SUBROUTINE PCLASCL( TYPE, CFROM, CTO, M, N, A, IA, JA, DESCA,
$ INFO )
*
* -- 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 TYPE
INTEGER IA, INFO, JA, M, N
REAL CFROM, CTO
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
COMPLEX A( * )
* ..
*
* Purpose
* =======
*
* PCLASCL multiplies the M-by-N complex distributed matrix sub( A )
* denoting A(IA:IA+M-1,JA:JA+N-1) by the real scalar CTO/CFROM. This
* is done without over/underflow as long as the final result
* CTO * A(I,J) / CFROM does not over/underflow. TYPE specifies that
* sub( A ) may be full, upper triangular, lower triangular or upper
* Hessenberg.
*
* 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
* =========
*
* TYPE (global input) CHARACTER
* TYPE indices the storage type of the input distributed
* matrix.
* = 'G': sub( A ) is a full matrix,
* = 'L': sub( A ) is a lower triangular matrix,
* = 'U': sub( A ) is an upper triangular matrix,
* = 'H': sub( A ) is an upper Hessenberg matrix.
*
* CFROM (global input) REAL
* CTO (global input) REAL
* The distributed matrix sub( A ) is multiplied by CTO/CFROM.
* A(I,J) is computed without over/underflow if the final
* result CTO * A(I,J) / CFROM can be represented without
* over/underflow. CFROM must be nonzero.
*
* 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.
*
* A (local input/local output) COMPLEX 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 ). On exit, this array contains the local
* pieces of the distributed matrix multiplied by CTO/CFROM.
*
* 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.
*
* INFO (local output) INTEGER
* = 0: successful exit
* < 0: If the i-th argument is an array and the j-entry had
* an illegal value, then INFO = -(i*100+j), if the i-th
* argument is a scalar and had an illegal value, then
* INFO = -i.
*
* =====================================================================
*
* .. 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 )
REAL ONE, ZERO
PARAMETER ( ZERO = 0.0E0, ONE = 1.0E0 )
* ..
* .. Local Scalars ..
LOGICAL DONE
INTEGER IACOL, IAROW, ICOFFA, ICTXT, ICURCOL, ICURROW,
$ IIA, II, INXTROW, IOFFA, IROFFA, ITYPE, J, JB,
$ JJA, JJ, JN, KK, LDA, LL, MYCOL, MYROW, MP,
$ NPCOL, NPROW, NQ
REAL BIGNUM, CFROM1, CFROMC, CTO1, CTOC, MUL, SMLNUM
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, CHK1MAT, INFOG2L, PXERBLA
* ..
* .. External Functions ..
LOGICAL LSAME, SISNAN
INTEGER ICEIL, NUMROC
REAL PSLAMCH
EXTERNAL SISNAN, ICEIL, LSAME, NUMROC, PSLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Test the input parameters
*
IF( NPROW.EQ.-1 ) THEN
INFO = -907
ELSE
INFO = 0
CALL CHK1MAT( M, 4, N, 6, IA, JA, DESCA, 9, INFO )
IF( INFO.EQ.0 ) THEN
IF( LSAME( TYPE, 'G' ) ) THEN
ITYPE = 0
ELSE IF( LSAME( TYPE, 'L' ) ) THEN
ITYPE = 1
ELSE IF( LSAME( TYPE, 'U' ) ) THEN
ITYPE = 2
ELSE IF( LSAME( TYPE, 'H' ) ) THEN
ITYPE = 3
ELSE
ITYPE = -1
END IF
IF( ITYPE.EQ.-1 ) THEN
INFO = -1
ELSE IF( CFROM.EQ.ZERO .OR. SISNAN(CFROM) ) THEN
INFO = -4
ELSE IF( SISNAN(CTO) ) THEN
INFO = -5
END IF
END IF
END IF
*
IF( INFO.NE.0 ) THEN
CALL PXERBLA( ICTXT, 'PCLASCL', -INFO )
RETURN
END IF
*
* Quick return if possible
*
IF( N.EQ.0 .OR. M.EQ.0 )
$ RETURN
*
* Get machine parameters
*
SMLNUM = PSLAMCH( ICTXT, 'S' )
BIGNUM = ONE / SMLNUM
*
CFROMC = CFROM
CTOC = CTO
*
* Compute local indexes
*
LDA = DESCA( LLD_ )
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
MP = NUMROC( M+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
IF( MYROW.EQ.IAROW )
$ MP = MP - IROFFA
NQ = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFFA
*
10 CONTINUE
CFROM1 = CFROMC*SMLNUM
IF( CFROM1.EQ.CFROMC ) THEN
! CFROMC is an inf. Multiply by a correctly signed zero for
! finite CTOC, or a NaN if CTOC is infinite.
MUL = CTOC / CFROMC
DONE = .TRUE.
CTO1 = CTOC
ELSE
CTO1 = CTOC / BIGNUM
IF( CTO1.EQ.CTOC ) THEN
! CTOC is either 0 or an inf. In both cases, CTOC itself
! serves as the correct multiplication factor.
MUL = CTOC
DONE = .TRUE.
CFROMC = ONE
ELSE IF( ABS( CFROM1 ).GT.ABS( CTOC ) .AND. CTOC.NE.ZERO ) THEN
MUL = SMLNUM
DONE = .FALSE.
CFROMC = CFROM1
ELSE IF( ABS( CTO1 ).GT.ABS( CFROMC ) ) THEN
MUL = BIGNUM
DONE = .FALSE.
