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575 lines
19 KiB
FortranFixed
575 lines
19 KiB
FortranFixed
*> \brief \b ZCHKTB
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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 ZCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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* NMAX, AB, AINV, B, X, XACT, WORK, 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, NNS, NOUT
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* DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER NSVAL( * ), NVAL( * )
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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 AB( * ), AINV( * ), B( * ), WORK( * ), X( * ),
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* $ XACT( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZCHKTB tests ZTBTRS, -RFS, and -CON, and ZLATBS.
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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 column dimension N.
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*> \endverbatim
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*>
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*> \param[in] NNS
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*> \verbatim
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*> NNS is INTEGER
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*> The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*> NSVAL is INTEGER array, dimension (NNS)
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*> The values of the number of right hand sides NRHS.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[in] TSTERR
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*> \verbatim
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*> TSTERR is LOGICAL
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*> Flag that indicates whether error exits are to be tested.
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*> \endverbatim
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*>
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*> \param[in] NMAX
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*> \verbatim
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*> NMAX is INTEGER
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*> The leading dimension of the work arrays.
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*> NMAX >= the maximum value of N in NVAL.
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*> \endverbatim
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*>
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*> \param[out] AB
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*> \verbatim
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*> AB is COMPLEX*16 array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AINV
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*> \verbatim
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*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> where NSMAX is the largest entry in NSVAL.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] XACT
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*> \verbatim
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*> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension
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*> (NMAX*max(3,NSMAX))
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension
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*> (max(NMAX,2*NSMAX))
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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 ZCHKTB( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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$ NMAX, AB, AINV, B, X, XACT, WORK, 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, NNS, NOUT
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DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER NSVAL( * ), NVAL( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 AB( * ), AINV( * ), B( * ), WORK( * ), X( * ),
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$ XACT( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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INTEGER NTYPE1, NTYPES
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PARAMETER ( NTYPE1 = 9, NTYPES = 17 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 8 )
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INTEGER NTRAN
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PARAMETER ( NTRAN = 3 )
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DOUBLE PRECISION ONE, ZERO
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PARAMETER ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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CHARACTER DIAG, NORM, TRANS, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, IDIAG, IK, IMAT, IN, INFO, IRHS, ITRAN,
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$ IUPLO, J, K, KD, LDA, LDAB, N, NERRS, NFAIL,
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$ NIMAT, NIMAT2, NK, NRHS, NRUN
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DOUBLE PRECISION AINVNM, ANORM, RCOND, RCONDC, RCONDI, RCONDO,
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$ SCALE
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* ..
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* .. Local Arrays ..
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CHARACTER TRANSS( NTRAN ), 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 ZLANTB, ZLANTR
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EXTERNAL LSAME, ZLANTB, ZLANTR
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, ZCOPY, ZERRTR, ZGET04,
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$ ZLACPY, ZLARHS, ZLASET, ZLATBS, ZLATTB, ZTBCON,
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$ ZTBRFS, ZTBSV, ZTBT02, ZTBT03, ZTBT05, ZTBT06,
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$ ZTBTRS
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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, IOUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, IOUNIT, 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 UPLOS / 'U', 'L' / , TRANSS / 'N', 'T', 'C' /
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* ..
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* .. Executable Statements ..
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*
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* Initialize constants and the random number seed.
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*
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PATH( 1: 1 ) = 'Zomplex precision'
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PATH( 2: 3 ) = 'TB'
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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 ZERRTR( PATH, NOUT )
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INFOT = 0
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*
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DO 140 IN = 1, NN
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*
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* Do for each value of N in NVAL
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*
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N = NVAL( IN )
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LDA = MAX( 1, N )
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XTYPE = 'N'
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NIMAT = NTYPE1
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NIMAT2 = NTYPES
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IF( N.LE.0 ) THEN
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NIMAT = 1
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NIMAT2 = NTYPE1 + 1
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END IF
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*
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NK = MIN( N+1, 4 )
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DO 130 IK = 1, NK
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*
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* Do for KD = 0, N, (3N-1)/4, and (N+1)/4. This order makes
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* it easier to skip redundant values for small values of N.
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*
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IF( IK.EQ.1 ) THEN
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KD = 0
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ELSE IF( IK.EQ.2 ) THEN
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KD = MAX( N, 0 )
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ELSE IF( IK.EQ.3 ) THEN
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KD = ( 3*N-1 ) / 4
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ELSE IF( IK.EQ.4 ) THEN
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KD = ( N+1 ) / 4
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END IF
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LDAB = KD + 1
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*
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DO 90 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 90
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*
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DO 80 IUPLO = 1, 2
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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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UPLO = UPLOS( IUPLO )
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*
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* Call ZLATTB to generate a triangular test matrix.
