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601 lines
20 KiB
601 lines
20 KiB
*> \brief \b ZCHKGE
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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 ZCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
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* NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
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* 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 NM, 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( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
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* $ NVAL( * )
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
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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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*> ZCHKGE tests ZGETRF, -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] NM
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*> \verbatim
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*> NM is INTEGER
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*> The number of values of M contained in the vector MVAL.
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*> \endverbatim
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*>
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*> \param[in] MVAL
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*> \verbatim
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*> MVAL is INTEGER array, dimension (NM)
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*> The values of the matrix row dimension M.
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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 maximum value permitted for M or N, used in dimensioning
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*> the 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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 COMPLEX*16 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(2*NMAX,2*NSMAX+NWORK))
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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 complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZCHKGE( DOTYPE, NM, MVAL, NN, NVAL, NNB, NBVAL, NNS,
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$ NSVAL, THRESH, TSTERR, NMAX, A, AFAC, AINV, B,
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$ 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 NM, 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( * ), MVAL( * ), NBVAL( * ), NSVAL( * ),
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$ NVAL( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
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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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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 = 11 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 8 )
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INTEGER NTRAN
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PARAMETER ( NTRAN = 3 )
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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, XTYPE
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CHARACTER*3 PATH
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INTEGER I, IM, IMAT, IN, INB, INFO, IOFF, IRHS, ITRAN,
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$ IZERO, K, KL, KU, LDA, LWORK, M, MODE, N, NB,
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$ NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
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DOUBLE PRECISION AINVNM, ANORM, ANORMI, ANORMO, CNDNUM, DUMMY,
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$ RCOND, RCONDC, RCONDI, RCONDO
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* ..
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* .. Local Arrays ..
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CHARACTER TRANSS( NTRAN )
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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, ZLANGE
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EXTERNAL DGET06, ZLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZERRGE, ZGECON,
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$ ZGERFS, ZGET01, ZGET02, ZGET03, ZGET04, ZGET07,
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$ ZGETRF, ZGETRI, ZGETRS, ZLACPY, ZLARHS, ZLASET,
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$ ZLATB4, ZLATMS
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DCMPLX, MAX, MIN
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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 / 1988, 1989, 1990, 1991 / ,
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$ 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 ) = 'Zomplex precision'
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PATH( 2: 3 ) = 'GE'
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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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CALL XLAENV( 1, 1 )
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IF( TSTERR )
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$ CALL ZERRGE( 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 M in MVAL
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*
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DO 120 IM = 1, NM
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M = MVAL( IM )
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LDA = MAX( 1, M )
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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 110 IN = 1, NN
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N = NVAL( IN )
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XTYPE = 'N'
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NIMAT = NTYPES
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IF( M.LE.0 .OR. 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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* Skip types 5, 6, or 7 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.5 .AND. IMAT.LE.7
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IF( ZEROT .AND. N.LT.IMAT-4 )
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$ GO TO 100
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*
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* Set up parameters with ZLATB4 and generate a test matrix
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* with ZLATMS.
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*
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CALL ZLATB4( PATH, IMAT, M, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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*
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SRNAMT = 'ZLATMS'
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CALL ZLATMS( M, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, 'No packing', A, LDA,
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$ WORK, INFO )
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*
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* Check error code from ZLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'ZLATMS', INFO, 0, ' ', M, 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 5-7, zero one or more columns 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.5 ) THEN
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IZERO = 1
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ELSE IF( IMAT.EQ.6 ) THEN
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IZERO = MIN( M, N )
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ELSE
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IZERO = MIN( M, N ) / 2 + 1
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END IF
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IOFF = ( IZERO-1 )*LDA
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IF( IMAT.LT.7 ) THEN
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DO 20 I = 1, M
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A( IOFF+I ) = ZERO
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20 CONTINUE
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ELSE
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CALL ZLASET( 'Full', M, N-IZERO+1, DCMPLX( ZERO ),
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$ DCMPLX( ZERO ), A( IOFF+1 ), LDA )
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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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* These lines, if used in place of the calls in the DO 60
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* loop, cause the code to bomb on a Sun SPARCstation.
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*
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* ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK )
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* ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK )
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*
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* Do for each blocksize 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 LU factorization of the matrix.
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*
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CALL ZLACPY( 'Full', M, N, A, LDA, AFAC, LDA )
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SRNAMT = 'ZGETRF'
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CALL ZGETRF( M, N, AFAC, LDA, IWORK, INFO )
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*
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* Check error code from ZGETRF.
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*
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IF( INFO.NE.IZERO )
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$ CALL ALAERH( PATH, 'ZGETRF', INFO, IZERO, ' ', M,
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$ N, -1, -1, NB, IMAT, NFAIL, NERRS,
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$ NOUT )
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TRFCON = .FALSE.
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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 ZLACPY( 'Full', M, N, AFAC, LDA, AINV, LDA )
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CALL ZGET01( M, N, A, LDA, AINV, LDA, IWORK, RWORK,
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$ RESULT( 1 ) )
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NT = 1
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*
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*+ TEST 2
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* Form the inverse if the factorization was successful
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* and compute the residual.
