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539 lines
16 KiB
539 lines
16 KiB
*> \brief \b ZDRVSY_RK
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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 ZDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
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* NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
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* 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, NOUT, NRHS
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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( * ), NVAL( * )
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), E( *),
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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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*> ZDRVSY_RK tests the driver routines ZSYSV_RK.
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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 side vectors to be generated for
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*> each linear system.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[in] TSTERR
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*> \verbatim
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*> TSTERR is LOGICAL
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*> Flag that indicates whether error exits are to be tested.
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*> \endverbatim
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*>
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*> \param[in] NMAX
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*> \verbatim
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*> NMAX is INTEGER
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*> The maximum value permitted for N, used in dimensioning the
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*> work arrays.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is 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] E
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*> \verbatim
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*> E is COMPLEX*16 array, dimension (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*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*16 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*16 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*16 array, dimension (NMAX*max(2,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 DOUBLE PRECISION 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 (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 ZDRVSY_RK( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR,
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$ NMAX, A, AFAC, E, AINV, B, X, XACT, WORK,
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$ 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, NOUT, NRHS
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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( * ), NVAL( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ), E( * ),
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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, NTESTS
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PARAMETER ( NTYPES = 11, NTESTS = 3 )
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INTEGER NFACT
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PARAMETER ( NFACT = 2 )
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* ..
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* .. Local Scalars ..
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LOGICAL ZEROT
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CHARACTER DIST, FACT, TYPE, UPLO, XTYPE
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CHARACTER*3 MATPATH, PATH
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INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
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$ IZERO, J, K, KL, KU, LDA, LWORK, MODE, N,
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$ NB, NBMIN, NERRS, NFAIL, NIMAT, NRUN, NT
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DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCONDC
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* ..
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* .. Local Arrays ..
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CHARACTER FACTS( NFACT ), UPLOS( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION ZLANSY
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EXTERNAL ZLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZERRVX, ZGET04,
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$ ZLACPY, ZLARHS, ZLATB4, ZLATMS, ZLATSY,
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$ ZSYSV_RK, ZSYT01_3, ZSYT02, ZSYTRF_RK, ZSYTRI_3
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* ..
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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, NUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, NUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN
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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' / , FACTS / 'F', 'N' /
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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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* Test path
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*
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PATH( 1: 1 ) = 'Zomplex precision'
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PATH( 2: 3 ) = 'SK'
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*
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* Path to generate matrices
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*
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MATPATH( 1: 1 ) = 'Zomplex precision'
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MATPATH( 2: 3 ) = 'SY'
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*
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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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LWORK = MAX( 2*NMAX, NMAX*NRHS )
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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 ZERRVX( PATH, NOUT )
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INFOT = 0
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*
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* Set the block size and minimum block size for which the block
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* routine should be used, which will be later returned by ILAENV.
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*
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NB = 1
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NBMIN = 2
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CALL XLAENV( 1, NB )
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CALL XLAENV( 2, NBMIN )
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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 180 IN = 1, NN
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N = NVAL( IN )
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LDA = MAX( N, 1 )
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XTYPE = 'N'
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NIMAT = NTYPES
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IF( N.LE.0 )
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$ NIMAT = 1
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*
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DO 170 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 170
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*
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* Skip types 3, 4, 5, or 6 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
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IF( ZEROT .AND. N.LT.IMAT-2 )
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$ GO TO 170
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*
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* Do first for UPLO = 'U', then for UPLO = 'L'
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*
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DO 160 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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*
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IF( IMAT.NE.NTYPES ) THEN
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*
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* Begin generate the test matrix A.
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*
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* Set up parameters with ZLATB4 for the matrix generator
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* based on the type of matrix to be generated.
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*
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CALL ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
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$ MODE, CNDNUM, DIST )
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*
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* Generate a matrix with ZLATMS.
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*
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SRNAMT = 'ZLATMS'
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CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
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$ WORK, INFO )
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*
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* Check error code from DLATMS and handle error.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
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$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 160
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END IF
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*
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* For types 3-6, zero one or more rows and columns of
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* the matrix to test that INFO is returned correctly.
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*
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IF( ZEROT ) THEN
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IF( IMAT.EQ.3 ) THEN
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IZERO = 1
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ELSE IF( IMAT.EQ.4 ) THEN
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IZERO = N
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ELSE
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IZERO = N / 2 + 1
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END IF
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*
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IF( IMAT.LT.6 ) THEN
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*
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* Set row and column IZERO to zero.
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*
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IF( IUPLO.EQ.1 ) THEN
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IOFF = ( IZERO-1 )*LDA
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DO 20 I = 1, IZERO - 1
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A( IOFF+I ) = ZERO
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20 CONTINUE
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IOFF = IOFF + IZERO
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DO 30 I = IZERO, N
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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30 CONTINUE
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ELSE
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IOFF = IZERO
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DO 40 I = 1, IZERO - 1
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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40 CONTINUE
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IOFF = IOFF - IZERO
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DO 50 I = IZERO, N
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A( IOFF+I ) = ZERO
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50 CONTINUE
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END IF
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ELSE
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IF( IUPLO.EQ.1 ) THEN
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*
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* Set the first IZERO rows and columns to zero.
