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|
SUBROUTINE PBDTRMM( ICONTXT, MATBLK, SIDE, UPLO, TRANSA, DIAG, M,
$ N, NB, ALPHA, A, LDA, B, LDB, IAROW, IACOL,
$ IBPOS, ABCOMM, ABWORK, 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 ABCOMM, ABWORK, DIAG, MATBLK, SIDE, TRANSA,
$ UPLO
INTEGER IACOL, IAROW, IBPOS, ICONTXT, LDA, LDB, M,
$ MULLEN, N, NB
DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PBDTRMM is a parallel blocked version of the Level 3 BLAS routine
* DTRMM.
* PBDTRMM performs one of the matrix-matrix operations based on block
* cyclic distribution.
*
* B := alpha*op( A )*B, or B := alpha*B*op( A ),
*
* op( A )*X = alpha*B, or X*op( A ) = alpha*B,
*
* where alpha is a scalar, X and B are M-bt-N matrices, A is a unit, or
* non-unit, upper or lower triangular matrix. op( A ) is one of
*
* op( A ) = A, A**T, or A**H
*
* where the size of the matrix op( A ) is M-by-M if SIDE = 'L', and N-
* by-N otherwise. The M-by-N matrix B is a column block (only one
* column of processors have B) if SIDE = 'L', and a row block otherwise
* (only one row of processors have B). The matrix X is overwritten on
* B.
*
* The first elements of the matrices A, and B should be located at
* the beginnings of their first blocks. (not the middle of the blocks.
*
* B can be broadcast columnwise or rowwise, or transposed if necessary.
* 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.
*
* MATBLK (input) CHARACTER*1
* MATBLK specifies whether op( A ) is a (full) block matrix or
* a single block as follows:
*
* MATBLK = 'M', op( A ) is a (full) block matrix
* MATBLK = 'B', op( A ) is a single block
*
* SIDE (input) CHARACTER*1
* SIDE specifies whether op( A ) multiplies B from the left or
* right as follows:
*
* SIDE = 'L', B := alpha*op( A )*B.
* SIDE = 'R', B := alpha*B*op( A ).
*
* UPLO (input) CHARACTER*1
* UPLO specifies whether the matrix A is an upper or lower
* triangular matrix as follows:
*
* UPLO = 'U', A is an upper triangular matrix.
* UPLO = 'L', A is a lower triangular matrix.
*
* TRANSA (input) CHARACTER*1
* TRANSA specifies the form of op( A ) to be used in the
* matrix multiplication as follows:
*
* TRANSA = 'N', op( A ) = A.
* TRANSA = 'T', op( A ) = A**T.
* TRANSA = 'C', op( A ) = A**H.
*
* DIAG (input) CHARACTER*1
* DIAG specifies whether or not A is unit triangular
* as follows:
*
* DIAG = 'U', A is assumed to be unit triangular.
* DIAG = 'N', A is not assumed to be unit triangular.
*
* M (input) INTEGER
* M specifies the (global) number of rows of B. M >= 0.
*
* N (input) INTEGER
* N specifies the (global) number of columns of B. N >= 0.
*
* NB (input) INTEGER
* NB specifies the row and column block size of matrix A.
* It also specifies the row block size of the matrix B if
* MATBLK = 'M' and SIDE = 'L', or MATBLK = 'B' and SIDE = 'R';
* and the column block size of the matrix B if MATBLK = 'M'
* and SIDE = 'R', or MATBLK = 'B' and SIDE = 'L'. NB >= 1.
*
* ALPHA (input) DOUBLE PRECISION
* ALPHA specifies the scalar alpha. When alpha is zero then
* A is not referenced and B need not be set before entry.
*
* A (input) DOUBLE PRECISION array of DIMENSION ( LDA, kq ),
* where kq is Mq (Kp is Mp) when SIDE = 'L' and is Nq (Kp is
* Np) when SIDE = 'R'.
* If SIDE = `L', the M-by-M part of the array A must contain
* the (global) triangular matrix, such that when UPLO = 'U',
* the leading M-by-M upper triangular part of the array A must
* contain the upper triangular part of the (global) matrix and
* the strictly lower triangular part of A is not referenced,
* and when UPLO = 'L', the leading M-by-M lower triangular
* part of the array A must contain the lower triangular part
* of the (global) matrix and the strictly upper triangular
* part of A is not referenced.
