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SUBROUTINE PBDTRSM( ICONTXT, MATBLK, SIDE, UPLO, TRANSA, DIAG, M,
$ N, NB, ALPHA, A, LDA, B, LDB, IAROW, IACOL,
$ IBPOS, ACOMM, ABWORK, 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 ABWORK, ACOMM, DIAG, MATBLK, SIDE, TRANSA,
$ UPLO
INTEGER IACOL, IAROW, IBPOS, ICONTXT, LDA, LDB, M, N,
$ NB
DOUBLE PRECISION ALPHA
* ..
* .. Array Arguments ..
DOUBLE PRECISION A( LDA, * ), B( LDB, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PBDTRSM is a parallel blocked version of he Level 3 BLAS routine
* DTRSM.
* PBDTRSM solves one of the matrix equations based on block
* cyclic distribution.
*
* op( A )*X = alpha*B, or X*op( A ) = alpha*B,
*
* where alpha is a scalar, X and B are m-by-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 processes have B) if SIDE = 'L', and a row block otherwise
* (only one row of processes 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.)
* When MATBLK = 'M', B can be moved or transposed to the starting
* column or row processes if necessary. The communication scheme is
* predetermined.
* And when MATBLK = 'B', A can be broadcast columnwise or rowwise 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 ) appears on the left or right
* of X as follows:
*
* SIDE = 'L', op( A )*X = alpha*B,
* SIDE = 'R', X*op( A ) = alpha*B.
*
* 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 number of rows of B. M >= 0.
*
* N (input) INTEGER
* N specifies the 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,
* 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
* processes which don't have the resultant column block or
* row block of B if MATBLK = 'M'.
*
* LDB (input) INTEGER
* LDB specifies the leading dimension of (local) B as declared
* in the calling (sub) program. LDB >= MAX(1,Mp).
*
* IAROW (input) INTEGER
* It specifies a row of process template which has the
* first block of A. When MATBLK = 'B', and all rows of
* processes have their own copies of A, set IAROW = -1.
*
* IACOL (input) INTEGER
* It specifies a column of process template which has the
* first block of A. When MATBLK = 'B', and all columns of
* processes 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
* (0 <= IBPOS < NPCOL). And if SIDE = 'R', it specifies a row
* of the template, which holds the row of blocks of B (0 <=
* IBPOS < NPROW).
* 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).
*
* ACOMM (input) CHARACTER*1
* When MATBLK = 'B', ACOMM specifies the communication scheme
* of a block of A. It follows topology definition of BLACS.
* When MATBLK = 'M', the argument is ignored.
*
* ABWORK (input) CHARACTER*1
* When MATBLK = 'M', ABWORK determines whether B is a
* workspace or not. If transposition of B is involved with
* the computation, the argument is ignored.
*
* ABWORK = 'Y': B is workspace in other processes.
* B is overwitten with temporal B in other
* processes. It is assumed that processes
* have sufficient space to store temporal
* (local) B.
* ABWORK = 'N': Data of B in other processes will be
* untouched (unchanged).
*
* And MATBLK = 'B', ABWORK determines whether A is a
* workspace or not.
*
* ABWORK = 'Y': A is workspace in other processes.
* A is sent to A position in other processes.
* It is assumed that processes have
* sufficient space to store a single block A.
* ABWORK = 'N': Data of A in other processes will be
* untouched (unchanged).
*
* WORK (workspace) DOUBLE PRECISION array of dimension Size(WORK).
* It will store copy of A or B if necessary.
*
* Communication Scheme
* ====================
*
* If MATBLK='M', the communication scheme of the routine is determined
* by the conditions and it is independent of machine characteristics,
* so that it is not an option of the routine. Increasing ring or
* Decreasing ring is used depeding on the following input conditions.
*
* COMM='Increasing ring' when UPLO = 'U', SIDE = 'L', TRANSA = 'T'/'C'
* or UPLO = 'U', SIDE = 'R', TRANSA = 'N'
* or UPLO = 'L', SIDE = 'L', TRANSA = 'N'
* or UPLO = 'L', SIDE = 'R', TRANSA = 'T'/'C'
*
* COMM='Decreasing ring' when UPLO = 'U', SIDE = 'L', TRANSA = 'N'
* or UPLO = 'U', SIDE = 'R', TRANSA = 'T'/'C'
* or UPLO = 'L', SIDE = 'L', TRANSA = 'T'/'C'
* or UPLO = 'L', SIDE = 'R', TRANSA = 'N'
*
* 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
* ==========================
*
* 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
*
* (1) MATBLK = 'M'
* (a) SIDE = 'Left'
* (i) TRANSA = 'N'
* Size(WORK) = N*Mp0 (if ABWORK <> 'Y')
* + N*NB*MAX[ 1, CEIL(Q-1,P) ]
* (ii) TRANSA = 'T'/'C'
* Size(WORK) = N*Mq0
* + MAX[ N*NB*MAX( CEIL(Mpb,LCMP), CEIL(Mqb,LCMQ) ),
* N*NB*CEIL(P-1,Q) ]
*
* (b) SIDE = 'Right'
* (i) TRANSA = 'N'
* Size(WORK) = M*Nq0 (if ABWORK <> 'Y')
* + M*NB*MAX[ 1, CEIL(P-1,Q) ]
* (ii) TRANSA = 'T'/'C'
* Size(WORK) = M*Np0
* + MAX[ M*NB*MAX( CEIL(Npb,LCMP), CEIL(Nqb,LCMQ) ),
* M*NB*CEIL(Q-1,P) ]
*
* (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
LOGICAL ADATA, AMAT, ASPACE, BDATA, BSPACE, LSIDE,
$ NOTRAN, UPPER
INTEGER ICURCOL, ICURROW, IDEST, II, IIN, IN, INFO,
$ IPART, IPT, IRDB, IRPB, J, JB, JJ, JJN, JN, KB,
$ KDIST, LCM, LDW, MBTROW, MLFCOL, MP, MQ,
$ MRTCOL, MTPROW, MYCOL, MYROW, NCOMM, NDIM,
$ NLENG, NPART, NPCOL, NPROW, NQ, NREST, NS,
$ NXTCOL, NXTROW
DOUBLE PRECISION DUMMY
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, NUMROC
EXTERNAL ICEIL, ILCM, LSAME, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DGEBR2D, DGEBS2D, DGEMM,
$ DGERV2D, DGESD2D, DTRBR2D, DTRBS2D, DTRSM,
$ PBDMATADD, PBDTRAN, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD
* ..
* .. 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' )
UPPER = LSAME( UPLO, 'U' )
NOTRAN = LSAME( TRANSA, 'N' )
*
INFO = 0
IF( ( .NOT.AMAT ).AND.
