SUBROUTINE PDNEPFCHK( N, A, IA, JA, DESCA, IASEED, Z, IZ, JZ, $ DESCZ, ANORM, FRESID, 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, IASEED, IZ, JA, JZ, N DOUBLE PRECISION ANORM, FRESID * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCZ( * ) DOUBLE PRECISION A( * ), WORK( * ), Z( * ) * .. * * Purpose * ======= * * PDNEPFCHK computes the residual * || sub(Z)*sub( A )*sub(Z)**T - sub( Ao ) || / (||sub( Ao )||*eps*N), * where Ao will be regenerated by the parallel random matrix generator, * sub( A ) = A(IA:IA+M-1,JA:JA+N-1), sub( Z ) = Z(IZ:IZ+N-1,JZ:JZ+N-1) * and ||.|| stands for the infinity 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 * ========= * * N (global input) INTEGER * The order of sub( A ) and sub( Z ). 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 N-by-N * distributed matrix sub( A ) to be checked. On exit, this * array contains the local pieces of the difference * sub(Z)*sub( A )*sub(Z)**T - sub( Ao ). * * IA (global input) INTEGER * A's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JA (global input) INTEGER * A's global column index, which points to the beginning of * the submatrix which is to be operated on. * * 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. * * Z (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_Z,LOCc(JZ+N-1)). On entry, this * array contains the local pieces of the N-by-N distributed * matrix sub( Z ). * * IZ (global input) INTEGER * Z's global row index, which points to the beginning of the * submatrix which is to be operated on. * * JZ (global input) INTEGER * Z's global column index, which points to the beginning of * the submatrix which is to be operated on. * * DESCZ (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix Z. * * 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 >= MAX( NpA0 * NB_A, MB_A * NqA0 ) where * * IROFFA = MOD( IA-1, MB_A ), * ICOFFA = MOD( JA-1, NB_A ), * IAROW = INDXG2P( IA, MB_A, MYROW, RSRC_A, NPROW ), * IACOL = INDXG2P( JA, NB_A, MYCOL, CSRC_A, NPCOL ), * NpA0 = NUMROC( N+IROFFA, MB_A, MYROW, IAROW, NPROW ), * NqA0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * * WORK is used to store a block of rows and 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, ZERO PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) * .. * .. Local Scalars .. INTEGER I, IACOL, IAROW, IB, ICTXT, IIA, IOFFA, IROFF, $ IW, J, JB, JJA, JN, LDA, LDW, MYCOL, MYROW, NP, $ NPCOL, NPROW DOUBLE PRECISION EPS * .. * .. Local Arrays .. INTEGER DESCW( DLEN_ ) * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, DMATADD, INFOG2L, $ PDGEMM, PDLACPY, PDLASET, 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 ) IROFF = MOD( IA-1, DESCA( MB_ ) ) NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW ) IF( MYROW.EQ.IAROW ) $ NP = NP - IROFF LDW = MAX( 1, NP ) * * First compute H <- H * Z**T * CALL DESCSET( DESCW, DESCA( MB_ ), N, DESCA( MB_ ), DESCA( NB_ ), $ IAROW, IACOL, ICTXT, DESCA( MB_ ) ) * DO 10 I = IA, IA + N - 1, DESCA( MB_ ) IB = MIN( IA+N-I, DESCA( MB_ ) ) * CALL PDLACPY( 'All', IB, N, A, I, JA, DESCA, WORK, 1, 1, $ DESCW ) CALL PDGEMM( 'No transpose', 'Transpose', IB, N, N, ONE, WORK, $ 1, 1, DESCW, Z, IZ, JZ, DESCZ, ZERO, A, I, JA, $ DESCA ) * DESCW( RSRC_ ) = MOD( DESCW( RSRC_ )+1, NPROW ) * 10 CONTINUE * * Then compute H <- Z * H = Z * H0 * Z**T * CALL DESCSET( DESCW, N, DESCA( NB_ ), DESCA( MB_ ), DESCA( NB_ ), $ IAROW, IACOL, ICTXT, LDW ) * DO 20 J = JA, JA + N - 1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * CALL PDLACPY( 'All', N, JB, A, IA, J, DESCA, WORK, 1, 1, $ DESCW ) CALL PDGEMM( 'No transpose', 'No transpose', N, JB, N, ONE, Z, $ IZ, JZ, DESCZ, WORK, 1, 1, DESCW, ZERO, A, IA, J, $ DESCA ) * DESCW( CSRC_ ) = MOD( DESCW( CSRC_ )+1, NPCOL ) * 20 CONTINUE * * Compute H - H0 * JN = MIN( ICEIL( JA, DESCA( NB_ ) )*DESCA( NB_ ), JA+N-1 ) LDA = DESCA( LLD_ ) IOFFA = IIA + ( JJA-1 )*LDA IW = 1 JB = JN - JA + 1 DESCW( CSRC_ ) = IACOL * * Handle first block of columns separately * IF( MYCOL.EQ.DESCW( CSRC_ ) ) THEN CALL PDMATGEN( ICTXT, 'N', 'N', DESCA( M_ ), DESCA( N_ ), $ DESCA( MB_ ), DESCA( NB_ ), WORK, LDW, $ DESCA( RSRC_ ), DESCA( CSRC_ ), IASEED, IIA-1, $ NP, JJA-1, JB, MYROW, MYCOL, NPROW, NPCOL ) CALL PDLASET( 'Lower', MAX( 0, N-2 ), JB, ZERO, ZERO, WORK, $ MIN( IW+2, N ), 1, DESCW ) CALL DMATADD( NP, JB, -ONE, WORK, LDW, ONE, A( IOFFA ), LDA ) JJA = JJA + JB IOFFA = IOFFA + JB*LDA END IF * IW = IW + DESCA( MB_ ) DESCW( CSRC_ ) = MOD( DESCW( CSRC_ )+1, NPCOL ) * DO 30 J = JN + 1, JA + N - 1, DESCA( NB_ ) JB = MIN( JA+N-J, DESCA( NB_ ) ) * IF( MYCOL.EQ.DESCW( CSRC_ ) ) THEN CALL PDMATGEN( ICTXT, 'N', 'N', DESCA( M_ ), DESCA( N_ ), $ DESCA( MB_ ), DESCA( NB_ ), WORK, LDW, $ DESCA( RSRC_ ), DESCA( CSRC_ ), IASEED, $ IIA-1, NP, JJA-1, JB, MYROW, MYCOL, NPROW, $ NPCOL ) CALL PDLASET( 'Lower', MAX( 0, N-IW-1 ), JB, ZERO, ZERO, $ WORK, MIN( N, IW+2 ), 1, DESCW ) CALL DMATADD( NP, JB, -ONE, WORK, LDW, ONE, A( IOFFA ), $ LDA ) JJA = JJA + JB IOFFA = IOFFA + JB*LDA END IF IW = IW + DESCA( MB_ ) DESCW( CSRC_ ) = MOD( DESCW( CSRC_ )+1, NPCOL ) 30 CONTINUE * * Calculate factor residual * FRESID = PDLANGE( 'I', N, N, A, IA, JA, DESCA, WORK ) / $ ( N*EPS*ANORM ) * RETURN * * End PDNEPFCHK * END