530 lines
16 KiB
Fortran
530 lines
16 KiB
Fortran
*> \brief \b DCHKPO
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
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* XACT, WORK, RWORK, IWORK, NOUT )
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*
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* .. Scalar Arguments ..
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* LOGICAL TSTERR
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* INTEGER NMAX, NN, NNB, NNS, NOUT
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* DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
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* DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
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* $ RWORK( * ), WORK( * ), X( * ), XACT( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DCHKPO tests DPOTRF, -TRI, -TRS, -RFS, and -CON
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] DOTYPE
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*> \verbatim
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*> DOTYPE is LOGICAL array, dimension (NTYPES)
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*> The matrix types to be used for testing. Matrices of type j
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*> (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
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*> .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*> NN is INTEGER
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*> The number of values of N contained in the vector NVAL.
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*> \endverbatim
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*>
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*> \param[in] NVAL
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*> \verbatim
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*> NVAL is INTEGER array, dimension (NN)
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*> The values of the matrix dimension N.
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*> \endverbatim
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*>
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*> \param[in] NNB
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*> \verbatim
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*> NNB is INTEGER
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*> The number of values of NB contained in the vector NBVAL.
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*> \endverbatim
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*>
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*> \param[in] NBVAL
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*> \verbatim
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*> NBVAL is INTEGER array, dimension (NNB)
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*> The values of the blocksize NB.
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*> \endverbatim
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*>
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*> \param[in] NNS
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*> \verbatim
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*> NNS is INTEGER
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*> The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*> NSVAL is INTEGER array, dimension (NNS)
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*> The values of the number of right hand sides NRHS.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[in] TSTERR
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*> \verbatim
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*> TSTERR is LOGICAL
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*> Flag that indicates whether error exits are to be tested.
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*> \endverbatim
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*>
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*> \param[in] NMAX
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*> \verbatim
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*> NMAX is INTEGER
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*> The maximum value permitted for N, used in dimensioning the
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*> work arrays.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AFAC
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*> \verbatim
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*> AFAC is DOUBLE PRECISION array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AINV
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*> \verbatim
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*> AINV is DOUBLE PRECISION array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
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*> where NSMAX is the largest entry in NSVAL.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] XACT
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*> \verbatim
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*> XACT is DOUBLE PRECISION array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension
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*> (NMAX*max(3,NSMAX))
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension
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*> (max(NMAX,2*NSMAX))
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The unit number for output.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DCHKPO( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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$ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
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$ XACT, WORK, RWORK, IWORK, NOUT )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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LOGICAL TSTERR
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INTEGER NMAX, NN, NNB, NNS, NOUT
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DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
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DOUBLE PRECISION A( * ), AFAC( * ), AINV( * ), B( * ),
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$ RWORK( * ), WORK( * ), X( * ), XACT( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D+0 )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 9 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 8 )
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* ..
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* .. Local Scalars ..
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LOGICAL ZEROT
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CHARACTER DIST, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, IMAT, IN, INB, INFO, IOFF, IRHS, IUPLO,
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$ IZERO, K, KL, KU, LDA, MODE, N, NB, NERRS,
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$ NFAIL, NIMAT, NRHS, NRUN
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DOUBLE PRECISION ANORM, CNDNUM, RCOND, RCONDC
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* ..
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* .. Local Arrays ..
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CHARACTER UPLOS( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DGET06, DLANSY
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EXTERNAL DGET06, DLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, DERRPO, DGET04, DLACPY,
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$ DLARHS, DLATB4, DLATMS, DPOCON, DPORFS, DPOT01,
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$ DPOT02, DPOT03, DPOT05, DPOTRF, DPOTRI, DPOTRS,
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$ XLAENV
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* ..
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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, NUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, NUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Data statements ..
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DATA ISEEDY / 1988, 1989, 1990, 1991 /
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DATA UPLOS / 'U', 'L' /
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants and the random number seed.
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*
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PATH( 1: 1 ) = 'Double precision'
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PATH( 2: 3 ) = 'PO'
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NRUN = 0
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NFAIL = 0
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NERRS = 0
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DO 10 I = 1, 4
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ISEED( I ) = ISEEDY( I )
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10 CONTINUE
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*
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* Test the error exits
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*
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IF( TSTERR )
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$ CALL DERRPO( PATH, NOUT )
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INFOT = 0
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CALL XLAENV( 2, 2 )
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*
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* Do for each value of N in NVAL
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*
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DO 120 IN = 1, NN
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N = NVAL( IN )
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LDA = MAX( N, 1 )
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XTYPE = 'N'
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NIMAT = NTYPES
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IF( N.LE.0 )
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$ NIMAT = 1
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*
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IZERO = 0
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DO 110 IMAT = 1, NIMAT
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*
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* Do the tests only if DOTYPE( IMAT ) is true.
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*
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IF( .NOT.DOTYPE( IMAT ) )
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$ GO TO 110
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*
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* Skip types 3, 4, or 5 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
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IF( ZEROT .AND. N.LT.IMAT-2 )
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$ GO TO 110
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*
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* Do first for UPLO = 'U', then for UPLO = 'L'
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*
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DO 100 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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*
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* Set up parameters with DLATB4 and generate a test matrix
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* with DLATMS.
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*
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CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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*
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SRNAMT = 'DLATMS'
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CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA, WORK,
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$ INFO )
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*
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* Check error code from DLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'DLATMS', INFO, 0, UPLO, N, N, -1,
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$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 100
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END IF
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*
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* For types 3-5, zero one row and column of the matrix to
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* test that INFO is returned correctly.
