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|
SUBROUTINE PBSSYMM( ICONTXT, MATBLK, SIDE, UPLO, M, N, NB, ALPHA,
$ A, LDA, B, LDB, BETA, C, LDC, IAROW, IACOL,
$ IBPOS, ICPOS, ACOMM, ABWORK, CWORK, 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 ABWORK, ACOMM, CWORK, MATBLK, SIDE, UPLO
INTEGER IACOL, IAROW, IBPOS, ICONTXT, ICPOS, LDA, LDB,
$ LDC, M, MULLEN, N, NB
REAL ALPHA, BETA
* ..
* .. Array Arguments ..
REAL A( LDA, * ), B( LDB, * ), C( LDC, * ),
$ WORK( * )
*
* Purpose
* =======
*
* PBSSYMM is a parallel blocked version of SSYMM.
* PBSSYMM performs one of the matrix-matrix operations
*
* C := alpha*A*B + beta*C,
*
* or
*
* C := alpha*B*A + beta*C,
*
* where alpha and beta are scalars, A is a symmetric matrix and B and
* C are m-by-n matrices.
*
* The first elements of the matrices A, B, and C should be located at
* the beginnings of their first blocks. (not the middle of the blocks.)
* B can be broadcast if necessary, and C is collected.
*
* 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 A is a (full) block matrix or
* a single block as follows:
*
* MATBLK = 'M', A is a (full) block matrix
* MATBLK = 'B', A is a single block
*
* SIDE (input) CHARACTER*1
* SIDE specifies whether the symmetric matrix A appears on the
* left or right in the operation as follows:
*
* SIDE = 'L', C := alpha*A*B + beta*C,
* SIDE = 'R', C := alpha*B*A + beta*C,
*
* UPLO (input) CHARACTER*1
* UPLO specifies whether the upper or lower triangular part of
* the symmetric matrix A is to be referenced as follows:
*
* UPLO = 'U', Only the upper triangular part of the
* symmetric matrix is to be referenced.
* UPLO = 'L', Only the lower triangular part of the
* symmetric matrix is to be referenced.
*
* M (input) INTEGER
* M specifies the (global) number of rows of the block matrix
* B and C. If SIDE = 'L', it also specifies the (global)
* number of rows and columns of the matrix A. M >= 0.
* If SIDE = 'R', M <= NB.
*
* N (input) INTEGER
* N specifies the (global) number of columns of the block
* matrix B and C. If SIDE = 'R', it also specifies the
* (global) number of rows and columns of the matrix A. M >= 0.
* If SIDE = 'L', N >= NB.
*
* NB (input) INTEGER
* NB specifies the row and column block size of matrix A.
* It also specifies the row block size of the matrices B and C
* if MATBLK = 'M' and SIDE = 'L', or MATBLK = 'B' and SIDE =
* 'R'; and the column block size of the matrices B and C if
* MATBLK = 'M' and SIDE = 'R', or MATBLK = 'B' and SIDE = 'L'.
* NB >= 1.
*
* ALPHA (input) REAL
* ALPHA specifies the scalar alpha.
*
* A (input) REAL array of DIMENSION ( LDA, ka ), where ka is Mq
* when SIDE = 'L' and is Nq otherwise.
* Before entry with SIDE = 'L', the M-by-M part of the (global)
* array A must contain the symmetric 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
* symmetric 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 (global) array A must
* contain the lower triangular part of the symmetric matrix and
* the strictly upper triangular part of A is not referenced.
* Before entry with SIDE = 'R', the N-by-N part of the (global)
* array A must contain the symmetric matrix, such that when
* UPLO = 'U', the leading n by n upper triangular part of the
* (global) array A must contain the upper triangular part of
* the symmetric 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 symmetric matrix and the
* strictly upper triangular part of A is not referenced.
*
* LDA (input) INTEGER
* On entry, LDA specifies the first dimension of (local) A as
* declared in the calling (sub) program. When SIDE = 'L',
* LDA >= MAX(1,Mp), otherwise LDA >= MAX(1,Np).
*
* B (input) REAL array of DIMENSION ( LDB, n ).
* The leading Mp-by-Nq part of the (local) array
* B must contain the matrix B.
*
* LDB (input) INTEGER
* On entry, LDB specifies the first dimension of (local) B as
* declared in the calling (sub) program. LDB >= MAX(1,Mp).
*
* BETA (input) REAL
* BETA specifies the scalar beta. When BETA is supplied as
* zero then C need not be set on input.