* And if SIDE = 'R', the N-by-N part of the (global) array A
* must contain the (global) matrix, such that when UPLO = 'U',
* the leading N-by-N upper triangular part of the array A must
* contain the upper triangular part of the (global) matrix and
* the strictly lower triangular part of A is not referenced,
* and when UPLO = 'L', the leading N-by-N lower triangular
* part of the array A must contain the lower triangular part
* of the (global) matrix and the strictly upper triangular
* part of A is not referenced.
* Note that when DIAG = `U', the diagonal elements of A are
* not referenced either, but are assumed to be unity.
*
* LDA (input) INTEGER
* LDA specifies the first dimension of A as declared in the
* calling (sub) program. LDA >= MAX(1,Mp) if SIDE = 'L', and
* LDA >= MAX(1,Np) otherwise.
*
* B (input/output) DOUBLE PRECISION array of DIMENSION
* ( LDB, Nq )
* On entry, the leading Mp-by-Nq part of the array B must
* contain the matrix B when SIDE = 'R', or the leading Mp-by-
* Nq part of the array B must contain the (local) matrix B
* otherwise.
* On exit B is overwritten by the transformed matrix. Input
* values of B would be changed after the computation in the
* processors which don't have the resultant column block or
* row block of B if MATBLK = 'M'.
*
* LDB (input) INTEGER
* LDB specifies the first dimension of (local) B as declared
* in the calling (sub) program. LDB >= MAX(1,Mp).
*
* IAROW (input) INTEGER
* It specifies a row of processor template which has the
* first block of A. When MATBLK = 'B', SIDE = 'R', and all
* rows of processors have their own copies of A, set IAROW
* = -1.
*
* IACOL (input) INTEGER
* It specifies a column of processor template which has the
* first block of A. When MATBLK = 'B', SIDE = 'L', and all
* columns of processors have their own copies of A, set
* IACOL = -1.
*
* IBPOS (input) INTEGER
* When MATBLK = 'M', if SIDE = 'L', IBPOS specifies a column of
* the process template, which holds the column of blocks of B
* (-1 <= IBPOS < NPCOL). And if SIDE = 'R', it specifies a row
* of the template, which holds the row of blocks of B (-1 <=
* IBPOS < NPROW). If all columns or rows of the template have
* their own copies of B, set IBPOS = -1.
* When MATBLK = 'B', if SIDE = 'L', it specifies a column of
* the template which has the first block of B (0 <= IBPOS
* < NPCOL), and if SIDE = 'R', it specifies a row of the
* template, which has the first block of B (0 <=IBPOS <NPROW).
*
* ABCOMM (input) CHARACTER*1
* When MATBLK = 'M', ABCOMM specifies the communication scheme
* of a row or column block of B if TRANSA <> 'N', and it is
* ignored if TRANSA = 'N'.
* When MATBLK = 'B', ABCOMM specifies the communication scheme
* of a block of A.
* It follows topology definition of BLACS.
*
* ABWORK (input) CHARACTER*1
* When MATBLK = 'M', ABWORK determines whether B is a
* workspace or not.
*
* ABWORK = 'Y': B is workspace in other processors.
* It is assumed that processors have
* sufficient space to store (local) B.
* ABWORK = 'N': Data of B in other processors will be
* untouched (unchanged).
*
* And MATBLK = 'B', ABWORK determines whether A is a
* workspace or not.
*
* ABWORK = 'Y': A is workspace in other processors.
* A is sent to A position in other processors.
* It is assumed that processors have
* sufficient space to store a single block A.
* ABWORK = 'N': Data of A in other processors will be
* untouched (unchanged).
*
* MULLEN (input) INTEGER
* When MATBLK = 'M', it specifies multiplication length of the
* optimum column number of A for multiplying A with B. The
* value depends on machine characteristics. When MATBLK = 'B',
* the argument is ignored.
*
* WORK (workspace) DOUBLE PRECISION array
* It will store copy of B, resultant B, and portion of A
* if necessary.
*
* Parameters Details
* ==================
*
* Lx It is a local portion of L owned by a processor, (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 processor template. Lx is equal to or
* less than Lx0 = CEIL( L, LB*x ) * LB.
