SUBROUTINE PDLAQSY( UPLO, N, A, IA, JA, DESCA, SR, SC, SCOND,
$ AMAX, EQUED )
*
* -- 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 EQUED, UPLO
INTEGER IA, JA, N
DOUBLE PRECISION AMAX, SCOND
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION A( * ), SC( * ), SR( * )
* ..
*
* Purpose
* =======
*
* PDLAQSY equilibrates a symmetric distributed matrix
* sub( A ) = A(IA:IA+N-1,JA:JA+N-1) using the scaling factors in the
* vectors SR and SC.
*
* 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 whether the upper or lower triangular part of the
* symmetric distributed matrix sub( A ) is to be referenced:
* = 'U': Upper triangular
* = 'L': Lower triangular
*
* N (global input) INTEGER
* The number of rows and columns to be operated on, i.e. the
* order of the distributed submatrix sub( A ). N >= 0.
*
* A (input/output) DOUBLE PRECISION pointer into the local
* memory to an array of local dimension (LLD_A,LOCc(JA+N-1)).
* On entry, the local pieces of the distributed symmetric
* matrix sub( A ). If UPLO = 'U', the leading N-by-N upper
* triangular part of sub( A ) contains the upper triangular
* part of the matrix, and the strictly lower triangular part
* of sub( A ) is not referenced. If UPLO = 'L', the leading
* N-by-N lower triangular part of sub( A ) contains the lower
* triangular part of the matrix, and the strictly upper trian-
* gular part of sub( A ) is not referenced.
* On exit, if EQUED = 'Y', the equilibrated matrix:
* diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).
*
* 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.
*
* SR (local input) DOUBLE PRECISION array, dimension LOCr(M_A)
* The scale factors for A(IA:IA+M-1,JA:JA+N-1). SR is aligned
* with the distributed matrix A, and replicated across every
* process column. SR is tied to the distributed matrix A.
*
* SC (local input) DOUBLE PRECISION array, dimension LOCc(N_A)
* The scale factors for sub( A ). SC is aligned with the dis-
* tributed matrix A, and replicated down every process row.
* SC is tied to the distributed matrix A.
*
* SCOND (global input) DOUBLE PRECISION
* Ratio of the smallest SR(i) (respectively SC(j)) to the
* largest SR(i) (respectively SC(j)), with IA <= i <= IA+N-1
* and JA <= j <= JA+N-1.
*
* AMAX (global input) DOUBLE PRECISION
* Absolute value of the largest distributed submatrix entry.
*
* EQUED (output) CHARACTER*1
* Specifies whether or not equilibration was done.
* = 'N': No equilibration.
* = 'Y': Equilibration was done, i.e., sub( A ) has been re-
* placed by:
* diag(SR(IA:IA+N-1)) * sub( A ) * diag(SC(JA:JA+N-1)).
*
* Internal Parameters
* ===================
*
* THRESH is a threshold value used to decide if scaling should be done
* based on the ratio of the scaling factors. If SCOND < THRESH,
* scaling is done.
*
* LARGE and SMALL are threshold values used to decide if scaling should
* be done based on the absolute size of the largest matrix element.
* If AMAX > LARGE or AMAX < SMALL, scaling is done.
*
* =====================================================================
*
* .. 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 )
DOUBLE PRECISION ONE, THRESH
PARAMETER ( ONE = 1.0D+0, THRESH = 0.1D+0 )
* ..
* .. Local Scalars ..
INTEGER IACOL, IAROW, ICTXT, II, IIA, IOFFA, IROFF, J,
$ JB, JJ, JJA, JN, KK, LDA, LL, MYCOL, MYROW, NP,
$ NPCOL, NPROW
DOUBLE PRECISION CJ, LARGE, SMALL
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L
* ..
* .. External Functions ..
LOGICAL LSAME
INTEGER ICEIL, NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL ICEIL, LSAME, NUMROC, PDLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MIN, MOD
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( N.LE.0 ) THEN
EQUED = 'N'
RETURN
END IF
*
* Get grid parameters and compute local indexes
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA,
$ IAROW, IACOL )
LDA = DESCA( LLD_ )
*
* Initialize LARGE and SMALL.
*
SMALL = PDLAMCH( ICTXT, 'Safe minimum' ) /
$ PDLAMCH( ICTXT, 'Precision' )
LARGE = ONE / SMALL
*
IF( SCOND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE ) THEN
*
* No equilibration
*
EQUED = 'N'
*
ELSE
*
II = IIA
JJ = JJA
JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 )
JB = JN-JA+1
*
* Replace A by diag(S) * A * diag(S).
*
IF( LSAME( UPLO, 'U' ) ) THEN
*
* Upper triangle of A(IA:IA+N-1,JA:JA+N-1) is stored.
* Handle first block separately
*
IOFFA = (JJ-1)*LDA
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
DO 20 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 10 KK = IIA, II+LL-JJ+1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
10 CONTINUE
IOFFA = IOFFA + LDA
20 CONTINUE
ELSE
IOFFA = IOFFA + JB*LDA
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 70 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
DO 40 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 30 KK = IIA, II+LL-JJ+1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
30 CONTINUE
IOFFA = IOFFA + LDA
40 CONTINUE
ELSE
DO 60 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 50 KK = IIA, II-1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
50 CONTINUE
IOFFA = IOFFA + LDA
60 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
70 CONTINUE
*
ELSE
*
* Lower triangle of A(IA:IA+N-1,JA:JA+N-1) is stored.
* Handle first block separately
*
IROFF = MOD( IA-1, DESCA( MB_ ) )
NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
IF( MYROW.EQ.IAROW )
$ NP = NP-IROFF
*
IOFFA = (JJ-1)*LDA
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
DO 90 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 80 KK = II+LL-JJ, IIA+NP-1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
80 CONTINUE
IOFFA = IOFFA + LDA
90 CONTINUE
ELSE
DO 110 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 100 KK = II, IIA+NP-1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
100 CONTINUE
IOFFA = IOFFA + LDA
110 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
* Loop over remaining block of columns
*
DO 160 J = JN+1, JA+N-1, DESCA( NB_ )
JB = MIN( JA+N-J, DESCA( NB_ ) )
*
IF( MYCOL.EQ.IACOL ) THEN
IF( MYROW.EQ.IAROW ) THEN
DO 130 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 120 KK = II+LL-JJ, IIA+NP-1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
120 CONTINUE
IOFFA = IOFFA + LDA
130 CONTINUE
ELSE
DO 150 LL = JJ, JJ + JB -1
CJ = SC( LL )
DO 140 KK = II, IIA+NP-1
A( IOFFA + KK ) = CJ*SR( KK )*A( IOFFA + KK )
140 CONTINUE
IOFFA = IOFFA + LDA
150 CONTINUE
END IF
JJ = JJ + JB
END IF
*
IF( MYROW.EQ.IAROW )
$ II = II + JB
IAROW = MOD( IAROW+1, NPROW )
IACOL = MOD( IACOL+1, NPCOL )
*
160 CONTINUE
*
END IF
*
EQUED = 'Y'
*
END IF
*
RETURN
*
* End of PDLAQSY
*
END