$ ( .NOT.LSAME( MATBLK, 'B' ) ) ) THEN
INFO = 2
ELSE IF( ( .NOT.LSIDE ).AND.
$ ( .NOT.LSAME( SIDE , 'R' ) ) ) 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.LSAME( DIAG , 'U' ) ).AND.
$ ( .NOT.LSAME( DIAG , 'N' ) ) ) 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, 'PBDTRSM ', INFO )
RETURN
END IF
*
* Start the operations.
*
* === If A is a matrix ===
*
IF( AMAT ) THEN
*
* Initialize parameters
*
IF( LSIDE ) THEN
NDIM = M
NS = N
ELSE
NDIM = N
NS = M
END IF
MP = NUMROC( NDIM, NB, MYROW, IAROW, NPROW )
MQ = NUMROC( NDIM, NB, MYCOL, IACOL, NPCOL )
*
IF( LDA.LT.MAX(1,MP) ) 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
*
BSPACE = LSAME( ABWORK, 'Y' )
IF( LSIDE ) THEN
IF( LDB.LT.MAX(1,MP) .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYCOL .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 14
ELSE IF( IBPOS.LT.0 .OR. IBPOS.GE.NPCOL ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
IF( MYCOL.EQ.IBPOS )
$ CALL PBDMATADD( ICONTXT, 'V', MP, NS, ZERO, DUMMY, 1, ALPHA,
$ B, LDB )
*
ELSE
IF( LDB.LT.MAX(1,M) .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYROW .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 14
ELSE IF( IBPOS.LT.0 .OR. IBPOS.GE.NPROW ) THEN
INFO = 17
END IF
IF( INFO.NE.0 ) GO TO 10
*
IF( MYROW.EQ.IBPOS )
$ CALL PBDMATADD( ICONTXT, 'V', NS, MQ, ZERO, DUMMY, 1, ALPHA,
$ B, LDB )
END IF
*
* When alpha = zero, quick return.
*
IF( ALPHA.EQ.ZERO ) RETURN
*
* MTPROW (Top)
* |
* MLFCOL <- MYCOL -> MRTCOL, MYROW
* (Left) (Right) |
* MBTROW (Bottom)
*
MLFCOL = MOD( NPCOL+MYCOL-1, NPCOL )
MRTCOL = MOD( MYCOL+1, NPCOL )
MTPROW = MOD( NPROW+MYROW-1, NPROW )
MBTROW = MOD( MYROW+1, NPROW )
LCM = ILCM( NPROW, NPCOL )
BDATA = .FALSE.
*
* Start the operations.
*
IF( UPPER ) THEN
IF( LSIDE.AND.NOTRAN .OR. .NOT.(LSIDE.OR.NOTRAN) ) THEN
*
* Form B := Up( A ) \ alpha * B.
* _ __________ _
* | | \_ | | |
* | | \_ | | |
* |B| := \_ A | \ alpha * |B|
* | | \_ | | |
* |_| \_| |_|
*
IPT = MP * NS + 1
ICURROW = MOD( ICEIL(NDIM,NB)+IAROW-1, NPROW )
ICURCOL = MOD( ICEIL(NDIM,NB)+IACOL-1, NPCOL )
*
IF( LSIDE ) THEN
IF( BSPACE ) THEN
IF( MYCOL.EQ.IBPOS ) THEN
IF( MYCOL.NE.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, MP, NS, B, LDB,
$ MYROW, ICURCOL )
CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY,
$ 1, ZERO, B, LDB )
END IF
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGERV2D( ICONTXT, MP, NS, B, LDB, MYROW, IBPOS )
ELSE
CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY, 1,
$ ZERO, B, LDB )
END IF
BDATA = .TRUE.
IPT = 1
*
ELSE
IF( MYCOL.EQ.IBPOS ) THEN
IF( MYCOL.EQ.ICURCOL ) THEN
CALL PBDMATADD( ICONTXT, 'V', MP, NS, ONE, B, LDB,
$ ZERO, WORK, MP )
ELSE
CALL DGESD2D( ICONTXT, MP, NS, B, LDB,
$ MYROW, ICURCOL )
END IF
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGERV2D( ICONTXT, MP, NS, WORK, MP,
$ MYROW, IBPOS )
END IF
END IF
IDEST = IBPOS
*
ELSE
CALL PBDTRAN( ICONTXT, 'Row', TRANSA, NS, NDIM, NB, B,
$ LDB, ZERO, WORK, MP, IBPOS, IACOL, IAROW,
$ ICURCOL, WORK(IPT) )
IDEST = ICURCOL
END IF
LDW = MAX( 1, MP )
*
IRPB = MOD( NPCOL+IDEST-MYCOL-1, NPCOL )
IRDB = NB * MOD( IRPB+1, NPCOL )
IRPB = NB * IRPB
NCOMM = NB * (NPCOL-1)
KB = MOD( NDIM, NB )
IF( KB.EQ.0 ) KB = NB
*
II = MP - NB + 1
IF( MYROW.EQ.ICURROW ) II = MP - KB + 1
IN = II
JJ = MQ - NB + 1
IF( MYCOL.EQ.ICURCOL ) JJ = MQ - KB + 1
JB = KB
*
* If B can be used as a working space,
*
IF( BDATA ) THEN
DO 20 J = 1, NDIM, NB
NLENG = NDIM - J - KB + 1
NXTROW = MOD( NPROW+ICURROW-1, NPROW )
NXTCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( MYROW.EQ.ICURROW ) IN = II - NB
*
IF( MYCOL.EQ.ICURCOL ) THEN
*
* Receive updated blocks from previous column of
* processes
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG+JB, NCOMM), NB, ICURROW,
$ MYROW, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(IPT), NPART,
$ MYROW, MRTCOL )
CALL PBDMATADD( ICONTXT, 'G', NPART, NS, ONE,
$ WORK(IPT), NPART, ONE,
$ B(II+NB-NPART,1), LDB )
END IF
*
* B(II,1) <== A(II,JJ) \ B(II,1), ( B(II,1) = WORK(II) )
* where A(II,JJ) is a upper triangular matrix
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DTRSM( 'Left', 'Upper', 'No', DIAG, JB, NS,
$ ONE, A(II,JJ), LDA, B(II,1), LDB )
CALL PBDMATADD( ICONTXT, 'G', JB, NS, ONE, B(II,1),
$ LDB, ZERO, WORK(IPT), JB )
CALL DGEBS2D( ICONTXT, 'Col', 'D-ring', JB, NS,
$ WORK(IPT), JB )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', 'D-ring', JB, NS,
$ WORK(IPT), JB, ICURROW, MYCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.0 ) THEN
*
* Update the (NPCOL-1) blocks first
*
NREST = MIN( NLENG, NCOMM )