*
* Memory Requirement of WORK
* ==========================
*
* Mqb = CEIL( M, NB*NPCOL )
* Npb = CEIL( N, NB*NPROW )
* Mq0 = NUMROC( M, NB, 0, 0, NPCOL ) ~= Mqb * NB
* Np0 = NUMROC( N, NB, 0, 0, NPROW ) ~= Npb * NB
* LCMQ = LCM / NPCOL
* LCMP = LCM / NPROW
* ISZCMP = CEIL(MULLEN, LCMQ*NB)
* SZCMP = ISZCMP * ISZCMP * LCMQ*NB * LCMP*NB
*
* (1) MATBLK = 'M'
* (a) SIDE = 'Left'
* (i) TRANSA = 'N'
* Size(WORK) = N * Mq0
* + Mp0 * N (if IBPOS <> -1 and ABWORK <> 'Y') ]
* + MAX[ SZCMP,
* N*CEIL(Mqb,LCMQ)*NB ( if IBPOS <> -1 ),
* N*CEIL(Mqb,LCMQ)*NB*MIN(LCMQ,CEIL(M,NB))
* ( if IBPOS = -1 ) ]
* (ii) TRANSA = 'T'/'C'
* Size(WORK) = N * Mq0 + SZCMP
* + Mp0 * N (if IBPOS <> -1 and ABWORK <> 'Y') ]
* (b) SIDE = 'Right'
* (i) TRANSA = 'N'
* Size(WORK) = Np0 * M
* + M * Nq0 (if IBPOS <> -1 and ABWORK <> 'Y') ]
* + MAX[ SZCMP,
* M*CEIL(Npb,LCMP)*NB ( if IBPOS <> -1 ),
* M*CEIL(Npb,LCMP)*NB*MIN(LCMP,CEIL(N,NB))
* ( if IBPOS = -1 ) ]
* (ii) TRANSA = 'T'/'C'
* Size(WORK) = Np0 * M + SZCMP
* + M * Nq0 (if IBPOS <> -1 and ABWORK <> 'Y') ]
*
* (2) MATBLK = 'B'
* (a) SIDE = 'Left'
* Size(WORK) = M * M (in IAROW; if IACOL <> -1 and ABWORK <> 'Y')
* (b) SIDE = 'Right'
* Size(WORK) = N * N (in IACOL; if IAROW <> -1 and ABWORK <> 'Y')
*
* Notes
* -----
* More precise space can be computed as
*
* CEIL(Mqb,LCMQ)*NB => NUMROC( NUMROC(M,NB,0,0,NPCOL), NB, 0, 0, LCMQ )
* = NUMROC( Mq0, NB, 0, 0, LCMQ )
* CEIL(Npb,LCMP)*NB => NUMROC( NUMROC(N,NB,0,0,NPROW), NB, 0, 0, LCMP )
* = NUMROC( Np0, NB, 0, 0, LCMP )
*
* =====================================================================
*
* ..
* .. Parameters ..
DOUBLE PRECISION ONE, ZERO
PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
* ..
* .. Local Scalars ..
CHARACTER*1 COMMA, COMMB, FORM
LOGICAL ADATA, AMAT, ASPACE, BDATA, BSPACE, LSIDE,
$ NOTRAN, NOUNIT, RSIDE, UPPER
INTEGER INFO, IPB, IPBZ, IPR, IPW, IQBZ, ISZCMP, ITER,
$ JJ, JNPBZ, JNQBZ, JPBZ, JQBZ, KI, KIZ, KJ, KJZ,
$ LCM, LCMP, LCMQ, LMW, LNW, LPBZ, LQBZ, MP,
$ MRCOL, MRROW, MYCOL, MYROW, MZCOL, MZROW, NDIM,
$ NP, NPCOL, NPROW, NQ, NS
DOUBLE PRECISION DUMMY, TBETA
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, NUMROC
EXTERNAL ICEIL, ILCM, LSAME, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DGEBR2D, DGEBS2D, DGEMM,
$ DGSUM2D, DTRBR2D, DTRBS2D, DTRMM, PBDLACPZ,
$ PBDMATADD, PBDTRAN, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Quick return if possible.
*
IF( M.EQ.0 .OR. N.EQ.0 ) RETURN
*
CALL BLACS_GRIDINFO( ICONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters.
*
AMAT = LSAME( MATBLK, 'M' )
LSIDE = LSAME( SIDE, 'L' )
RSIDE = LSAME( SIDE, 'R' )
UPPER = LSAME( UPLO, 'U' )
NOTRAN = LSAME( TRANSA, 'N' )
NOUNIT = LSAME( DIAG, 'N' )
*
INFO = 0
IF( ( .NOT.AMAT ).AND.
$ ( .NOT.LSAME( MATBLK, 'B' ) ) ) THEN
INFO = 2
ELSE IF( ( .NOT.LSIDE ) .AND. ( .NOT.RSIDE ) ) THEN
INFO = 3
ELSE IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO , 'L' ) ) ) THEN
INFO = 4
ELSE IF( ( .NOT.NOTRAN ).AND.
