618 lines
21 KiB
Fortran
618 lines
21 KiB
Fortran
*> \brief \b DCHKTR
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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 DCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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* THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
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* 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( * ), AINV( * ), B( * ), RWORK( * ),
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* $ 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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*> DCHKTR tests DTRTRI, -TRS, -RFS, and -CON, and DLATRS(3)
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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 column 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 leading dimension of the work arrays.
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*> NMAX >= the maximum value of N in NVAL.
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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] 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 DCHKTR( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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$ THRESH, TSTERR, NMAX, A, AINV, B, X, XACT,
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$ 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( * ), AINV( * ), B( * ), RWORK( * ),
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$ 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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INTEGER NTYPE1, NTYPES
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PARAMETER ( NTYPE1 = 10, NTYPES = 18 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 10 )
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INTEGER NTRAN
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PARAMETER ( NTRAN = 3 )
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D0, ZERO = 0.0D0 )
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* ..
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* .. Local Scalars ..
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CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, IDIAG, IMAT, IN, INB, INFO, IRHS, ITRAN,
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$ IUPLO, K, LDA, N, NB, NERRS, NFAIL, NRHS, NRUN
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DOUBLE PRECISION AINVNM, ANORM, BIGNUM, DLAMCH, DUMMY, RCOND,
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$ RCONDC, RCONDI, RCONDO, RES, SCALE
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* ..
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* .. Local Arrays ..
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CHARACTER TRANSS( NTRAN ), UPLOS( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS ), SCALE3( 2 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLANTR
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EXTERNAL LSAME, DLANTR
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, DCOPY, DERRTR, DGET04,
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$ DLACPY, DLAMCH, DSCAL, DLARHS, DLATRS, DLATRS3,
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$ DLATTR, DTRCON, DTRRFS, DTRT01, DTRT02, DTRT03,
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$ DTRT05, DTRT06, DTRTRI, DTRTRS, 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, IOUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, IOUNIT, 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' / , TRANSS / 'N', 'T', 'C' /
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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 ) = 'TR'
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BIGNUM = DLAMCH('Overflow') / DLAMCH('Precision')
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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 DERRTR( 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 120 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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LDA = MAX( 1, N )
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XTYPE = 'N'
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*
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DO 80 IMAT = 1, NTYPE1
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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 80
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*
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DO 70 IUPLO = 1, 2
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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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UPLO = UPLOS( IUPLO )
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*
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* Call DLATTR to generate a triangular test matrix.
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*
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SRNAMT = 'DLATTR'
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CALL DLATTR( IMAT, UPLO, 'No transpose', DIAG, ISEED, N,
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$ A, LDA, X, WORK, INFO )
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*
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* Set IDIAG = 1 for non-unit matrices, 2 for unit.
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*
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IF( LSAME( DIAG, 'N' ) ) THEN
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IDIAG = 1
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ELSE
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IDIAG = 2
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END IF
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*
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DO 60 INB = 1, NNB
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*
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* Do for each blocksize in NBVAL
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*
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NB = NBVAL( INB )
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CALL XLAENV( 1, NB )
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*
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*+ TEST 1
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* Form the inverse of A.
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*
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CALL DLACPY( UPLO, N, N, A, LDA, AINV, LDA )
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SRNAMT = 'DTRTRI'
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CALL DTRTRI( UPLO, DIAG, N, AINV, LDA, INFO )
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*
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* Check error code from DTRTRI.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DTRTRI', INFO, 0, UPLO // DIAG,
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$ N, N, -1, -1, NB, IMAT, NFAIL, NERRS,
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$ NOUT )
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*
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* Compute the infinity-norm condition number of A.
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*
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ANORM = DLANTR( 'I', UPLO, DIAG, N, N, A, LDA, RWORK )
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AINVNM = DLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
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$ RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCONDI = ONE
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ELSE
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RCONDI = ( ONE / ANORM ) / AINVNM
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END IF
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*
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* Compute the residual for the triangular matrix times
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* its inverse. Also compute the 1-norm condition number
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* of A.
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*
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CALL DTRT01( UPLO, DIAG, N, A, LDA, AINV, LDA, RCONDO,
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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 )UPLO, DIAG, N, NB, IMAT,
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$ 1, RESULT( 1 )
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NFAIL = NFAIL + 1
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END IF
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NRUN = NRUN + 1
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*
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* Skip remaining tests if not the first block size.
