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554 lines
17 KiB
554 lines
17 KiB
2 years ago
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*> \brief \b DCHKGT
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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 DCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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* A, AF, B, X, 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 NN, 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( * ), NSVAL( * ), NVAL( * )
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* DOUBLE PRECISION A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
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* $ 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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*> DCHKGT tests DGTTRF, -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] 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[out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (NMAX*4)
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*> \endverbatim
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*>
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*> \param[out] AF
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*> \verbatim
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*> AF is DOUBLE PRECISION array, dimension (NMAX*4)
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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 (2*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 DCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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$ A, AF, B, X, 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 NN, 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( * ), NSVAL( * ), NVAL( * )
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DOUBLE PRECISION A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
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$ 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 ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 12 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 7 )
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* ..
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* .. Local Scalars ..
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LOGICAL TRFCON, ZEROT
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CHARACTER DIST, NORM, TRANS, TYPE
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CHARACTER*3 PATH
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INTEGER I, IMAT, IN, INFO, IRHS, ITRAN, IX, IZERO, J,
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$ K, KL, KOFF, KU, LDA, M, MODE, N, NERRS, NFAIL,
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$ NIMAT, NRHS, NRUN
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DOUBLE PRECISION AINVNM, ANORM, COND, RCOND, RCONDC, RCONDI,
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$ RCONDO
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* ..
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* .. Local Arrays ..
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CHARACTER TRANSS( 3 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS ), Z( 3 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DASUM, DGET06, DLANGT
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EXTERNAL DASUM, DGET06, DLANGT
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, DCOPY, DERRGE, DGET04,
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$ DGTCON, DGTRFS, DGTT01, DGTT02, DGTT05, DGTTRF,
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$ DGTTRS, DLACPY, DLAGTM, DLARNV, DLATB4, DLATMS,
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$ DSCAL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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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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* .. Data statements ..
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DATA ISEEDY / 0, 0, 0, 1 / , TRANSS / 'N', 'T',
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$ 'C' /
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* ..
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* .. Executable Statements ..
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*
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PATH( 1: 1 ) = 'Double precision'
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PATH( 2: 3 ) = 'GT'
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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 DERRGE( PATH, NOUT )
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INFOT = 0
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*
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DO 110 IN = 1, NN
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*
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* Do for each value of N in NVAL.
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*
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N = NVAL( IN )
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M = MAX( N-1, 0 )
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LDA = MAX( 1, 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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DO 100 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 100
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*
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* Set up parameters with DLATB4.
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*
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CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ COND, DIST )
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*
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ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
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IF( IMAT.LE.6 ) THEN
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*
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* Types 1-6: generate matrices of known condition number.
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*
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KOFF = MAX( 2-KU, 3-MAX( 1, N ) )
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SRNAMT = 'DLATMS'
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CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
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$ ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK,
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$ INFO )
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*
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* Check the 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, ' ', N, N, KL,
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$ KU, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 100
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END IF
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IZERO = 0
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*
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IF( N.GT.1 ) THEN
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CALL DCOPY( N-1, AF( 4 ), 3, A, 1 )
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CALL DCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 )
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END IF
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CALL DCOPY( N, AF( 2 ), 3, A( M+1 ), 1 )
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ELSE
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*
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* Types 7-12: generate tridiagonal matrices with
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* unknown condition numbers.
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*
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IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
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*
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* Generate a matrix with elements from [-1,1].
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*
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CALL DLARNV( 2, ISEED, N+2*M, A )
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IF( ANORM.NE.ONE )
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$ CALL DSCAL( N+2*M, ANORM, A, 1 )
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ELSE IF( IZERO.GT.0 ) THEN
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*
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* Reuse the last matrix by copying back the zeroed out
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* elements.
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*
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IF( IZERO.EQ.1 ) THEN
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A( N ) = Z( 2 )
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IF( N.GT.1 )
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$ A( 1 ) = Z( 3 )
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ELSE IF( IZERO.EQ.N ) THEN
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A( 3*N-2 ) = Z( 1 )
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A( 2*N-1 ) = Z( 2 )
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ELSE
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A( 2*N-2+IZERO ) = Z( 1 )
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A( N-1+IZERO ) = Z( 2 )
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A( IZERO ) = Z( 3 )
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END IF
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END IF
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*
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* If IMAT > 7, set one column of the matrix to 0.
