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|
SUBROUTINE PBCHERK( ICONTXT, MATBLK, UPLO, TRANS, N, K, NB, ALPHA,
$ A, LDA, BETA, C, LDC, IAPOS, ICROW, ICCOL,
$ ACOMM, AWORK, 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 ACOMM, AWORK, CWORK, MATBLK, TRANS, UPLO
INTEGER IAPOS, ICCOL, ICONTXT, ICROW, K, LDA, LDC,
$ MULLEN, N, NB
REAL ALPHA, BETA
* ..
* .. Array Arguments ..
COMPLEX A( LDA, * ), C( LDC, * ), WORK( * )
* ..
*
* Purpose
* =======
*
* PBCHERK is a parallel blocked version of CHERK.
* PBCHERK performs one of the Hermitian rank k operations
*
* C := alpha*A*A' + beta*C,
*
* or
*
* C := alpha*A'*A + beta*C,
*
* where alpha and beta are scalars, C is an N-by-N Hermitian matrix
* and A is an N-by-K matrix in the first case and a K-by-N matrix
* in the second case.
*
* The first elements of the matrices A, and C should be located at
* the beginnings of their first blocks. (not the middle of the blocks.)
* A can be broadcast if necessary and then transposed. The communica-
* tion 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 C is a (full) block matrix or
* a single block as follows:
*
* MATBLK = 'M', C is a (full) block matrix,
* MATBLK = 'B', C is a single block.
*
* UPLO (input) CHARACTER*1
* UPLO specifies whether the upper or lower triangular part of
* the array C is to be referenced as follows:
*
* UPLO = 'U', Only the upper triangular part of C
* is to be referenced.
* UPLO = 'L', Only the lower triangular part of C
* is to be referenced.
*
* TRANS (input) CHARACTER*1
* TRANS specifies the operation to be performed as follows:
*
* TRANS = 'N', C := alpha*A*A' + beta*C.
* TRANS = 'C', C := alpha*A'*A + beta*C.
*
* N (input) INTEGER
* N specifies the order of the matrix C. N >= 0.
*
* K (input) INTEGER
* If TRANS = 'N', K specifies the number of columns of the
* matrix A, and if TRANS = 'C', K specifies the number of rows
* of the matrix A. K >= 0.
*
* NB (input) INTEGER
* NB specifies the row and column block size of the matrix C.
* It also specifies the row block size of the matrix A if
* MATBLK = 'M' and TRANS = 'N', or MATBLK = 'B' and TRANS='C';
* and the column block size of the matrix A if MATBLK = 'M' and
* TRANS = 'C', or MATBLK = 'B' and TRANS = 'N'. NB >= 1.
*
* ALPHA (input) REAL
* ALPHA specifies the scalar alpha.
*
* A (input) COMPLEX array of local DIMENSION ( LDA, ka ),
* where ka is Kq when TRANS = 'N', or Nq otherwise.
* If TRANS = 'N', the leading Np-by-Kq part of the array A
* must contain the (local) matrix A, otherwise the leading Kp-
* by-Nq part of the array A must contain the (local) matrix A.
*
* LDA (input) INTEGER
* LDA specifies the leading dimension of (local) A as declared
* in the calling (sub) program.
* LDA >= MAX(1,Np) if MATBLK = 'M' & TRANS = 'N',
* or MATBLK = 'B' & TRANS = 'C',
* LDA >= MAX(1,Kp) if MATBLK = 'M' & TRANS = 'C',
* or MATBLK = 'B' & TRANS = 'N'.
* BETA (input) REAL
* BETA specifies the scalar beta.
*
* C (input/output) COMPLEX array of local DIMENSION ( LDC, Nq ).
* On entry with UPLO = 'U', the leading N-by-N upper triangular
* part of the (global) array C must contain the upper triangu-
* lar part of the Hermitian matrix and the strictly lower
* triangular part of C is not referenced. On exit, the upper
* triangular part of the array C is overwritten by the upper
* triangular part of the updated matrix.
* On entry with UPLO='L', the leading N-by-N lower triangular
* part of the (global) array C must contain the lower
* triangular part of the Hermitian matrix and the strictly
* upper triangular part of C is not referenced. On exit,
* the lower triangular part of the array C is overwritten by
* the lower triangular part of the updated matrix.