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*
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IF( INB.NE.1 )
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$ GO TO 60
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*
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DO 40 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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XTYPE = 'N'
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*
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DO 30 ITRAN = 1, NTRAN
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*
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* Do for op(A) = A, A**T, or A**H.
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*
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TRANS = TRANSS( ITRAN )
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IF( ITRAN.EQ.1 ) THEN
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NORM = 'O'
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RCONDC = RCONDO
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ELSE
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NORM = 'I'
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RCONDC = RCONDI
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END IF
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*
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*+ TEST 2
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* Solve and compute residual for op(A)*x = b.
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*
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SRNAMT = 'DLARHS'
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CALL DLARHS( PATH, XTYPE, UPLO, TRANS, N, N, 0,
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$ IDIAG, NRHS, A, LDA, XACT, LDA, B,
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$ LDA, ISEED, INFO )
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XTYPE = 'C'
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CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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*
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SRNAMT = 'DTRTRS'
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CALL DTRTRS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
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$ X, LDA, INFO )
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*
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* Check error code from DTRTRS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DTRTRS', INFO, 0,
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$ UPLO // TRANS // DIAG, N, N, -1,
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$ -1, NRHS, IMAT, NFAIL, NERRS,
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$ NOUT )
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*
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* This line is needed on a Sun SPARCstation.
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*
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IF( N.GT.0 )
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$ DUMMY = A( 1 )
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*
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CALL DTRT02( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
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$ X, LDA, B, LDA, WORK, RESULT( 2 ) )
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*
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*+ TEST 3
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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( 3 ) )
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*
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*+ TESTS 4, 5, and 6
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* Use iterative refinement to improve the solution
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* and compute error bounds.
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*
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SRNAMT = 'DTRRFS'
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CALL DTRRFS( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
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$ B, LDA, X, LDA, RWORK,
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$ RWORK( NRHS+1 ), WORK, IWORK,
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$ INFO )
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*
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* Check error code from DTRRFS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DTRRFS', INFO, 0,
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$ UPLO // TRANS // DIAG, N, N, -1,
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$ -1, NRHS, IMAT, NFAIL, NERRS,
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$ NOUT )
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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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CALL DTRT05( UPLO, TRANS, DIAG, N, NRHS, A, LDA,
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$ B, LDA, X, LDA, XACT, LDA, RWORK,
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$ RWORK( NRHS+1 ), RESULT( 5 ) )
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*
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* Print information about the tests that did not
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* pass the threshold.
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*
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DO 20 K = 2, 6
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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, TRANS,
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$ DIAG, N, NRHS, IMAT, K, RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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20 CONTINUE
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NRUN = NRUN + 5
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30 CONTINUE
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40 CONTINUE
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*
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*+ TEST 7
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* Get an estimate of RCOND = 1/CNDNUM.
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*
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DO 50 ITRAN = 1, 2
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IF( ITRAN.EQ.1 ) THEN
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NORM = 'O'
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RCONDC = RCONDO
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ELSE
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NORM = 'I'
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RCONDC = RCONDI
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END IF
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SRNAMT = 'DTRCON'
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CALL DTRCON( NORM, UPLO, DIAG, N, A, LDA, RCOND,
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$ WORK, IWORK, INFO )
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*
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* Check error code from DTRCON.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'DTRCON', INFO, 0,
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$ NORM // UPLO // DIAG, N, N, -1, -1,
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$ -1, IMAT, NFAIL, NERRS, NOUT )
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*
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CALL DTRT06( RCOND, RCONDC, UPLO, DIAG, N, A, LDA,
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$ RWORK, RESULT( 7 ) )
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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( 7 ).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 = 9997 )NORM, UPLO, N, IMAT,
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$ 7, RESULT( 7 )
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NFAIL = NFAIL + 1
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END IF
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NRUN = NRUN + 1
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50 CONTINUE
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60 CONTINUE
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70 CONTINUE
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80 CONTINUE
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*
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* Use pathological test matrices to test DLATRS.
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*
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DO 110 IMAT = NTYPE1 + 1, NTYPES
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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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DO 100 IUPLO = 1, 2
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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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UPLO = UPLOS( IUPLO )
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DO 90 ITRAN = 1, NTRAN
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*
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* Do for op(A) = A, A**T, and A**H.
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*
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TRANS = TRANSS( ITRAN )
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*
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* Call DLATTR to generate a triangular test matrix.