*
* C (input/output) REAL array of DIMENSION ( LDC, n ).
* On entry, the leading Mp-by-Nq part of the array C must
* contain the (local) matrix C, except when beta is zero, in
* which case C need not be set on entry.
* On exit, the array C is overwritten by the Mp-by-Nq updated
* matrix. Input values of C would be changed after the
* computation in the processes which don't have the resultant
* column block or row block of C.
*
* LDC (input) INTEGER
* LDC specifies the first dimension of C as declared
* in the calling (sub) program. LDC >= 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
* (-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).
* IBPOS should be the same as ICPOS if MATBLK = 'B'.
*
* ICPOS (input) INTEGER
* When MATBLK = 'M', if SIDE = 'L', ICPOS specifies a column of
* the process template, which holds the column of blocks of C
* (0 <= ICPOS < NPCOL). And if SIDE = 'R', it specifies a row
* of the template, which holds the row of blocks of C (0 <=
* ICPOS < NPROW).
* When MATBLK = 'B', if SIDE = 'L', it specifies a column of
* the template which has the first block of C (0 <= ICPOS
* < NPCOL), and if SIDE = 'R', it specifies a row of the
* template, which has the first block of C (0 <=ICPOS <NPROW).
* ICPOS should be the same as IBPOS if MATBLK = 'B'.
*
* ACOMM (input) CHARACTER*1
* When MATBLK = 'B', ACOMM specifies the communication scheme
* of a block of A. And it is ignored when MATBLK = 'M'.
* 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 processes.
* B is sent to B position in other processes.
* It is assumed that processes have
* sufficient space to store (local) B.
* ABWORK = 'N': Data in B 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': A is data space, not to be touched.
*
* CWORK (input) CHARACTER*1
* When MATBLK = 'M', CWORK determines whether C is a
* workspace or not.
*
* CWORK = 'Y': C is workspace in other processes.
* It is assumed that processes have
* sufficient space to store temporary
* (local) C.
* CWORK = 'N': Data in C will be untouched (unchanged)
* in other processes.
*
* And MATBLK = 'B', it is ignored.
*
* MULLEN (input) INTEGER
* It specifies multiplication length of the optimum column
* number of A for multiplying A with B. The value depends on
* machine characteristics.
*
* WORK (workspace) REAL array of dimension Size(WORK).
* It will store copies of B and/or C (see Requirements).
*
* 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.
*
* Communication Scheme
* ====================
*
* When MATBLK = 'M', the communication schemes of the routine are
* fixed as fan-out and fan-in schemes (COMM = '1-tree').
*
* 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'
* Size(WORK) = 2 * N * Mq0
* + N * Mp0 ( if CWORK <> 'Y' )
* + N * Mp0 ( if IBPOS <> -1 and ABWORK <> 'Y' )
* + MAX[ SZCMP,
* N*CEIL(Mqb,LCMQ)*NB*MIN(LCMQ,CEIL(M,NB)) ]
* (b) SIDE = 'Right'
* Size(WORK) = 2 * M * Np0
* + M * Nq0 ( if CWORK <> 'Y' )
* + M * Nq0 ( if IBPOS <> -1 and ABWORK <> 'Y' )
* + MAX[ SZCMP,
* M*CEIL(Npb,LCMP)*NB*MIN(LCMP,CEIL(N,NB)) ]
*
* (2) MATBLK = 'B'
* (a) SIDE = 'Left'
* Size(WORK) = M * M ( if IACOL <> -1 and ABWORK <> 'Y' )
* (b) SIDE = 'Right'
* Size(WORK) = N * N ( 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 ..
REAL ONE, ZERO
PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
* ..
* .. Local Scalars ..
CHARACTER*1 FORM, COMMA
LOGICAL ADATA, AMAT, ASPACE, BDATA, BSPACE, CDATA,
$ CSPACE, LSIDE, RSIDE, UPPER
INTEGER INFO, IPB, IPBZ, IPC, IPD, IPT, IPW, IQBZ,
$ ISZCMP, ITER, JJ, JNPBZ, JNQBZ, JPBZ, JQBZ, KI,
$ KIZ, KJ, KJZ, LCM, LCMP, LCMQ, LMW, LNW, LPBZ,
$ LQBZ, MRCOL, MRROW, MYCOL, MYROW, MZCOL, MZROW,
$ NDIM, NP, NP1, NPCOL, NPROW, NQ
REAL DUMMY
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, NUMROC
EXTERNAL ICEIL, ILCM, LSAME, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, PBSDZERO, PBSLACPZ, PBSMATADD,
$ PBSTRAN, PXERBLA, SGEBR2D, SGEBS2D, SGEMM,
$ SGSUM2D, SSYMM, STRBR2D, STRBS2D
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible.