*
* LDC (input) INTEGER
* LDC specifies the leading dimension of (local) C as declared
* in the calling (sub) program. LDC >= MAX(1,Np).
*
* IAPOS (input) INTEGER
* If TRANS = 'N', IAPOS specifies a column of process
* template, which holds the first block of A. And if TRANS =
* 'C', IAPOS specifies a row of the template, which holds the
* first block of A. If MATBLK = 'M' and all columns or rows
* of processes have a copy of A, then set IAPOS = -1.
*
* ICROW (input) INTEGER
* It specifies a row of process template which has the
* first block of C. It also represents the first (row)
* process of the column block C if TRANS = 'N'.
* When MATBLK = 'B', and all rows of processes have their
* own copies of C, set ICROW = -1.
*
* ICCOL (input) INTEGER
* It specifies a column of process template which has the
* first block of C. It also represents the first (column)
* process of the row block C if TRANS = 'C'.
* When MATBLK = 'B', and all columns of processes have
* their own copies of C, set ICCOL = -1.
*
* ACOMM (input) CHARACTER*1
* When MATBLK = 'M', ACOMM specifies the communication scheme
* of column or row block of A if communication is necessary.
* It follows topology definition of BLACS.
* When MATBLK = 'B', the argument is ignored.
*
* AWORK (input) CHARACTER*1
* When MATBLK = 'M', AWORK determines whether A is a
* workspace or not.
*
* AWORK = '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 (local) A.
* AWORK = 'N': Data in A will be untouched (unchanged).
*
* When MATBLK = 'B', it is ignored.
*
* CWORK (input) CHARACTER*1
* When MATBLK = 'M', CWORK determines whether the other
* triangular part of C is accessed and modified or not.
*
* CWORK = 'N': if UPLO = 'U', only upper triangular portion
* portion of the matrix C is accessed and the
* lower triangular portion is untouched.
* Likewise if UPLO = 'L', only lower triangular
* portion of the matrix C is accessed and the
* upper triangular portion is untouched.
* CWORK = 'Y': if UPLO = 'U', only lower triangular portion
* of the matrix C may be accessed and modified
* for fast computation. And if UPLO = 'L', the
* upper triangular portion of the matrix C may
* be accessed and modified for fast computation.
*
* And when MATBLK = 'B', CWORK determines whether C is a
* workspace or not.
*
* CWORK = 'Y': C is workspace in other processes.
* C is sent to C position in other processes.
* It is assumed that processes have
* sufficient space to store C.
* CWORK = 'N': Data in C will be untouched (unchanged)
* in other processes.
*
* MULLEN (input) INTEGER
* When MATBLK = 'M', MULLEN specifies multiplication length of
* the optimum column number of a row block A if TRANS = 'C',
* or A' if TRANS = 'N' for multiplying A with A'. The value
* depends on machine characteristics.
* When MATBLK = 'B', it is ignored.
*
* WORK (workspace) COMPLEX array of dimension Size(WORK).
* It will store copy of A and/or A'.
*
* 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
* ==========================
*
