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SUBROUTINE PCQRT16( TRANS, M, N, NRHS, A, IA, JA, DESCA, X, IX,
$ JX, DESCX, B, IB, JB, DESCB, RWORK, RESID )
*
* -- 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, IX, JA, JB, JX, M, N, NRHS
REAL RESID
* ..
* .. Array Arguments ..
INTEGER DESCA( * ), DESCB( * ), DESCX( * )
REAL RWORK( * )
COMPLEX A( * ), B( * ), X( * )
* ..
*
* Purpose
* =======
*
* PCQRT16 computes the residual for a solution of a system of linear
* equations sub( A )*sub( X ) = B or sub( A' )*sub( X ) = B:
* RESID = norm(B - sub( A )*sub( X ) ) /
* ( max(m,n) * norm(sub( A ) ) * norm(sub( X ) ) * EPS ),
* where EPS is the machine epsilon, sub( A ) denotes
* A(IA:IA+N-1,JA,JA+N-1), and 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
* =========
*
* TRANS (global input) CHARACTER*1
* Specifies the form of the system of equations:
* = 'N': sub( A )*sub( X ) = sub( B )
* = 'T': sub( A' )*sub( X )= sub( B ), where A' is the
* transpose of sub( A ).
* = 'C': sub( A' )*sub( X )= B, where A' is the conjugate
* transpose of sub( A ).
*
* 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.
*
* NRHS (global input) INTEGER
* The number of right hand sides, i.e., the number of columns
* of the distributed submatrix sub( B ). NRHS >= 0.
*
* A (local input) COMPLEX pointer into the local
* memory to an array of dimension (LLD_A,LOCc(JA+N-1)).
* The original M x N matrix 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) COMPLEX pointer into the local
* memory to an array of dimension (LLD_X,LOCc(JX+NRHS-1)). This
* array contains the local pieces of the computed solution
* distributed vectors for the system of linear equations.
*
* 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/local output) COMPLEX pointer into
* the local memory to an array of dimension
* (LLD_B,LOCc(JB+NRHS-1)). On entry, this array contains the
* local pieces of the distributes right hand side vectors for
* the system of linear equations. On exit, sub( B ) is over-
* written with the difference sub( B ) - sub( A )*sub( X ) or
* sub( B ) - sub( A )'*sub( X ).
*
* 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.
*
* RWORK (local workspace) REAL array, dimension (LRWORK)
* LWORK >= 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 ),
* Nq0 = NUMROC( N+ICOFFA, NB_A, MYCOL, IACOL, NPCOL ),
*
* INDXG2P and NUMROC are ScaLAPACK tool functions; MYROW,
* MYCOL, NPROW and NPCOL can be determined by calling the
* subroutine BLACS_GRIDINFO.
*
* RESID (global output) REAL
* The maximum over the number of right hand sides of
* norm( sub( B )- sub( A )*sub( X ) ) /
* ( max(m,n) * norm( sub( A ) ) * norm( sub( X ) ) * EPS ).
*
* =====================================================================
*
* .. 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 )
REAL ZERO, ONE
PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
COMPLEX CONE
PARAMETER ( CONE = ( 1.0E+0, 0.0E+0 ) )
* ..
* .. Local Scalars ..
INTEGER ICTXT, IDUMM, J, MYCOL, MYROW, N1, N2, NPCOL,
$ NPROW
REAL ANORM, BNORM, EPS, XNORM
* ..
* .. Local Arrays ..
REAL TEMP( 2 )
* ..
* .. External Functions ..
LOGICAL LSAME
REAL PCLANGE, PSLAMCH
EXTERNAL LSAME, PCLANGE, PSLAMCH
* ..
* .. External Subroutines ..
EXTERNAL BLACS_GRIDINFO, PCGEMM, PSCASUM,
$ SGAMX2D
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
* Get grid parameters
*
ICTXT = DESCA( CTXT_ )
CALL BLACS_GRIDINFO( ICTXT, NPROW, NPCOL, MYROW, MYCOL )
*
* Quick exit if M = 0 or N = 0 or NRHS = 0
*
IF( M.LE.0 .OR. N.LE.0 .OR. NRHS.EQ.0 ) THEN
RESID = ZERO
RETURN
END IF
*
IF( LSAME( TRANS, 'T' ) .OR. LSAME( TRANS, 'C' ) ) THEN
ANORM = PCLANGE( 'I', M, N, A, IA, JA, DESCA, RWORK )
N1 = N
N2 = M
ELSE
ANORM = PCLANGE( '1', M, N, A, IA, JA, DESCA, RWORK )
N1 = M
N2 = N
END IF
*
EPS = PSLAMCH( ICTXT, 'Epsilon' )
*
* Compute B - sub( A )*sub( X ) (or B - sub( A' )*sub( X ) ) and
* store in B.
*
CALL PCGEMM( TRANS, 'No transpose', N1, NRHS, N2, -CONE, A, IA,
$ JA, DESCA, X, IX, JX, DESCX, CONE, B, IB, JB, DESCB )
*
* Compute the maximum over the number of right hand sides of
* norm( sub( B ) - sub( A )*sub( X ) ) /
* ( max(m,n) * norm( sub( A ) ) * norm( sub( X ) ) * EPS ).
*
RESID = ZERO
DO 10 J = 1, NRHS
*
CALL PSCASUM( N1, BNORM, B, IB, JB+J-1, DESCB, 1 )
CALL PSCASUM( N2, XNORM, X, IX, JX+J-1, DESCX, 1 )
*
* Only the process columns owning the vector operands will have
* the correct result, the other will have zero.
*
TEMP( 1 ) = BNORM
TEMP( 2 ) = XNORM
CALL SGAMX2D( ICTXT, 'All', ' ', 2, 1, TEMP, 2, IDUMM, IDUMM,
$ -1, -1, IDUMM )
BNORM = TEMP( 1 )
XNORM = TEMP( 2 )
*
* Every processes have ANORM, BNORM and XNORM now.
*
IF( ANORM.EQ.ZERO .AND. BNORM.EQ.ZERO ) THEN
RESID = ZERO
ELSE IF( ANORM.LE.ZERO .OR. XNORM.LE.ZERO ) THEN
RESID = ONE / EPS
ELSE
RESID = MAX( RESID, ( ( BNORM / ANORM ) / XNORM ) /
$ ( MAX( M, N )*EPS ) )
END IF
*
10 CONTINUE
*
RETURN
*
* End of PCQRT16
*
END
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