$ ( .NOT.LSAME( TRANSA, 'T' ) ).AND.
$ ( .NOT.LSAME( TRANSA, 'C' ) ) ) THEN
INFO = 5
ELSE IF( ( .NOT.NOUNIT ).AND.
$ ( .NOT.LSAME( DIAG , 'U' ) ) ) THEN
INFO = 6
ELSE IF( M .LT. 0 ) THEN
INFO = 7
ELSE IF( N .LT. 0 ) THEN
INFO = 8
ELSE IF( NB .LT. 1 ) THEN
INFO = 9
END IF
*
10 CONTINUE
IF( INFO .NE. 0 ) THEN
CALL PXERBLA( ICONTXT, 'PBDTRMM ', INFO )
RETURN
END IF
*
* Start the operations.
*
* === If A is a matrix ===
*
IF( AMAT ) THEN
IF( LSIDE ) THEN
NDIM = M
NS = N
ELSE
NDIM = N
NS = M
END IF
NP = NUMROC( NDIM, NB, MYROW, IAROW, NPROW )
NQ = NUMROC( NDIM, NB, MYCOL, IACOL, NPCOL )
*
IF( LDA.LT.MAX(1,NP) ) THEN
INFO = 12
ELSE IF( IAROW.LT.0 .OR. IAROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( IACOL.LT.0 .OR. IACOL.GE.NPCOL ) THEN
INFO = 16
END IF
*
* 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 )
BDATA = .FALSE.
BSPACE = LSAME( ABWORK, 'Y' )
COMMB = ABCOMM
IF( LSAME( COMMB, ' ' ) ) COMMB = '1'
*
* PART 1: Distribute a column (or row) block B or its transpose B'
* ================================================================
*
IF( LSIDE ) THEN
*
* Form B := alpha*op( A )*B.
* _ _____________ _
* | | |\_ | | |
* | | | \_ | | |
* | | | \_ | | |
* |B| = alpha * | op(A) | * |B|
* | | | \_ | | |
* | | | \_ | | |
* |_| |____________\| |_|
*
IF( LDB.LT.MAX(1,NP) .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYCOL .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 14
ELSE IF( IBPOS.LT.-1 .OR. IBPOS.GE.NPCOL ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
IF( NOTRAN ) THEN
*
* Transpose a column block of B to WORK(IPB)
*
IPB = 1
IPR = N * NQ + IPB
CALL PBDTRAN( ICONTXT, 'Col', 'T', M, N, NB, B, LDB, ZERO,
$ WORK(IPB), N, IAROW, IBPOS, -1, IACOL,
$ WORK(IPR) )
*
IF( BSPACE ) THEN
CALL PBDMATADD( ICONTXT, 'G', NP, N, ZERO, DUMMY, 1, ZERO,
$ B, LDB )
BDATA = .TRUE.
IPW = IPR
ELSE
CALL PBDMATADD( ICONTXT, 'G', NP, N, ZERO, DUMMY, 1, ZERO,
$ WORK(IPR), NP )
IPW = NP * N + IPR
END IF
*
* if TRANSA = 'Transpose' or 'Conjugate'
*
ELSE
*
* Broadcast B if necessary
*
IPR = 1
IPB = N * NQ + IPR
IPW = IPB
*
IF( IBPOS.EQ.-1 ) THEN
BDATA = .TRUE.
ELSE
IF( BSPACE ) THEN
IF( MYCOL.EQ.IBPOS ) THEN
CALL DGEBS2D( ICONTXT, 'Row', COMMB, NP, N, B, LDB )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', COMMB, NP, N, B, LDB,
$ MYROW, IBPOS )
END IF
BDATA = .TRUE.
ELSE
IF( MYCOL.EQ.IBPOS ) THEN
CALL PBDMATADD( ICONTXT, 'V', NP, N, ONE, B, LDB,
$ ZERO, WORK(IPB), NP )
CALL DGEBS2D( ICONTXT, 'Row', COMMB, NP, N,
$ WORK(IPB), NP )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', COMMB, NP, N,
$ WORK(IPB), NP, MYROW, IBPOS )
END IF
IPW = NP * N + IPB
END IF
END IF
*
CALL PBDMATADD( ICONTXT, 'G', N, NQ, ZERO, DUMMY, 1, ZERO,
$ WORK(IPR), N )
END IF
*
* If SIDE = 'Right'
*
ELSE
*
* Form B := alpha*B*op( A ).
