DOUBLE PRECISION FUNCTION PDQRT17( TRANS, IRESID, M, N, NRHS, A, $ IA, JA, DESCA, X, IX, JX, $ DESCX, B, IB, JB, DESCB, WORK, $ RWORK ) * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * May 1, 1997 * * .. Scalar Arguments .. CHARACTER TRANS INTEGER IA, IB, IRESID, IX, JA, JB, JX, M, N, NRHS * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCB( * ), DESCX( * ) DOUBLE PRECISION A( * ), B( * ), WORK( * ), X( * ) DOUBLE PRECISION RWORK( * ) * .. * * Purpose * ======= * * PDQRT17 computes the ratio * * || R'*op( sub( A ) ) ||/(||sub( A )||*alpha*max(M,N,NRHS)*eps) * * where R = op( sub( A ) )*sub( X ) - B, op(A) is A or A', and * * alpha = ||B|| if IRESID = 1 (zero-residual problem) * alpha = ||R|| if IRESID = 2 (otherwise). * * 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 * ========= * * TRANS (global input) CHARACTER*1 * Specifies whether or not the transpose of sub( A ) is used. * = 'N': No transpose, op( sub( A ) ) = sub( A ). * = 'T': Transpose, op( sub( A ) ) = sub( A' ). * * IRESID (global input) INTEGER * IRESID = 1 indicates zero-residual problem. * IRESID = 2 indicates non-zero residual. * * 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. * If TRANS = 'N', the number of rows of the distributed * submatrix sub( B ). * If TRANS = 'T', the number of rows of the distributed * submatrix sub( X ). * * 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. * If TRANS = 'N', the number of rows of the distributed * submatrix sub( X ). Otherwise N is the number of rows of * the distributed submatrix sub( B ). * * NRHS (global input) INTEGER * The number of right hand sides, i.e., the number of columns * of the distributed submatrices sub( X ) and sub( B ). * NRHS >= 0. * * A (local input) DOUBLE PRECISION 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 M-by-N * submatrix 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. * * X (local input) DOUBLE PRECISION pointer into the local * memory to an array of dimension (LLD_X,LOCc(JX+NRHS-1)). * If TRANS = 'N', this array contains the local pieces of the * N-by-NRHS distributed submatrix sub( X ). Otherwise, this * array contains the local pieces of the M-by-NRHS distributed * submatrix sub( X ). * * IX (global input) INTEGER * The row index in the global array X indicating the first * row of sub( X ). * * JX (global input) INTEGER * The column index in the global array X indicating the * first column of sub( X ). * * DESCX (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix X. * * B (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_B,LOCc(JB+NRHS-1)). * If TRANS='N', this array contains the local pieces of the * distributed M-by-NRHS submatrix operand sub( B ). Otherwise, * this array contains the local pieces of the distributed * N-by-NRHS submatrix operand sub( B ). * * IB (global input) INTEGER * The row index in the global array B indicating the first * row of sub( B ). * * JB (global input) INTEGER * The column index in the global array B indicating the * first column of sub( B ). * * DESCB (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix B. * * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK) * If TRANS = 'N', LWORK >= Mp0 * NRHSq0 + NRHSp0 * Nq0 * otherwise LWORK >= Np0 * NRHSq0 + NRHSp0 * Mq0 * * RWORK (local workspace) DOUBLE PRECISION array, dimension (LRWORK) * LRWORK >= Nq0, if TRANS = 'N', and LRWORK >= Mp0 otherwise. * * 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 ), * Mp0 = NUMROC( M+IROFFA, MB_A, MYROW, IAROW, NPROW ), * Np0 = NUMROC( N+ICOFFA, NB_A, MYROW, IAROW, NPROW ), * Mq0 = NUMROC( M+IROFFA, NB_A, MYCOL, IACOL, NPCOL ), * Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ), * * IROFFB = MOD( IB-1, MB_B ), ICOFFB = MOD( JB-1, NB_B ), * IBROW = INDXG2P( IB, MB_B, MYROW, RSRC_B, NPROW ), * IBCOL = INDXG2P( JB, NB_B, MYCOL, CSRC_B, NPCOL ), * NRHSp0 = NUMROC( NRHS+ICOFFB, NB_B, MYROW, IBROW, NPROW ), * NRHSq0 = NUMROC( NRHS+ICOFFB, NB_B, MYCOL, IBCOL, 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 ) DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 ) * .. * .. Local Scalars .. INTEGER IACOL, IBCOL, IBROW, ICOFFB, ICTXT, INFO, $ IOFFA, IROFFB, ISCL, IW, IW2, JW, JW2, MYCOL, $ NRHSQ, NRHSP, MYROW, NCOLS, NPCOL, NPROW, $ NROWS, NROWSP DOUBLE PRECISION ERR, NORMA, NORMB, NORMRS, NORMX, SMLNUM * .. * .. Local Arrays .. INTEGER DESCW( DLEN_ ), DESCW2( DLEN_ ) * .. * .. External Functions .. LOGICAL LSAME INTEGER INDXG2P, NUMROC DOUBLE PRECISION PDLAMCH, PDLANGE EXTERNAL INDXG2P, LSAME, NUMROC, PDLAMCH, PDLANGE * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DESCSET, PDGEMM, PDLACPY, $ PDLASCL, PXERBLA * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Executable Statements .. * PDQRT17 = ZERO * * Get grid parameters * ICTXT = DESCA( CTXT_ ) CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * INFO = 0 IF( LSAME( TRANS, 'N' ) ) THEN NROWS = M NCOLS = N IOFFA = MOD( JA-1, DESCA( NB_ ) ) ELSE IF( LSAME( TRANS, 'T' ) ) THEN NROWS = N NCOLS = M IOFFA = MOD( IA-1, DESCA( MB_ ) ) ELSE CALL PXERBLA( ICTXT, 'PDQRT17', -1 ) RETURN END IF * IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.LE.0 ) $ RETURN * IROFFB = MOD( IA-1, DESCA( MB_ ) ) ICOFFB = MOD( JA-1, DESCA( NB_ ) ) IBROW = INDXG2P( IB, DESCB( MB_ ), MYROW, DESCB( RSRC_ ), $ NPROW ) IACOL = INDXG2P( JA, DESCA( NB_ ), MYCOL, DESCA( CSRC_ ), $ NPCOL ) IBCOL = INDXG2P( JB, DESCB( NB_ ), MYCOL, DESCB( CSRC_ ), $ NPCOL ) * NRHSQ = NUMROC( NRHS+ICOFFB, DESCB( NB_ ), MYCOL, IBCOL, NPCOL ) NRHSP = NUMROC( NRHS+IROFFB, DESCB( NB_ ), MYROW, IBROW, NPROW ) NROWSP = NUMROC( NROWS+IROFFB, DESCA( MB_ ), MYROW, IBROW, NPROW ) * * Assign array descriptor DESCW for workspace WORK, where DESCW * holds a copy of the distributed submatrix sub( B ) * CALL DESCSET( DESCW, NROWS+IROFFB, NRHS+ICOFFB, DESCB( MB_ ), $ DESCB( NB_ ), IBROW, IBCOL, ICTXT, MAX( 1, $ NROWSP ) ) * * Assign array descriptor DESCW2 for workspace WORK, where DESCW2 * holds a copy of the distributed submatrix sub( X**T ) * CALL DESCSET( DESCW2, NRHS+ICOFFB, NCOLS+IOFFA, DESCX( NB_ ), $ DESCX( MB_ ), IBROW, IACOL, ICTXT, MAX( 1, $ NRHSP ) ) * NORMA = PDLANGE( 'One-norm', M, N, A, IA, JA, DESCA, RWORK ) SMLNUM = PDLAMCH( ICTXT, 'Safe minimum' ) SMLNUM = SMLNUM / PDLAMCH( ICTXT, 'Precision' ) ISCL = 0 * * compute residual and scale it * IW = 1 + IROFFB JW = 1 + ICOFFB CALL PDLACPY( 'All', NROWS, NRHS, B, IB, JB, DESCB, WORK, IW, JW, $ DESCW ) CALL PDGEMM( TRANS, 'No transpose', NROWS, NRHS, NCOLS, -ONE, A, $ IA, JA, DESCA, X, IX, JX, DESCX, ONE, WORK, IW, JW, $ DESCW ) NORMRS = PDLANGE( 'Max', NROWS, NRHS, WORK, IW, JW, DESCW, $ RWORK ) IF( NORMRS.GT.SMLNUM ) THEN ISCL = 1 CALL PDLASCL( 'General', NORMRS, ONE, NROWS, NRHS, WORK, $ IW, JW, DESCW, INFO ) END IF * * compute R'*sub( A ) * IW2 = 1 + ICOFFB JW2 = 1 + IOFFA CALL PDGEMM( 'Transpose', TRANS, NRHS, NCOLS, NROWS, ONE, WORK, $ IW, JW, DESCW, A, IA, JA, DESCA, ZERO, $ WORK( NROWSP*NRHSQ+1 ), IW2, JW2, DESCW2 ) * * compute and properly scale error * ERR = PDLANGE( 'One-norm', NRHS, NCOLS, WORK( NROWSP*NRHSQ+1 ), $ IW2, JW2, DESCW2, RWORK ) IF( NORMA.NE.ZERO ) $ ERR = ERR / NORMA * IF( ISCL.EQ.1 ) $ ERR = ERR*NORMRS * IF( IRESID.EQ.1 ) THEN NORMB = PDLANGE( 'One-norm', NROWS, NRHS, B, IB, JB, DESCB, $ RWORK ) IF( NORMB.NE.ZERO ) $ ERR = ERR / NORMB ELSE NORMX = PDLANGE( 'One-norm', NCOLS, NRHS, X, IX, JX, DESCX, $ RWORK ) IF( NORMX.NE.ZERO ) $ ERR = ERR / NORMX END IF * PDQRT17 = ERR / ( PDLAMCH( ICTXT, 'Epsilon' ) * $ DBLE( MAX( M, N, NRHS ) ) ) * RETURN * * End of PDQRT17 * END