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*
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IF( ZEROT ) THEN
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IF( IMAT.EQ.3 ) THEN
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IZERO = 1
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ELSE IF( IMAT.EQ.4 ) THEN
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IZERO = N
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ELSE
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IZERO = N / 2 + 1
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END IF
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IOFF = ( IZERO-1 )*LDA
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*
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* Set row and column IZERO of A to 0.
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*
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IF( IUPLO.EQ.1 ) THEN
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DO 20 I = 1, IZERO - 1
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A( IOFF+I ) = ZERO
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20 CONTINUE
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IOFF = IOFF + IZERO
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DO 30 I = IZERO, N
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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30 CONTINUE
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ELSE
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IOFF = IZERO
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DO 40 I = 1, IZERO - 1
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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40 CONTINUE
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IOFF = IOFF - IZERO
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DO 50 I = IZERO, N
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A( IOFF+I ) = ZERO
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50 CONTINUE
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END IF
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ELSE
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IZERO = 0
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END IF
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*
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* Do for each value of NB in NBVAL
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*
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DO 90 INB = 1, NNB
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NB = NBVAL( INB )
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CALL XLAENV( 1, NB )
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*
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* Compute the L*L' or U'*U factorization of the matrix.
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*
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CALL DLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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SRNAMT = 'DPOTRF'
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CALL DPOTRF( UPLO, N, AFAC, LDA, INFO )
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*
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* Check error code from DPOTRF.
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*
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IF( INFO.NE.IZERO ) THEN
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CALL ALAERH( PATH, 'DPOTRF', INFO, IZERO, UPLO, N,
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$ N, -1, -1, NB, IMAT, NFAIL, NERRS,
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$ NOUT )
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GO TO 90
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END IF
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*
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* Skip the tests if INFO is not 0.
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*
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IF( INFO.NE.0 )
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$ GO TO 90
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*
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*+ TEST 1
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* Reconstruct matrix from factors and compute residual.
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*
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CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
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CALL DPOT01( UPLO, N, A, LDA, AINV, LDA, RWORK,
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$ RESULT( 1 ) )
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*
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*+ TEST 2
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* Form the inverse and compute the residual.
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*
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CALL DLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
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SRNAMT = 'DPOTRI'
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CALL DPOTRI( UPLO, N, AINV, LDA, INFO )
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*
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* Check error code from DPOTRI.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DPOTRI', INFO, 0, UPLO, N, N,
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$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
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*
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CALL DPOT03( UPLO, N, A, LDA, AINV, LDA, WORK, LDA,
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$ RWORK, RCONDC, RESULT( 2 ) )
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*
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* Print information about the tests that did not pass
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* the threshold.
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*
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DO 60 K = 1, 2
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IF( RESULT( K ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALAHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
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$ RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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60 CONTINUE
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NRUN = NRUN + 2
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*
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* Skip the rest of the tests unless this is the first
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* blocksize.
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*
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IF( INB.NE.1 )
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$ GO TO 90
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*
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DO 80 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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*
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*+ TEST 3
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* Solve and compute residual for A * X = B .
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*
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SRNAMT = 'DLARHS'
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CALL DLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
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$ NRHS, A, LDA, XACT, LDA, B, LDA,
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$ ISEED, INFO )
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CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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*
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SRNAMT = 'DPOTRS'
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CALL DPOTRS( UPLO, N, NRHS, AFAC, LDA, X, LDA,
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$ INFO )
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*
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* Check error code from DPOTRS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DPOTRS', INFO, 0, UPLO, N,
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$ N, -1, -1, NRHS, IMAT, NFAIL,
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$ NERRS, NOUT )
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*
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CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
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CALL DPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
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$ LDA, RWORK, RESULT( 3 ) )
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*
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*+ TEST 4
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* Check solution from generated exact solution.
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*
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CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 4 ) )
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*
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*+ TESTS 5, 6, and 7
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* Use iterative refinement to improve the solution.
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*
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SRNAMT = 'DPORFS'
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CALL DPORFS( UPLO, N, NRHS, A, LDA, AFAC, LDA, B,
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$ LDA, X, LDA, RWORK, RWORK( NRHS+1 ),
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$ WORK, IWORK, INFO )
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*
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* Check error code from DPORFS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DPORFS', INFO, 0, UPLO, N,
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$ N, -1, -1, NRHS, IMAT, NFAIL,
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$ NERRS, NOUT )
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*
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CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 5 ) )
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CALL DPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
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$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
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$ RESULT( 6 ) )
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*
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* Print information about the tests that did not pass
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* the threshold.
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*
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DO 70 K = 3, 7
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IF( RESULT( K ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALAHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
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$ IMAT, K, RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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70 CONTINUE
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NRUN = NRUN + 5
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80 CONTINUE
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*
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*+ TEST 8
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* Get an estimate of RCOND = 1/CNDNUM.
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*
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ANORM = DLANSY( '1', UPLO, N, A, LDA, RWORK )
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SRNAMT = 'DPOCON'
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CALL DPOCON( UPLO, N, AFAC, LDA, ANORM, RCOND, WORK,
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$ IWORK, INFO )
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*
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* Check error code from DPOCON.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DPOCON', INFO, 0, UPLO, N, N,
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$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
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*
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RESULT( 8 ) = DGET06( RCOND, RCONDC )
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*
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* Print the test ratio if it is .GE. THRESH.
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*
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IF( RESULT( 8 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 8,
|
|
$ RESULT( 8 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
|
|
$ I2, ', test ', I2, ', ratio =', G12.5 )
|
|
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
|
|
$ I2, ', test(', I2, ') =', G12.5 )
|
|
9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
|
|
$ ', test(', I2, ') =', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of DCHKPO
|
|
*
|
|
END
|