NPART = NUMROC( NREST, NB, ICURROW, MYROW+1, NPROW )
IIN = IN + NB - NPART
*
CALL DGEMM( 'No', 'No', NPART, NS, JB, -ONE,
$ A(IIN,JJ), LDA, WORK(IPT), JB, ONE,
$ B(IIN,1), LDB )
*
* Send updated blocks to next column of processes
*
IF( NPCOL.GT.1 )
$ CALL DGESD2D( ICONTXT, NPART, NS, B(IIN,1), LDB,
$ MYROW, MLFCOL)
*
* Update the rest of the matrix
*
CALL DGEMM( 'No', 'No', IIN-1, NS, JB, -ONE,
$ A(1,JJ), LDA, WORK(IPT), JB, ONE, B,
$ LDB )
END IF
*
* Send the solution blocks to destination (IDEST column)
*
JJN = J + KB - 1
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, JJN-JB), NB, MYROW,
$ ICURROW+1, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, B(II+NB,1), LDB,
$ MYROW, MRTCOL)
END IF
*
IF( NLENG.GT.0 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, JJN), NB, MYROW, ICURROW,
$ NPROW )
CALL DGESD2D( ICONTXT, NPART, NS, B(IN+NB,1), LDB,
$ MYROW, MLFCOL )
END IF
*
JJ = JJ - NB
END IF
*
II = IN
JB = NB
ICURROW = NXTROW
ICURCOL = NXTCOL
20 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURCOL = MOD( ICURCOL+1, NPCOL )
IF( ICURCOL.NE.IDEST ) THEN
KDIST = MOD( NPCOL+IDEST-ICURCOL, NPCOL )
NPART = NUMROC( MIN(NDIM, KDIST*NB), NB, MYROW, IAROW,
$ NPROW )
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, NPART, NS, B, LDB,
$ MYROW, IDEST )
ELSE IF( MYCOL.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NPART, NS, B, LDB,
$ MYROW, ICURCOL )
END IF
END IF
*
* If B can't be used as a working space,
*
ELSE
IF( MYCOL.NE.ICURCOL )
$ CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY, 1,
$ ZERO, WORK, MP )
*
DO 30 J = 1, NDIM, NB
NLENG = NDIM - J - KB + 1
NXTROW = MOD( NPROW+ICURROW-1, NPROW )
NXTCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( MYROW.EQ.ICURROW ) IN = II - NB
*
IF( MYCOL.EQ.ICURCOL ) THEN
*
* Receive updated blocks from previous column of
* processes
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG+JB, NCOMM), NB, ICURROW,
$ MYROW, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(IPT), NPART,
$ MYROW, MRTCOL )
CALL PBDMATADD( ICONTXT, 'G', NPART, NS, ONE,
$ WORK(IPT), NPART, ONE,
$ WORK(II+NB-NPART), MP )
END IF
*
* B(II,1) <== A(II,JJ) \ B(II,1), ( B(II,1) = WORK(II) )
* where A(II,JJ) is a upper triangular matrix
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DTRSM( 'Left', 'Upper', 'No', DIAG, JB, NS,
$ ONE, A(II,JJ), LDA, WORK(II), LDW )
CALL PBDMATADD( ICONTXT, 'G', JB, NS, ONE, WORK(II),
$ MP, ZERO, WORK(IPT), JB )
CALL DGEBS2D( ICONTXT, 'Col', 'D-ring', JB, NS,
$ WORK(IPT), JB )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', 'D-ring', JB, NS,
$ WORK(IPT), JB, ICURROW, MYCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.0 ) THEN
*
* Update the (NPCOL-1) blocks first
*
NREST = MIN( NLENG, NCOMM )
NPART = NUMROC( NREST, NB, ICURROW, MYROW+1, NPROW )
IIN = IN + NB - NPART
*
CALL DGEMM( 'No', 'No', NPART, NS, JB, -ONE,
$ A(IIN,JJ), LDA, WORK(IPT), JB, ONE,
$ WORK(IIN), LDW )
*
* Send updated blocks to next column of processes
*
IF( NPCOL.GT.1 )
$ CALL DGESD2D( ICONTXT, NPART, NS, WORK(IIN), MP,
$ MYROW, MLFCOL)
*
* Update the rest of the matrix
*
CALL DGEMM( 'No','No', IIN-1, NS, JB, -ONE, A(1,JJ),
$ LDA, WORK(IPT),JB, ONE, WORK, LDW )
END IF
*
* Send the solution blocks to destination (IDEST column)
*
JJN = J + KB - 1
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, JJN-JB), NB, MYROW,
$ ICURROW+1, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(II+NB), MP,
$ MYROW, MRTCOL )
END IF
*
IF( NLENG.GT.0 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, JJN), NB, MYROW, ICURROW,
$ NPROW )
CALL DGESD2D( ICONTXT, NPART, NS, WORK(IN+NB), MP,
$ MYROW, MLFCOL )
END IF
*
JJ = JJ - NB
END IF
*
II = IN
JB = NB
ICURROW = NXTROW
ICURCOL = NXTCOL
30 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURCOL = MOD( ICURCOL+1, NPCOL )
IF( ICURCOL.NE.IDEST ) THEN
KDIST = MOD( NPCOL+IDEST-ICURCOL, NPCOL )
NPART = NUMROC( MIN(NDIM, KDIST*NB), NB, MYROW, IAROW,
$ NPROW )
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, NPART, NS, WORK, MP,
$ MYROW, IDEST )
ELSE IF( MYCOL.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NPART, NS, WORK, MP,
$ MYROW, ICURCOL )
END IF
END IF
END IF
*
IF( LSIDE ) THEN
IF( .NOT.BDATA .AND. MYCOL.EQ.IDEST )
$ CALL PBDMATADD( ICONTXT, 'V', MP, NS, ONE, WORK, MP,
$ ZERO, B, LDB )
ELSE
CALL PBDTRAN( ICONTXT, 'Col', TRANSA, NDIM, NS, NB, WORK,
$ MP, ZERO, B, LDB, IAROW, IDEST, IBPOS,
$ IACOL, WORK(IPT) )
END IF
*
ELSE IF( ( LSIDE .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LSIDE .AND. NOTRAN ) ) THEN
*
*
* Form B := alpha * B / Up( A ).
