INCX+1), INCX, A(JPBZ+1,JQBZ+1), LDA)
ELSE
CALL CGERC( NP-JPBZ, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+1), 1, A(JPBZ+1,JQBZ+1), LDA )
END IF
END IF
*
* Update data in the lower triangular matrix
* and save data in the upper triangular matrix
*
ELSE
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( XDATA ) THEN
CALL CGERC( NP-JNPBZ, LNW, ALPHA, X(JNPBZ*INCX+1), INCX,
$ WORK(JQBZ+IPT), 1, A(JNPBZ+1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, X(JPBZ*INCX+1), INCX,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGERC( NP-JNPBZ, LNW, ALPHA, WORK(JNPBZ+1), 1,
$ WORK(JQBZ+IPT), 1, A(JNPBZ+1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+1), 1,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( XDATA ) THEN
CALL CGERC( NP-JNPBZ, LNW, TALPHA, WORK(JNPBZ+IPT), 1,
$ X(JQBZ*INCX+1), INCX, A(JNPBZ+1,JQBZ+1),LDA)
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ X(JQBZ*INCX+1), INCX, WORK(IPW), MAX(1,LMW))
ELSE
CALL CGERC( NP-JNPBZ, LNW, TALPHA, WORK(JNPBZ+IPT), 1,
$ WORK(JQBZ+1), 1, A(JNPBZ+1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+1), 1, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
IF( MYCOL.EQ.IACOL ) KZ = JZ
*
DO 60 KJ = 0, LCMQ-1
50 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 50
END IF
KIZ = MAX( 0, KI*NB-IZ )
KJZ = MAX( 0, KJ*NB-JZ )
IF( KJZ.GE.LNW )
$ GO TO 70
FORM = 'G'
IF( MZROW.EQ.MZCOL )
$ FORM = 'H'
MZCOL = MZCOL + NPCOL
*
CALL PBCTRAD1( ICONTXT, 'Lower', FORM, KIZ, NB, KZ, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, ONE,
$ A( JPBZ+1, JQBZ+KJZ+1 ), LDA,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
KZ = 0
60 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
IZ = 0
JZ = 0
70 CONTINUE
END IF
*
80 CONTINUE
*
* PART 3: Transpose X' (X is already distributed)
* ===============================================
*
IF( COLUMN ) THEN
IF( XDATA ) THEN
CALL PBCTRNV( ICONTXT, 'Col', 'T', N, NB, NZ, X, INCX, ZERO,
$ WORK(IPT), 1, IAROW, -1, -1, IACOL, WORK(IPW) )
ELSE
CALL PBCTRNV( ICONTXT, 'Col', 'T', N, NB, NZ, WORK, 1, ZERO,
$ WORK(IPT), 1, IAROW, -1, -1, IACOL, WORK(IPW) )
END IF
*
ELSE
IF( XDATA ) THEN
CALL PBCTRNV( ICONTXT, 'Row', 'T', N, NB, NZ, X, INCX, ZERO,
$ WORK(IPT), 1, -1, IACOL, IAROW, -1, WORK(IPW) )
ELSE
CALL PBCTRNV( ICONTXT, 'Row', 'T', N, NB, NZ, WORK, 1, ZERO,
$ WORK(IPT), 1, -1, IACOL, IAROW, -1, WORK(IPW) )
END IF
END IF
*
* PART 4: Update A with Y and X'
* =====================================
*
IF( NP.EQ.0 .OR. NQ.EQ.0 ) RETURN
IF( MYROW.EQ.IAROW ) IZ = NZ
IF( MYCOL.EQ.IACOL ) JZ = NZ
*
* If A is a Hermitian upper triangular matrix,
*
IF( UPPER ) THEN
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 110 JJ = 1, ICEIL(NQ+JZ, IQBZ)
LMW = MIN( IPBZ-IZ, NP-JPBZ )
LNW = MIN( IQBZ-JZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the lower triangular part
*
IF( ASPACE ) THEN
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( YDATA ) THEN
CALL CGERC( JNPBZ, LNW, TALPHA, Y, INCY, WORK(JQBZ+IPT),
$ 1, A(1,JQBZ+1), LDA )
ELSE
CALL CGERC( JNPBZ, LNW, TALPHA, WORK(IPY), 1,
$ WORK(JQBZ+IPT), 1, A(1,JQBZ+1), LDA )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( YDATA ) THEN
CALL CGERC( JNPBZ, LNW, ALPHA, WORK(IPT), 1,
$ Y(JQBZ*INCY+1), INCY, A(1,JQBZ+1), LDA )
ELSE
CALL CGERC( JNPBZ, LNW, ALPHA, WORK(IPT), 1,
$ WORK(JQBZ+IPY), 1, A(1,JQBZ+1), LDA )
END IF
END IF
*
* Update data in the upper triangular matrix
* and save data in the lower triangular matrix
*
ELSE
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( YDATA ) THEN
CALL CGERC( JPBZ, LNW, TALPHA, Y, INCY,
$ WORK(JQBZ+IPT), 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, Y(JPBZ*INCY+1), INCY,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGERC( JPBZ, LNW, TALPHA, WORK(IPY), 1,