*
IF( M.EQ.0 .OR. N.EQ.0 .OR. ( ALPHA.EQ.ZERO .AND. BETA.EQ.ONE ) )
$ RETURN
*
CALL BLACS_GRIDINFO( ICONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
AMAT = LSAME( MATBLK, 'M' )
UPPER = LSAME( UPLO, 'U' )
LSIDE = LSAME( SIDE, 'L' )
RSIDE = LSAME( SIDE, 'R' )
*
* Test the input parameters.
*
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( M .LT.0 ) THEN
INFO = 5
ELSE IF( N .LT.0 ) THEN
INFO = 6
ELSE IF( NB .LT.1 ) THEN
INFO = 7
END IF
*
10 CONTINUE
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICONTXT, 'PBSSYMM ', INFO )
RETURN
END IF
*
* === If A is a general matrix ( MATBLK = 'M' ) ===
*
IF( LSAME( MATBLK, 'M' ) ) THEN
IF( LSIDE ) THEN
NDIM = M
ELSE
NDIM = N
END IF
NP = NUMROC( NDIM, NB, MYROW, IAROW, NPROW )
NQ = NUMROC( NDIM, NB, MYCOL, IACOL, NPCOL )
*
NP1 = MAX( 1, NP )
IF( LDA.LT.NP1 ) THEN
INFO = 10
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
*
* Quick return if alpha = zero
*
IF( ALPHA.EQ.ZERO ) THEN
IF( LSIDE .AND. MYCOL.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'V', NP, N, ZERO, DUMMY, 1, BETA,
$ C, LDC )
ELSE IF( .NOT.LSIDE .AND. MYROW.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, BETA,
$ C, LDC )
END IF
RETURN
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.
IF( IBPOS.EQ.-1 ) BDATA = .TRUE.
CDATA = .FALSE.
BSPACE = LSAME( ABWORK, 'Y' )
CSPACE = LSAME( CWORK, 'Y' )
*
* PART 1: Distribute a column (or row) block B and its transpose
* ==============================================================
*
IF( LSIDE ) THEN
*
* Form C := alpha*A*B + beta*C, if SIDE = 'Left'.
* _ _____________ _ _
* | | |\_ | | | | |
* | | | \_ | | | | |
* | | | \_ | | | | |
* |C| = alpha * | A_ | * |B| + beta * |C|
* | | | \_ | | | | |
* | | | \_ | | | | |
* |_| |____________\| |_| |_|
*
IF( LDB.LT.NP1 .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYCOL .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 12
ELSE IF( LDC.LT.NP1 .AND. ( CSPACE .OR.
$ ICPOS.EQ.MYCOL .OR. ICPOS.EQ.-1 ) ) THEN
INFO = 15
ELSE IF( IBPOS.LT.-1 .OR. IBPOS.GE.NPCOL ) THEN
INFO = 18
ELSE IF( ICPOS.LT.0 .OR. ICPOS.GE.NPCOL ) THEN
INFO = 19
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Initialize parameters
*
IF( CSPACE ) THEN
IPD = 1
CDATA = .TRUE.
IF( MYCOL.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'G', NP, N, ZERO, DUMMY, 1, BETA,
$ C, LDC )
ELSE
CALL PBSMATADD( ICONTXT, 'G', NP, N, ZERO, DUMMY, 1, ZERO,
$ C, LDC )
END IF
ELSE
IPC = 1
IPD = N * NP + IPC
CALL PBSMATADD( ICONTXT, 'G', NP, N, ZERO, DUMMY, 1, ZERO,
$ WORK(IPC), NP )
END IF
*
CALL PBSMATADD( ICONTXT, 'G', N, NQ, ZERO, DUMMY, 1, ZERO,
$ WORK(IPD), N )
*
IPT = N * NQ + IPD
IPB = N * NQ + IPT
IPW = N * NP + IPB
*
* Broadcast B if necessary
*
IF( .NOT.BDATA ) THEN
IF( BSPACE ) THEN
IF( MYCOL.EQ.IBPOS ) THEN
CALL SGEBS2D( ICONTXT, 'Row', '1-tree', NP, N, B, LDB )
ELSE
CALL SGEBR2D( ICONTXT, 'Row', '1-tree', NP, N, B, LDB,
$ MYROW, IBPOS )
END IF
BDATA = .TRUE.
