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