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*
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SRNAMT = 'ZLATTB'
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CALL ZLATTB( IMAT, UPLO, 'No transpose', DIAG, ISEED,
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$ N, KD, AB, LDAB, X, WORK, RWORK, INFO )
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*
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* Set IDIAG = 1 for non-unit matrices, 2 for unit.
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*
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IF( LSAME( DIAG, 'N' ) ) THEN
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IDIAG = 1
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ELSE
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IDIAG = 2
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END IF
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*
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* Form the inverse of A so we can get a good estimate
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* of RCONDC = 1/(norm(A) * norm(inv(A))).
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*
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CALL ZLASET( 'Full', N, N, DCMPLX( ZERO ),
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$ DCMPLX( ONE ), AINV, LDA )
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IF( LSAME( UPLO, 'U' ) ) THEN
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DO 20 J = 1, N
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CALL ZTBSV( UPLO, 'No transpose', DIAG, J, KD,
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$ AB, LDAB, AINV( ( J-1 )*LDA+1 ), 1 )
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20 CONTINUE
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ELSE
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DO 30 J = 1, N
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CALL ZTBSV( UPLO, 'No transpose', DIAG, N-J+1,
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$ KD, AB( ( J-1 )*LDAB+1 ), LDAB,
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$ AINV( ( J-1 )*LDA+J ), 1 )
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30 CONTINUE
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END IF
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*
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* Compute the 1-norm condition number of A.
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*
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ANORM = ZLANTB( '1', UPLO, DIAG, N, KD, AB, LDAB,
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$ RWORK )
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AINVNM = ZLANTR( '1', UPLO, DIAG, N, N, AINV, LDA,
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$ RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCONDO = ONE
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ELSE
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RCONDO = ( ONE / ANORM ) / AINVNM
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END IF
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*
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* Compute the infinity-norm condition number of A.
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*
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ANORM = ZLANTB( 'I', UPLO, DIAG, N, KD, AB, LDAB,
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$ RWORK )
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AINVNM = ZLANTR( 'I', UPLO, DIAG, N, N, AINV, LDA,
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$ RWORK )
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IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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RCONDI = ONE
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ELSE
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RCONDI = ( ONE / ANORM ) / AINVNM
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END IF
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*
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DO 60 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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XTYPE = 'N'
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*
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DO 50 ITRAN = 1, NTRAN
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*
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* Do for op(A) = A, A**T, or A**H.
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*
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TRANS = TRANSS( ITRAN )
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IF( ITRAN.EQ.1 ) THEN
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NORM = 'O'
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RCONDC = RCONDO
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ELSE
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NORM = 'I'
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RCONDC = RCONDI
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END IF
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*
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*+ TEST 1
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* Solve and compute residual for op(A)*x = b.
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*
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SRNAMT = 'ZLARHS'
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CALL ZLARHS( PATH, XTYPE, UPLO, TRANS, N, N, KD,
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$ IDIAG, NRHS, AB, LDAB, XACT, LDA,
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$ B, LDA, ISEED, INFO )
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XTYPE = 'C'
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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*
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SRNAMT = 'ZTBTRS'
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CALL ZTBTRS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
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$ LDAB, X, LDA, INFO )
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*
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* Check error code from ZTBTRS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'ZTBTRS', INFO, 0,
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$ UPLO // TRANS // DIAG, N, N, KD,
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$ KD, NRHS, IMAT, NFAIL, NERRS,
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$ NOUT )
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*
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CALL ZTBT02( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
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$ LDAB, X, LDA, B, LDA, WORK, RWORK,
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$ RESULT( 1 ) )
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*
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*+ TEST 2
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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( 2 ) )
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*
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*+ TESTS 3, 4, and 5
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* Use iterative refinement to improve the solution
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* and compute error bounds.
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*
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SRNAMT = 'ZTBRFS'
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CALL ZTBRFS( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
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$ LDAB, B, LDA, X, LDA, RWORK,
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$ RWORK( NRHS+1 ), WORK,
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$ RWORK( 2*NRHS+1 ), INFO )
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*
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* Check error code from ZTBRFS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'ZTBRFS', INFO, 0,
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$ UPLO // TRANS // DIAG, N, N, KD,
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$ KD, NRHS, IMAT, NFAIL, NERRS,
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$ NOUT )
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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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CALL ZTBT05( UPLO, TRANS, DIAG, N, KD, NRHS, AB,
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$ LDAB, B, LDA, X, LDA, XACT, LDA,
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$ RWORK, RWORK( NRHS+1 ),
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$ RESULT( 4 ) )
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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 40 K = 1, 5
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IF( RESULT( K ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALAHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9999 )UPLO, TRANS,
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$ DIAG, N, KD, NRHS, IMAT, K, RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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40 CONTINUE
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NRUN = NRUN + 5
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50 CONTINUE
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60 CONTINUE
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*
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*+ TEST 6
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* Get an estimate of RCOND = 1/CNDNUM.