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*
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IF( M.EQ.N .AND. INFO.EQ.0 ) THEN
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CALL ZLACPY( 'Full', N, N, AFAC, LDA, AINV, LDA )
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SRNAMT = 'ZGETRI'
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NRHS = NSVAL( 1 )
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LWORK = NMAX*MAX( 3, NRHS )
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CALL ZGETRI( N, AINV, LDA, IWORK, WORK, LWORK,
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$ INFO )
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*
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* Check error code from ZGETRI.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'ZGETRI', INFO, 0, ' ', N, N,
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$ -1, -1, NB, IMAT, NFAIL, NERRS,
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$ NOUT )
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*
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* Compute the residual for the matrix times its
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* inverse. Also compute the 1-norm condition number
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* of A.
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*
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CALL ZGET03( N, A, LDA, AINV, LDA, WORK, LDA,
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$ RWORK, RCONDO, RESULT( 2 ) )
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ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK )
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*
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* Compute the infinity-norm condition number of A.
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*
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ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK )
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AINVNM = ZLANGE( 'I', N, N, AINV, LDA, RWORK )
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IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCONDI = ONE
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ELSE
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RCONDI = ( ONE / ANORMI ) / AINVNM
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END IF
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NT = 2
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ELSE
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*
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* Do only the condition estimate if INFO > 0.
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*
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TRFCON = .TRUE.
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ANORMO = ZLANGE( 'O', M, N, A, LDA, RWORK )
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ANORMI = ZLANGE( 'I', M, N, A, LDA, RWORK )
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RCONDO = ZERO
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RCONDI = ZERO
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END IF
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*
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* Print information about the tests so far that did not
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* pass the threshold.
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*
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DO 30 K = 1, NT
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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 )M, 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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30 CONTINUE
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NRUN = NRUN + NT
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*
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* Skip the remaining tests if this is not the first
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* block size or if M .ne. N. Skip the solve tests if
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* the matrix is singular.
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*
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IF( INB.GT.1 .OR. M.NE.N )
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$ GO TO 90
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IF( TRFCON )
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$ GO TO 70
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*
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DO 60 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 50 ITRAN = 1, NTRAN
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TRANS = TRANSS( ITRAN )
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IF( ITRAN.EQ.1 ) THEN
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RCONDC = RCONDO
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ELSE
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RCONDC = RCONDI
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END IF
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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 = 'ZLARHS'
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CALL ZLARHS( PATH, XTYPE, ' ', TRANS, N, N, KL,
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$ KU, NRHS, A, LDA, XACT, LDA, B,
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$ LDA, ISEED, INFO )
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XTYPE = 'C'
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*
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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SRNAMT = 'ZGETRS'
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CALL ZGETRS( TRANS, N, NRHS, AFAC, LDA, IWORK,
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$ X, LDA, INFO )
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*
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* Check error code from ZGETRS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'ZGETRS', INFO, 0, TRANS,
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$ N, N, -1, -1, NRHS, IMAT, NFAIL,
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$ NERRS, NOUT )
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*
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
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$ LDA )
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CALL ZGET02( TRANS, N, N, NRHS, A, LDA, X, LDA,
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$ WORK, 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 ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 4 ) )
|
|
*
|
|
*+ TESTS 5, 6, and 7
|
|
* Use iterative refinement to improve the
|
|
* solution.
|
|
*
|
|
SRNAMT = 'ZGERFS'
|
|
CALL ZGERFS( TRANS, N, NRHS, A, LDA, AFAC, LDA,
|
|
$ IWORK, B, LDA, X, LDA, RWORK,
|
|
$ RWORK( NRHS+1 ), WORK,
|
|
$ RWORK( 2*NRHS+1 ), INFO )
|
|
*
|
|
* Check error code from ZGERFS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZGERFS', INFO, 0, TRANS,
|
|
$ N, N, -1, -1, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
*
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 5 ) )
|
|
CALL ZGET07( TRANS, N, NRHS, A, LDA, B, LDA, X,
|
|
$ LDA, XACT, LDA, RWORK, .TRUE.,
|
|
$ RWORK( NRHS+1 ), RESULT( 6 ) )
|
|
*
|
|
* Print information about the tests that did not
|
|
* pass the threshold.
|
|
*
|
|
DO 40 K = 3, 7
|
|
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
|
|
40 CONTINUE
|
|
NRUN = NRUN + 5
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
*
|
|
*+ TEST 8
|
|
* Get an estimate of RCOND = 1/CNDNUM.
|
|
*
|
|
70 CONTINUE
|
|
DO 80 ITRAN = 1, 2
|
|
IF( ITRAN.EQ.1 ) THEN
|
|
ANORM = ANORMO
|
|
RCONDC = RCONDO
|
|
NORM = 'O'
|
|
ELSE
|
|
ANORM = ANORMI
|
|
RCONDC = RCONDI
|
|
NORM = 'I'
|
|
END IF
|
|
SRNAMT = 'ZGECON'
|
|
CALL ZGECON( NORM, N, AFAC, LDA, ANORM, RCOND,
|
|
$ WORK, RWORK, INFO )
|
|
*
|
|
* Check error code from ZGECON.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZGECON', INFO, 0, NORM, N,
|
|
$ N, -1, -1, -1, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
* This line is needed on a Sun SPARCstation.
|
|
*
|
|
DUMMY = RCOND
|
|
*
|
|
RESULT( 8 ) = DGET06( RCOND, RCONDC )
|
|
*
|
|
* 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 = 9997 )NORM, N, IMAT, 8,
|
|
$ RESULT( 8 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
*
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' M = ', I5, ', N =', I5, ', NB =', I4, ', 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 ZCHKGE
|
|
*
|
|
END
|
|
|