IPW = IPB
ELSE
IF( MYCOL.EQ.IBPOS ) THEN
CALL PBSMATADD( ICONTXT, 'V', NP, N, ONE, B, LDB, ZERO,
$ WORK(IPB), NP )
CALL SGEBS2D( ICONTXT, 'Row', '1-tree', NP, N,
$ WORK(IPB), NP )
ELSE
CALL SGEBR2D( ICONTXT, 'Row', '1-tree', NP, N,
$ WORK(IPB), NP, MYROW, IBPOS )
END IF
END IF
END IF
*
* Transpose col block of B to WORK(IPT), where B is distributed
*
IF( BDATA ) THEN
CALL PBSTRAN( ICONTXT, 'Col', 'T', M, N, NB, B, LDB, ZERO,
$ WORK(IPT), N, IAROW, -1, -1, IACOL,
$ WORK(IPW) )
ELSE
CALL PBSTRAN( ICONTXT, 'Col', 'T', M, N, NB, WORK(IPB), NP,
$ ZERO, WORK(IPT),N, IAROW, -1, -1, IACOL,
$ WORK(IPW) )
END IF
*
ELSE
*
* Form C := alpha*B*A + beta*C, if SIDE = 'Right'.
* _____________
* |\_ |
* | \_ |
* ___________ _____________ | \_ | ___________
* |____C______| = a*|______B______|*| A_ |+b*|____C______|
* | \_ |
* | \_ |
* |____________\|
*
IF( LDB.LT.MAX(1,M) .AND. ( BSPACE .OR.
$ IBPOS.EQ.MYROW .OR. IBPOS.EQ.-1 ) ) THEN
INFO = 12
ELSE IF( LDC.LT.MAX(1,M) .AND. ( CSPACE .OR.
$ ICPOS.EQ.MYROW .OR. ICPOS.EQ.-1 ) ) THEN
INFO = 15
ELSE IF( IBPOS.LT.-1 .OR. IBPOS.GE.NPROW ) THEN
INFO = 18
ELSE IF( ICPOS.LT.0 .OR. ICPOS.GE.NPROW ) THEN
INFO = 19
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Initialize parameters
*
IF( CSPACE ) THEN
IPD = 1
CDATA = .TRUE.
IF( MYROW.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, BETA,
$ C, LDC )
ELSE
CALL PBSMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, ZERO,
$ C, LDC )
END IF
ELSE
IPC = 1
IPD = M * NQ + IPC
CALL PBSMATADD( ICONTXT, 'G', M, NQ, ZERO, DUMMY, 1, ZERO,
$ WORK(IPC), M )
END IF
*
CALL PBSMATADD( ICONTXT, 'G', NP, M, ZERO, DUMMY, 1, ZERO,
$ WORK(IPD), NP )
*
IPT = M * NP + IPD
IPB = M * NP + IPT
IPW = M * NQ + IPB
*
* Broadcast B if necessary
*
IF( .NOT.BDATA ) THEN
IF( BSPACE ) THEN
IF( MYROW.EQ.IBPOS ) THEN
CALL SGEBS2D( ICONTXT, 'Col', '1-tree', M, NQ, B, LDB )
ELSE
CALL SGEBR2D( ICONTXT, 'Col', '1-tree', M, NQ, B, LDB,
$ IBPOS, MYCOL )
END IF
BDATA = .TRUE.
