619 lines
20 KiB
Fortran
619 lines
20 KiB
Fortran
*> \brief \b ZDRVPO
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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 ZDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
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* A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
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* RWORK, 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 NVAL( * )
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* DOUBLE PRECISION RWORK( * ), S( * )
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* COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ),
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* $ BSAV( * ), 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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*> ZDRVPO tests the driver routines ZPOSV 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 (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] ASAV
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*> \verbatim
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*> ASAV 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] BSAV
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*> \verbatim
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*> BSAV 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] S
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*> \verbatim
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*> S is DOUBLE PRECISION array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension
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*> (NMAX*max(3,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[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 ZDRVPO( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, NMAX,
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$ A, AFAC, ASAV, B, BSAV, X, XACT, S, WORK,
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$ RWORK, 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 NVAL( * )
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DOUBLE PRECISION RWORK( * ), S( * )
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COMPLEX*16 A( * ), AFAC( * ), ASAV( * ), B( * ),
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$ BSAV( * ), WORK( * ), X( * ), XACT( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 9 )
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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 EQUIL, NOFACT, PREFAC, ZEROT
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CHARACTER DIST, EQUED, FACT, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, IEQUED, IFACT, IMAT, IN, INFO, IOFF, IUPLO,
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$ IZERO, K, K1, KL, KU, LDA, MODE, N, NB, NBMIN,
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$ NERRS, NFACT, NFAIL, NIMAT, NRUN, NT
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DOUBLE PRECISION AINVNM, AMAX, ANORM, CNDNUM, RCOND, RCONDC,
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$ ROLDC, SCOND
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* ..
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* .. Local Arrays ..
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CHARACTER EQUEDS( 2 ), FACTS( 3 ), 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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LOGICAL LSAME
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DOUBLE PRECISION DGET06, ZLANHE
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EXTERNAL LSAME, DGET06, ZLANHE
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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, ZLAIPD, ZLAQHE, ZLARHS, ZLASET, ZLATB4,
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$ ZLATMS, ZPOEQU, ZPOSV, ZPOSVX, ZPOT01, ZPOT02,
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$ ZPOT05, ZPOTRF, ZPOTRI
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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
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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' /
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DATA FACTS / 'F', 'N', 'E' /
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DATA EQUEDS / 'N', 'Y' /
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants and the random number seed.
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*
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PATH( 1: 1 ) = 'Zomplex precision'
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PATH( 2: 3 ) = 'PO'
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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 130 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 120 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 120
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*
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* Skip types 3, 4, or 5 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.3 .AND. IMAT.LE.5
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IF( ZEROT .AND. N.LT.IMAT-2 )
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$ GO TO 120
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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 110 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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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, UPLO, 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 110
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END IF
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*
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* For types 3-5, zero one row and column of the matrix to
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* test that INFO is returned correctly.
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*
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IF( ZEROT ) THEN
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IF( IMAT.EQ.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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IOFF = ( IZERO-1 )*LDA
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*
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* Set row and column IZERO of A to 0.
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*
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IF( IUPLO.EQ.1 ) THEN
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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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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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CALL ZLAIPD( N, A, LDA+1, 0 )
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*
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* Save a copy of the matrix A in ASAV.
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*
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CALL ZLACPY( UPLO, N, N, A, LDA, ASAV, LDA )
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*
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DO 100 IEQUED = 1, 2
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EQUED = EQUEDS( IEQUED )
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IF( IEQUED.EQ.1 ) THEN
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NFACT = 3
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ELSE
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NFACT = 1
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END IF
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*
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DO 90 IFACT = 1, NFACT
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FACT = FACTS( IFACT )
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PREFAC = LSAME( FACT, 'F' )
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NOFACT = LSAME( FACT, 'N' )
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EQUIL = LSAME( FACT, 'E' )
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*
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IF( ZEROT ) THEN
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IF( PREFAC )
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$ GO TO 90
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RCONDC = ZERO
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*
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ELSE IF( .NOT.LSAME( FACT, 'N' ) ) THEN
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*
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* Compute the condition number for comparison with
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* the value returned by ZPOSVX (FACT = 'N' reuses
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* the condition number from the previous iteration
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* with FACT = 'F').
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*
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CALL ZLACPY( UPLO, N, N, ASAV, LDA, AFAC, LDA )
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IF( EQUIL .OR. IEQUED.GT.1 ) THEN
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*
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* Compute row and column scale factors to
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* equilibrate the matrix A.
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*
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CALL ZPOEQU( N, AFAC, LDA, S, SCOND, AMAX,
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$ INFO )
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IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
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IF( IEQUED.GT.1 )
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$ SCOND = ZERO
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*
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* Equilibrate the matrix.
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*
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CALL ZLAQHE( UPLO, N, AFAC, LDA, S, SCOND,
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$ AMAX, EQUED )
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END IF
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END IF
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*
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* Save the condition number of the
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* non-equilibrated system for use in ZGET04.
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*
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IF( EQUIL )
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$ ROLDC = RCONDC
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*
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* Compute the 1-norm of A.
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*
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ANORM = ZLANHE( '1', UPLO, N, AFAC, LDA, RWORK )
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*
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* Factor the matrix A.
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*
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CALL ZPOTRF( UPLO, N, AFAC, LDA, INFO )
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*
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* Form the inverse of A.
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*
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CALL ZLACPY( UPLO, N, N, AFAC, LDA, A, LDA )
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CALL ZPOTRI( UPLO, N, A, LDA, INFO )
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*
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* Compute the 1-norm condition number of A.
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*
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AINVNM = ZLANHE( '1', UPLO, N, A, LDA, RWORK )
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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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* Restore the matrix A.