* __________
* \_ |
* __________ __________ \_ |
* |_____B____| := alpha * |_____B____| / \_ A |
* \_ |
* \_|
*
IPT = NS * MQ + 1
ICURROW = IAROW
ICURCOL = IACOL
*
IF( LSIDE ) THEN
CALL PBDTRAN( ICONTXT, 'Col', TRANSA, NDIM, NS, NB, B,
$ LDB, ZERO, WORK, NS, IAROW, IBPOS, ICURROW,
$ IACOL, WORK(IPT) )
IDEST = ICURROW
*
ELSE
IF( BSPACE ) THEN
IF( MYROW.EQ.IBPOS ) THEN
IF( MYROW.NE.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, MQ, B, LDB,
$ ICURROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY,
$ 1, ZERO, B, LDB )
END IF
ELSE IF( MYROW.EQ.ICURROW ) THEN
CALL DGERV2D( ICONTXT, NS, MQ, B, LDB, IBPOS, MYCOL )
ELSE
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY, 1,
$ ZERO, B, LDB )
END IF
BDATA = .TRUE.
IPT = 1
*
ELSE
IF( MYROW.EQ.IBPOS ) THEN
IF( MYROW.EQ.ICURROW ) THEN
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ONE, B, LDB,
$ ZERO, WORK, NS )
ELSE
CALL DGESD2D( ICONTXT, NS, MQ, B, LDB,
$ ICURROW, MYCOL )
END IF
ELSE IF( MYROW.EQ.ICURROW ) THEN
CALL DGERV2D( ICONTXT, NS, MQ, WORK, NS,
$ IBPOS, MYCOL )
END IF
END IF
IDEST = IBPOS
END IF
*
IRPB = MOD( NPROW+MYROW-IDEST-1, NPROW )
IRDB = NB * MOD( IRPB+1, NPROW )
IRPB = NB * IRPB
NCOMM = NB * (NPROW-1)
*
II = 1
JJ = 0
JN = 0
*
* If B can be used as a working space,
*
IF( BDATA ) THEN
DO 40 J = 1, NDIM, NB
NLENG = NDIM - J + 1
JB = MIN( NLENG, NB )
NXTROW = MOD( ICURROW+1, NPROW )
NXTCOL = MOD( ICURCOL+1, NPCOL )
IF( MYCOL.EQ.ICURCOL ) JN = JJ + JB
*
IF( MYROW.EQ.ICURROW ) THEN
*
* Receive updated blocks from previous row of processes
*
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG, NCOMM), NB, MYCOL,
$ ICURCOL, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, WORK(IPT), NS,
$ MTPROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, NPART, ONE,
$ WORK(IPT), NS, ONE, B(1,JJ+1), LDB )
END IF
*
* B(1,JJ+1) <== A(II,JJ+1) \ B(1,JJ+1),
* ( B(1,JJ+1) = WORK(JJN) )
* where A(II,JJ+1) is a upper triangular matrix
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DTRSM( 'Right', 'Upper', 'No', DIAG, NS, JB,
$ ONE, A(II,JJ+1), LDA, B(1,JJ+1), LDB )
CALL PBDMATADD( ICONTXT, 'G', NS, JB, ONE,
$ B(1,JJ+1), LDB, ZERO, WORK(IPT),
$ NS )
CALL DGEBS2D( ICONTXT, 'Row', 'I-ring', NS, JB,
$ WORK(IPT), NS )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', 'I-ring', NS, JB,
$ WORK(IPT), NS, MYROW, ICURCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.JB ) THEN
*
* Update the (NPROW-1) blocks first
*
NREST = MIN( NLENG-JB, NCOMM )
NPART = NUMROC( NREST, NB, MYCOL, ICURCOL+1, NPCOL )
*
CALL DGEMM( 'No', 'No', NS, NPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JN+1), LDA, ONE,
$ B(1,JN+1), LDB )
*
* Send updated blocks to next column of processes
*
IF( NPROW.GT.1 )
$ CALL DGESD2D( ICONTXT, NS, NPART, B(1,JN+1), LDB,
$ MBTROW, MYCOL )
*
* Update the rest of the matrix
*
IPART = NUMROC( NLENG-JB-NREST, NB, MYCOL+LCM,
$ ICURCOL+NPROW, NPCOL )
CALL DGEMM( 'No', 'No', NS,IPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JN+NPART+1), LDA,
$ ONE, B(1,JN+NPART+1), LDB )
END IF
*
* Send the solution blocks to destination (IDEST row)
*
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, J-1), NB, ICURCOL,
$ MYCOL+1, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, B(1,JJ-NPART+1),
$ LDB, MTPROW, MYCOL )
END IF
*
IF( NLENG.GT.JB .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, J+JB-1), NB, ICURCOL,
$ MYCOL, NPCOL )
CALL DGESD2D( ICONTXT, NS, NPART, B(1,JN-NPART+1),
$ LDB, MBTROW, MYCOL )
END IF
*
II = II + JB
END IF
*
JJ = JN
ICURROW = NXTROW
ICURCOL = NXTCOL
40 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURROW = MOD( NPROW+ICURROW-1, NPROW )
IF( ICURROW.NE.IDEST ) THEN
KDIST = MOD( NPROW+ICURROW-IDEST-1, NPROW )
IF( ICEIL(NDIM,NB).GT.MOD(IDEST-IAROW+NPROW,NPROW) )
$ THEN
NPART = NUMROC( KDIST*NB+JB, NB, MYCOL+KDIST,
$ ICURCOL-1, NPCOL )
ELSE
NPART = NUMROC( NDIM, NB, MYCOL, IACOL, NPCOL )
END IF
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, NPART, B(1,JJ-NPART+1),
$ LDB, IDEST, MYCOL )
ELSE IF( MYROW.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NS, NPART, B(1,JJ-NPART+1),
$ LDB, ICURROW, MYCOL )
END IF
END IF
*
* If B can't be used as a working space,
*
ELSE
IF( MYROW.NE.ICURROW )
$ CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY, 1,
$ ZERO, WORK, NS )
*
DO 50 J = 1, NDIM, NB
NLENG = NDIM - J + 1
JB = MIN( NLENG, NB )
NXTROW = MOD( ICURROW+1, NPROW )
NXTCOL = MOD( ICURCOL+1, NPCOL )
IF( MYCOL.EQ.ICURCOL ) JN = JJ + JB
*
IF( MYROW.EQ.ICURROW ) THEN
*
* Receive updated blocks from previous row of processes
*
JJN = JJ * NS + 1
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG, NCOMM), NB, MYCOL,
$ ICURCOL, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, WORK(IPT), NS,
$ MTPROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, NPART, ONE,
$ WORK(IPT), NS, ONE, WORK(JJN), NS )
END IF
*
* B(1,JJ+1) <== A(II,JJ+1) \ B(1,JJ+1),
* ( B(1,JJ+1) = WORK(JJN) )
* where A(II,JJ+1) is a upper triangular matrix
