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SUBROUTINE PSLASE2( UPLO, M, N, ALPHA, BETA, A, IA, JA, DESCA )
*
* -- ScaLAPACK auxiliary routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER UPLO
INTEGER IA, JA, M, N
REAL ALPHA, BETA
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL A( * )
* ..
*
* Purpose
* =======
*
* PSLASE2 initializes an M-by-N distributed matrix sub( A ) denoting
* A(IA:IA+M-1,JA:JA+N-1) to BETA on the diagonal and ALPHA on the
* offdiagonals. PSLASE2 requires that only dimension of the matrix
* operand is distributed.
*
* Notes
* =====
*
* Each global data object is described by an associated description
* vector. This vector stores the information required to establish
* the mapping between an object element and its corresponding process
* and memory location.
*
* Let A be a generic term for any 2D block cyclicly distributed array.
* Such a global array has an associated description vector DESCA.
* In the following comments, the character _ should be read as
* "of the global array".
*
* NOTATION STORED IN EXPLANATION
* --------------- -------------- --------------------------------------
* DTYPE_A(global) DESCA( DTYPE_ )The descriptor type. In this case,
* DTYPE_A = 1.
* CTXT_A (global) DESCA( CTXT_ ) The BLACS context handle, indicating
* the BLACS process grid A is distribu-
* ted over. The context itself is glo-
* bal, but the handle (the integer
* value) may vary.
* M_A (global) DESCA( M_ ) The number of rows in the global
* array A.
* N_A (global) DESCA( N_ ) The number of columns in the global
* array A.
* MB_A (global) DESCA( MB_ ) The blocking factor used to distribute
* the rows of the array.
* NB_A (global) DESCA( NB_ ) The blocking factor used to distribute
* the columns of the array.
* RSRC_A (global) DESCA( RSRC_ ) The process row over which the first
* row of the array A is distributed.
* CSRC_A (global) DESCA( CSRC_ ) The process column over which the
* first column of the array A is
* distributed.
* LLD_A (local) DESCA( LLD_ ) The leading dimension of the local
* array. LLD_A >= MAX(1,LOCr(M_A)).
*
* Let K be the number of rows or columns of a distributed matrix,
* and assume that its process grid has dimension p x q.
* LOCr( K ) denotes the number of elements of K that a process
* would receive if K were distributed over the p processes of its
* process column.
* Similarly, LOCc( K ) denotes the number of elements of K that a
* process would receive if K were distributed over the q processes of
* its process row.
* The values of LOCr() and LOCc() may be determined via a call to the
* ScaLAPACK tool function, NUMROC:
* LOCr( M ) = NUMROC( M, MB_A, MYROW, RSRC_A, NPROW ),
* LOCc( N ) = NUMROC( N, NB_A, MYCOL, CSRC_A, NPCOL ).
* An upper bound for these quantities may be computed by:
* LOCr( M ) <= ceil( ceil(M/MB_A)/NPROW )*MB_A
* LOCc( N ) <= ceil( ceil(N/NB_A)/NPCOL )*NB_A
*
* Arguments
* =========
*
* UPLO (global input) CHARACTER
* Specifies the part of the distributed matrix sub( A ) to be
* set:
* = 'U': Upper triangular part is set; the strictly lower
* triangular part of sub( A ) is not changed;
* = 'L': Lower triangular part is set; the strictly upper
* triangular part of sub( A ) is not changed;
* Otherwise: All of the matrix sub( A ) is set.
*
* M (global input) INTEGER
* The number of rows to be operated on i.e the number of rows
* of the distributed submatrix sub( A ). M >= 0.
*
* N (global input) INTEGER
* The number of columns to be operated on i.e the number of
* columns of the distributed submatrix sub( A ). N >= 0.
*
* ALPHA (global input) REAL
* The constant to which the offdiagonal elements are to be
* set.
*
* BETA (global input) REAL
* The constant to which the diagonal elements are to be set.
*
* A (local output) REAL pointer into the local memory
* to an array of dimension (LLD_A,LOCc(JA+N-1)). This array
* contains the local pieces of the distributed matrix sub( A )
* to be set. On exit, the leading M-by-N submatrix sub( A )
* is set as follows:
*
* if UPLO = 'U', A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=j-1, 1<=j<=N,
* if UPLO = 'L', A(IA+i-1,JA+j-1) = ALPHA, j+1<=i<=M, 1<=j<=N,
* otherwise, A(IA+i-1,JA+j-1) = ALPHA, 1<=i<=M, 1<=j<=N,
* IA+i.NE.JA+j,
* and, for all UPLO, A(IA+i-1,JA+i-1) = BETA, 1<=i<=min(M,N).
*
* IA (global input) INTEGER
* The row index in the global array A indicating the first
* row of sub( A ).
*
* JA (global input) INTEGER
* The column index in the global array A indicating the
* first column of sub( A ).
*
* DESCA (global and local input) INTEGER array of dimension DLEN_.
* The array descriptor for the distributed matrix A.