* _____________
* |\_ |
* | \_ |
* _____________ _____________ | \_ |
* |______B______| = alpha * |______B______| * | op(A) |
* | \_ |
* | \_ |
* |____________\|
*
IF( LDB.LT.MAX(1,M) .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYROW .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 14
ELSE IF( IBPOS.LT.-1 .OR. IBPOS.GE.NPROW ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
IF( NOTRAN ) THEN
*
* Transpose a column block of B to WORK(IPB),
*
IPB = 1
IPR = NP * M + IPB
CALL PBDTRAN( ICONTXT, 'Row', 'T', M, N, NB, B, LDB, ZERO,
$ WORK(IPB), NP, IBPOS, IACOL, IAROW, -1,
$ WORK(IPR) )
*
IF( BSPACE ) THEN
CALL PBDMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, ZERO,
$ B, LDB )
BDATA = .TRUE.
IPW = IPR
ELSE
CALL PBDMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, ZERO,
$ WORK(IPR), M )
IPW = M * NQ + IPR
END IF
*
* If TRANSA = 'Transpose' or 'Conjugate'
*
ELSE
*
* Broadcast B if necessary
*
IPR = 1
IPB = NP * M + IPR
IPW = IPB
*
IF( IBPOS.EQ.-1 ) THEN
BDATA = .TRUE.
ELSE
IF( BSPACE ) THEN
IF( MYROW.EQ.IBPOS ) THEN
CALL DGEBS2D( ICONTXT, 'Col', COMMB, M, NQ, B, LDB )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', COMMB, M, NQ, B, LDB,
$ IBPOS, MYCOL )
END IF
BDATA = .TRUE.
ELSE
IF( MYROW.EQ.IBPOS ) THEN
CALL PBDMATADD( ICONTXT, 'G', M, NQ, ONE, B, LDB,
$ ZERO, WORK(IPB), M )
CALL DGEBS2D( ICONTXT, 'Col', COMMB, M, NQ,
$ WORK(IPB), M )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', COMMB, M, NQ,
$ WORK(IPB), M, IBPOS, MYCOL )
END IF
IPW = M * NQ + IPB
END IF
END IF
*
CALL PBDMATADD( ICONTXT, 'G', NP, M, ZERO, DUMMY, 1, ZERO,
$ WORK(IPR), NP )
END IF
END IF
*
* PART 2: Compute B locally
* =========================
*
IF( NP.EQ.0 .OR. NQ.EQ.0 ) GO TO 100
*
IF( UPPER ) THEN
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
ITER = ICEIL( NQ, IQBZ )
JPBZ = 0
JQBZ = 0
*
DO 50 JJ = 0, ITER-1
LMW = MIN( IPBZ, NP-JPBZ )
LNW = MIN( IQBZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
JNQBZ = JQBZ + LNW
*
* Copy the upper triangular matrix A to WORK(IPW)
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
*
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 = KI * NB
KJZ = KJ * NB
IF( KJZ.GE.LNW ) GO TO 40
FORM = 'G'
IF( MZROW.EQ.MZCOL ) FORM = 'T'
MZCOL = MZCOL + NPCOL
*
CALL PBDLACPZ( ICONTXT, 'Upper', FORM, DIAG, KIZ, NB,
$ A(JPBZ+1,JQBZ+KJZ+1), LDA,
$ WORK(KJZ*LMW+IPW), LMW,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
30 CONTINUE
40 CONTINUE
*
* If SIDE = 'Left',
*
IF( LSIDE ) THEN
*
* Compute B if A is not transposed
*
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGEMM( 'No', 'Trans', LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, ZERO, B(JPBZ+1,1), LDB )
CALL DGEMM( 'No', 'Trans', JPBZ, NS, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*NS+IPB), NS,
$ ONE, B, LDB )
ELSE
CALL DGEMM( 'No', 'Trans', LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, ZERO, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', 'Trans', JPBZ, NS, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*NS+IPB), NS,
$ ONE, WORK(IPR), NP )
END IF
*
* Compute B if A is (conjugate) transposed
*
ELSE
IF( BDATA ) THEN
CALL DGEMM( TRANSA, 'No', NS, LNW, LMW, ALPHA,
$ B(JPBZ+1,1), LDB, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( TRANSA, 'No', NS, LNW, JPBZ, ALPHA,
$ B, LDB, A(1,JQBZ+1), LDA, ONE,
$ WORK(NS*JQBZ+IPR), NS )
ELSE