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DTRSM( 'Right', 'Upper', 'No', DIAG, NS, JB,
$ ONE, A(II,JJ+1), LDA, WORK(JJN), NS )
CALL PBDMATADD( ICONTXT, 'G', NS, JB, ONE,
$ WORK(JJN), NS, ZERO, WORK(IPT), NS )
CALL DGEBS2D( ICONTXT, 'Row', 'I-ring', NS, JB,
$ WORK(IPT), NS )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', 'I-ring', NS, JB,
$ WORK(IPT), NS, MYROW, ICURCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.JB ) THEN
*
* Update the (NPROW-1) blocks first
*
NREST = MIN( NLENG-JB, NCOMM )
NPART = NUMROC( NREST, NB, MYCOL, ICURCOL+1, NPCOL )
*
CALL DGEMM( 'No', 'No', NS, NPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JN+1), LDA, ONE,
$ WORK(JN*NS+1), NS )
*
* Send updated blocks to next column of processes
*
IF( NPROW.GT.1 )
$ CALL DGESD2D( ICONTXT, NS, NPART, WORK(JN*NS+1),
$ NS, MBTROW, MYCOL )
*
* Update the rest of the matrix
*
IPART = NUMROC( NLENG-JB-NREST, NB, MYCOL+LCM,
$ ICURCOL+NPROW, NPCOL )
CALL DGEMM( 'No', 'No', NS,IPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JN+NPART+1), LDA,
$ ONE, WORK((JN+NPART)*NS+1), NS )
END IF
*
* Send the solution blocks to destination (IDEST row)
*
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, J-1), NB, ICURCOL,
$ MYCOL+1, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART,
$ WORK((JJ-NPART)*NS+1), NS,
$ MTPROW, MYCOL )
END IF
*
IF( NLENG.GT.JB .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, J+JB-1), NB, ICURCOL,
$ MYCOL, NPCOL )
CALL DGESD2D( ICONTXT, NS, NPART,
$ WORK((JN-NPART)*NS+1), NS,
$ MBTROW, MYCOL )
END IF
*
II = II + JB
END IF
*
JJ = JN
ICURROW = NXTROW
ICURCOL = NXTCOL
50 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURROW = MOD( NPROW+ICURROW-1, NPROW )
IF( ICURROW.NE.IDEST ) THEN
KDIST = MOD( NPROW+ICURROW-IDEST-1, NPROW )
IF( ICEIL(NDIM,NB).GT.MOD(IDEST-IAROW+NPROW,NPROW) )
$ THEN
NPART = NUMROC( KDIST*NB+JB, NB, MYCOL+KDIST,
$ ICURCOL-1, NPCOL )
ELSE
NPART = NUMROC( NDIM, NB, MYCOL, IACOL, NPCOL )
END IF
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, NPART,
$ WORK((JJ-NPART)*NS+1), NS,
$ IDEST, MYCOL )
ELSE IF( MYROW.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NS, NPART,
$ WORK((JJ-NPART)*NS+1), NS,
$ ICURROW, MYCOL )
END IF
END IF
END IF
*
IF( LSIDE ) THEN
CALL PBDTRAN( ICONTXT, 'Row', TRANSA, NS, NDIM, NB, WORK,
$ NS, ZERO, B, LDB, IDEST, IACOL, IAROW,
$ IBPOS, WORK(IPT) )
ELSE
IF( .NOT.BDATA .AND. MYROW.EQ.IDEST )
$ CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ONE, WORK, NS,
$ ZERO, B, LDB )
END IF
END IF
*
* if ( LSAME( UPLO, 'L' ) then
*
ELSE
*
IF( LSIDE.AND.NOTRAN .OR. .NOT.(LSIDE.OR.NOTRAN) ) THEN
*
* Form B := Lo( A ) \ alpha * B.
* _ _ _
* | | | \_ | |
* | | | \_ | |
* |B| := | A \_ \ alpha * |B|
* | | | \_ | |
* |_| |_________| |_|
*
IPT = MP * NS + 1
ICURROW = IAROW
ICURCOL = IACOL
*
IF( LSIDE ) THEN
IF( BSPACE ) THEN
IF( MYCOL.EQ.IBPOS ) THEN
IF( MYCOL.NE.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, MP, NS, B, LDB,
$ MYROW, ICURCOL )
CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY,
$ 1, ZERO, B, LDB )
END IF
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGERV2D( ICONTXT, MP, NS, B, LDB, MYROW, IBPOS )
ELSE
CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY, 1,
$ ZERO, B, LDB )
END IF
BDATA = .TRUE.
IPT = 1
*
ELSE
IF( MYCOL.EQ.IBPOS ) THEN
IF( MYCOL.EQ.ICURCOL ) THEN
CALL PBDMATADD( ICONTXT, 'V', MP, NS, ONE, B, LDB,
$ ZERO, WORK, MP )
ELSE
CALL DGESD2D( ICONTXT, MP, NS, B, LDB,
$ MYROW, ICURCOL )
END IF
ELSE IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGERV2D( ICONTXT, MP, NS, WORK, MP,
$ MYROW, IBPOS )
END IF
END IF
IDEST = IBPOS
*
ELSE
CALL PBDTRAN( ICONTXT, 'Row', TRANSA, NS, NDIM, NB, B,
$ LDB, ZERO, WORK, MP, IBPOS, IACOL, IAROW,
$ ICURCOL, WORK(IPT) )
IDEST = IACOL
END IF
*
LDW = MAX( 1, MP )
IRPB = MOD( NPCOL+MYCOL-IDEST-1, NPCOL )
IRDB = NB * MOD( IRPB+1, NPCOL )
IRPB = NB * IRPB
NCOMM = NB * (NPCOL-1)
*
II = 1
IN = 1
JJ = 1
*
* If B can be used as a working space,
*
IF( BDATA ) THEN
DO 60 J = 1, NDIM, NB
NLENG = NDIM - J + 1
JB = MIN( NLENG, NB )
NXTROW = MOD( ICURROW+1, NPROW )
NXTCOL = MOD( ICURCOL+1, NPCOL )
IF( MYROW.EQ.ICURROW ) IN = II + JB
*
IF( MYCOL.EQ.ICURCOL ) THEN
*
* Receive updated blocks from previous column of
* processes
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG, NCOMM), NB, MYROW,
$ ICURROW, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(IPT), NPART,
$ MYROW, MLFCOL )
CALL PBDMATADD( ICONTXT, 'G', NPART, NS, ONE,
$ WORK(IPT), NPART, ONE, B(II,1),
$ LDB )
END IF
*
* B(II,1) <== A(II,JJ) \ B(II,1), ( B(II,1) = WORK(II) )
* where A(II,JJ) is a lower triangular matrix
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DTRSM( 'Left', 'Lower', 'No', DIAG, JB, NS,
$ ONE, A(II,JJ), LDA, B(II,1), LDB )
CALL PBDMATADD( ICONTXT, 'G', JB, NS, ONE, B(II,1),
$ LDB, ZERO, WORK(IPT), JB )
CALL DGEBS2D( ICONTXT, 'Col', 'I-ring', JB, NS,
$ WORK(IPT), JB )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', 'I-ring', JB, NS,