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*
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IF( .NOT.ZEROT ) THEN
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IZERO = 0
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ELSE IF( IMAT.EQ.8 ) THEN
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IZERO = 1
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Z( 2 ) = A( N )
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A( N ) = ZERO
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IF( N.GT.1 ) THEN
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Z( 3 ) = A( 1 )
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A( 1 ) = ZERO
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END IF
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ELSE IF( IMAT.EQ.9 ) THEN
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IZERO = N
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Z( 1 ) = A( 3*N-2 )
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Z( 2 ) = A( 2*N-1 )
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A( 3*N-2 ) = ZERO
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A( 2*N-1 ) = ZERO
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ELSE
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IZERO = ( N+1 ) / 2
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DO 20 I = IZERO, N - 1
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A( 2*N-2+I ) = ZERO
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A( N-1+I ) = ZERO
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A( I ) = ZERO
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20 CONTINUE
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A( 3*N-2 ) = ZERO
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A( 2*N-1 ) = ZERO
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END IF
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END IF
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*
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*+ TEST 1
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* Factor A as L*U and compute the ratio
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* norm(L*U - A) / (n * norm(A) * EPS )
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*
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CALL DCOPY( N+2*M, A, 1, AF, 1 )
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SRNAMT = 'DGTTRF'
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CALL DGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ),
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$ IWORK, INFO )
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*
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* Check error code from DGTTRF.
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*
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IF( INFO.NE.IZERO )
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$ CALL ALAERH( PATH, 'DGTTRF', INFO, IZERO, ' ', N, N, 1,
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$ 1, -1, IMAT, NFAIL, NERRS, NOUT )
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TRFCON = INFO.NE.0
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*
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CALL DGTT01( N, A, A( M+1 ), A( N+M+1 ), AF, AF( M+1 ),
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$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, WORK, LDA,
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$ RWORK, RESULT( 1 ) )
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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( 1 ).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 )N, IMAT, 1, RESULT( 1 )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
NRUN = NRUN + 1
|
||
|
|
*
|
||
|
|
DO 50 ITRAN = 1, 2
|
||
|
|
TRANS = TRANSS( ITRAN )
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
NORM = 'O'
|
||
|
|
ELSE
|
||
|
|
NORM = 'I'
|
||
|
|
END IF
|
||
|
|
ANORM = DLANGT( NORM, N, A, A( M+1 ), A( N+M+1 ) )
|
||
|
|
*
|
||
|
|
IF( .NOT.TRFCON ) THEN
|
||
|
|
*
|
||
|
|
* Use DGTTRS to solve for one column at a time of inv(A)
|
||
|
|
* or inv(A^T), computing the maximum column sum as we
|
||
|
|
* go.
|
||
|
|
*
|
||
|
|
AINVNM = ZERO
|
||
|
|
DO 40 I = 1, N
|
||
|
|
DO 30 J = 1, N
|
||
|
|
X( J ) = ZERO
|
||
|
|
30 CONTINUE
|
||
|
|
X( I ) = ONE
|
||
|
|
CALL DGTTRS( TRANS, N, 1, AF, AF( M+1 ),
|
||
|
|
$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
|
||
|
|
$ LDA, INFO )
|
||
|
|
AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
|
||
|
|
40 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute RCONDC = 1 / (norm(A) * norm(inv(A))
|
||
|
|
*
|
||
|
|
IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
|
||
|
|
RCONDC = ONE
|
||
|
|
ELSE
|
||
|
|
RCONDC = ( ONE / ANORM ) / AINVNM
|
||
|
|
END IF
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
RCONDO = RCONDC
|
||
|
|
ELSE
|
||
|
|
RCONDI = RCONDC
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
RCONDC = ZERO
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
*+ TEST 7
|
||
|
|
* Estimate the reciprocal of the condition number of the
|
||
|
|
* matrix.
|
||
|
|
*
|
||
|
|
SRNAMT = 'DGTCON'
|
||
|
|
CALL DGTCON( NORM, N, AF, AF( M+1 ), AF( N+M+1 ),
|
||
|
|
$ AF( N+2*M+1 ), IWORK, ANORM, RCOND, WORK,
|
||
|
|
$ IWORK( N+1 ), INFO )
|
||
|
|
*
|
||
|
|
* Check error code from DGTCON.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGTCON', INFO, 0, NORM, N, N, -1,
|
||
|
|
$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
RESULT( 7 ) = DGET06( RCOND, RCONDC )
|
||
|
|
*
|
||
|
|
* Print the test ratio if it is .GE. THRESH.
|
||
|
|
*
|
||
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 7,
|
||
|
|
$ RESULT( 7 )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
NRUN = NRUN + 1
|
||
|
|
50 CONTINUE
|
||
|
|
*
|
||
|
|
* Skip the remaining tests if the matrix is singular.
