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SUBROUTINE PCQRT13( SCALE, M, N, A, IA, JA, DESCA, NORMA, ISEED,
$ WORK )
*
* -- ScaLAPACK routine (version 1.7) --
* University of Tennessee, Knoxville, Oak Ridge National Laboratory,
* and University of California, Berkeley.
* May 1, 1997
*
* .. Scalar Arguments ..
INTEGER IA, ISEED, JA, M, N, SCALE
REAL NORMA
* ..
* .. Array Arguments ..
INTEGER DESCA( * )
REAL WORK( * )
COMPLEX A( * )
* ..
*
* Purpose
* =======
*
* PCQRT13 generates a full-rank matrix that may be scaled to have
* large or small norm.
*
* 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
* =========
*
* SCALE (global input) INTEGER
* SCALE = 1: normally scaled matrix
* SCALE = 2: matrix scaled up
* SCALE = 3: matrix scaled down
*
* 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 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 ).
*
* 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.
*
* NORMA (global output) REAL
* The one-norm of A.
*
* ISEED (global input/global output) INTEGER
* Seed for random number generator.
*
* WORK (local workspace) REAL array, dimension (LWORK)
* LWORK >= Nq0, where
*
* ICOFFA = MOD( JA-1, NB_A ),
* IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), and
* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ).
*
* INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW,
* MYCOL, NPROW and NPCOL can be determined by calling the
* subroutine BLACS_GRIDINFO.
*
* =====================================================================
*
* .. 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
PARAMETER ( ONE = 1.0E0 )
* ..
* .. Local Scalars ..
INTEGER I, IACOL, IAROW, ICOFFA, ICTXT, IIA, INFO,
$ IROFFA, J, JJA, MP, MYCOL, MYROW, NPCOL,
$ NPROW, NQ
REAL ASUM, BIGNUM, SMLNUM
COMPLEX AJJ
* ..
* .. External Functions ..
INTEGER NUMROC
REAL PCLANGE, PSLAMCH
EXTERNAL NUMROC, PCLANGE, PSLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, INFOG2L, PCLASCL, PCMATGEN,
$ PCELGET, PCELSET, PSCASUM,
$ PSLABAD
* ..
* .. Intrinsic Functions ..
INTRINSIC CMPLX, MOD, REAL, SIGN
* ..
* .. Executable Statements ..
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
IF( M.LE.0 .OR. N.LE.0 )
$ RETURN
*
* generate the matrix
*
IROFFA = MOD( IA-1, DESCA( MB_ ) )
ICOFFA = MOD( JA-1, DESCA( NB_ ) )
CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA,
$ JJA, IAROW, IACOL )
MP = NUMROC( M+IROFFA, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFFA, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
IF( MYROW.EQ.IAROW )
$ MP = MP - IROFFA
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFFA
*
CALL PCMATGEN( ICTXT, 'N', 'N', DESCA( M_ ), DESCA( N_ ),
$ DESCA( MB_ ), DESCA( NB_ ), A, DESCA( LLD_ ),
$ DESCA( RSRC_ ), DESCA( CSRC_ ), ISEED, IIA-1, MP,
$ JJA-1, NQ, MYROW, MYCOL, NPROW, NPCOL )
*
DO 10 J = JA, JA+N-1
I = IA + J - JA
IF( I.LE.IA+M-1 ) THEN
CALL PSCASUM( M, ASUM, A, IA, J, DESCA, 1 )
CALL PCELGET( 'Column', ' ', AJJ, A, I, J, DESCA )
AJJ = AJJ + CMPLX( SIGN( ASUM, REAL( AJJ ) ) )
CALL PCELSET( A, I, J, DESCA, AJJ )
END IF
10 CONTINUE
*
* scaled versions
*
IF( SCALE.NE.1 ) THEN
*
NORMA = PCLANGE( 'M', M, N, A, IA, JA, DESCA, WORK )
SMLNUM = PSLAMCH( ICTXT, 'Safe minimum' )
BIGNUM = ONE / SMLNUM
CALL PSLABAD( ICTXT, SMLNUM, BIGNUM )
SMLNUM = SMLNUM / PSLAMCH( ICTXT, 'Epsilon' )
BIGNUM = ONE / SMLNUM
*
IF( SCALE.EQ.2 ) THEN
*
* matrix scaled up
*
CALL PCLASCL( 'General', NORMA, BIGNUM, M, N, A, IA,
$ JA, DESCA, INFO )
*
ELSE IF( SCALE.EQ.3 ) THEN
*
* matrix scaled down
*
CALL PCLASCL( 'General', NORMA, SMLNUM, M, N, A, IA,
$ JA, DESCA, INFO )
*
END IF
*
END IF
*
NORMA = PCLANGE( 'One-norm', M, N, A, IA, JA, DESCA, WORK )
*
RETURN
*
* End of PCQRT13
*
END
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