CALL DGEMM( TRANSA, 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( TRANSA, 'No', NS, LNW, JPBZ, ALPHA,
$ WORK(IPB), NP, A(1,JQBZ+1), LDA, ONE,
$ WORK(NS*JQBZ+IPR), NS )
END IF
END IF
*
* If SIDE = 'Right',
*
ELSE
*
* Compute B if A is not transposed
*
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGEMM( 'Trans', 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, B(1,JQBZ+1), NS )
CALL DGEMM( 'Trans', 'No', NS, LNW, JPBZ, ALPHA,
$ WORK(IPB), NP, A(1,JQBZ+1), LDA, ONE,
$ B(1,JQBZ+1), NS )
ELSE
CALL DGEMM( 'Trans', 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( 'Trans', 'No', NS, LNW, JPBZ, ALPHA,
$ WORK(IPB), NP, A(1,JQBZ+1), LDA, ONE,
$ WORK(NS*JQBZ+IPR), NS )
END IF
*
* Compute B if A is (conjugate) transposed
*
ELSE
IF( BDATA ) THEN
CALL DGEMM( 'No', TRANSA, LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), B(1,JQBZ+1), LDB,
$ ZERO, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', TRANSA, JPBZ, NS, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, B(1,JQBZ+1), LDB,
$ ONE, WORK(IPR), NP )
ELSE
CALL DGEMM( 'No', TRANSA, LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, ZERO, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', TRANSA, JPBZ, NS, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*NS+IPB), NS,
$ ONE, WORK(IPR), NP )
END IF
END IF
END IF
*
JPBZ = JNPBZ
JQBZ = JNQBZ
50 CONTINUE
*
* If A is a lower triangular matrix,
*
ELSE
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
ITER = ICEIL( NQ, IQBZ )
JPBZ = 0
JQBZ = 0
TBETA = ZERO
*
DO 90 JJ = 0, ITER-1
LMW = MIN( IPBZ, NP-JPBZ )
LNW = MIN( IQBZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
JNQBZ = JQBZ + LNW
*
* Copy the lower triangular matrix A to WORK(IPW)
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
*
DO 70 KJ = 0, LCMQ-1
60 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 60
END IF
KIZ = KI * NB
KJZ = KJ * NB
IF( KJZ.GE.LNW ) GO TO 80
FORM = 'G'
IF( MZROW.EQ.MZCOL ) FORM = 'T'
MZCOL = MZCOL + NPCOL
*
CALL PBDLACPZ( ICONTXT, 'Lower', FORM, DIAG, KIZ, NB,
$ A(JPBZ+1,JQBZ+KJZ+1), LDA,
$ WORK(KJZ*LMW+IPW), LMW,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
70 CONTINUE
80 CONTINUE
*
* If SIDE = 'Left',
*
IF( LSIDE ) THEN
*
* Compute B if A is not transposed
*
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGEMM( 'No', 'Trans', LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, TBETA, B(JPBZ+1,1), LDB )
CALL DGEMM( 'No', 'Trans', NP-JNPBZ, NS, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, WORK(JQBZ*NS+IPB),
$ NS, TBETA, B(JNPBZ+1,1), LDB )
ELSE
CALL DGEMM( 'No', 'Trans', LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, TBETA, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', 'Trans', NP-JNPBZ, NS, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, WORK(JQBZ*NS+IPB),
$ NS, TBETA, WORK(JNPBZ+IPR), NP )
END IF
*
* Compute B if A is (conjugate) transposed
*
ELSE
IF( BDATA ) THEN
CALL DGEMM( TRANSA, 'No', NS, LNW, LMW, ALPHA,
$ B(JPBZ+1,1), LDB, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( TRANSA, 'No', NS, LNW, NP-JNPBZ, ALPHA,
$ B(JNPBZ+1,1), LDB, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, WORK(NS*JQBZ+IPR), NS )
ELSE
CALL DGEMM( TRANSA, 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( TRANSA, 'No', NS, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPB), NP, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, WORK(NS*JQBZ+IPR), NS )