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*
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DO 70 ITRAN = 1, 2
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IF( ITRAN.EQ.1 ) THEN
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NORM = 'O'
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RCONDC = RCONDO
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ELSE
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NORM = 'I'
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RCONDC = RCONDI
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END IF
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SRNAMT = 'ZTBCON'
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CALL ZTBCON( NORM, UPLO, DIAG, N, KD, AB, LDAB,
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$ RCOND, WORK, RWORK, INFO )
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*
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* Check error code from ZTBCON.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'ZTBCON', INFO, 0,
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$ NORM // UPLO // DIAG, N, N, KD, KD,
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$ -1, IMAT, NFAIL, NERRS, NOUT )
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*
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CALL ZTBT06( RCOND, RCONDC, UPLO, DIAG, N, KD, AB,
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$ LDAB, RWORK, RESULT( 6 ) )
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*
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* Print the test ratio if it is .GE. THRESH.
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*
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IF( RESULT( 6 ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALAHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9998 ) 'ZTBCON', NORM, UPLO,
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$ DIAG, N, KD, IMAT, 6, RESULT( 6 )
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NFAIL = NFAIL + 1
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END IF
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NRUN = NRUN + 1
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70 CONTINUE
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80 CONTINUE
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90 CONTINUE
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*
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* Use pathological test matrices to test ZLATBS.
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*
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DO 120 IMAT = NTYPE1 + 1, NIMAT2
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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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DO 110 IUPLO = 1, 2
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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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UPLO = UPLOS( IUPLO )
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DO 100 ITRAN = 1, NTRAN
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*
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* Do for op(A) = A, A**T, and A**H.
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*
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TRANS = TRANSS( ITRAN )
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*
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* Call ZLATTB to generate a triangular test matrix.
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*
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SRNAMT = 'ZLATTB'
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CALL ZLATTB( IMAT, UPLO, TRANS, DIAG, ISEED, N, KD,
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$ AB, LDAB, X, WORK, RWORK, INFO )
|
|
*
|
|
*+ TEST 7
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|
* Solve the system op(A)*x = b
|
|
*
|
|
SRNAMT = 'ZLATBS'
|
|
CALL ZCOPY( N, X, 1, B, 1 )
|
|
CALL ZLATBS( UPLO, TRANS, DIAG, 'N', N, KD, AB,
|
|
$ LDAB, B, SCALE, RWORK, INFO )
|
|
*
|
|
* Check error code from ZLATBS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZLATBS', INFO, 0,
|
|
$ UPLO // TRANS // DIAG // 'N', N, N,
|
|
$ KD, KD, -1, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
CALL ZTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
|
|
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
|
|
$ WORK, RESULT( 7 ) )
|
|
*
|
|
*+ TEST 8
|
|
* Solve op(A)*x = b again with NORMIN = 'Y'.
|
|
*
|
|
CALL ZCOPY( N, X, 1, B, 1 )
|
|
CALL ZLATBS( UPLO, TRANS, DIAG, 'Y', N, KD, AB,
|
|
$ LDAB, B, SCALE, RWORK, INFO )
|
|
*
|
|
* Check error code from ZLATBS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZLATBS', INFO, 0,
|
|
$ UPLO // TRANS // DIAG // 'Y', N, N,
|
|
$ KD, KD, -1, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
CALL ZTBT03( UPLO, TRANS, DIAG, N, KD, 1, AB, LDAB,
|
|
$ SCALE, RWORK, ONE, B, LDA, X, LDA,
|
|
$ WORK, RESULT( 8 ) )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )'ZLATBS', UPLO, TRANS,
|
|
$ DIAG, 'N', N, KD, IMAT, 7, RESULT( 7 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
IF( RESULT( 8 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )'ZLATBS', UPLO, TRANS,
|
|
$ DIAG, 'Y', N, KD, IMAT, 8, RESULT( 8 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 2
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' UPLO=''', A1, ''', TRANS=''', A1, ''',
|
|
$ DIAG=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I5,
|
|
$ ', type ', I2, ', test(', I2, ')=', G12.5 )
|
|
9998 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''',',
|
|
$ I5, ',', I5, ', ... ), type ', I2, ', test(', I2, ')=',
|
|
$ G12.5 )
|
|
9997 FORMAT( 1X, A, '( ''', A1, ''', ''', A1, ''', ''', A1, ''', ''',
|
|
$ A1, ''',', I5, ',', I5, ', ... ), type ', I2, ', test(',
|
|
$ I1, ')=', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of ZCHKTB
|
|
*
|
|
END
|