* Npb = CEIL( N, NB*NPROW )
* Nqb = CEIL( N, NB*NPCOL )
* Np0 = NUMROC( N, NB, 0, 0, NPROW ) ~= Npb * NB
* Nq0 = NUMROC( N, NB, 0, 0, NPCOL ) ~= Nqb * NB
* LCMQ = LCM / NPCOL
* LCMP = LCM / NPROW
* ISZCMP = CEIL(MULLEN, LCMQ*NB)
* SZCMP = ISZCMP * ISZCMP * LCMQ*NB * LCMP*NB
*
* (1) MATBLK = 'M'
* (a) TRANS = 'N'
* Size(WORK) = K * Nq0
* + K * Np0 ( if IAPOS <> -1 and AWORK <> 'Y' )
* + MAX[ SZCMP ( if CWORK <> 'Y' ),
* K*CEIL(Nqb,LCMQ)*NB*MIN(LCMQ,CEIL(N,NB) ]
* (b) TRANS = 'C'
* Size(WORK) = K * Np0
* + K * Nq0 ( if IAPOS <> -1 and AWORK <> 'Y' )
* + MAX[ SZCMP ( if CWORK <> 'Y' ),
* K*CEIL(Npb,LCMP)*NB*MIN(LCMP,CEIL(N,NB) ]
*
* (2) MATBLK = 'B'
* (a) TRANS = 'N' (on a row of processes ICROW only )
* Size(WORK) = N * (N+1) / 2 ( if CWORK = 'Y')
* Size(WORK) = N * N ( if CWORK <> 'Y')
* (b) TRANS = 'C' (on a column of processes ICCOL only )
* Size(WORK) = N * (N+1) / 2 ( if CWORK = 'Y')
* Size(WORK) = N * N ( if CWORK <> 'Y')
*
* Notes
* -----
* More precise space can be computed as
*
* CEIL(Nqb,LCMQ)*NB => NUMROC( NUMROC(N,NB,0,0,NPCOL), NB, 0, 0, LCMQ )
* = NUMROC( Nq0, 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 RONE, RZERO
PARAMETER ( RONE = 1.0E+0, RZERO = 0.0E+0 )
COMPLEX ONE, ZERO
PARAMETER ( ONE = ( 1.0E+0, 0.0E+0 ),
$ ZERO = ( 0.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
CHARACTER*1 COMMA, FORM
LOGICAL ADATA, ASPACE, CMAT, CSPACE, NOTRAN, UPPER
INTEGER INFO, IPBZ, IPT, IPW, IQBZ, ISZCMP, JJ, JNPBZ,
$ JPBZ, JQBZ, KI, KIZ, KJ, KJZ, LCM, LCMP, LCMQ,
$ LKK, LMW, LNW, LPBZ, LQBZ, MRCOL, MRROW, MYCOL,
$ MYROW, MZCOL, MZROW, NP, NPCOL, NPROW, NQ
COMPLEX TALPHA, TBETA
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, ILCM, NUMROC
EXTERNAL ICEIL, ILCM, LSAME, NUMROC
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CGEBR2D, CGEBS2D, CGEMM, CHERK,
$ PBCMATADD, PBCT1CPY, PBCT2CPY, PBCT3CPY,
$ PBCTRADD, PBCTRAN, PXERBLA
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MAX, MIN
* ..
* .. Executable Statements ..
*
* Quick return if possible.
*
IF( N.EQ.0 .OR.
$ ( ( ALPHA.EQ.RZERO .OR. K.EQ.0 ) .AND. BETA.EQ.RONE ) )
$ RETURN
*
CALL BLACS_GRIDINFO( ICONTXT, NPROW, NPCOL, MYROW, MYCOL )
*
CMAT = LSAME( MATBLK, 'M' )
UPPER = LSAME( UPLO, 'U' )
NOTRAN = LSAME( TRANS, 'N' )
*
* Test the input parameters.
*
INFO = 0
IF( ( .NOT.CMAT ).AND.
$ ( .NOT.LSAME( MATBLK, 'B' ) ) ) THEN
INFO = 2
ELSE IF( ( .NOT.UPPER ).AND.
$ ( .NOT.LSAME( UPLO, 'L' ) ) ) THEN
INFO = 3
ELSE IF( ( .NOT.NOTRAN ).AND.
$ ( .NOT.LSAME( TRANS, 'C' ) ) ) THEN
INFO = 4
ELSE IF( N .LT.0 ) THEN
INFO = 5
ELSE IF( K .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, 'PBCHERK ', INFO )
RETURN
END IF
*
* Start the operations.
*
* === If C is a matrix ===
*
IF( CMAT ) THEN
NP = NUMROC( N, NB, MYROW, ICROW, NPROW )
NQ = NUMROC( N, NB, MYCOL, ICCOL, NPCOL )
*
IF( LDC.LT.MAX(1,NP) ) THEN
INFO = 13
ELSE IF( ICROW.LT.0 .OR. ICROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( ICCOL.LT.0 .OR. ICCOL.GE.NPCOL ) THEN
INFO = 16
END IF
*
ADATA = .FALSE.
IF( IAPOS.EQ.-1 ) ADATA = .TRUE.
