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593 lines
19 KiB
593 lines
19 KiB
2 years ago
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*> \brief \b CDRVGT
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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 CDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
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* 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, NOUT, NRHS
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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER IWORK( * ), NVAL( * )
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* REAL RWORK( * )
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* COMPLEX A( * ), AF( * ), B( * ), WORK( * ), X( * ),
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* $ 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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*> CDRVGT tests CGTSV and -SVX.
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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] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand sides, NRHS >= 0.
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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 REAL
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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 COMPLEX 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 COMPLEX 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 COMPLEX array, dimension (NMAX*NRHS)
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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 array, dimension (NMAX*NRHS)
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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 array, dimension (NMAX*NRHS)
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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 array, dimension
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*> (NMAX*max(3,NRHS))
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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 REAL array, dimension (NMAX+2*NRHS)
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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 complex_lin
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*
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* =====================================================================
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SUBROUTINE CDRVGT( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, AF,
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$ 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, NOUT, NRHS
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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER IWORK( * ), NVAL( * )
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REAL RWORK( * )
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COMPLEX A( * ), AF( * ), B( * ), WORK( * ), X( * ),
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$ 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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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+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 = 6 )
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* ..
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* .. Local Scalars ..
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LOGICAL TRFCON, ZEROT
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CHARACTER DIST, FACT, TRANS, TYPE
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CHARACTER*3 PATH
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INTEGER I, IFACT, IMAT, IN, INFO, ITRAN, IX, IZERO, J,
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$ K, K1, KL, KOFF, KU, LDA, M, MODE, N, NERRS,
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$ NFAIL, NIMAT, NRUN, NT
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REAL AINVNM, ANORM, ANORMI, ANORMO, COND, RCOND,
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$ RCONDC, RCONDI, 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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REAL RESULT( NTESTS ), Z( 3 )
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* ..
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* .. External Functions ..
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REAL CLANGT, SCASUM, SGET06
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EXTERNAL CLANGT, SCASUM, SGET06
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, CCOPY, CERRVX, CGET04,
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$ CGTSV, CGTSVX, CGTT01, CGTT02, CGTT05, CGTTRF,
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$ CGTTRS, CLACPY, CLAGTM, CLARNV, CLASET, CLATB4,
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$ CLATMS, CSSCAL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX, 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 ) = 'Complex 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 CERRVX( PATH, NOUT )
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INFOT = 0
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*
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DO 140 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 130 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 130
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*
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* Set up parameters with CLATB4.
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*
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CALL CLATB4( 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 = 'CLATMS'
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CALL CLATMS( 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 CLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'CLATMS', INFO, 0, ' ', N, N, KL,
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$ KU, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 130
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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 CCOPY( N-1, AF( 4 ), 3, A, 1 )
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CALL CCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 )
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END IF
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CALL CCOPY( 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 CLARNV( 2, ISEED, N+2*M, A )
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IF( ANORM.NE.ONE )
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$ CALL CSSCAL( 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 ) = REAL( A( N ) )
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A( N ) = ZERO
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IF( N.GT.1 ) THEN
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Z( 3 ) = REAL( 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 ) = REAL( A( 3*N-2 ) )
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Z( 2 ) = REAL( 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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DO 120 IFACT = 1, 2
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IF( IFACT.EQ.1 ) THEN
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FACT = 'F'
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ELSE
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FACT = 'N'
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END IF
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*
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* Compute the condition number for comparison with
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* the value returned by CGTSVX.
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*
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IF( ZEROT ) THEN
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IF( IFACT.EQ.1 )
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$ GO TO 120
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RCONDO = ZERO
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RCONDI = ZERO
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*
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ELSE IF( IFACT.EQ.1 ) THEN
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CALL CCOPY( N+2*M, A, 1, AF, 1 )
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*
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* Compute the 1-norm and infinity-norm of A.
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*
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ANORMO = CLANGT( '1', N, A, A( M+1 ), A( N+M+1 ) )
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ANORMI = CLANGT( 'I', N, A, A( M+1 ), A( N+M+1 ) )
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*
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* Factor the matrix A.
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*
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CALL CGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ),
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$ AF( N+2*M+1 ), IWORK, INFO )
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*
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* Use CGTTRS to solve for one column at a time of
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* inv(A), computing the maximum column sum as we go.