IPW = IPB
ELSE
IF( MYROW.EQ.IBPOS ) THEN
CALL PBSMATADD( ICONTXT, 'V', M, NQ, ONE, B, LDB, ZERO,
$ WORK(IPB), M )
CALL SGEBS2D( ICONTXT, 'Col', '1-tree', M, NQ,
$ WORK(IPB), M )
ELSE
CALL SGEBR2D( ICONTXT, 'Col', '1-tree', M, NQ,
$ WORK(IPB), M, IBPOS, MYCOL )
END IF
END IF
END IF
*
* Transpose row block of B to WORK(IPT), where B is distributed
*
IF( BDATA ) THEN
CALL PBSTRAN( ICONTXT, 'Row', 'T', M, N, NB, B, LDB, ZERO,
$ WORK(IPT), NP, -1, IACOL, IAROW, -1,
$ WORK(IPW) )
ELSE
CALL PBSTRAN( ICONTXT, 'Row', 'T', M, N, NB, WORK(IPB), M,
$ ZERO, WORK(IPT), NP, -1, IACOL, IAROW, -1,
$ WORK(IPW) )
END IF
END IF
*
* PART 2: Compute C (= WORK(IPC)) and WORK(IPD)
* =============================================
*
IF( NP.EQ.0 .OR. NQ.EQ.0 ) GO TO 160
*
* If A is a symmetric upper triangular matrix,
*
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 80 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 PBSLACPZ( ICONTXT, 'Upper', FORM, 'No', KIZ, NB,
$ A(JPBZ+1,JQBZ+KJZ+1), LDA,
$ WORK(KJZ*LMW+IPW), LMW,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
30 CONTINUE
40 CONTINUE
*
* Compute C if SIDE = 'Left'
*
IF( LSIDE ) THEN
IF( CDATA ) THEN
CALL SGEMM( 'No', 'Trans', LMW, N, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*N+IPT), N,
$ ONE, C(JPBZ+1,1), LDC )
CALL SGEMM( 'No', 'Trans', JPBZ, N, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*N+IPT), N,
$ ONE, C, LDC )
ELSE
CALL SGEMM( 'No', 'Trans', LMW, N, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*N+IPT), N,
$ ZERO, WORK(JPBZ+IPC), NP1 )
CALL SGEMM( 'No', 'Trans', JPBZ, N, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*N+IPT), N,
$ ONE, WORK(IPC), NP1 )
END IF
*
* Compute C if SIDE = 'Right'
*
ELSE
IF( BDATA ) THEN
CALL SGEMM( 'No', 'Trans', LMW, M, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), B(1,JQBZ+1), LDB,
$ ONE, WORK(JPBZ+IPD), NP1 )
CALL SGEMM( 'No', 'Trans', JPBZ, M, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, B(1,JQBZ+1), LDB, ONE,
$ WORK(IPD), NP1 )
ELSE
CALL SGEMM( 'No', 'Trans', LMW, M, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*M+IPB),
$ M, ZERO, WORK(JPBZ+IPD), NP1 )
CALL SGEMM( 'No', 'Trans', JPBZ, M, LNW, ALPHA,
$ A(1,JQBZ+1), LDA, WORK(JQBZ*M+IPB), M,
$ ONE, WORK(IPD), NP1 )
END IF
END IF
*
* Delete the diagonal elements of upper tri. matrix WORK(IPW)
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
*
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 = KI * NB
KJZ = KJ * NB
IF( KJZ.GE.LNW ) GO TO 70
IF( MZROW.EQ.MZCOL )
$ CALL PBSDZERO( KIZ, NB, WORK(KJZ*LMW+IPW), LMW,
$ LPBZ, LQBZ, LNW-KJZ )
MZCOL = MZCOL + NPCOL
60 CONTINUE
70 CONTINUE
*
* Compute C if SIDE = 'Left'
*
IF( LSIDE ) THEN
IF( BDATA ) THEN
CALL SGEMM( 'Trans', 'No', N, LNW, LMW, ALPHA,
$ B(JPBZ+1,1), LDB, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(N*JQBZ+IPD), N )
CALL SGEMM( 'Trans', 'No', N, LNW, JPBZ, ALPHA, B, LDB,
$ A(1,JQBZ+1), LDA, ONE, WORK(N*JQBZ+IPD),N )