$ WORK(IPT), JB, ICURROW, MYCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.JB ) THEN
*
* Update the (NPCOL-1) blocks first
*
NREST = MIN( NLENG-JB, NCOMM )
NPART = NUMROC( NREST, NB, MYROW, ICURROW+1, NPROW )
*
CALL DGEMM( 'No', 'No', NPART, NS, JB, -ONE,
$ A(IN,JJ), LDA, WORK(IPT), JB, ONE,
$ B(IN,1), LDB )
*
* Send updated blocks to next column of processes
*
IF( NPCOL.GT.1 )
$ CALL DGESD2D( ICONTXT, NPART, NS, B(IN,1), LDB,
$ MYROW, MRTCOL )
*
* Update the rest of the matrix
*
IPART = NUMROC( NLENG-JB-NREST, NB, MYROW+LCM,
$ ICURROW+NPCOL, NPROW )
CALL DGEMM( 'No', 'No', IPART, NS, JB, -ONE,
$ A(IN+NPART,JJ), LDA, WORK(IPT), JB,
$ ONE, B(IN+NPART,1), LDB )
END IF
*
* Send the solution blocks to destination (IDEST column)
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, J-1), NB, ICURROW,
$ MYROW+1, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, B(II-NPART,1),
$ LDB, MYROW, MLFCOL )
END IF
*
IF( NLENG.GT.JB .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB,J+JB-1), NB, ICURROW,
$ MYROW, NPROW )
CALL DGESD2D( ICONTXT, NPART, NS, B(IN-NPART,1),
$ LDB, MYROW, MRTCOL )
END IF
*
JJ = JJ + JB
END IF
*
II = IN
ICURROW = NXTROW
ICURCOL = NXTCOL
60 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( ICURCOL.NE.IDEST ) THEN
KDIST = MOD( NPCOL+ICURCOL-IDEST-1, NPCOL )
IF( ICEIL(NDIM,NB).GT.MOD(IDEST-IACOL+NPCOL,NPCOL) )
$ THEN
NPART = NUMROC( KDIST*NB+JB, NB, MYROW+KDIST,
$ ICURROW-1, NPROW )
ELSE
NPART = NUMROC( NDIM, NB, MYROW, IAROW, NPROW )
END IF
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, NPART, NS, B(II-NPART,1), LDB,
$ MYROW, IDEST )
ELSE IF( MYCOL.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NPART, NS, B(II-NPART,1), LDB,
$ MYROW, ICURCOL )
END IF
END IF
*
* If B can't be used as a working space,
*
ELSE
IF( MYCOL.NE.ICURCOL )
$ CALL PBDMATADD( ICONTXT, 'G', MP, NS, ZERO, DUMMY, 1,
$ ZERO, WORK, MP )
*
DO 70 J = 1, NDIM, NB
NLENG = NDIM - J + 1
JB = MIN( NLENG, NB )
NXTROW = MOD( ICURROW+1, NPROW )
NXTCOL = MOD( ICURCOL+1, NPCOL )
IF( MYROW.EQ.ICURROW ) IN = II + JB
*
IF( MYCOL.EQ.ICURCOL ) THEN
*
* Receive updated blocks from previous column of
* processes
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG, NCOMM), NB, MYROW,
$ ICURROW, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(IPT), NPART,
$ MYROW, MLFCOL )
CALL PBDMATADD( ICONTXT, 'G', NPART, NS, ONE,
$ WORK(IPT), NPART, ONE, WORK(II),
$ MP )
END IF
*
* B(II,1) <== A(II,JJ) \ B(II,1), ( B(II,1) = WORK(II) )
* where A(II,JJ) is a lower triangular matrix
*
IF( MYROW.EQ.ICURROW ) THEN
CALL DTRSM( 'Left', 'Lower', 'No', DIAG, JB, NS,
$ ONE, A(II,JJ), LDA, WORK(II), LDW )
CALL PBDMATADD( ICONTXT, 'G', JB, NS, ONE, WORK(II),
$ MP, ZERO, WORK(IPT), JB )
CALL DGEBS2D( ICONTXT, 'Col', 'I-ring', JB, NS,
$ WORK(IPT), JB )
ELSE
CALL DGEBR2D( ICONTXT, 'Col', 'I-ring', JB, NS,
$ WORK(IPT), JB, ICURROW, MYCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.JB ) THEN
*
* Update the (NPCOL-1) blocks first
*
NREST = MIN( NLENG-JB, NCOMM )
NPART = NUMROC( NREST, NB, MYROW, ICURROW+1, NPROW )
*
CALL DGEMM( 'No', 'No', NPART, NS, JB, -ONE,
$ A(IN,JJ), LDA, WORK(IPT), JB, ONE,
$ WORK(IN), LDW )
*
* Send updated blocks to next column of processes
*
IF( NPCOL.GT.1 )
$ CALL DGESD2D( ICONTXT, NPART, NS, WORK(IN), MP,
$ MYROW, MRTCOL )
*
* Update the rest of the matrix
*
IPART = NUMROC( NLENG-JB-NREST, NB, MYROW+LCM,
$ ICURROW+NPCOL, NPROW )
CALL DGEMM( 'No', 'No', IPART, NS, JB, -ONE,
$ A(IN+NPART,JJ), LDA, WORK(IPT), JB,
$ ONE, WORK(IN+NPART), LDW )
END IF
*
* Send the solution blocks to destination (IDEST column)
*
IF( J.GT.1 .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, J-1), NB, ICURROW,
$ MYROW+1, NPROW )
CALL DGERV2D( ICONTXT, NPART, NS, WORK(II-NPART),
$ MP, MYROW, MLFCOL )
END IF
*
IF( NLENG.GT.JB .AND. NPCOL.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB,J+JB-1), NB, ICURROW,
$ MYROW, NPROW )
CALL DGESD2D( ICONTXT, NPART, NS, WORK(IN-NPART),
$ MP, MYROW, MRTCOL )
END IF
*
JJ = JJ + JB
END IF
*
II = IN
ICURROW = NXTROW
ICURCOL = NXTCOL
70 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( ICURCOL.NE.IDEST ) THEN
KDIST = MOD( NPCOL+ICURCOL-IDEST-1, NPCOL )
IF( ICEIL(NDIM,NB).GT.MOD(IDEST-IACOL+NPCOL,NPCOL) )
$ THEN
NPART = NUMROC( KDIST*NB+JB, NB, MYROW+KDIST,
$ ICURROW-1, NPROW )
ELSE
NPART = NUMROC( NDIM, NB, MYROW, IAROW, NPROW )
END IF
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DGESD2D( ICONTXT, NPART, NS, WORK(II-NPART), MP,
$ MYROW, IDEST )
ELSE IF( MYCOL.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NPART, NS, WORK(II-NPART), MP,
$ MYROW, ICURCOL )
END IF
END IF
END IF
*
IF( LSIDE ) THEN
IF( .NOT.BDATA .AND. MYCOL.EQ.IDEST )
$ CALL PBDMATADD( ICONTXT, 'V', MP, NS, ONE, WORK, MP,
$ ZERO, B, LDB )
ELSE
CALL PBDTRAN( ICONTXT, 'Col', TRANSA, NDIM, NS, NB, WORK,
$ MP, ZERO, B, LDB, IAROW, IDEST, IBPOS,
$ IACOL, WORK(IPT) )
END IF
*
ELSE IF( ( LSIDE .AND. .NOT.NOTRAN ) .OR.