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*
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SRNAMT = 'DLATTR'
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|
CALL DLATTR( IMAT, UPLO, TRANS, DIAG, ISEED, N, A,
|
|
$ LDA, X, WORK, INFO )
|
|
*
|
|
*+ TEST 8
|
|
* Solve the system op(A)*x = b.
|
|
*
|
|
SRNAMT = 'DLATRS'
|
|
CALL DCOPY( N, X, 1, B, 1 )
|
|
CALL DLATRS( UPLO, TRANS, DIAG, 'N', N, A, LDA, B,
|
|
$ SCALE, RWORK, INFO )
|
|
*
|
|
* Check error code from DLATRS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'DLATRS', INFO, 0,
|
|
$ UPLO // TRANS // DIAG // 'N', N, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
|
|
$ RWORK, ONE, B, LDA, X, LDA, WORK,
|
|
$ RESULT( 8 ) )
|
|
*
|
|
*+ TEST 9
|
|
* Solve op(A)*X = b again with NORMIN = 'Y'.
|
|
*
|
|
CALL DCOPY( N, X, 1, B( N+1 ), 1 )
|
|
CALL DLATRS( UPLO, TRANS, DIAG, 'Y', N, A, LDA,
|
|
$ B( N+1 ), SCALE, RWORK, INFO )
|
|
*
|
|
* Check error code from DLATRS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'DLATRS', INFO, 0,
|
|
$ UPLO // TRANS // DIAG // 'Y', N, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA, SCALE,
|
|
$ RWORK, ONE, B( N+1 ), LDA, X, LDA, WORK,
|
|
$ RESULT( 9 ) )
|
|
*
|
|
*+ TEST 10
|
|
* Solve op(A)*X = B
|
|
*
|
|
SRNAMT = 'DLATRS3'
|
|
CALL DCOPY( N, X, 1, B, 1 )
|
|
CALL DCOPY( N, X, 1, B( N+1 ), 1 )
|
|
CALL DSCAL( N, BIGNUM, B( N+1 ), 1 )
|
|
CALL DLATRS3( UPLO, TRANS, DIAG, 'N', N, 2, A, LDA,
|
|
$ B, MAX(1, N), SCALE3, RWORK, WORK, NMAX,
|
|
$ INFO )
|
|
*
|
|
* Check error code from DLATRS3.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'DLATRS3', INFO, 0,
|
|
$ UPLO // TRANS // DIAG // 'N', N, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA,
|
|
$ SCALE3( 1 ), RWORK, ONE, B( 1 ), LDA,
|
|
$ X, LDA, WORK, RESULT( 10 ) )
|
|
CALL DSCAL( N, BIGNUM, X, 1 )
|
|
CALL DTRT03( UPLO, TRANS, DIAG, N, 1, A, LDA,
|
|
$ SCALE3( 2 ), RWORK, ONE, B( N+1 ), LDA,
|
|
$ X, LDA, WORK, RES )
|
|
RESULT( 10 ) = MAX( RESULT( 10 ), RES )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
IF( RESULT( 8 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9996 )'DLATRS', UPLO, TRANS,
|
|
$ DIAG, 'N', N, IMAT, 8, RESULT( 8 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
IF( RESULT( 9 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9996 )'DLATRS', UPLO, TRANS,
|
|
$ DIAG, 'Y', N, IMAT, 9, RESULT( 9 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
IF( RESULT( 10 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9996 )'DLATRS3', UPLO, TRANS,
|
|
$ DIAG, 'N', N, IMAT, 10, RESULT( 10 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 3
|
|
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, ''', DIAG=''', A1, ''', N=', I5, ', NB=',
|
|
$ I4, ', type ', I2, ', test(', I2, ')= ', G12.5 )
|
|
9998 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''', DIAG=''', A1,
|
|
$ ''', N=', I5, ', NB=', I4, ', type ', I2, ', test(',
|
|
$ I2, ')= ', G12.5 )
|
|
9997 FORMAT( ' NORM=''', A1, ''', UPLO =''', A1, ''', N=', I5, ',',
|
|
$ 11X, ' type ', I2, ', test(', I2, ')=', G12.5 )
|
|
9996 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
|
|
$ A1, ''',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
|
|
$ G12.5 )
|
|
RETURN
|
|
*
|
|
* End of DCHKTR
|
|
*
|
|
END
|