$ WORK(JQBZ+IPT), 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPY), 1,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( YDATA ) THEN
CALL CGERC( JPBZ, LNW, ALPHA, WORK(IPT), 1,
$ Y(JQBZ*INCY+1), INCY, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ Y(JQBZ*INCY+1), INCY, WORK(IPW), MAX(1,LMW))
ELSE
CALL CGERC( JPBZ, LNW, ALPHA, WORK(IPT), 1,
$ WORK(JQBZ+IPY), 1, A(1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+IPY), 1, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
IF( MYCOL.EQ.IACOL ) KZ = JZ
*
DO 100 KJ = 0, LCMQ-1
90 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 90
END IF
KIZ = MAX( 0, KI*NB-IZ )
KJZ = MAX( 0, KJ*NB-JZ )
IF( KJZ.GE.LNW )
$ GO TO 110
FORM = 'G'
IF( MZROW.EQ.MZCOL )
$ FORM = 'H'
MZCOL = MZCOL + NPCOL
CALL PBCTRAD1( ICONTXT, 'Upper', FORM, KIZ, NB, KZ, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, ONE,
$ A( JPBZ+1, JQBZ+KJZ+1 ), LDA,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
KZ = 0
100 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
IZ = 0
JZ = 0
110 CONTINUE
*
* If A is a Hermitian lower triangular matrix,
*
ELSE
*
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 140 JJ = 1, ICEIL(NQ+JZ, IQBZ)
LMW = MIN( IPBZ-IZ, NP-JPBZ )
LNW = MIN( IQBZ-JZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the upper triangular part
*
IF( ASPACE ) THEN
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( YDATA ) THEN
CALL CGERC( NP-JPBZ, LNW, TALPHA, Y(JPBZ*INCY+1), INCY,
$ WORK(JQBZ+IPT), 1, A(JPBZ+1,JQBZ+1), LDA )
ELSE
CALL CGERC( NP-JPBZ, LNW, TALPHA, WORK(JPBZ+IPY), 1,
$ WORK(JQBZ+IPT), 1, A(JPBZ+1,JQBZ+1), LDA )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( YDATA ) THEN
CALL CGERC( NP-JPBZ, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ Y(JQBZ*INCY+1), INCY, A(JPBZ+1,JQBZ+1), LDA)
ELSE
CALL CGERC( NP-JPBZ, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+IPY), 1, A(JPBZ+1,JQBZ+1), LDA )
END IF
END IF
*
* Update data in the lower triangular matrix
* and save data in the upper triangular matrix
*
ELSE
*
* if XYDIST = 'Column'
*
IF( COLUMN ) THEN
IF( YDATA ) THEN
CALL CGERC( NP-JNPBZ, LNW, TALPHA, Y(JNPBZ*INCY+1),
$ INCY, WORK(JQBZ+IPT), 1, A(JNPBZ+1,JQBZ+1),
$ LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, Y(JPBZ*INCY+1), INCY,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGERC( NP-JNPBZ, LNW, TALPHA, WORK(JNPBZ+IPY), 1,
$ WORK(JQBZ+IPT), 1, A(JNPBZ+1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, TALPHA, WORK(JPBZ+IPY), 1,
$ WORK(JQBZ+IPT), 1, WORK(IPW), MAX(1,LMW) )
END IF
*
* if XYDIST = 'Row'
*
ELSE
IF( YDATA ) THEN
CALL CGERC( NP-JNPBZ, LNW, ALPHA, WORK(JNPBZ+IPT), 1,
$ Y(JQBZ*INCY+1), INCY, A(JNPBZ+1,JQBZ+1),LDA)
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ Y(JQBZ*INCY+1), INCY, WORK(IPW), MAX(1,LMW))
ELSE
CALL CGERC( NP-JNPBZ, LNW, ALPHA, WORK(JNPBZ+IPT), 1,
$ WORK(JQBZ+IPY), 1, A(JNPBZ+1,JQBZ+1), LDA )
CALL PBCVECADD( ICONTXT, 'G', LMW*LNW, ZERO, DUMMY, 1,
$ ZERO, WORK(IPW), 1 )
CALL CGERC( LMW, LNW, ALPHA, WORK(JPBZ+IPT), 1,
$ WORK(JQBZ+IPY), 1, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
IF( MYCOL.EQ.IACOL ) KZ = JZ
*
DO 130 KJ = 0, LCMQ-1
120 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 120
END IF
KIZ = MAX( 0, KI*NB-IZ )
KJZ = MAX( 0, KJ*NB-JZ )
IF( KJZ.GE.LNW )
$ GO TO 140
FORM = 'G'
IF( MZROW.EQ.MZCOL )
$ FORM = 'H'
MZCOL = MZCOL + NPCOL
*
CALL PBCTRAD1( ICONTXT, 'Lower', FORM, KIZ, NB, KZ, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, ONE,
$ A( JPBZ+1, JQBZ+KJZ+1 ), LDA,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
KZ = 0
130 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
IZ = 0
JZ = 0
140 CONTINUE
END IF
*
RETURN
*
* End of PBCHER2
*
END
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