END IF
END IF
*
* If SIDE = 'Right',
*
ELSE
*
* Compute B if A is not transposed
*
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGEMM( 'Trans', 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, B(1,JQBZ+1), LDB )
CALL DGEMM( 'Trans', 'No', NS, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPB), NP, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, B(1,JQBZ+1), LDB )
ELSE
CALL DGEMM( 'Trans', 'No', NS, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW),
$ MAX(1,LMW), ZERO, WORK(NS*JQBZ+IPR), NS )
CALL DGEMM( 'Trans', 'No', NS, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPB), NP, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, WORK(NS*JQBZ+IPR), NS )
END IF
*
* Compute B if A is (conjugate) transposed
*
ELSE
IF( BDATA ) THEN
CALL DGEMM( 'No', TRANSA, LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), B(1,JQBZ+1), LDB,
$ TBETA, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', TRANSA, NP-JNPBZ, NS, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, B(1,JQBZ+1), LDB,
$ TBETA, WORK(JNPBZ+IPR), NP )
ELSE
CALL DGEMM( 'No', TRANSA, LMW, NS, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*NS+IPB),
$ NS, TBETA, WORK(JPBZ+IPR), NP )
CALL DGEMM( 'No', TRANSA, NP-JNPBZ, NS, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1),LDA, WORK(JQBZ*NS+IPB),
$ NS, TBETA, WORK(JNPBZ+IPR), NP )
END IF
END IF
END IF
*
TBETA = ONE
JPBZ = JNPBZ
JQBZ = JNQBZ
90 CONTINUE
END IF
*
100 CONTINUE
*
* PART 3: Collect B, and transpose it if necessary
* ================================================
*
IF( LSIDE ) THEN
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGSUM2D( ICONTXT, 'Row', '1-tree', NP, NS, B, LDB,
$ MYROW, IBPOS )
ELSE
IF( MYCOL.EQ.IBPOS ) THEN
CALL PBDMATADD( ICONTXT, 'V', NP, NS, ONE, WORK(IPR),
$ NP, ZERO, B, LDB )
CALL DGSUM2D( ICONTXT, 'Row', '1-tree', NP, NS, B, LDB,
$ MYROW, IBPOS )
ELSE
CALL DGSUM2D( ICONTXT, 'Row', '1-tree', NP, NS,
$ WORK(IPR), NP, MYROW, IBPOS )
IF( IBPOS.EQ.-1 )
$ CALL PBDMATADD( ICONTXT, 'V', NP, NS, ONE, WORK(IPR),
$ NP, ZERO, B, LDB )
END IF
END IF
*
ELSE
CALL DGSUM2D( ICONTXT, 'Col', '1-tree', NS, NQ, WORK(IPR),
$ NS, IAROW, MYCOL)
CALL PBDTRAN( ICONTXT, 'Row', TRANSA, N, M, NB, WORK(IPR),
$ NS, ZERO, B, LDB, IAROW, IACOL, IAROW, IBPOS,
$ WORK(IPB) )
END IF
*
ELSE
IF( NOTRAN ) THEN
IF( BDATA ) THEN
CALL DGSUM2D( ICONTXT, 'Col', '1-tree', NS, NQ, B, LDB,
$ IBPOS, MYCOL )
ELSE
IF( MYROW.EQ.IBPOS ) THEN
CALL PBDMATADD( ICONTXT, 'G', NS, NQ, ONE, WORK(IPR),
$ NS, ZERO, B, LDB )
CALL DGSUM2D( ICONTXT, 'Col', '1-tree', NS,NQ, B, LDB,
$ IBPOS, MYCOL )
ELSE
CALL DGSUM2D( ICONTXT, 'Col', '1-tree', NS, NQ,
$ WORK(IPR), NS, IBPOS, MYCOL )
IF( IBPOS.EQ.-1 )
$ CALL PBDMATADD( ICONTXT, 'G', NS, NQ, ONE, WORK(IPR),
$ NS, ZERO, B, LDB )
END IF
END IF
*
ELSE
CALL DGSUM2D( ICONTXT, 'Row', '1-tree', NP, NS, WORK(IPR),
$ NP, MYROW, IACOL)
CALL PBDTRAN( ICONTXT, 'Col', TRANSA, N, M, NB, WORK(IPR),
$ NP, ZERO, B, LDB, IAROW, IACOL, IBPOS, IACOL,
$ WORK(IPB) )
END IF
END IF
*
* === If A is just a block ===
*
ELSE
ADATA = .FALSE.
ASPACE = LSAME( ABWORK, 'Y' )
COMMA = ABCOMM
IF( LSAME( COMMA, ' ' ) ) COMMA = '1'
*
IF( LSIDE .AND. MYROW.EQ.IAROW ) THEN
*
* Form B := alpha*op( A )*B.
* _____________ _ _____________
* |______B______| = |_| * |______B______|
* op(A)
*
IF( IACOL.EQ.-1 ) ADATA = .TRUE.