CTOC = CTO1
ELSE
MUL = CTOC / CFROMC
DONE = .TRUE.
END IF
END IF
*
IOFFA = ( JJA - 1 ) * LDA
ICURROW = IAROW
ICURCOL = IACOL
*
IF( ITYPE.EQ.0 ) THEN
*
* Full matrix
*
DO 30 JJ = JJA, JJA+NQ-1
DO 20 II = IIA, IIA+MP-1
A( IOFFA+II ) = A( IOFFA+II ) * MUL
20 CONTINUE
IOFFA = IOFFA + LDA
30 CONTINUE
*
ELSE IF( ITYPE.EQ.1 ) THEN
*
* Lower triangular matrix
*
II = IIA
JJ = JJA
JB = JN-JA+1
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 50 LL = JJ, JJ + JB -1
DO 40 KK = II+LL-JJ, IIA+MP-1
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
40 CONTINUE
IOFFA = IOFFA + LDA
50 CONTINUE
ELSE
DO 70 LL = JJ, JJ + JB -1
DO 60 KK = II, IIA+MP-1
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
60 CONTINUE
IOFFA = IOFFA + LDA
70 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 120 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 90 LL = JJ, JJ + JB -1
DO 80 KK = II+LL-JJ, IIA+MP-1
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
80 CONTINUE
IOFFA = IOFFA + LDA
90 CONTINUE
ELSE
DO 110 LL = JJ, JJ + JB -1
DO 100 KK = II, IIA+MP-1
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
100 CONTINUE
IOFFA = IOFFA + LDA
110 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
120 CONTINUE
*
ELSE IF( ITYPE.EQ.2 ) THEN
*
* Upper triangular matrix
*
II = IIA
JJ = JJA
JB = JN-JA+1
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 140 LL = JJ, JJ + JB -1
DO 130 KK = IIA, MIN(II+LL-JJ,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
130 CONTINUE
IOFFA = IOFFA + LDA
140 CONTINUE
ELSE
DO 160 LL = JJ, JJ + JB -1
DO 150 KK = IIA, MIN(II-1,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
150 CONTINUE
IOFFA = IOFFA + LDA
160 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 210 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 180 LL = JJ, JJ + JB -1
DO 170 KK = IIA, MIN(II+LL-JJ,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK )*MUL
170 CONTINUE
IOFFA = IOFFA + LDA
180 CONTINUE
ELSE
DO 200 LL = JJ, JJ + JB -1
DO 190 KK = IIA, MIN(II-1,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
190 CONTINUE
IOFFA = IOFFA + LDA
200 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
210 CONTINUE
*
ELSE IF( ITYPE.EQ.3 ) THEN
*
* Upper Hessenberg matrix
*
II = IIA
JJ = JJA
JB = JN-JA+1
*
* Only one process row
*
IF( NPROW.EQ.1 ) THEN
*
* Handle first block of columns separately
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 230 LL = JJ, JJ+JB-1
DO 220 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
A( IOFFA+KK ) = A( IOFFA+KK )*MUL
220 CONTINUE
IOFFA = IOFFA + LDA
230 CONTINUE
JJ = JJ + JB
END IF
*
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 260 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.ICURCOL ) THEN
DO 250 LL = JJ, JJ+JB-1
DO 240 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
A( IOFFA+KK ) = A( IOFFA+KK )*MUL
240 CONTINUE
IOFFA = IOFFA + LDA
250 CONTINUE
JJ = JJ + JB
END IF
*
II = II + JB
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
260 CONTINUE
*
ELSE
*
* Handle first block of columns separately
*
INXTROW = MOD( ICURROW+1, NPROW )
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 280 LL = JJ, JJ + JB -1
DO 270 KK = IIA, MIN(II+LL-JJ+1,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
270 CONTINUE
IOFFA = IOFFA + LDA
280 CONTINUE
ELSE
DO 300 LL = JJ, JJ + JB -1
DO 290 KK = IIA, MIN(II-1,IIA+MP-1)
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
290 CONTINUE
IOFFA = IOFFA + LDA
300 CONTINUE
IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+MP-1 )
$ A( II+(JJ+JB-2)*LDA ) = A( II+(JJ+JB-2)*LDA ) * MUL
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = INXTROW
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 350 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.ICURCOL ) THEN
IF( MYROW.EQ.ICURROW ) THEN
DO 320 LL = JJ, JJ + JB -1
DO 310 KK = IIA, MIN( II+LL-JJ+1, IIA+MP-1 )
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
310 CONTINUE
IOFFA = IOFFA + LDA
320 CONTINUE
ELSE
DO 340 LL = JJ, JJ + JB -1
DO 330 KK = IIA, MIN( II-1, IIA+MP-1 )
A( IOFFA+KK ) = A( IOFFA+KK ) * MUL
330 CONTINUE
IOFFA = IOFFA + LDA
340 CONTINUE
IF( MYROW.EQ.INXTROW .AND. II.LE.IIA+MP-1 )
$ A( II+(JJ+JB-2)*LDA ) = A( II+(JJ+JB-2)*LDA ) *
$ MUL
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.ICURROW )
$ II = II + JB
ICURROW = INXTROW
ICURROW = MOD( ICURROW+1, NPROW )
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
350 CONTINUE
*
END IF
*
END IF
*
IF( .NOT.DONE )
$ GO TO 10
*
RETURN
*
* End of PCLASCL
*
END