ELSE
CALL SGEMM( 'Trans', 'No', N, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP1, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(N*JQBZ+IPD), N )
CALL SGEMM( 'Trans', 'No', N, LNW, JPBZ, ALPHA,
$ WORK(IPB), NP1, A(1,JQBZ+1), LDA, ONE,
$ WORK(N*JQBZ+IPD), N )
END IF
*
* Compute C if SIDE = 'Right'
*
ELSE
IF( CDATA ) THEN
CALL SGEMM( 'Trans', 'No', M, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPT), NP1, WORK(IPW), MAX(1,LMW),
$ ONE, C(1,JQBZ+1), LDC )
CALL SGEMM( 'Trans', 'No', M, LNW, JPBZ, ALPHA,
$ WORK(IPT), NP1, A(1,JQBZ+1), LDA, ONE,
$ C(1,JQBZ+1), LDC )
ELSE
CALL SGEMM( 'Trans', 'No', M, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPT), NP1, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(M*JQBZ+IPC), M )
CALL SGEMM( 'Trans', 'No', M, LNW, JPBZ, ALPHA,
$ WORK(IPT), NP1, A(1,JQBZ+1), LDA, ONE,
$ WORK(M*JQBZ+IPC), M )
END IF
END IF
*
JPBZ = JNPBZ
JQBZ = JNQBZ
80 CONTINUE
*
* If A is a symmetric 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
*
DO 150 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 100 KJ = 0, LCMQ-1
90 CONTINUE
IF( MZROW.LT.MZCOL ) THEN
MZROW = MZROW + NPROW
KI = KI + 1
GO TO 90
END IF
KIZ = KI * NB
KJZ = KJ * NB
IF( KJZ.GE.LNW ) GO TO 110
FORM = 'G'
IF( MZROW.EQ.MZCOL ) FORM = 'T'
MZCOL = MZCOL + NPCOL
*
CALL PBSLACPZ( ICONTXT, 'Lower', FORM, 'No', KIZ, NB,
$ A(JPBZ+1,JQBZ+KJZ+1), LDA,
$ WORK(KJZ*LMW+IPW), LMW, LPBZ, LQBZ,
$ LMW, LNW-KJZ )
100 CONTINUE
110 CONTINUE
*
* Compute C if SIDE = 'Left'
*
IF( LSIDE ) THEN
IF( CDATA ) THEN
CALL SGEMM( 'No', 'Trans', LMW, N, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*N+IPT), N,
$ ONE, C(JPBZ+1,1), LDC )
CALL SGEMM( 'No', 'Trans', NP-JNPBZ, N, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, WORK(JQBZ*N+IPT),
$ N, ONE, C(JNPBZ+1,1), LDC )
ELSE
CALL SGEMM( 'No', 'Trans', LMW, N, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*N+IPT), N,
$ ONE, WORK(JPBZ+IPC), NP1 )
CALL SGEMM( 'No', 'Trans', NP-JNPBZ, N, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, WORK(JQBZ*N+IPT),
$ N, ONE, WORK(JNPBZ+IPC), NP1 )
END IF
*
* Compute C if SIDE = 'Right'
*
ELSE
IF( BDATA ) THEN
CALL SGEMM( 'No', 'Trans', LMW, M, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), B(1,JQBZ+1), LDB,
$ ONE, WORK(JPBZ+IPD), NP1 )
CALL SGEMM( 'No', 'Trans', NP-JNPBZ, M, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, B(1,JQBZ+1), LDB,
$ ONE, WORK(JNPBZ+IPD), NP1 )
ELSE
CALL SGEMM( 'No', 'Trans', LMW, M, LNW, ALPHA,
$ WORK(IPW), MAX(1,LMW), WORK(JQBZ*M+IPB), M,
$ ONE, WORK(JPBZ+IPD), NP1 )
CALL SGEMM( 'No', 'Trans', NP-JNPBZ, M, LNW, ALPHA,
$ A(JNPBZ+1,JQBZ+1), LDA, WORK(JQBZ*M+IPB),
$ M, ONE, WORK(JNPBZ+IPD), NP1 )
END IF
END IF
*
* Delete the diagonal elements of lower tri. matrix WORK(IPW)
*
MZROW = MRROW
MZCOL = MRCOL
KI = 0
*
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 = KI * NB
KJZ = KJ * NB
IF( KJZ.GE.LNW ) GO TO 140
IF( MZROW.EQ.MZCOL )