CSPACE = LSAME( CWORK, 'Y' )
ASPACE = LSAME( AWORK, 'Y' )
COMMA = ACOMM
IF( LSAME( COMMA, ' ' ) ) COMMA = '1'
*
* LCM : the least common multiple of NPROW and NPCOL
*
LCM = ILCM( NPROW, NPCOL )
LCMP = LCM / NPROW
LCMQ = LCM / NPCOL
LPBZ = LCMP * NB
LQBZ = LCMQ * NB
*
MRROW = MOD( NPROW+MYROW-ICROW, NPROW )
MRCOL = MOD( NPCOL+MYCOL-ICCOL, NPCOL )
TALPHA = CMPLX( ALPHA )
TBETA = CMPLX( BETA )
LKK = MAX( 1, K )
*
* PART 1: Distribute a column (or row) block A and its transpose A
* ================================================================
*
IF( NOTRAN ) THEN
*
* Form C := alpha*A*A' + beta*C.
* _____________ _ _____________
* |\_ | | | |\_ |
* | \_ | | | | \_ |
* | \_ | | | _____________ | \_ |
* | C_ | = a * |A| * |_____(A')____| + b * | C_ |
* | \_ | | | | \_ |
* | \_ | | | | \_ |
* |____________\| |_| |____________\|
*
IF( LDA.LT.MAX(1,NP) .AND. ( ASPACE .OR.
$ IAPOS.EQ.MYCOL .OR. IAPOS.EQ.-1 ) ) THEN
INFO = 10
ELSE IF( IAPOS.LT.-1 .OR. IAPOS.GE.NPCOL ) THEN
INFO = 14
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast A if necessary
*
IPT = 1
IF( .NOT.ADATA ) THEN
IF( ASPACE ) THEN
IF( MYCOL.EQ.IAPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Row', COMMA, NP, K, A, LDA )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMA, NP, K, A, LDA,
$ MYROW, IAPOS )
END IF
ADATA = .TRUE.
ELSE
IF( MYCOL.EQ.IAPOS ) THEN
CALL PBCMATADD( ICONTXT, 'V', NP, K, ONE, A, LDA, ZERO,
$ WORK, NP )
CALL CGEBS2D( ICONTXT, 'Row', COMMA, NP, K, WORK, NP )
ELSE
CALL CGEBR2D( ICONTXT, 'Row', COMMA, NP, K, WORK, NP,
$ MYROW, IAPOS )
END IF
IPT = NP * K + 1
END IF
END IF
*
* Transpose col block of A to WORK(IPT), where A is distributed
*
IPW = K * NQ + IPT
IF( ADATA ) THEN
CALL PBCTRAN( ICONTXT, 'Col', 'C', N, K, NB, A, LDA, ZERO,
$ WORK(IPT), K, ICROW, -1, -1, ICCOL,
$ WORK(IPW) )
ELSE
CALL PBCTRAN( ICONTXT, 'Col', 'C', N, K, NB, WORK, NP, ZERO,
$ WORK(IPT), K, ICROW, -1, -1, ICCOL,
$ WORK(IPW) )
END IF
*
ELSE
*
* Form C := alpha*A'*A + beta*C.
* _____________ _ _____________
* |\_ | | | |\_ |
* | \_ | | | | \_ |
* | \_ | | | _____________ | \_ |
* | C_ | = a * ( A')*|______A______| + b * | C_ |
* | \_ | | | | \_ |
* | \_ | | | | \_ |
* |____________\| |_| |____________\|
*
IF( LDA.LT.MAX(1,K) .AND. ( ASPACE .OR.
$ IAPOS.EQ.MYROW .OR. IAPOS.EQ.-1 ) ) THEN
INFO = 10
ELSE IF( IAPOS.LT.-1 .OR. IAPOS.GE.NPROW ) THEN
INFO = 14
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Broadcast A if necessary
*
IPT= 1
IF( .NOT.ADATA ) THEN
IF( ASPACE ) THEN
IF( MYROW.EQ.IAPOS ) THEN
CALL CGEBS2D( ICONTXT, 'Col', COMMA, K, NQ, A, LDA )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMA, K, NQ, A, LDA,
$ IAPOS, MYCOL )
END IF
ADATA = .TRUE.