NQ = NUMROC( N, NB, MYCOL, IBPOS, NPCOL )
*
IF( LDA.LT.MAX(1,M) .AND. ( ASPACE .OR.
$ IACOL.EQ.MYCOL .OR. IACOL.EQ.-1 ) ) THEN
INFO = 12
ELSE IF( LDB .LT. M ) THEN
INFO = 14
ELSE IF( IAROW.LT. 0 .OR. IAROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( IACOL.LT.-1 .OR. IACOL.GE.NPCOL ) THEN
INFO = 16
ELSE IF( IBPOS.LT. 0 .OR. IBPOS.GE.NPCOL ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast A if necessary
*
IF( .NOT. ADATA ) THEN
IF( ASPACE ) THEN
IF( MYCOL.EQ.IACOL ) THEN
CALL DTRBS2D( ICONTXT, 'Row', COMMA, UPLO, DIAG, M, M,
$ A, LDA )
ELSE
CALL DTRBR2D( ICONTXT, 'Row', COMMA, UPLO, DIAG, M, M,
$ A, LDA, MYROW, IACOL )
END IF
ADATA = .TRUE.
ELSE
IF( MYCOL.EQ.IACOL ) THEN
CALL DTRBS2D( ICONTXT, 'Row', COMMA, UPLO, DIAG, M, M,
$ A, LDA )
CALL PBDMATADD( ICONTXT, UPLO, M, M, ONE, A, LDA, ZERO,
$ WORK, M )
ELSE
CALL DTRBR2D( ICONTXT, 'Row', COMMA, UPLO, DIAG, M, M,
$ WORK, M, MYROW, IACOL )
END IF
END IF
END IF
*
* Compute DTRMM
*
IF( ADATA ) THEN
CALL DTRMM( 'Left', UPLO, TRANSA, DIAG, M, NQ, ALPHA,
$ A, LDA, B, LDB )
ELSE
CALL DTRMM( 'Left', UPLO, TRANSA, DIAG, M, NQ, ALPHA,
$ WORK, M, B, LDB )
END IF
*
ELSE IF( LSAME( SIDE, 'R' ) .AND. MYCOL.EQ.IACOL ) THEN
*
* Form B := alpha*B*op( A ).
* _ _
* | | | |
* | | | |
* | | | | _
* |B| = |B| * |_|
* | | | | op(A)
* | | | |
* |_| |_|
*
IF( IAROW.EQ.-1 ) ADATA = .TRUE.
MP = NUMROC( M, NB, MYROW, IBPOS, NPROW )
*
IF( LDA.LT.MAX(1,N) .AND. ( ASPACE .OR.
$ IAROW.EQ.MYROW .OR. IAROW.EQ.-1 ) ) THEN
INFO = 12
ELSE IF( LDB .LT.MAX(1,MP) ) THEN
INFO = 14
ELSE IF( IAROW.LT.-1 .OR. IAROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( IACOL.LT. 0 .OR. IACOL.GE.NPCOL ) THEN
INFO = 16
ELSE IF( IBPOS.LT. 0 .OR. IBPOS.GE.NPROW ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast B if necessary
*
IF( .NOT.ADATA ) THEN
IF( ASPACE ) THEN
IF( MYROW.EQ.IAROW ) THEN
CALL DTRBS2D( ICONTXT, 'Col', COMMA, UPLO, DIAG, N, N,
$ A, LDA )
ELSE
CALL DTRBR2D( ICONTXT, 'Col', COMMA, UPLO, DIAG, N, N,
$ A, LDA, IAROW, MYCOL )
END IF
ADATA = .TRUE.
ELSE
IF( MYROW.EQ.IAROW ) THEN
CALL DTRBS2D( ICONTXT, 'Col', COMMA, UPLO, DIAG, N, N,
$ A, LDA )
CALL PBDMATADD( ICONTXT, UPLO, N, N, ONE, A, LDA, ZERO,
$ WORK, N )
ELSE
CALL DTRBR2D( ICONTXT, 'Col', COMMA, UPLO, DIAG, N, N,
$ WORK, N, IAROW, MYCOL )
END IF
END IF
END IF
*
* Compute DTRMM
*
IF( ADATA ) THEN
CALL DTRMM( 'Right', UPLO, TRANSA, DIAG, MP, N, ALPHA,
$ A, LDA, B, LDB )
ELSE
CALL DTRMM( 'Right', UPLO, TRANSA, DIAG, MP, N, ALPHA,
$ WORK, N, B, LDB )
END IF
END IF
END IF
*
RETURN
*
* End of PBDTRMM
*
END
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