|
||
|
|
*
|
||
|
|
IF( TRFCON )
|
||
|
|
$ GO TO 100
|
||
|
|
*
|
||
|
|
DO 90 IRHS = 1, NNS
|
||
|
|
NRHS = NSVAL( IRHS )
|
||
|
|
*
|
||
|
|
* Generate NRHS random solution vectors.
|
||
|
|
*
|
||
|
|
IX = 1
|
||
|
|
DO 60 J = 1, NRHS
|
||
|
|
CALL DLARNV( 2, ISEED, N, XACT( IX ) )
|
||
|
|
IX = IX + LDA
|
||
|
|
60 CONTINUE
|
||
|
|
*
|
||
|
|
DO 80 ITRAN = 1, 3
|
||
|
|
TRANS = TRANSS( ITRAN )
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
RCONDC = RCONDO
|
||
|
|
ELSE
|
||
|
|
RCONDC = RCONDI
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Set the right hand side.
|
||
|
|
*
|
||
|
|
CALL DLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ),
|
||
|
|
$ A( N+M+1 ), XACT, LDA, ZERO, B, LDA )
|
||
|
|
*
|
||
|
|
*+ TEST 2
|
||
|
|
* Solve op(A) * X = B and compute the residual.
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
||
|
|
SRNAMT = 'DGTTRS'
|
||
|
|
CALL DGTTRS( TRANS, N, NRHS, AF, AF( M+1 ),
|
||
|
|
$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
|
||
|
|
$ LDA, INFO )
|
||
|
|
*
|
||
|
|
* Check error code from DGTTRS.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGTTRS', INFO, 0, TRANS, N, N,
|
||
|
|
$ -1, -1, NRHS, IMAT, NFAIL, NERRS,
|
||
|
|
$ NOUT )
|
||
|
|
*
|
||
|
|
CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
||
|
|
CALL DGTT02( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
|
||
|
|
$ X, LDA, WORK, LDA, RESULT( 2 ) )
|
||
|
|
*
|
||
|
|
*+ TEST 3
|
||
|
|
* Check solution from generated exact solution.
|
||
|
|
*
|
||
|
|
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
||
|
|
$ RESULT( 3 ) )
|
||
|
|
*
|
||
|
|
*+ TESTS 4, 5, and 6
|
||
|
|
* Use iterative refinement to improve the solution.
|
||
|
|
*
|
||
|
|
SRNAMT = 'DGTRFS'
|
||
|
|
CALL DGTRFS( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
|
||
|
|
$ AF, AF( M+1 ), AF( N+M+1 ),
|
||
|
|
$ AF( N+2*M+1 ), IWORK, B, LDA, X, LDA,
|
||
|
|
$ RWORK, RWORK( NRHS+1 ), WORK,
|
||
|
|
$ IWORK( N+1 ), INFO )
|
||
|
|
*
|
||
|
|
* Check error code from DGTRFS.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'DGTRFS', INFO, 0, TRANS, N, N,
|
||
|
|
$ -1, -1, NRHS, IMAT, NFAIL, NERRS,
|
||
|
|
$ NOUT )
|
||
|
|
*
|
||
|
|
CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
||
|
|
$ RESULT( 4 ) )
|
||
|
|
CALL DGTT05( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
|
||
|
|
$ B, LDA, X, LDA, XACT, LDA, RWORK,
|
||
|
|
$ RWORK( NRHS+1 ), RESULT( 5 ) )
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 70 K = 2, 6
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS, IMAT,
|
||
|
|
$ K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
70 CONTINUE
|
||
|
|
NRUN = NRUN + 5
|
||
|
|
80 CONTINUE
|
||
|
|
90 CONTINUE
|
||
|
|
*
|
||
|
|
100 CONTINUE
|
||
|
|
110 CONTINUE
|
||
|
|
*
|
||
|
|
* Print a summary of the results.
|
||
|
|
*
|
||
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
||
|
|
*
|
||
|
|
9999 FORMAT( 12X, 'N =', I5, ',', 10X, ' type ', I2, ', test(', I2,
|
||
|
|
$ ') = ', G12.5 )
|
||
|
|
9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
|
||
|
|
$ I2, ', test(', I2, ') = ', G12.5 )
|
||
|
|
9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
|
||
|
|
$ ', test(', I2, ') = ', G12.5 )
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of DCHKGT
|
||
|
|
*
|
||
|
|
END
|