*
* =====================================================================
*
* .. Parameters ..
INTEGER BLOCK_CYCLIC_2D, CSRC_, CTXT_, DLEN_, DTYPE_,
$ LLD_, MB_, M_, NB_, N_, RSRC_
PARAMETER ( BLOCK_CYCLIC_2D = 1, DLEN_ = 9, DTYPE_ = 1,
$ CTXT_ = 2, M_ = 3, N_ = 4, MB_ = 5, NB_ = 6,
$ RSRC_ = 7, CSRC_ = 8, LLD_ = 9 )
* ..
* .. Local Scalars ..
INTEGER HEIGHT, IACOL, IAROW, IBASE, ICOFFA, II, IIA,
$ IIBEG, IIEND, IINXT, ILEFT, IRIGHT, IROFFA,
$ ITOP, JJ, JJA, JJBEG, JJEND, JJNXT, LDA, MBA,
$ MP, MPA, MYCOL, MYDIST, MYROW, NBA, NPCOL,
$ NPROW, NQ, NQA, WIDE
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, SLASET
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, NUMROC
EXTERNAL ICEIL, LSAME, NUMROC
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
IF( M.EQ.0 .OR. N.EQ.0 )
$ RETURN
*
* Get grid parameters
*
CALL BLACS_GRIDINFO( DESCA( CTXT_ ), NPROW, NPCOL, MYROW, MYCOL )
*
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
MBA = DESCA( MB_ )
NBA = DESCA( NB_ )
LDA = DESCA( LLD_ )
IROFFA = MOD( IA-1, MBA )
ICOFFA = MOD( JA-1, NBA )
*
IF( N.LE.( NBA-ICOFFA ) ) THEN
*
* It is assumed that the local columns JJA:JJA+N-1 of the matrix
* A are in the same process column (IACOL).
*
* N
* JJA JJA+N-1
* / --------------------- \
* IROFFA| | | |
* \ |...................| | ( IAROW )
* IIA |x | | MB_A
* | x | |
* |--x----------------| /
* | x |
* | x | ITOP
* | x | |
* | x | /-------\
* |-------x-----------| |-------x-----------|
* | x | | x |
* | x | | x |
* | x | | x |
* | x | | x |
* |------------x------| |------------x------|
* | x | \____________/
* | x | |
* | x | IBASE
* | x |
* |-----------------x-| Local picture
* | x|
* | |
* | |
* | |
* |-------------------|
* | |
* . .
* . .
* . (IACOL) .
*
IF( MYCOL.EQ.IACOL ) THEN
*
MPA = NUMROC( M+IROFFA, MBA, MYROW, IAROW, NPROW )
IF( MPA.LE.0 )
$ RETURN
IF( MYROW.EQ.IAROW )
$ MPA = MPA - IROFFA
MYDIST = MOD( MYROW-IAROW+NPROW, NPROW )
ITOP = MYDIST * MBA - IROFFA
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
ITOP = MAX( 0, ITOP )
IIBEG = IIA
IIEND = IIA + MPA - 1
IINXT = MIN( ICEIL( IIBEG, MBA ) * MBA, IIEND )
*
10 CONTINUE
IF( ( N-ITOP ).GT.0 ) THEN
CALL SLASET( UPLO, IINXT-IIBEG+1, N-ITOP, ALPHA, BETA,
$ A( IIBEG+(JJA+ITOP-1)*LDA ), LDA )
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBA - IROFFA
IIBEG = IINXT +1
IINXT = MIN( IINXT+MBA, IIEND )
GO TO 10
END IF
*
ELSE IF( LSAME( UPLO, 'L' ) ) THEN
*
II = IIA
JJ = JJA
MP = MPA
IBASE = MIN( ITOP+MBA, N )
ITOP = MIN( MAX( 0, ITOP ), N )
*
20 CONTINUE
IF( JJ.LE.( JJA+N-1 ) ) THEN
HEIGHT = IBASE - ITOP
CALL SLASET( 'All', MP, ITOP-JJ+JJA, ALPHA, ALPHA,
$ A( II+(JJ-1)*LDA ), LDA )
CALL SLASET( UPLO, MP, HEIGHT, ALPHA, BETA,
$ A( II+(JJA+ITOP-1)*LDA ), LDA )
MP = MAX( 0, MP - HEIGHT )
II = II + HEIGHT
JJ = JJA + IBASE
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBA - IROFFA
IBASE = MIN( ITOP + MBA, N )
ITOP = MIN( ITOP, N )
GO TO 20
END IF
*
ELSE
*
II = IIA
JJ = JJA
MP = MPA
IBASE = MIN( ITOP+MBA, N )
ITOP = MIN( MAX( 0, ITOP ), N )
*
30 CONTINUE
IF( JJ.LE.( JJA+N-1 ) ) THEN
HEIGHT = IBASE - ITOP
CALL SLASET( 'All', MPA, ITOP-JJ+JJA, ALPHA, ALPHA,
$ A( IIA+(JJ-1)*LDA ), LDA )
CALL SLASET( 'All', MPA-MP, HEIGHT, ALPHA, ALPHA,
$ A( IIA+(JJA+ITOP-1)*LDA ), LDA )
CALL SLASET( 'All', MP, HEIGHT, ALPHA, BETA,
$ A( II+(JJA+ITOP-1)*LDA ), LDA )
MP = MAX( 0, MP - HEIGHT )
II = II + HEIGHT
JJ = JJA + IBASE
MYDIST = MYDIST + NPROW
ITOP = MYDIST * MBA - IROFFA
IBASE = MIN( ITOP + MBA, N )
ITOP = MIN( ITOP, N )
GO TO 30
END IF
*
END IF
*
END IF
*
ELSE IF( M.LE.( MBA-IROFFA ) ) THEN
*
* It is assumed that the local rows IIA:IIA+M-1 of the matrix A
* are in the same process row (IAROW).