ELSE
IF( MYROW.EQ.IAPOS ) THEN
CALL PBCMATADD( ICONTXT, 'G', K, NQ, ONE, A, LDA, ZERO,
$ WORK, K )
CALL CGEBS2D( ICONTXT, 'Col', COMMA, K, NQ, WORK, K )
ELSE
CALL CGEBR2D( ICONTXT, 'Col', COMMA, K, NQ, WORK, K,
$ IAPOS, MYCOL )
END IF
IPT = K * NQ + 1
END IF
END IF
*
* Transpose row block of A to WORK(IPT), where A is distributed
*
IPW = NP * K + IPT
IF( ADATA ) THEN
CALL PBCTRAN( ICONTXT, 'Row', 'C', K, N, NB, A, LDA, ZERO,
$ WORK(IPT), NP, -1, ICCOL, ICROW, -1,
$ WORK(IPW) )
ELSE
CALL PBCTRAN( ICONTXT, 'Row', 'C', K, N, NB, WORK,K, ZERO,
$ WORK(IPT), NP, -1, ICCOL, ICROW, -1,
$ WORK(IPW) )
END IF
END IF
*
* PART 2: Update C with A and A'
* ==============================
*
IF( NP.EQ.0 .OR. NQ.EQ.0 ) RETURN
*
* If C is a Hermitian upper triangular matrix,
*
IF( UPPER ) THEN
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 40 JJ = 1, ICEIL(NQ, IQBZ)
LMW = MIN( IPBZ, NP-JPBZ )
LNW = MIN( IQBZ, NQ-JQBZ )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the lower triangular part
*
IF( CSPACE ) THEN
*
* Update C := alpha*A*A' + beta*C, if TRANS = 'N'
*
IF( NOTRAN ) THEN
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', JNPBZ, LNW, K, TALPHA,
$ A, LDA, WORK(JQBZ*K+IPT), LKK, TBETA,
$ C(1,JQBZ+1), LDC )
ELSE
CALL CGEMM( 'No', 'No', JNPBZ, LNW, K, TALPHA,
$ WORK, NP, WORK(JQBZ*K+IPT), LKK, TBETA,
$ C(1,JQBZ+1), LDC )
END IF
*
* Update C := alpha*A'*A + beta*C, if TRANS = 'C'
*
ELSE
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', JNPBZ, LNW, K, TALPHA,
$ WORK(IPT), NP, A(1,JQBZ+1), LDA, TBETA,
$ C(1,JQBZ+1), LDC )
ELSE
CALL CGEMM( 'No', 'No', JNPBZ, LNW, K, TALPHA,
$ WORK(IPT), NP, WORK(JQBZ*K+1), LKK,
$ TBETA, C(1,JQBZ+1), LDC )
END IF
END IF
*
* Update data in the upper triangular matrix
* and save data in the lower triangular matrix
*
ELSE
*
* Update C := alpha*A*A' + beta*C, if TRANS = 'N'
*
IF( NOTRAN ) THEN
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', JPBZ, LNW, K, TALPHA,
$ A, LDA, WORK(JQBZ*K+IPT), LKK, TBETA,
$ C(1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ A(JPBZ+1,1), LDA, WORK(JQBZ*K+IPT), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGEMM( 'No', 'No', JPBZ, LNW, K, TALPHA,
$ WORK, NP, WORK(JQBZ*K+IPT), LKK, TBETA,
$ C(1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+1), NP, WORK(JQBZ*K+IPT), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
END IF
*
* Update C := alpha*A'*A + beta*C, if TRANS = 'C'
*
ELSE
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', JPBZ, LNW, K, TALPHA,
$ WORK(IPT), NP, A(1,JQBZ+1), LDA,
$ TBETA, C(1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, A(1,JQBZ+1), LDA,
$ ZERO, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGEMM( 'No', 'No', JPBZ, LNW, K, TALPHA,
$ WORK(IPT), NP, WORK(JQBZ*K+1), LKK,
$ TBETA, C(1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, WORK(JQBZ*K+1), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
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 = 'H'
MZCOL = MZCOL + NPCOL
*
CALL PBCTRADD( ICONTXT, 'Upper', FORM, KIZ, NB, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, TBETA,
