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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
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