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*
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AINVNM = ZERO
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DO 40 I = 1, N
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DO 30 J = 1, N
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X( J ) = ZERO
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30 CONTINUE
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X( I ) = ONE
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CALL CGTTRS( 'No transpose', N, 1, AF, AF( M+1 ),
|
||
|
|
$ AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
|
||
|
|
$ LDA, INFO )
|
||
|
|
AINVNM = MAX( AINVNM, SCASUM( N, X, 1 ) )
|
||
|
|
40 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute the 1-norm condition number of A.
|
||
|
|
*
|
||
|
|
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
|
||
|
|
RCONDO = ONE
|
||
|
|
ELSE
|
||
|
|
RCONDO = ( ONE / ANORMO ) / AINVNM
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Use CGTTRS to solve for one column at a time of
|
||
|
|
* inv(A'), computing the maximum column sum as we go.
|
||
|
|
*
|
||
|
|
AINVNM = ZERO
|
||
|
|
DO 60 I = 1, N
|
||
|
|
DO 50 J = 1, N
|
||
|
|
X( J ) = ZERO
|
||
|
|
50 CONTINUE
|
||
|
|
X( I ) = ONE
|
||
|
|
CALL CGTTRS( 'Conjugate transpose', N, 1, AF,
|
||
|
|
$ AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ),
|
||
|
|
$ IWORK, X, LDA, INFO )
|
||
|
|
AINVNM = MAX( AINVNM, SCASUM( N, X, 1 ) )
|
||
|
|
60 CONTINUE
|
||
|
|
*
|
||
|
|
* Compute the infinity-norm condition number of A.
|
||
|
|
*
|
||
|
|
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
|
||
|
|
RCONDI = ONE
|
||
|
|
ELSE
|
||
|
|
RCONDI = ( ONE / ANORMI ) / AINVNM
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
DO 110 ITRAN = 1, 3
|
||
|
|
TRANS = TRANSS( ITRAN )
|
||
|
|
IF( ITRAN.EQ.1 ) THEN
|
||
|
|
RCONDC = RCONDO
|
||
|
|
ELSE
|
||
|
|
RCONDC = RCONDI
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Generate NRHS random solution vectors.
|
||
|
|
*
|
||
|
|
IX = 1
|
||
|
|
DO 70 J = 1, NRHS
|
||
|
|
CALL CLARNV( 2, ISEED, N, XACT( IX ) )
|
||
|
|
IX = IX + LDA
|
||
|
|
70 CONTINUE
|
||
|
|
*
|
||
|
|
* Set the right hand side.
|
||
|
|
*
|
||
|
|
CALL CLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ),
|
||
|
|
$ A( N+M+1 ), XACT, LDA, ZERO, B, LDA )
|
||
|
|
*
|
||
|
|
IF( IFACT.EQ.2 .AND. ITRAN.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* --- Test CGTSV ---
|
||
|
|
*
|
||
|
|
* Solve the system using Gaussian elimination with
|
||
|
|
* partial pivoting.
|
||
|
|
*
|
||
|
|
CALL CCOPY( N+2*M, A, 1, AF, 1 )
|
||
|
|
CALL CLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
||
|
|
*
|
||
|
|
SRNAMT = 'CGTSV '
|
||
|
|
CALL CGTSV( N, NRHS, AF, AF( M+1 ), AF( N+M+1 ), X,
|
||
|
|
$ LDA, INFO )
|
||
|
|
*
|
||
|
|
* Check error code from CGTSV .
|
||
|
|
*
|
||
|
|
IF( INFO.NE.IZERO )
|
||
|
|
$ CALL ALAERH( PATH, 'CGTSV ', INFO, IZERO, ' ',
|
||
|
|
$ N, N, 1, 1, NRHS, IMAT, NFAIL,
|
||
|
|
$ NERRS, NOUT )
|
||
|
|
NT = 1
|
||
|
|
IF( IZERO.EQ.0 ) THEN
|
||
|
|
*
|
||
|
|
* Check residual of computed solution.
|
||
|
|
*
|
||
|
|
CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK,
|
||
|
|
$ LDA )
|
||
|
|
CALL CGTT02( TRANS, N, NRHS, A, A( M+1 ),
|
||
|
|
$ A( N+M+1 ), X, LDA, WORK, LDA,
|
||
|
|
$ RESULT( 2 ) )
|
||
|
|
*
|
||
|
|
* Check solution from generated exact solution.
|
||
|
|
*
|
||
|
|
CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
||
|
|
$ RESULT( 3 ) )
|
||
|
|
NT = 3
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 80 K = 2, NT
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALADHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9999 )'CGTSV ', N, IMAT,
|
||
|
|
$ K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
80 CONTINUE
|
||
|
|
NRUN = NRUN + NT - 1
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* --- Test CGTSVX ---
|
||
|
|
*
|
||
|
|
IF( IFACT.GT.1 ) THEN
|
||
|
|
*
|
||
|
|
* Initialize AF to zero.