$ C( JPBZ+1, JQBZ+KJZ+1 ), LDC,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
30 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
40 CONTINUE
*
* If C is a Hermitian lower triangular matrix,
*
ELSE
*
ISZCMP = ICEIL( MULLEN, LQBZ )
IF( ISZCMP.LE.0 ) ISZCMP = 1
IPBZ = ISZCMP * LPBZ
IQBZ = ISZCMP * LQBZ
JPBZ = 0
JQBZ = 0
*
DO 70 JJ = 1, ICEIL(NQ, IQBZ)
LMW = MIN( IPBZ, MAX(NP-JPBZ, 0) )
LNW = MIN( IQBZ, MAX(NQ-JQBZ, 0) )
JNPBZ = JPBZ + LMW
*
* Modify (change) data in the upper triangular part
*
IF( CSPACE ) THEN
*
* Update C := alpha*A*A' + beta*C, if TRANS = 'N'
*
IF( NOTRAN ) THEN
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', NP-JPBZ, LNW, K, TALPHA,
$ A(JPBZ+1,1), LDA, WORK(JQBZ*K+IPT), LKK,
$ TBETA, C(JPBZ+1,JQBZ+1), LDC )
ELSE
CALL CGEMM( 'No', 'No', NP-JPBZ, LNW, K, TALPHA,
$ WORK(JPBZ+1), NP, WORK(JQBZ*K+IPT), LKK,
$ TBETA, C(JPBZ+1,JQBZ+1), LDC )
END IF
*
* Update C := alpha*A'*A + beta*C, if TRANS = 'C'
*
ELSE
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', NP-JPBZ, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, A(1,JQBZ+1), LDA,
$ TBETA, C(JPBZ+1,JQBZ+1), LDC )
ELSE
CALL CGEMM( 'No', 'No', NP-JPBZ, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, WORK(JQBZ*K+1), LKK,
$ TBETA, C(JPBZ+1,JQBZ+1), LDC )
END IF
END IF
*
* Update data in the lower triangular matrix
* and save data in the upper triangular matrix
*
ELSE
*
* Update C := alpha*A*A' + beta*C, if TRANS = 'N'
*
IF( NOTRAN ) THEN
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', NP-JNPBZ, LNW, K, TALPHA,
$ A(JNPBZ+1,1), LDA, WORK(JQBZ*K+IPT), LKK,
$ TBETA, C(JNPBZ+1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ A(JPBZ+1,1), LDA, WORK(JQBZ*K+IPT), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGEMM( 'No', 'No', NP-JNPBZ, LNW, K, TALPHA,
$ WORK(JNPBZ+1), NP, WORK(JQBZ*K+IPT), LKK,
$ TBETA, C(JNPBZ+1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+1), NP, WORK(JQBZ*K+IPT), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
END IF
*
* Update C := alpha*A'*A + beta*C, if TRANS = 'C'
*
ELSE
IF( ADATA ) THEN
CALL CGEMM( 'No', 'No', NP-JNPBZ, LNW, K, TALPHA,
$ WORK(JNPBZ+IPT), NP, A(1,JQBZ+1), LDA,
$ TBETA, C(JNPBZ+1,JQBZ+1), LDC )
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, A(1,JQBZ+1), LDA,
$ ZERO, WORK(IPW), MAX(1,LMW) )
ELSE
CALL CGEMM( 'No', 'No', NP-JNPBZ, LNW, K, TALPHA,
$ WORK(JNPBZ+IPT), NP, WORK(JQBZ*K+1), LKK,
$ TBETA, C(JNPBZ+1,JQBZ+1), LDC)
CALL CGEMM( 'No', 'No', LMW, LNW, K, TALPHA,
$ WORK(JPBZ+IPT), NP, WORK(JQBZ*K+1), LKK,
$ ZERO, WORK(IPW), MAX(1,LMW) )
END IF
END IF
*
* Compute diagonal blocks.
*
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
FORM = 'G'
IF( MZROW.EQ.MZCOL )
$ FORM = 'H'
MZCOL = MZCOL + NPCOL
*
CALL PBCTRADD( ICONTXT, 'Lower', FORM, KIZ, NB, ONE,
$ WORK( KJZ*LMW+IPW ), LMW, TBETA,
$ C( JPBZ+1, JQBZ+KJZ+1 ), LDC,
$ LPBZ, LQBZ, LMW, LNW-KJZ )
60 CONTINUE
END IF
*
JPBZ = JNPBZ
JQBZ = JQBZ + LNW
70 CONTINUE
END IF
*
* === If C is just a block ===
*
ELSE
IF( NOTRAN .AND. MYROW.EQ.ICROW ) THEN
*
* Form C := alpha * A * (A') + beta * C.