$ CALL PBSDZERO( KIZ, NB, WORK(KJZ*LMW+IPW), LMW,
$ LPBZ, LQBZ, LNW-KJZ )
MZCOL = MZCOL + NPCOL
130 CONTINUE
140 CONTINUE
*
* Compute C if SIDE = 'Left'
*
IF( LSIDE ) THEN
IF( BDATA ) THEN
CALL SGEMM( 'Trans', 'No', N, LNW, LMW, ALPHA,
$ B(JPBZ+1,1), LDB, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(N*JQBZ+IPD), N )
CALL SGEMM( 'Trans', 'No', N, LNW, NP-JNPBZ, ALPHA,
$ B(JNPBZ+1,1), LDB, A(JNPBZ+1,JQBZ+1), LDA,
$ ONE, WORK(N*JQBZ+IPD), N )
ELSE
CALL SGEMM( 'Trans', 'No', N, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPB), NP, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(N*JQBZ+IPD), N )
CALL SGEMM( 'Trans', 'No', N, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPB), NP, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, WORK(N*JQBZ+IPD), N )
END IF
*
* Compute C if SIDE = 'Right'
*
ELSE
IF( CDATA ) THEN
CALL SGEMM( 'Trans', 'No', M, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPT), NP, WORK(IPW), MAX(1,LMW),
$ ONE, C(1,JQBZ+1), LDC )
CALL SGEMM( 'Trans', 'No', M, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPT), NP, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, C(1,JQBZ+1), LDC )
ELSE
CALL SGEMM( 'Trans', 'No', M, LNW, LMW, ALPHA,
$ WORK(JPBZ+IPT), NP1, WORK(IPW), MAX(1,LMW),
$ ZERO, WORK(M*JQBZ+IPC), M )
CALL SGEMM( 'Trans', 'No', M, LNW, NP-JNPBZ, ALPHA,
$ WORK(JNPBZ+IPT), NP1, A(JNPBZ+1,JQBZ+1),
$ LDA, ONE, WORK(M*JQBZ+IPC), M )
END IF
END IF
*
JPBZ = JNPBZ
JQBZ = JNQBZ
150 CONTINUE
END IF
*
160 CONTINUE
*
* PART 3: Collect and Add C, C := C + op(WORK(IPC))+op(WORK(IPD))
* ===============================================================
*
* C is a column block if SIDE = 'Left'
*
IF( LSIDE ) THEN
IF( CDATA ) THEN
CALL SGSUM2D( ICONTXT, 'Row', '1-tree', NP, N, C, LDC,
$ MYROW, ICPOS )
ELSE
IF( MYCOL.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'V', NP, N, ONE, WORK(IPC), NP,
$ BETA, C, LDC )
CALL SGSUM2D( ICONTXT, 'Row', '1-tree', NP, N, C, LDC,
$ MYROW, ICPOS )
ELSE
CALL SGSUM2D( ICONTXT, 'Row', '1-tree', NP, N, WORK(IPC),
$ NP, MYROW, ICPOS )
END IF
END IF
*
CALL SGSUM2D( ICONTXT, 'Col', '1-tree', N, NQ, WORK(IPD), N,
$ IAROW, MYCOL )
CALL PBSTRAN( ICONTXT, 'Row', 'T', N, M, NB, WORK(IPD), N,
$ ONE, C, LDC, IAROW, IACOL, IAROW, ICPOS,
$ WORK(IPT) )
*
* C is a row block if SIDE = 'Right'
*
ELSE
IF( CDATA ) THEN
CALL SGSUM2D( ICONTXT, 'Col', '1-tree', M, NQ, C, LDC,
$ ICPOS, MYCOL )
ELSE
IF( MYROW.EQ.ICPOS ) THEN
CALL PBSMATADD( ICONTXT, 'G', M, NQ, ONE, WORK(IPC), M,
$ BETA, C, LDC )
CALL SGSUM2D( ICONTXT, 'Col', '1-tree', M, NQ, C, LDC,
$ ICPOS, MYCOL )
ELSE
CALL SGSUM2D( ICONTXT, 'Col', '1-tree', M, NQ,
$ WORK(IPC), M, ICPOS, MYCOL )
END IF
END IF
*
CALL SGSUM2D( ICONTXT, 'Row', '1-tree', NP, M, WORK(IPD), NP,
$ MYROW, IACOL )
CALL PBSTRAN( ICONTXT, 'Col', 'T', N, M, NB, WORK(IPD), NP,
$ ONE, C, LDC, IAROW, IACOL, ICPOS, IACOL,
$ WORK(IPT) )
END IF
*
* === If A is just a block ( MATBLK = 'B' ) ===
*
ELSE
ADATA = .FALSE.