$ ( .NOT.LSIDE .AND. NOTRAN ) ) THEN
*
* Form B := alpha * B / Lo( A ).
* _
* | \_
* __________ __________ | \_
* |_____B____| := alpha * |_____B____| / | A \_
* | \_
* |_________|
*
IPT = NS * MQ + 1
ICURROW = MOD( ICEIL(NDIM,NB)+IAROW-1, NPROW )
ICURCOL = MOD( ICEIL(NDIM,NB)+IACOL-1, NPCOL )
*
IF( LSIDE ) THEN
CALL PBDTRAN( ICONTXT, 'Col', TRANSA, NDIM, NS, NB, B,
$ LDB, ZERO, WORK, NS, IAROW, IBPOS, ICURROW,
$ IACOL, WORK(IPT) )
IDEST = ICURROW
*
ELSE
IF( BSPACE ) THEN
IF( MYROW.EQ.IBPOS ) THEN
IF( MYROW.NE.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, MQ, B, LDB,
$ ICURROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY,
$ 1, ZERO, B, LDB )
END IF
ELSE IF( MYROW.EQ.ICURROW ) THEN
CALL DGERV2D( ICONTXT, NS, MQ, B, LDB, IBPOS, MYCOL )
ELSE
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY, 1,
$ ZERO, B, LDB )
END IF
BDATA = .TRUE.
IPT = 1
*
ELSE
IF( MYROW.EQ.IBPOS ) THEN
IF( MYROW.EQ.ICURROW ) THEN
CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ONE, B, LDB,
$ ZERO, WORK, NS )
ELSE
CALL DGESD2D( ICONTXT, NS, MQ, B, LDB,
$ ICURROW, MYCOL )
END IF
ELSE IF( MYROW.EQ.ICURROW ) THEN
CALL DGERV2D( ICONTXT, NS, MQ, WORK, NS,
$ IBPOS, MYCOL )
END IF
END IF
IDEST = IBPOS
END IF
*
IRPB = MOD( NPROW+IDEST-MYROW-1, NPROW )
IRDB = NB * MOD( IRPB+1, NPROW )
IRPB = NB * IRPB
NCOMM = NB * (NPROW-1)
KB = MOD( NDIM, NB )
IF( KB.EQ.0 ) KB = NB
*
II = MP - NB + 1
IF( MYROW.EQ.ICURROW ) II = MP - KB + 1
JJ = MQ - NB
IF( MYCOL.EQ.ICURCOL ) JJ = MQ - KB
JN = JJ
JB = KB
*
* If B can be used as a working space,
*
IF( BDATA ) THEN
DO 80 J = 1, NDIM, NB
NLENG = NDIM - J - KB + 1
NXTROW = MOD( NPROW+ICURROW-1, NPROW )
NXTCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( MYCOL.EQ.ICURCOL ) JN = JJ - NB
*
IF( MYROW.EQ.ICURROW ) THEN
*
* Receive updated blocks from previous row of processes
*
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG+JB, NCOMM), NB, ICURCOL,
$ MYCOL, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, WORK(IPT), NS,
$ MBTROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, NPART, ONE,
$ WORK(IPT), NS, ONE,
$ B(1,JJ+NB-NPART+1), LDB )
END IF
*
* B(1,JJ+1) <== A(II,JJ+1) / B(1,JJ+1)
* ( B(1,JJ+1) = WORK(JJ*NS+1) )
* where A(II,JJ+1) is a lower triangular matrix
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DTRSM( 'Right', 'Lower', 'No', DIAG, NS, JB,
$ ONE, A(II,JJ+1), LDA, B(1,JJ+1), LDB )
CALL PBDMATADD( ICONTXT, 'G', NS, JB, ONE,
$ B(1,JJ+1), LDB, ZERO, WORK(IPT), NS )
CALL DGEBS2D( ICONTXT, 'Row', 'D-ring', NS, JB,
$ WORK(IPT), NS )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', 'D-ring', NS, JB,
$ WORK(IPT), NS, MYROW, ICURCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.0 ) THEN
*
* Update the (NPROW-1) blocks first
*
NREST = MIN( NLENG, NCOMM )
NPART = NUMROC( NREST, NB, ICURCOL, MYCOL+1, NPCOL )
JJN = JN + NB - NPART
CALL DGEMM( 'No', 'No', NS, NPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JJN+1), LDA, ONE,
$ B(1,JJN+1), LDB )
*
* Send updated blocks to next column of processes
*
IF( NPROW.GT.1 )
$ CALL DGESD2D( ICONTXT, NS, NPART, B(1,JJN+1), LDB,
$ MTPROW, MYCOL )
*
* Update the rest of the matrix
*
CALL DGEMM( 'No','No', NS, JJN, JB, -ONE, WORK(IPT),
$ NS, A(II,1), LDA, ONE, B, LDB )
END IF
*
* Send the solution blocks to destination (IDEST row)
*
JJN = J + KB - 1
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, JJN-JB), NB, MYCOL,
$ ICURCOL+1, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, B(1,JJ+NB+1), LDB,
$ MBTROW, MYCOL )
END IF
*
IF( NLENG.GT.0 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, JJN), NB, MYCOL, ICURCOL,
$ NPCOL )
CALL DGESD2D( ICONTXT, NS, NPART, B(1,JN+NB+1), LDB,
$ MTPROW, MYCOL )
END IF
*
II = II - NB
END IF
*
JJ = JN
JB = NB
ICURROW = NXTROW
ICURCOL = NXTCOL
80 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURROW = MOD( ICURROW+1, NPROW )
IF( ICURROW.NE.IDEST ) THEN
KDIST = MOD( NPROW+IDEST-ICURROW, NPROW )
NPART = NUMROC( MIN(NDIM, KDIST*NB), NB, MYCOL, IACOL,
$ NPCOL )
IF( MYROW.EQ.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, NPART, B, LDB,
