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616 lines
19 KiB
FortranFixed
616 lines
19 KiB
FortranFixed
*> \brief \b ZDRVHP
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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 ZDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
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* A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
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* 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( * ),
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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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*> ZDRVHP tests the driver routines ZHPSV 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 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
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*> (NMAX*(NMAX+1)/2)
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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
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*> (NMAX*(NMAX+1)/2)
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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
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*> (NMAX*(NMAX+1)/2)
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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
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*> (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 ZDRVHP( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
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$ A, AFAC, AINV, B, X, XACT, WORK, RWORK, IWORK,
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$ 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( * ),
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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 = 10, NTESTS = 6 )
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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, PACKIT, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, I1, I2, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
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$ IZERO, J, K, K1, KL, KU, LDA, MODE, N, NB,
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$ NBMIN, NERRS, NFAIL, NIMAT, NPP, NRUN, NT
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DOUBLE PRECISION AINVNM, ANORM, CNDNUM, RCOND, RCONDC
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* ..
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* .. Local Arrays ..
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CHARACTER FACTS( NFACT )
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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, ZLANHP
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EXTERNAL DGET06, ZLANHP
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, XLAENV, ZCOPY, ZERRVX,
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$ ZGET04, ZHPSV, ZHPSVX, ZHPT01, ZHPTRF, ZHPTRI,
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$ ZLACPY, ZLAIPD, ZLARHS, ZLASET, ZLATB4, ZLATMS,
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$ ZPPT02, ZPPT05
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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 DCMPLX, 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 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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PATH( 1: 1 ) = 'Z'
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PATH( 2: 3 ) = 'HP'
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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 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 testing.
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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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NPP = N*( N+1 ) / 2
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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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IF( IUPLO.EQ.1 ) THEN
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UPLO = 'U'
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PACKIT = 'C'
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ELSE
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UPLO = 'L'
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PACKIT = 'R'
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END IF
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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, N, 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( N, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, PACKIT, A, LDA, WORK,
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$ 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, UPLO, N, N, -1,
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$ -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 the
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* 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 )*IZERO / 2
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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 + I
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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 + N - I
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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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IOFF = 0
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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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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 + J
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70 CONTINUE
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ELSE
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*
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* Set the last IZERO rows and columns to zero.
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*
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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 + N - J
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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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*
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* Set the imaginary part of the diagonals.
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*
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IF( IUPLO.EQ.1 ) THEN
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CALL ZLAIPD( N, A, 2, 1 )
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ELSE
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CALL ZLAIPD( N, A, N, -1 )
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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 ZHPSVX.
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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 = ZLANHP( '1', UPLO, N, A, RWORK )
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*
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* Factor the matrix A.
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*
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CALL ZCOPY( NPP, A, 1, AFAC, 1 )
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CALL ZHPTRF( UPLO, N, AFAC, IWORK, 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 ZCOPY( NPP, AFAC, 1, AINV, 1 )
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CALL ZHPTRI( UPLO, N, AINV, IWORK, WORK, INFO )
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AINVNM = ZLANHP( '1', UPLO, N, AINV, 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( PATH, 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 ZHPSV ---
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*
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IF( IFACT.EQ.2 ) THEN
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CALL ZCOPY( NPP, A, 1, AFAC, 1 )
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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 ZHPSV.
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*
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SRNAMT = 'ZHPSV '
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CALL ZHPSV( UPLO, N, NRHS, AFAC, IWORK, X, LDA,
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$ 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 ZHPSV .
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*
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IF( INFO.NE.K ) THEN
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CALL ALAERH( PATH, 'ZHPSV ', INFO, K, UPLO, N,
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$ 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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* Reconstruct matrix from factors and compute
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* residual.
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*
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CALL ZHPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
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$ RWORK, RESULT( 1 ) )
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*
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* 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 ZPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
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$ RWORK, RESULT( 2 ) )
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*
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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 )'ZHPSV ', UPLO, N,
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$ IMAT, K, RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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110 CONTINUE
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NRUN = NRUN + NT
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120 CONTINUE
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END IF
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*
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* --- Test ZHPSVX ---
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*
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IF( IFACT.EQ.2 .AND. NPP.GT.0 )
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$ CALL ZLASET( 'Full', NPP, 1, DCMPLX( ZERO ),
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$ DCMPLX( ZERO ), AFAC, NPP )
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CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
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$ DCMPLX( ZERO ), X, LDA )
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*
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* Solve the system and compute the condition number and
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* error bounds using ZHPSVX.
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*
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SRNAMT = 'ZHPSVX'
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CALL ZHPSVX( FACT, UPLO, N, NRHS, A, AFAC, IWORK, B,
|
|
$ LDA, X, LDA, RCOND, RWORK,
|
|
$ RWORK( NRHS+1 ), WORK, RWORK( 2*NRHS+1 ),
|
|
$ INFO )
|
|
*
|
|
* Adjust the expected value of INFO to account for
|
|
* pivoting.
|
|
*
|
|
K = IZERO
|
|
IF( K.GT.0 ) THEN
|
|
130 CONTINUE
|
|
IF( IWORK( K ).LT.0 ) THEN
|
|
IF( IWORK( K ).NE.-K ) THEN
|
|
K = -IWORK( K )
|
|
GO TO 130
|
|
END IF
|
|
ELSE IF( IWORK( K ).NE.K ) THEN
|
|
K = IWORK( K )
|
|
GO TO 130
|
|
END IF
|
|
END IF
|
|
*
|
|
* Check the error code from ZHPSVX.
|
|
*
|
|
IF( INFO.NE.K ) THEN
|
|
CALL ALAERH( PATH, 'ZHPSVX', INFO, K, FACT // UPLO,
|
|
$ N, N, -1, -1, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
GO TO 150
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
IF( IFACT.GE.2 ) THEN
|
|
*
|
|
* Reconstruct matrix from factors and compute
|
|
* residual.
|
|
*
|
|
CALL ZHPT01( UPLO, N, A, AFAC, IWORK, AINV, LDA,
|
|
$ RWORK( 2*NRHS+1 ), RESULT( 1 ) )
|
|
K1 = 1
|
|
ELSE
|
|
K1 = 2
|
|
END IF
|
|
*
|
|
* Compute residual of the computed solution.
|
|
*
|
|
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
|
CALL ZPPT02( UPLO, N, NRHS, A, X, LDA, WORK, LDA,
|
|
$ RWORK( 2*NRHS+1 ), RESULT( 2 ) )
|
|
*
|
|
* Check solution from generated exact solution.
|
|
*
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 3 ) )
|
|
*
|
|
* Check the error bounds from iterative refinement.
|
|
*
|
|
CALL ZPPT05( UPLO, N, NRHS, A, B, LDA, X, LDA,
|
|
$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
|
|
$ RESULT( 4 ) )
|
|
ELSE
|
|
K1 = 6
|
|
END IF
|
|
*
|
|
* Compare RCOND from ZHPSVX with the computed value
|
|
* in RCONDC.
|
|
*
|
|
RESULT( 6 ) = DGET06( RCOND, RCONDC )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
DO 140 K = K1, 6
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9998 )'ZHPSVX', FACT, UPLO,
|
|
$ N, IMAT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
140 CONTINUE
|
|
NRUN = NRUN + 7 - K1
|
|
*
|
|
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 )
|
|
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N =', I5,
|
|
$ ', type ', I2, ', test ', I2, ', ratio =', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of ZDRVHP
|
|
*
|
|
END
|