SUBROUTINE PDDBLASCHK( SYMM, UPLO, TRANS, N, BWL, BWU, NRHS, X, $ IX, JX, DESCX, IASEED, A, IA, JA, DESCA, $ IBSEED, ANORM, RESID, WORK, WORKSIZ ) * * * -- ScaLAPACK routine (version 1.7) -- * University of Tennessee, Knoxville, Oak Ridge National Laboratory, * and University of California, Berkeley. * November 15, 1997 * * .. Scalar Arguments .. CHARACTER SYMM, TRANS, UPLO INTEGER BWL, BWU, IA, IASEED, IBSEED, $ IX, JA, JX, N, NRHS, WORKSIZ DOUBLE PRECISION ANORM, RESID * .. * .. Array Arguments .. INTEGER DESCA( * ), DESCX( * ) DOUBLE PRECISION A( * ), WORK( * ), X( * ) * .. External Functions .. LOGICAL LSAME * .. * * Purpose * ======= * * PDDBLASCHK computes the residual * || sub( A )*sub( X ) - B || / (|| sub( A ) ||*|| sub( X ) ||*eps*N) * to check the accuracy of the factorization and solve steps in the * LU and Cholesky decompositions, where sub( A ) denotes * A(IA:IA+N-1,JA,JA+N-1), sub( X ) denotes X(IX:IX+N-1, JX:JX+NRHS-1). * * 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 * ========= * * SYMM (global input) CHARACTER * if SYMM = 'S', sub( A ) is a symmetric distributed band * matrix, otherwise sub( A ) is a general distributed matrix. * * UPLO (global input) CHARACTER * if SYMM = 'S', then * if UPLO = 'L', the lower half of the matrix is stored * if UPLO = 'U', the upper half of the matrix is stored * if SYMM != 'S' or 'H', then * if UPLO = 'D', the matrix is stable during factorization * without interchanges * if UPLO != 'D', the matrix is general * * TRANS if TRANS= 'T', A 'Transpose' is used as the * coefficient matrix in the solve. * * 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. * * NRHS (global input) INTEGER * The number of right-hand-sides, i.e the number of columns * of the distributed matrix sub( X ). NRHS >= 1. * * X (local input) DOUBLE PRECISION pointer into the local memory * to an array of dimension (LLD_X,LOCq(JX+NRHS-1). This array * contains the local pieces of the answer vector(s) sub( X ) of * sub( A ) sub( X ) - B, split up over a column of processes. * * IX (global input) INTEGER * The row index in the global array X indicating the first * row of sub( X ). * * DESCX (global and local input) INTEGER array of dimension DLEN_. * The array descriptor for the distributed matrix X. * * IASEED (global input) INTEGER * The seed number to generate the original matrix Ao. * * 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. * * IBSEED (global input) INTEGER * The seed number to generate the original matrix B. * * ANORM (global input) DOUBLE PRECISION * The 1-norm or infinity norm of the distributed matrix * sub( A ). * * RESID (global output) DOUBLE PRECISION * The residual error: * ||sub( A )*sub( X )-B|| / (||sub( A )||*||sub( X )||*eps*N). * * WORK (local workspace) DOUBLE PRECISION array, dimension (LWORK) * IF SYMM='S' * LWORK >= max(5,max(max(bwl,bwu)*(max(bwl,bwu)+2),NB))+2*NB * IF SYMM!='S' or 'H' * LWORK >= max(5,max(max(bwl,bwu)*(max(bwl,bwu)+2),NB))+2*NB * * WORKSIZ (local input) size of WORK. * * ===================================================================== * * Code Developer: Andrew J. Cleary, University of Tennessee. * Current address: Lawrence Livermore National Labs. * This version released: August, 2001. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 ) 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 ) INTEGER INT_ONE PARAMETER ( INT_ONE = 1 ) * .. * .. Local Scalars .. INTEGER IACOL, IAROW, ICTXT, $ IIA, IIX, IPB, IPW, $ IXCOL, IXROW, J, JJA, JJX, LDA, $ MYCOL, MYROW, NB, NP, NPCOL, NPROW, NQ INTEGER BW, INFO, IPPRODUCT, WORK_MIN DOUBLE PRECISION DIVISOR, EPS, RESID1, NORMX * .. * .. Local Arrays .. * .. * .. External Subroutines .. EXTERNAL BLACS_GRIDINFO, DGAMX2D, DGEBR2D, $ DGEBS2D, DGEMM, DGERV2D, DGESD2D, $ DGSUM2D, DLASET, PBDTRAN, PDMATGEN * .. * .. External Functions .. INTEGER IDAMAX, NUMROC DOUBLE PRECISION PDLAMCH EXTERNAL IDAMAX, NUMROC, PDLAMCH * .. * .. Intrinsic Functions .. INTRINSIC ABS, DBLE, MAX, MIN, MOD * .. * .. Executable Statements .. * * Get needed initial parameters * ICTXT = DESCA( CTXT_ ) NB = DESCA( NB_ ) * IF( LSAME( SYMM, 'S' ) ) THEN BW = BWL WORK_MIN = MAX(5,MAX(MAX(BWL,BWU)*(MAX(BWL,BWU)+2),NB))+2*NB ELSE BW = MAX(BWL, BWU) WORK_MIN = MAX(5,MAX(MAX(BWL,BWU)*(MAX(BWL,BWU)+2),NB))+2*NB ENDIF * IF ( WORKSIZ .LT. WORK_MIN ) THEN CALL PXERBLA( ICTXT, 'PDBLASCHK', -18 ) RETURN END IF * CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL ) * EPS = PDLAMCH( ICTXT, 'eps' ) RESID = 0.0D+0 DIVISOR = ANORM * EPS * DBLE( N ) * CALL INFOG2L( IA, JA, DESCA, NPROW, NPCOL, MYROW, MYCOL, IIA, JJA, $ IAROW, IACOL ) CALL INFOG2L( IX, JX, DESCX, NPROW, NPCOL, MYROW, MYCOL, IIX, JJX, $ IXROW, IXCOL ) NP = NUMROC( (BWL+BWU+1), DESCA( MB_ ), MYROW, 0, NPROW ) NQ = NUMROC( N, DESCA( NB_ ), MYCOL, 0, NPCOL ) * IPB = 1 IPPRODUCT = 1 + DESCA( NB_ ) IPW = 1 + 2*DESCA( NB_ ) * LDA = DESCA( LLD_ ) * * Regenerate A * IF( LSAME( SYMM, 'S' )) THEN CALL PDBMATGEN( ICTXT, UPLO, 'D', BW, BW, N, BW+1, $ DESCA( NB_ ), A, DESCA( LLD_ ), 0, 0, $ IASEED, MYROW, MYCOL, NPROW, NPCOL ) ELSE * CALL PDBMATGEN( ICTXT, 'N', UPLO, BWL, BWU, N, $ DESCA( MB_ ), DESCA( NB_ ), A, $ DESCA( LLD_ ), 0, 0, IASEED, MYROW, $ MYCOL, NPROW, NPCOL ) ENDIF * * Loop over the rhs * RESID = 0.0 * DO 40 J = 1, NRHS * * Multiply A * current column of X * * CALL PDGBDCMV( BWL+BWU+1, BWL, BWU, TRANS, N, A, 1, DESCA, $ 1, X( 1 + (J-1)*DESCX( LLD_ )), 1, DESCX, $ WORK( IPPRODUCT ), WORK( IPW ), $ (MAX(BWL,BWU)+2)*MAX(BWL,BWU), INFO ) * * * Regenerate column of B * CALL PDMATGEN( DESCX( CTXT_ ), 'No', 'No', DESCX( M_ ), $ DESCX( N_ ), DESCX( MB_ ), DESCX( NB_ ), $ WORK( IPB ), DESCX( LLD_ ), DESCX( RSRC_ ), $ DESCX( CSRC_ ), IBSEED, 0, NQ, J-1, 1, MYCOL, $ MYROW, NPCOL, NPROW ) * * Figure || A * X - B || & || X || * CALL PDAXPY( N, -ONE, WORK( IPPRODUCT ), 1, 1, DESCX, 1, $ WORK( IPB ), 1, 1, DESCX, 1 ) * CALL PDNRM2( N, NORMX, $ X, 1, J, DESCX, 1 ) * CALL PDNRM2( N, RESID1, $ WORK( IPB ), 1, 1, DESCX, 1 ) * * * Calculate residual = ||Ax-b|| / (||x||*||A||*eps*N) * RESID1 = RESID1 / ( NORMX*DIVISOR ) * RESID = MAX( RESID, RESID1 ) * 40 CONTINUE * RETURN * * End of PDBLASCHK * END