ASPACE = LSAME( ABWORK, 'Y' )
COMMA = ACOMM
IF( LSAME( COMMA, ' ' ) ) COMMA = '1'
*
IF( LSIDE .AND. MYROW.EQ.IAROW ) THEN
*
* Form C := alpha*A*B + beta*C
* _____________ _ _____________ _____________
* |______C______| = a*|_|*|______B______| + b*|______C______|
* 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 = 10
ELSE IF( LDB.LT.MAX(1,M) ) THEN
INFO = 12
ELSE IF( LDC.LT.MAX(1,M) ) THEN
INFO = 15
ELSE IF( IAROW.LT.0 .OR. IAROW.GE.NPROW ) THEN
INFO = 16
ELSE IF( IACOL.LT.-1.OR. IACOL.GE.NPCOL ) THEN
INFO = 17
ELSE IF( IBPOS.LT.0 .OR. IBPOS.GE.NPCOL ) THEN
INFO = 18
ELSE IF( ICPOS.NE.IBPOS ) THEN
INFO = 19
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 STRBS2D( ICONTXT, 'Row', COMMA, UPLO, 'No', M, M,
$ A, LDA )
ELSE
CALL STRBR2D( ICONTXT, 'Row', COMMA, UPLO, 'No', M, M,
$ A, LDA, MYROW, IACOL )
END IF
ADATA = .TRUE.
ELSE
IF( MYCOL.EQ.IACOL ) THEN
CALL STRBS2D( ICONTXT, 'Row', COMMA, UPLO, 'No', M, M,
$ A, LDA )
CALL PBSMATADD( ICONTXT, UPLO, M, M, ONE, A, LDA, ZERO,
$ WORK, M )
ELSE
CALL STRBR2D( ICONTXT, 'Row', COMMA, UPLO, 'No', M, M,
$ WORK, M, MYROW, IACOL )
END IF
END IF
END IF
*
* Compute SSYMM
*
IF( ADATA ) THEN
CALL SSYMM( 'Left', UPLO, M, NQ, ALPHA, A, LDA, B, LDB,
$ BETA, C, LDC )
ELSE
CALL SSYMM( 'Left', UPLO, M, NQ, ALPHA, WORK, M, B, LDB,
$ BETA, C, LDC )
END IF
*
ELSE IF( LSAME( SIDE, 'R' ) .AND. MYCOL.EQ.IACOL ) THEN
*
* Form B := alpha*B*A + beta*C.
* _ _ _
* | | | | | |
* | | | | | |
* | | | | _ | |
* |C| = alpha * |B| * |_| + beta * |C|
* | | | | A | |
* | | | | | |
* |_| |_| |_|
*
IF( IAROW.EQ.-1 ) ADATA = .TRUE.
NP = NUMROC( M, NB, MYROW, IBPOS, NPROW )
*
IF( LDA.LT.MAX(1,N) .AND. ( ASPACE .OR.
$ IAROW.EQ.MYROW .OR. IAROW.EQ.-1 ) ) THEN
INFO = 10
ELSE IF( LDB.LT.MAX(1,NP) ) THEN
INFO = 12
ELSE IF( LDC.LT.MAX(1,NP) ) THEN
INFO = 15
ELSE IF( IAROW.LT.-1.OR. IAROW.GE.NPROW ) THEN
INFO = 16
ELSE IF( IACOL.LT.0 .OR. IACOL.GE.NPCOL ) THEN
INFO = 17
ELSE IF( IBPOS.LT.0 .OR. IBPOS.GE.NPROW ) THEN
INFO = 18
ELSE IF( ICPOS.NE.IBPOS ) THEN
INFO = 19
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 STRBS2D( ICONTXT, 'Col', COMMA, UPLO, 'No', N, N,
$ A, LDA )
ELSE
CALL STRBR2D( ICONTXT, 'Col', COMMA, UPLO, 'No', N, N,
$ A, LDA, IAROW, MYCOL )
END IF
ADATA = .TRUE.
ELSE
IF( MYROW.EQ.IAROW ) THEN
CALL STRBS2D( ICONTXT, 'Col', COMMA, UPLO, 'No', N, N,
$ A, LDA )
CALL PBSMATADD( ICONTXT, UPLO, N, N, ONE, A, LDA, ZERO,
$ WORK, N )
ELSE
CALL STRBR2D( ICONTXT, 'Col', COMMA, UPLO, 'No', N, N,
$ WORK, N, IAROW, MYCOL )
END IF
END IF
END IF
*
* Compute SSYMM
*
IF( ADATA ) THEN
CALL SSYMM( 'Right', UPLO, NP, N, ALPHA, A, LDA, B, LDB,
$ BETA, C, LDC )
ELSE
CALL SSYMM( 'Right', UPLO, NP, N, ALPHA, WORK, N, B, LDB,
$ BETA, C, LDC )
END IF
END IF
END IF
*
RETURN
*
* End of PBSSYMM
*
END
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