|
||
|
|
*
|
||
|
|
DO 90 I = 1, 3*N - 2
|
||
|
|
AF( I ) = ZERO
|
||
|
|
90 CONTINUE
|
||
|
|
END IF
|
||
|
|
CALL CLASET( 'Full', N, NRHS, CMPLX( ZERO ),
|
||
|
|
$ CMPLX( ZERO ), X, LDA )
|
||
|
|
*
|
||
|
|
* Solve the system and compute the condition number and
|
||
|
|
* error bounds using CGTSVX.
|
||
|
|
*
|
||
|
|
SRNAMT = 'CGTSVX'
|
||
|
|
CALL CGTSVX( FACT, 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,
|
||
|
|
$ RCOND, RWORK, RWORK( NRHS+1 ), WORK,
|
||
|
|
$ RWORK( 2*NRHS+1 ), INFO )
|
||
|
|
*
|
||
|
|
* Check the error code from CGTSVX.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.IZERO )
|
||
|
|
$ CALL ALAERH( PATH, 'CGTSVX', INFO, IZERO,
|
||
|
|
$ FACT // TRANS, N, N, 1, 1, NRHS, IMAT,
|
||
|
|
$ NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
IF( IFACT.GE.2 ) THEN
|
||
|
|
*
|
||
|
|
* Reconstruct matrix from factors and compute
|
||
|
|
* residual.
|
||
|
|
*
|
||
|
|
CALL CGTT01( N, A, A( M+1 ), A( N+M+1 ), AF,
|
||
|
|
$ AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ),
|
||
|
|
$ IWORK, WORK, LDA, RWORK, RESULT( 1 ) )
|
||
|
|
K1 = 1
|
||
|
|
ELSE
|
||
|
|
K1 = 2
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
IF( INFO.EQ.0 ) THEN
|
||
|
|
TRFCON = .FALSE.
|
||
|
|
*
|
||
|
|
* Check residual of computed solution.
|
||
|
|
*
|
||
|
|
CALL CLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
||
|
|
CALL CGTT02( TRANS, N, NRHS, A, A( M+1 ),
|
||
|
|
$ A( N+M+1 ), X, LDA, WORK, LDA,
|
||
|
|
$ RESULT( 2 ) )
|
||
|
|
*
|
||
|
|
* Check solution from generated exact solution.
|
||
|
|
*
|
||
|
|
CALL CGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
||
|
|
$ RESULT( 3 ) )
|
||
|
|
*
|
||
|
|
* Check the error bounds from iterative refinement.
|
||
|
|
*
|
||
|
|
CALL CGTT05( TRANS, N, NRHS, A, A( M+1 ),
|
||
|
|
$ A( N+M+1 ), B, LDA, X, LDA, XACT, LDA,
|
||
|
|
$ RWORK, RWORK( NRHS+1 ), RESULT( 4 ) )
|
||
|
|
NT = 5
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 100 K = K1, NT
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALADHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9998 )'CGTSVX', FACT, TRANS,
|
||
|
|
$ N, IMAT, K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
100 CONTINUE
|
||
|
|
*
|
||
|
|
* Check the reciprocal of the condition number.
|
||
|
|
*
|
||
|
|
RESULT( 6 ) = SGET06( RCOND, RCONDC )
|
||
|
|
IF( RESULT( 6 ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALADHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9998 )'CGTSVX', FACT, TRANS, N,
|
||
|
|
$ IMAT, K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
NRUN = NRUN + NT - K1 + 2
|
||
|
|
*
|
||
|
|
110 CONTINUE
|
||
|
|
120 CONTINUE
|
||
|
|
130 CONTINUE
|
||
|
|
140 CONTINUE
|
||
|
|
*
|
||
|
|
* Print a summary of the results.
|
||
|
|
*
|
||
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
||
|
|
*
|
||
|
|
9999 FORMAT( 1X, A, ', N =', I5, ', type ', I2, ', test ', I2,
|
||
|
|
$ ', ratio = ', G12.5 )
|
||
|
|
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', TRANS=''', A1, ''', N =',
|
||
|
|
$ I5, ', type ', I2, ', test ', I2, ', ratio = ', G12.5 )
|
||
|
|
RETURN
|
||
|
|
*
|
||
|
|
* End of CDRVGT
|
||
|
|
*
|
||
|
|
END
|