SUBROUTINE PDLAFCHK( AFORM, DIAG, M, N, A, IA, JA, DESCA, IASEED, $ ANORM, FRESID, WORK ) * * -- 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 AFORM, DIAG INTEGER IA, IASEED, JA, M, N DOUBLE PRECISION ANORM, FRESID * .. * .. Array Arguments .. INTEGER DESCA( * ) DOUBLE PRECISION A( * ), WORK( * ) * .. * * Purpose * ======= * * PDLAFCHK computes the residual * || sub( A ) - sub( Ao ) || / (|| sub( Ao ) ||*eps*MAX(M,N)), * where Ao will be regenerated by the parallel random matrix generator, * sub( A ) = A( IA:IA+M-1, JA:JA+N-1 ) and ||.|| stands for the infini- * ty 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 * ========= * * AFORM (global input) CHARACTER * sub( A ) is overwritten with: * - a symmetric matrix, if AFORM = 'S'; * - a Hermitian matrix, if AFORM = 'H'; * - the transpose of what would normally be generated, * if AFORM = 'T'; * - the conjugate transpose of what would normally be * generated, if AFORM = 'C'; * - otherwise a random matrix. * * DIAG (global input) CHARACTER * if DIAG = 'D' : sub( A ) is diagonally dominant. * * 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) DOUBLE PRECISION pointer into the * local memory to an array of dimension (LLD_A,LOCc(JA+N-1)). * On entry, this array contains the local pieces of the M-by-N * distributed matrix sub( A ) to be checked. On exit, this * array contains the local pieces of the difference * sub( A ) - sub( Ao ). * * 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. * * IASEED (global input) INTEGER * The seed number to generate the original matrix Ao. * * ANORM (global input) DOUBLE PRECISION * The Infinity norm of sub( A ). * * FRESID (global output) DOUBLE PRECISION * The maximum (worst) factorizational error. * * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK). * LWORK >= MpA0 * NB_A, where * * IROFFA = MOD( IA-1, MB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * MpA0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), * * WORK is used to store a block of columns of sub( A ). * 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 ) DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D+0 ) * .. * .. Local Scalars .. INTEGER IACOL, IAROW, ICOFF, ICTXT, IIA, IOFFA, IROFF, $ JB, JJ, JJA, JN, LDA, LDW, MP, MYCOL, MYROW, $ NPCOL, NPROW, NQ DOUBLE PRECISION EPS * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DMATADD, INFOG2L, PDMATGEN * .. * .. External Functions .. INTEGER ICEIL, NUMROC DOUBLE PRECISION PDLAMCH, PDLANGE EXTERNAL ICEIL, NUMROC, PDLAMCH, PDLANGE * .. * .. Intrinsic Functions .. INTRINSIC MAX, MIN, MOD * .. * .. Executable Statements .. * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) EPS = PDLAMCH( ICTXT, 'eps' ) CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) * * Compute sub( A ) := sub( A ) - sub( Ao ) * 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 JN = MIN( ICEIL( JA, DESCA( NB_ ) ) * DESCA( NB_ ), JA+N-1 ) LDW = MAX( 1, MP ) LDA = DESCA( LLD_ ) IOFFA = IIA + ( JJA - 1 )*LDA * * Handle first block of columns separately * IF( MYCOL.EQ.IACOL ) THEN JB = JN-JA+1 CALL PDMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ), DESCA( N_ ), $ DESCA( MB_ ), DESCA( NB_ ), WORK, LDW, $ DESCA( RSRC_ ), DESCA( CSRC_ ), IASEED, IIA-1, $ MP, JJA-1, JB, MYROW, MYCOL, NPROW, NPCOL ) CALL DMATADD( MP, JB, -ONE, WORK, LDW, ONE, A( IOFFA ), LDA ) JJA = JJA + JB NQ = NQ - JB IOFFA = IOFFA + JB * LDA END IF * * Handle the remaning blocks of columns * DO 10 JJ = JJA, JJA+NQ-1, DESCA( NB_ ) JB = MIN( DESCA( NB_ ), JJA+NQ-JJ ) IOFFA = IIA + ( JJ - 1 ) * LDA CALL PDMATGEN( ICTXT, AFORM, DIAG, DESCA( M_ ), DESCA( N_ ), $ DESCA( MB_ ), DESCA( NB_ ), WORK, LDW, $ DESCA( RSRC_ ), DESCA( CSRC_ ), IASEED, IIA-1, $ MP, JJ-1, JB, MYROW, MYCOL, NPROW, NPCOL ) CALL DMATADD( MP, JB, -ONE, WORK, LDW, ONE, A( IOFFA ), LDA ) 10 CONTINUE * * Calculate factor residual * FRESID = PDLANGE( 'I', M, N, A, IA, JA, DESCA, WORK ) / $ ( MAX( M, N ) * EPS * ANORM ) * RETURN * * End PDLAFCHK * END