SUBROUTINE PZLAQGE( M, N, A, IA, JA, DESCA, R, C, ROWCND, COLCND,
$ AMAX, EQUED )
*
* -- ScaLAPACK auxiliary routine (version 1.5) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
CHARACTER EQUED
INTEGER IA, JA, M, N
DOUBLE PRECISION AMAX, COLCND, ROWCND
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
DOUBLE PRECISION C( * ), R( * )
COMPLEX*16 A( * )
* ..
*
* Purpose
* =======
*
* PZLAQGE equilibrates a general M-by-N distributed matrix
* sub( A ) = A(IA:IA+M-1,JA:JA+N-1) using the row and scaling
* factors in the vectors R and C.
*
* 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
* =========
*
* 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*16 pointer into the
* local memory to an array of dimension (LLD_A,LOCc(JA+N-1))
* containing on entry the M-by-N matrix sub( A ). On exit,
* the equilibrated distributed matrix. See EQUED for the
* form of the equilibrated distributed submatrix.
*
* 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.
*
* R (local input) DOUBLE PRECISION array, dimension LOCr(M_A)
* The row scale factors for sub( A ). R is aligned with the
* distributed matrix A, and replicated across every process
* column. R is tied to the distributed matrix A.
*
* C (local input) DOUBLE PRECISION array, dimension LOCc(N_A)
* The column scale factors of sub( A ). C is aligned with the
* distributed matrix A, and replicated down every process
* row. C is tied to the distributed matrix A.
*
* ROWCND (global input) DOUBLE PRECISION
* The global ratio of the smallest R(i) to the largest R(i),
* IA <= i <= IA+M-1.
*
* COLCND (global input) DOUBLE PRECISION
* The global ratio of the smallest C(i) to the largest C(i),
* JA <= j <= JA+N-1.
*
* AMAX (global input) DOUBLE PRECISION
* Absolute value of largest distributed submatrix entry.
*
* EQUED (global output) CHARACTER
* Specifies the form of equilibration that was done.
* = 'N': No equilibration
* = 'R': Row equilibration, i.e., sub( A ) has been pre-
* multiplied by diag(R(IA:IA+M-1)),
* = 'C': Column equilibration, i.e., sub( A ) has been post-
* multiplied by diag(C(JA:JA+N-1)),
* = 'B': Both row and column equilibration, i.e., sub( A )
* has been replaced by
* diag(R(IA:IA+M-1)) * sub( A ) * diag(C(JA:JA+N-1)).
*
* Internal Parameters
* ===================
*
* THRESH is a threshold value used to decide if row or column scaling
* should be done based on the ratio of the row or column scaling
* factors. If ROWCND < THRESH, row scaling is done, and if
* COLCND < THRESH, column scaling is done.
*
* LARGE and SMALL are threshold values used to decide if row scaling
* should be done based on the absolute size of the largest matrix
* element. If AMAX > LARGE or AMAX < SMALL, row 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 I, IACOL, IAROW, ICOFF, ICTXT, IIA, IOFFA,
$ IROFF, J, JJA, LDA, MP, MYCOL, MYROW, NPCOL,
$ NPROW, NQ
DOUBLE PRECISION CJ, LARGE, SMALL
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L
* ..
* .. External Functions ..
INTEGER NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL NUMROC, PDLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC MOD
* ..
* .. Executable Statements ..
*
* Quick return if possible
*
IF( M.LE.0 .OR. 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 )
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
MP = NUMROC( M+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYROW.EQ.IAROW )
$ MP = MP - IROFF
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFF
LDA = DESCA( LLD_ )
*
* Initialize LARGE and SMALL.
*
SMALL = PDLAMCH( ICTXT, 'Safe minimum' ) /
$ PDLAMCH( ICTXT, 'Precision' )
LARGE = ONE / SMALL
*
IF( ROWCND.GE.THRESH .AND. AMAX.GE.SMALL .AND. AMAX.LE.LARGE )
$ THEN
*
* No row scaling
*
IF( COLCND.GE.THRESH ) THEN
*
* No column scaling
*
EQUED = 'N'
*
ELSE
*
* Column scaling
*
IOFFA = (JJA-1)*LDA
DO 20 J = JJA, JJA+NQ-1
CJ = C( J )
DO 10 I = IIA, IIA+MP-1
A( IOFFA + I ) = CJ*A( IOFFA + I )
10 CONTINUE
IOFFA = IOFFA + LDA
20 CONTINUE
EQUED = 'C'
END IF
*
ELSE IF( COLCND.GE.THRESH ) THEN
*
* Row scaling, no column scaling
*
IOFFA = (JJA-1)*LDA
DO 40 J = JJA, JJA+NQ-1
DO 30 I = IIA, IIA+MP-1
A( IOFFA + I ) = R( I )*A( IOFFA + I )
30 CONTINUE
IOFFA = IOFFA + LDA
40 CONTINUE
EQUED = 'R'
*
ELSE
*
* Row and column scaling
*
IOFFA = (JJA-1)*LDA
DO 60 J = JJA, JJA+NQ-1
CJ = C( J )
DO 50 I = IIA, IIA+MP-1
A( IOFFA + I ) = CJ*R( I )*A( IOFFA + I )
50 CONTINUE
IOFFA = IOFFA + LDA
60 CONTINUE
EQUED = 'B'
*
END IF
*
RETURN
*
* End of PZLAQGE
*
END