$ IDEST, MYCOL )
ELSE IF( MYROW.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NS, NPART, B, LDB,
$ ICURROW, MYCOL )
END IF
END IF
*
* If B can't be used as a working space,
*
ELSE
IF( MYROW.NE.ICURROW )
$ CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ZERO, DUMMY, 1,
$ ZERO, WORK, NS )
*
DO 90 J = 1, NDIM, NB
NLENG = NDIM - J - KB + 1
NXTROW = MOD( NPROW+ICURROW-1, NPROW )
NXTCOL = MOD( NPCOL+ICURCOL-1, NPCOL )
IF( MYCOL.EQ.ICURCOL ) JN = JJ - NB
*
IF( MYROW.EQ.ICURROW ) THEN
*
* Receive updated blocks from previous row of processes
*
JJN = JJ * NS + 1
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(NLENG+JB, NCOMM), NB, ICURCOL,
$ MYCOL, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART, WORK(IPT), NS,
$ MBTROW, MYCOL )
CALL PBDMATADD( ICONTXT, 'G', NS, NPART, ONE,
$ WORK(IPT), NS, ONE,
$ WORK((JJ+NB-NPART)*NS+1), NS )
END IF
*
* B(1,JJ+1) <== A(II,JJ+1) / B(1,JJ+1)
* ( B(1,JJ+1) = WORK(JJ*NS+1) )
* where A(II,JJ+1) is a lower triangular matrix
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL DTRSM( 'Right', 'Lower', 'No', DIAG, NS, JB,
$ ONE, A(II,JJ+1),LDA, WORK(JJ*NS+1),NS )
CALL PBDMATADD( ICONTXT, 'G', NS, JB, ONE,
$ WORK(JJ*NS+1), NS, ZERO, WORK(IPT),
$ NS )
CALL DGEBS2D( ICONTXT, 'Row', 'D-ring', NS, JB,
$ WORK(IPT), NS )
ELSE
CALL DGEBR2D( ICONTXT, 'Row', 'D-ring', NS, JB,
$ WORK(IPT), NS, MYROW, ICURCOL )
END IF
*
* Update the rest of data and prepare for the next step
*
IF( NLENG.GT.0 ) THEN
*
* Update the (NPROW-1) blocks first
*
NREST = MIN( NLENG, NCOMM )
NPART = NUMROC( NREST, NB, ICURCOL, MYCOL+1, NPCOL )
JJN = JN + NB - NPART
CALL DGEMM( 'No', 'No', NS, NPART, JB, -ONE,
$ WORK(IPT), NS, A(II,JJN+1), LDA, ONE,
$ WORK(JJN*NS+1), NS )
*
* Send updated blocks to next column of processes
*
IF( NPROW.GT.1 )
$ CALL DGESD2D( ICONTXT, NS, NPART, WORK(JJN*NS+1),
$ NS, MTPROW, MYCOL )
*
* Update the rest of the matrix
*
CALL DGEMM( 'No','No', NS, JJN, JB, -ONE, WORK(IPT),
$ NS, A(II,1), LDA, ONE, WORK, NS )
END IF
*
* Send the solution blocks to destination (IDEST row)
*
JJN = J + KB - 1
IF( J.GT.1 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRPB, JJN-JB), NB, MYCOL,
$ ICURCOL+1, NPCOL )
CALL DGERV2D( ICONTXT, NS, NPART,
$ WORK((JJ+NB)*NS+1), NS,
$ MBTROW, MYCOL )
END IF
*
IF( NLENG.GT.0 .AND. NPROW.GT.1 ) THEN
NPART = NUMROC( MIN(IRDB, JJN), NB, MYCOL, ICURCOL,
$ NPCOL )
CALL DGESD2D( ICONTXT, NS, NPART,
$ WORK((JN+NB)*NS+1), NS,
$ MTPROW, MYCOL )
END IF
*
II = II - NB
END IF
*
JJ = JN
JB = NB
ICURROW = NXTROW
ICURCOL = NXTCOL
90 CONTINUE
*
* Uncopied solutions are moved to the first column of procs.
*
ICURROW = MOD( ICURROW+1, NPROW )
IF( ICURROW.NE.IDEST ) THEN
KDIST = MOD( NPROW+IDEST-ICURROW, NPROW )
NPART = NUMROC( MIN(NDIM, KDIST*NB), NB, MYCOL, IACOL,
$ NPCOL )
IF( MYROW.EQ.ICURROW ) THEN
CALL DGESD2D( ICONTXT, NS, NPART, WORK, NS,
$ IDEST, MYCOL )
ELSE IF( MYROW.EQ.IDEST ) THEN
CALL DGERV2D( ICONTXT, NS, NPART, WORK, NS,
$ ICURROW, MYCOL )
END IF
END IF
END IF
*
IF( LSIDE ) THEN
CALL PBDTRAN( ICONTXT, 'Row', TRANSA, NS, NDIM, NB, WORK,
$ NS, ZERO, B, LDB, IDEST, IACOL, IAROW,
$ IBPOS, WORK(IPT) )
ELSE
IF( .NOT.BDATA .AND. MYROW.EQ.IDEST )
$ CALL PBDMATADD( ICONTXT, 'G', NS, MQ, ONE, WORK, NS,
$ ZERO, B, LDB )
END IF
END IF
END IF
*
* === If A is just a block ===
*
ELSE
ADATA = .FALSE.
ASPACE = LSAME( ABWORK, 'Y' )
COMMA = ACOMM
IF( LSAME( COMMA, ' ' ) ) COMMA = '1'
*
IF( LSIDE .AND. MYROW.EQ.IAROW ) THEN
*
* Form B := op( A ) \ alpha * 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. MAX(1,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 DTRSM
*
IF( ADATA ) THEN
CALL DTRSM( 'Left', UPLO, TRANSA, DIAG, M, NQ, ALPHA,
$ A, LDA, B, LDB )
ELSE
CALL DTRSM( '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 DTRSM
*
IF( ADATA ) THEN
CALL DTRSM( 'Right', UPLO, TRANSA, DIAG, MP, N, ALPHA,
$ A, LDA, B, LDB )
ELSE
CALL DTRSM( 'Right', UPLO, TRANSA, DIAG, MP, N, ALPHA,
$ WORK, N, B, LDB )
END IF
END IF
END IF
*
RETURN
*
* End of PBDTRSM
*
END
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