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*
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CALL ZLACPY( UPLO, N, N, ASAV, LDA, A, LDA )
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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,
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$ ISEED, INFO )
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XTYPE = 'C'
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, BSAV, LDA )
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*
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IF( NOFACT ) THEN
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*
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* --- Test ZPOSV ---
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*
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* Compute the L*L' or U'*U factorization of the
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* matrix and solve the system.
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*
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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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SRNAMT = 'ZPOSV '
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CALL ZPOSV( UPLO, N, NRHS, AFAC, LDA, X, LDA,
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$ INFO )
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*
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* Check error code from ZPOSV .
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*
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IF( INFO.NE.IZERO ) THEN
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CALL ALAERH( PATH, 'ZPOSV ', INFO, IZERO,
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$ UPLO, N, N, -1, -1, NRHS, IMAT,
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$ NFAIL, NERRS, NOUT )
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GO TO 70
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ELSE IF( INFO.NE.0 ) THEN
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GO TO 70
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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 ZPOT01( UPLO, N, A, LDA, AFAC, LDA, RWORK,
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$ 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,
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$ LDA )
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CALL ZPOT02( UPLO, N, NRHS, A, LDA, X, LDA,
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$ WORK, LDA, 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
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* pass the threshold.
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*
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DO 60 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 )'ZPOSV ', UPLO,
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$ N, IMAT, K, RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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60 CONTINUE
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NRUN = NRUN + NT
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70 CONTINUE
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END IF
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*
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* --- Test ZPOSVX ---
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*
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IF( .NOT.PREFAC )
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$ CALL ZLASET( UPLO, N, N, DCMPLX( ZERO ),
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$ DCMPLX( ZERO ), AFAC, LDA )
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CALL ZLASET( 'Full', N, NRHS, DCMPLX( ZERO ),
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$ DCMPLX( ZERO ), X, LDA )
|
|
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
|
|
*
|
|
* Equilibrate the matrix if FACT='F' and
|
|
* EQUED='Y'.
|
|
*
|
|
CALL ZLAQHE( UPLO, N, A, LDA, S, SCOND, AMAX,
|
|
$ EQUED )
|
|
END IF
|
|
*
|
|
* Solve the system and compute the condition number
|
|
* and error bounds using ZPOSVX.
|
|
*
|
|
SRNAMT = 'ZPOSVX'
|
|
CALL ZPOSVX( FACT, UPLO, N, NRHS, A, LDA, AFAC,
|
|
$ LDA, EQUED, S, B, LDA, X, LDA, RCOND,
|
|
$ RWORK, RWORK( NRHS+1 ), WORK,
|
|
$ RWORK( 2*NRHS+1 ), INFO )
|
|
*
|
|
* Check the error code from ZPOSVX.
|
|
*
|
|
IF( INFO.NE.IZERO ) THEN
|
|
CALL ALAERH( PATH, 'ZPOSVX', INFO, IZERO,
|
|
$ FACT // UPLO, N, N, -1, -1, NRHS,
|
|
$ IMAT, NFAIL, NERRS, NOUT )
|
|
GO TO 90
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
IF( .NOT.PREFAC ) THEN
|
|
*
|
|
* Reconstruct matrix from factors and compute
|
|
* residual.
|
|
*
|
|
CALL ZPOT01( UPLO, N, A, LDA, AFAC, 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, BSAV, LDA, WORK,
|
|
$ LDA )
|
|
CALL ZPOT02( UPLO, N, NRHS, ASAV, LDA, X, LDA,
|
|
$ WORK, LDA, RWORK( 2*NRHS+1 ),
|
|
$ RESULT( 2 ) )
|
|
*
|
|
* Check solution from generated exact solution.
|
|
*
|
|
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
|
|
$ 'N' ) ) ) THEN
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
|
|
$ RCONDC, RESULT( 3 ) )
|
|
ELSE
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA,
|
|
$ ROLDC, RESULT( 3 ) )
|
|
END IF
|
|
*
|
|
* Check the error bounds from iterative
|
|
* refinement.
|
|
*
|
|
CALL ZPOT05( UPLO, N, NRHS, ASAV, LDA, B, LDA,
|
|
$ X, LDA, XACT, LDA, RWORK,
|
|
$ RWORK( NRHS+1 ), RESULT( 4 ) )
|
|
ELSE
|
|
K1 = 6
|
|
END IF
|
|
*
|
|
* Compare RCOND from ZPOSVX with the computed value
|
|
* in RCONDC.
|
|
*
|
|
RESULT( 6 ) = DGET06( RCOND, RCONDC )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
DO 80 K = K1, 6
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9997 )'ZPOSVX', FACT,
|
|
$ UPLO, N, EQUED, IMAT, K, RESULT( K )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9998 )'ZPOSVX', FACT,
|
|
$ UPLO, N, IMAT, K, RESULT( K )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
80 CONTINUE
|
|
NRUN = NRUN + 7 - K1
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( 1X, A, ', UPLO=''', A1, ''', N =', I5, ', type ', I1,
|
|
$ ', test(', I1, ')=', G12.5 )
|
|
9998 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
|
|
$ ', type ', I1, ', test(', I1, ')=', G12.5 )
|
|
9997 FORMAT( 1X, A, ', FACT=''', A1, ''', UPLO=''', A1, ''', N=', I5,
|
|
$ ', EQUED=''', A1, ''', type ', I1, ', test(', I1, ') =',
|
|
$ G12.5 )
|
|
RETURN
|
|
*
|
|
* End of ZDRVPO
|
|
*
|
|
END
|