*
* ICOFFA
* / \JJA
* IIA ------------------ .... --------
* | .x | | | / | | \
* | . x | | | ILEFT| | | |
* | . x | | | | | |
* | . x | | \ x | |
* | . |x | | |x | | IRIGHT
* | . | x | | | x | |
* (IAROW) | . | x | | | x | |
* | . | x| | | x| |
* | . | x | | x /
* | . | |x | | |
* | . | | x | | |
* | . | | x | | |
* | . | | x| | |
* IIA+M-1 ------------------ .... -------
* NB_A
* (IACOL) Local picture
*
IF( MYROW.EQ.IAROW ) THEN
*
NQA = NUMROC( N+ICOFFA, NBA, MYCOL, IACOL, NPCOL )
IF( NQA.LE.0 )
$ RETURN
IF( MYCOL.EQ.IACOL )
$ NQA = NQA - ICOFFA
MYDIST = MOD( MYCOL-IACOL+NPCOL, NPCOL )
ILEFT = MYDIST * NBA - ICOFFA
*
IF( LSAME( UPLO, 'L' ) ) THEN
*
ILEFT = MAX( 0, ILEFT )
JJBEG = JJA
JJEND = JJA + NQA - 1
JJNXT = MIN( ICEIL( JJBEG, NBA ) * NBA, JJEND )
*
40 CONTINUE
IF( ( M-ILEFT ).GT.0 ) THEN
CALL SLASET( UPLO, M-ILEFT, JJNXT-JJBEG+1, ALPHA,
$ BETA, A( IIA+ILEFT+(JJBEG-1)*LDA ), LDA )
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBA - ICOFFA
JJBEG = JJNXT +1
JJNXT = MIN( JJNXT+NBA, JJEND )
GO TO 40
END IF
*
ELSE IF( LSAME( UPLO, 'U' ) ) THEN
*
II = IIA
JJ = JJA
NQ = NQA
IRIGHT = MIN( ILEFT+NBA, M )
ILEFT = MIN( MAX( 0, ILEFT ), M )
*
50 CONTINUE
IF( II.LE.( IIA+M-1 ) ) THEN
WIDE = IRIGHT - ILEFT
CALL SLASET( 'All', ILEFT-II+IIA, NQ, ALPHA, ALPHA,
$ A( II+(JJ-1)*LDA ), LDA )
CALL SLASET( UPLO, WIDE, NQ, ALPHA, BETA,
$ A( IIA+ILEFT+(JJ-1)*LDA ), LDA )
NQ = MAX( 0, NQ - WIDE )
II = IIA + IRIGHT
JJ = JJ + WIDE
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBA - ICOFFA
IRIGHT = MIN( ILEFT + NBA, M )
ILEFT = MIN( ILEFT, M )
GO TO 50
END IF
*
ELSE
*
II = IIA
JJ = JJA
NQ = NQA
IRIGHT = MIN( ILEFT+NBA, M )
ILEFT = MIN( MAX( 0, ILEFT ), M )
*
60 CONTINUE
IF( II.LE.( IIA+M-1 ) ) THEN
WIDE = IRIGHT - ILEFT
CALL SLASET( 'All', ILEFT-II+IIA, NQA, ALPHA, ALPHA,
$ A( II+(JJA-1)*LDA ), LDA )
CALL SLASET( 'All', WIDE, NQA-NQ, ALPHA, ALPHA,
$ A( IIA+ILEFT+(JJA-1)*LDA ), LDA )
CALL SLASET( 'All', WIDE, NQ, ALPHA, BETA,
$ A( IIA+ILEFT+(JJ-1)*LDA ), LDA )
NQ = MAX( 0, NQ - WIDE )
II = IIA + IRIGHT
JJ = JJ + WIDE
MYDIST = MYDIST + NPCOL
ILEFT = MYDIST * NBA - ICOFFA
IRIGHT = MIN( ILEFT + NBA, M )
ILEFT = MIN( ILEFT, M )
GO TO 60
END IF
*
END IF
*
END IF
*
END IF
*
RETURN
*
* End of PSLASE2
*
END
|