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*
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IOFF = 0
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DO 70 J = 1, N
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I2 = MIN( J, IZERO )
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DO 60 I = 1, I2
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A( IOFF+I ) = ZERO
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60 CONTINUE
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IOFF = IOFF + LDA
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70 CONTINUE
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ELSE
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*
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* Set the first IZERO rows and columns to zero.
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*
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IOFF = 0
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DO 90 J = 1, N
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I1 = MAX( J, IZERO )
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DO 80 I = I1, N
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A( IOFF+I ) = ZERO
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80 CONTINUE
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IOFF = IOFF + LDA
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90 CONTINUE
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END IF
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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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ELSE
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*
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* IMAT = NTYPES: Use a special block diagonal matrix to
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* test alternate code for the 2-by-2 blocks.
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*
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CALL ZLATSY( UPLO, N, A, LDA, ISEED )
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END IF
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*
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DO 150 IFACT = 1, NFACT
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*
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* Do first for FACT = 'F', then for other values.
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*
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FACT = FACTS( IFACT )
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*
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* Compute the condition number for comparison with
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* the value returned by ZSYSVX_ROOK.
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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 150
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RCONDC = ZERO
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*
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ELSE IF( IFACT.EQ.1 ) THEN
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*
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* Compute the 1-norm of A.
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*
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ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
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*
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* Factor the matrix A.
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*
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CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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CALL ZSYTRF_RK( UPLO, N, AFAC, LDA, E, IWORK, AINV,
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$ LWORK, INFO )
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*
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* Compute inv(A) and take its norm.
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*
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CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
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LWORK = (N+NB+1)*(NB+3)
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*
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* We need to compute the inverse to compute
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* RCONDC that is used later in TEST3.
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*
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CALL ZSYTRI_3( UPLO, N, AINV, LDA, E, IWORK,
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$ WORK, LWORK, INFO )
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AINVNM = ZLANSY( '1', UPLO, N, AINV, LDA, RWORK )
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*
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* Compute the 1-norm condition number of A.
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*
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCONDC = ONE
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ELSE
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RCONDC = ( ONE / ANORM ) / AINVNM
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END IF
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END IF
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*
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* Form an exact solution and set the right hand side.
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*
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SRNAMT = 'ZLARHS'
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CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N, KL, KU,
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$ NRHS, A, LDA, XACT, LDA, B, LDA, ISEED,
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$ INFO )
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XTYPE = 'C'
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*
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* --- Test ZSYSV_RK ---
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*
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IF( IFACT.EQ.2 ) THEN
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CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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*
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* Factor the matrix and solve the system using
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* ZSYSV_RK.
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*
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SRNAMT = 'ZSYSV_RK'
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CALL ZSYSV_RK( UPLO, N, NRHS, AFAC, LDA, E, IWORK,
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$ X, LDA, WORK, LWORK, INFO )
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*
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* Adjust the expected value of INFO to account for
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* pivoting.
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*
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K = IZERO
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IF( K.GT.0 ) THEN
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100 CONTINUE
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IF( IWORK( K ).LT.0 ) THEN
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IF( IWORK( K ).NE.-K ) THEN
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K = -IWORK( K )
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GO TO 100
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END IF
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ELSE IF( IWORK( K ).NE.K ) THEN
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K = IWORK( K )
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GO TO 100
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END IF
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END IF
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*
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* Check error code from ZSYSV_RK and handle error.
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*
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IF( INFO.NE.K ) THEN
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CALL ALAERH( PATH, 'ZSYSV_RK', INFO, K, UPLO,
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$ N, N, -1, -1, NRHS, IMAT, NFAIL,
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$ NERRS, NOUT )
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GO TO 120
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ELSE IF( INFO.NE.0 ) THEN
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GO TO 120
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END IF
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*
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*+ TEST 1 Reconstruct matrix from factors and compute
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* residual.
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*
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CALL ZSYT01_3( UPLO, N, A, LDA, AFAC, LDA, E,
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$ IWORK, AINV, LDA, RWORK,
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$ RESULT( 1 ) )
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*
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*+ TEST 2 Compute residual of the computed solution.
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*
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
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CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
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$ LDA, RWORK, 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 ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 3 ) )
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NT = 3
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*
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* Print information about the tests that did not pass
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* the threshold.
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*
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DO 110 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 ALADHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9999 )'ZSYSV_RK', UPLO,
|
|
$ N, IMAT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
110 CONTINUE
|
|
NRUN = NRUN + NT
|
|
120 CONTINUE
|
|
END IF
|
|
*
|
|
150 CONTINUE
|
|
*
|
|
160 CONTINUE
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I2,
|
|
$ ', test ', I2, ', ratio =', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of ZDRVSY_RK
|
|
*
|
|
END
|
|
|