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SUBROUTINE PZLASCHK( SYMM, DIAG, N, NRHS, X, IX, JX, DESCX,
$ IASEED, IA, JA, DESCA, IBSEED, ANORM, RESID,
$ 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 DIAG, SYMM
INTEGER IA, IASEED, IBSEED, IX, JA, JX, N, NRHS
DOUBLE PRECISION ANORM, RESID
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCX( * )
COMPLEX*16 WORK( * ), X( * )
* ..
*
* Purpose
* =======
*
* PZLASCHK 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 = 'H', sub( A ) is a hermitian distributed matrix,
* otherwise sub( A ) is a general distributed matrix.
*
* DIAG (global input) CHARACTER
* If DIAG = 'D', sub( A ) is diagonally dominant.
*
* 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 >= 0.
*
* X (local input) COMPLEX*16 pointer into the local memory
* to an array of dimension (LLD_X,LOCc(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 ).
*
* 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.
*
* IASEED (global input) INTEGER
* The seed number to generate the original matrix 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.
*
* 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) COMPLEX*16 array, dimension (LWORK)
* LWORK >= MAX(1,Np)*NB_X + Nq*NB_X + MAX( MAX(NQ*MB_A,2*NB_X),
* NB_X * NUMROC( NUMROC(N,MB_X,0,0,NPCOL), MB_X, 0, 0, LCMQ ) )
*
* =====================================================================
*
* .. 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 )
COMPLEX*16 ZERO, ONE
PARAMETER ( ONE = ( 1.0D+0, 0.0D+0 ),
$ ZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
INTEGER IACOL, IAROW, IB, ICOFF, ICTXT, ICURCOL, IDUMM,
$ II, IIA, IIX, IOFFX, IPA, IPB, IPW, IPX, IROFF,
$ IXCOL, IXROW, J, JBRHS, JJ, JJA, JJX, LDX,
$ MYCOL, MYROW, NP, NPCOL, NPROW, NQ
DOUBLE PRECISION DIVISOR, EPS, RESID1
COMPLEX*16 BETA
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, DGEBR2D, DGEBS2D,
$ DGERV2D, DGESD2D, PBZTRAN,
$ PZMATGEN, ZGAMX2D, ZGEMM, ZGSUM2D,
$ ZLASET
* ..
* .. External Functions ..
INTEGER IZAMAX, NUMROC
DOUBLE PRECISION PDLAMCH
EXTERNAL IZAMAX, NUMROC, PDLAMCH
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, MAX, MIN, MOD
* ..
* .. Executable Statements ..
*
* Get needed initial parameters
*
ICTXT = DESCA( CTXT_ )
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 )
IROFF = MOD( IA-1, DESCA( MB_ ) )
ICOFF = MOD( JA-1, DESCA( NB_ ) )
NP = NUMROC( N+IROFF, DESCA( MB_ ), MYROW, IAROW, NPROW )
NQ = NUMROC( N+ICOFF, DESCA( NB_ ), MYCOL, IACOL, NPCOL )
*
LDX = MAX( 1, NP )
IPB = 1
IPX = IPB + NP * DESCX( NB_ )
IPA = IPX + NQ * DESCX( NB_ )
*
IF( MYROW.EQ.IAROW )
$ NP = NP - IROFF
IF( MYCOL.EQ.IACOL )
$ NQ = NQ - ICOFF
*
ICURCOL = IXCOL
*
* Loop over the rhs
*
DO 40 J = 1, NRHS, DESCX( NB_ )
JBRHS = MIN( DESCX( NB_ ), NRHS-J+1 )
*
* Transpose x from ICURCOL to all rows
*
IOFFX = IIX + ( JJX - 1 ) * DESCX( LLD_ )
CALL PBZTRAN( ICTXT, 'Column', 'Transpose', N, JBRHS,
$ DESCX( MB_ ), X( IOFFX ), DESCX( LLD_ ), ZERO,
$ WORK( IPX ), JBRHS, IXROW, ICURCOL, -1, IACOL,
$ WORK( IPA ) )
*
* Regenerate B in IXCOL
*
IF( MYCOL.EQ.ICURCOL ) THEN
CALL PZMATGEN( ICTXT, 'N', 'N', DESCX( M_ ), DESCX( N_ ),
$ DESCX( MB_ ), DESCX( NB_ ), WORK( IPB ), LDX,
$ IXROW, IXCOL, IBSEED, IIX-1, NP, JJX-1,
$ JBRHS, MYROW, MYCOL, NPROW, NPCOL )
BETA = ONE
ELSE
BETA = ZERO
END IF
*
IF( NQ.GT.0 ) THEN
DO 10 II = IIA, IIA+NP-1, DESCA( MB_ )
IB = MIN( DESCA( MB_ ), IIA+NP-II )
*
* Regenerate ib rows of the matrix A(IA:IA+N-1,JA:JA+N-1).