* _
* | |
* | |
* _ _____________ | | _
* |_| = alpha * |______A______| * (A') + beta * |_|
* C | | C
* | |
* |_|
*
NQ = NUMROC( K, NB, MYCOL, IAPOS, NPCOL )
CSPACE = LSAME( CWORK, 'Y' )
*
IF( LDA.LT.MAX(1,N) ) THEN
INFO = 10
ELSE IF( LDC.LT.MAX(1,N) .AND. ( CSPACE .OR.
$ ICCOL.EQ.MYCOL .OR. ICCOL.EQ.-1 ) ) THEN
INFO = 13
ELSE IF( IAPOS.LT.0 .OR. IAPOS.GE.NPCOL ) THEN
INFO = 14
ELSE IF( ICROW.LT.0 .OR. ICROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( ICCOL.LT.-1 .OR. ICCOL.GE.NPCOL ) THEN
INFO = 16
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Compute C
*
IF( MYCOL.EQ.ICCOL ) THEN
CALL CHERK( UPLO, TRANS, N, NQ, ALPHA, A,LDA, BETA, C,LDC )
CALL PBCT1CPY( UPLO, JJ, N, C, LDC, WORK )
CALL CGSUM2D( ICONTXT, 'Row', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
CALL PBCT2CPY( UPLO, JJ, N, C, LDC, WORK )
*
ELSE
IF( LSAME( CWORK, 'Y' ) ) THEN
CALL CHERK( UPLO, TRANS, N, NQ, ALPHA, A, LDA, RZERO,
$ C, LDC )
CALL PBCT1CPY( UPLO, JJ, N, C, LDC, WORK )
CALL CGSUM2D( ICONTXT, 'Row', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
ELSE
CALL CHERK( UPLO, TRANS, N, NQ, ALPHA, A, LDA, RZERO,
$ WORK, N )
CALL PBCT3CPY( UPLO, JJ, N, WORK )
CALL CGSUM2D( ICONTXT, 'Row', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
END IF
END IF
*
ELSE IF( LSAME( TRANS, 'C' ) .AND. MYCOL.EQ.ICCOL ) THEN
*
* Form B := alpha*B / op( A ).
* _
* | |
* | |
* _ _____________ | | _
* |_| = alpha * |_____(A')____| * |A| + beta * |_|
* C | | C
* | |
* |_|
*
NP = NUMROC( K, NB, MYROW, IAPOS, NPROW )
CSPACE = LSAME( CWORK, 'Y' )
*
IF( LDA.LT.MAX(1,NP) ) THEN
INFO = 10
ELSE IF( LDC.LT.MAX(1,N) .AND. ( CSPACE .OR.
$ ICROW.EQ.MYROW .OR. ICROW.EQ.-1 ) ) THEN
INFO = 13
ELSE IF( IAPOS.LT.0 .OR. IAPOS.GE.NPROW ) THEN
INFO = 14
ELSE IF( ICROW.LT.-1 .OR. ICROW.GE.NPROW ) THEN
INFO = 15
ELSE IF( ICCOL.LT.0 .OR. ICCOL.GE.NPCOL ) THEN
INFO = 16
END IF
IF( INFO.NE.0 ) GO TO 10
*
* Compute C
*
IF( MYROW.EQ.ICROW ) THEN
CALL CHERK( UPLO, TRANS, N, NP, ALPHA, A,LDA, BETA, C,LDC )
CALL PBCT1CPY( UPLO, JJ, N, C, LDC, WORK )
CALL CGSUM2D( ICONTXT, 'Col', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
CALL PBCT2CPY( UPLO, JJ, N, C, LDC, WORK )
*
ELSE
IF( LSAME( CWORK, 'Y' ) ) THEN
CALL CHERK( UPLO, TRANS, N, NP, ALPHA, A, LDA, RZERO,
$ C, LDC )
CALL PBCT1CPY( UPLO, JJ, N, C, LDC, WORK )
CALL CGSUM2D( ICONTXT, 'Col', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
ELSE
CALL CHERK( UPLO, TRANS, N, NP, ALPHA, A, LDA, RZERO,
$ WORK, N )
CALL PBCT3CPY( UPLO, JJ, N, WORK )
CALL CGSUM2D( ICONTXT, 'Col', '1-tree', 1, JJ, WORK, 1,
$ ICROW, ICCOL )
END IF
END IF
END IF
END IF
*
RETURN
*
* End of PBCHERK
*
END
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