*
CALL PZMATGEN( ICTXT, SYMM, DIAG, DESCA( M_ ),
$ DESCA( N_ ), DESCA( MB_ ), DESCA( NB_ ),
$ WORK( IPA ), IB, DESCA( RSRC_ ),
$ DESCA( CSRC_ ), IASEED, II-1, IB,
$ JJA-1, NQ, MYROW, MYCOL, NPROW, NPCOL )
*
* Compute B <= B - A * X.
*
CALL ZGEMM( 'No transpose', 'Transpose', IB, JBRHS, NQ,
$ -ONE, WORK( IPA ), IB, WORK( IPX ), JBRHS,
$ BETA, WORK( IPB+II-IIA ), LDX )
*
10 CONTINUE
*
ELSE IF( MYCOL.NE.ICURCOL ) THEN
*
CALL ZLASET( 'All', NP, JBRHS, ZERO, ZERO, WORK( IPB ),
$ LDX )
*
END IF
*
* Add B rowwise to ICURCOL
*
CALL ZGSUM2D( ICTXT, 'Row', ' ', NP, JBRHS, WORK( IPB ), LDX,
$ MYROW, ICURCOL )
*
IF( MYCOL.EQ.ICURCOL ) THEN
*
* Figure || A * X - B || & || X ||
*
IPW = IPA + JBRHS
DO 20 JJ = 0, JBRHS - 1
IF( NP.GT.0 ) THEN
II = IZAMAX( NP, WORK( IPB+JJ*LDX ), 1 )
WORK( IPA+JJ ) = ABS( WORK( IPB+II-1+JJ*LDX ) )
WORK( IPW+JJ ) = ABS( X( IOFFX + IZAMAX( NP,
$ X( IOFFX + JJ*DESCX( LLD_ ) ), 1 )-1+JJ*
$ DESCX( LLD_ ) ) )
ELSE
WORK( IPA+JJ ) = ZERO
WORK( IPW+JJ ) = ZERO
END IF
20 CONTINUE
*
* After ZGAMX2D computation,
* WORK(IPB) has the maximum of || Ax - b ||, and
* WORK(IPX) has the maximum of || X ||.
*
CALL ZGAMX2D( ICTXT, 'Column', ' ', 1, 2*JBRHS,
$ WORK( IPA ), 1, IDUMM, IDUMM, -1, 0, ICURCOL )
*
* Calculate residual = ||Ax-b|| / (||x||*||A||*eps*N)
*
IF( MYROW.EQ.0 ) THEN
DO 30 JJ = 0, JBRHS - 1
RESID1 = DBLE( WORK( IPA+JJ ) ) /
$ ( DBLE( WORK( IPW+JJ ) )*DIVISOR )
IF( RESID.LT.RESID1 )
$ RESID = RESID1
30 CONTINUE
IF( MYCOL.NE.0 )
$ CALL DGESD2D( ICTXT, 1, 1, RESID, 1, 0, 0 )
END IF
*
ELSE IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
*
CALL DGERV2D( ICTXT, 1, 1, RESID1, 1, 0, ICURCOL )
IF( RESID.LT.RESID1 )
$ RESID = RESID1
*
END IF
*
IF( MYCOL.EQ.ICURCOL )
$ JJX = JJX + JBRHS
ICURCOL = MOD( ICURCOL+1, NPCOL )
*
40 CONTINUE
*
IF( MYROW.EQ.0 .AND. MYCOL.EQ.0 ) THEN
CALL DGEBS2D( ICTXT, 'All', ' ', 1, 1, RESID, 1 )
ELSE
CALL DGEBR2D( ICTXT, 'All', ' ', 1, 1, RESID, 1, 0, 0 )
END IF
*
RETURN
*
* End of PZLASCHK
*
END
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