595 lines
20 KiB
Fortran
595 lines
20 KiB
Fortran
*> \brief \b ZCHKPB
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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 ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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* THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
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* 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, NNB, 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 NBVAL( * ), NSVAL( * ), 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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*> ZCHKPB tests ZPBTRF, -TRS, -RFS, and -CON.
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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] NNB
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*> \verbatim
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*> NNB is INTEGER
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*> The number of values of NB contained in the vector NBVAL.
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*> \endverbatim
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*>
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*> \param[in] NBVAL
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*> \verbatim
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*> NBVAL is INTEGER array, dimension (NBVAL)
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*> The values of the blocksize NB.
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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 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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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*> \date November 2011
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*
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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZCHKPB( DOTYPE, NN, NVAL, NNB, NBVAL, NNS, NSVAL,
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$ THRESH, TSTERR, NMAX, A, AFAC, AINV, B, X,
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$ XACT, WORK, RWORK, NOUT )
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*
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* -- LAPACK test routine (version 3.4.0) --
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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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* November 2011
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*
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* .. Scalar Arguments ..
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LOGICAL TSTERR
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INTEGER NMAX, NN, NNB, 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 NBVAL( * ), NSVAL( * ), 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 = 8, NTESTS = 7 )
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INTEGER NBW
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PARAMETER ( NBW = 4 )
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* ..
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* .. Local Scalars ..
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LOGICAL ZEROT
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CHARACTER DIST, PACKIT, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, I1, I2, IKD, IMAT, IN, INB, INFO, IOFF,
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$ IRHS, IUPLO, IW, IZERO, K, KD, KL, KOFF, KU,
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$ LDA, LDAB, MODE, N, NB, NERRS, NFAIL, NIMAT,
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$ NKD, NRHS, NRUN
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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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INTEGER ISEED( 4 ), ISEEDY( 4 ), KDVAL( NBW )
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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, ZLANGE, ZLANHB
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EXTERNAL DGET06, ZLANGE, ZLANHB
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, XLAENV, ZCOPY, ZERRPO,
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$ ZGET04, ZLACPY, ZLAIPD, ZLARHS, ZLASET, ZLATB4,
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$ ZLATMS, ZPBCON, ZPBRFS, ZPBT01, ZPBT02, ZPBT05,
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$ ZPBTRF, ZPBTRS, ZSWAP
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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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* .. Scalars in Common ..
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LOGICAL LERR, OK
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CHARACTER*32 SRNAMT
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INTEGER INFOT, NUNIT
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* ..
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* .. Common blocks ..
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COMMON / INFOC / INFOT, NUNIT, OK, LERR
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA ISEEDY / 1988, 1989, 1990, 1991 /
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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 ) = 'PB'
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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 ZERRPO( PATH, NOUT )
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INFOT = 0
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KDVAL( 1 ) = 0
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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 90 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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*
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* Set limits on the number of loop iterations.
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*
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NKD = MAX( 1, MIN( N, 4 ) )
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NIMAT = NTYPES
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IF( N.EQ.0 )
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$ NIMAT = 1
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*
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KDVAL( 2 ) = N + ( N+1 ) / 4
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KDVAL( 3 ) = ( 3*N-1 ) / 4
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KDVAL( 4 ) = ( N+1 ) / 4
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*
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DO 80 IKD = 1, NKD
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*
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* Do for KD = 0, (5*N+1)/4, (3N-1)/4, and (N+1)/4. This order
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* makes it easier to skip redundant values for small values
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* of N.
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*
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KD = KDVAL( IKD )
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LDAB = KD + 1
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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 70 IUPLO = 1, 2
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KOFF = 1
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IF( IUPLO.EQ.1 ) THEN
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UPLO = 'U'
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KOFF = MAX( 1, KD+2-N )
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PACKIT = 'Q'
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ELSE
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UPLO = 'L'
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PACKIT = 'B'
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END IF
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*
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DO 60 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 60
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*
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* Skip types 2, 3, or 4 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.2 .AND. IMAT.LE.4
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IF( ZEROT .AND. N.LT.IMAT-1 )
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$ GO TO 60
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*
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IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 1 ) ) THEN
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*
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* Set up parameters with ZLATB4 and generate a test
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* matrix with ZLATMS.
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*
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CALL ZLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
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$ MODE, 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, KD, KD, PACKIT,
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$ A( KOFF ), LDAB, WORK, 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,
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$ N, KD, KD, -1, IMAT, NFAIL, NERRS,
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$ NOUT )
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GO TO 60
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END IF
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ELSE IF( IZERO.GT.0 ) THEN
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*
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* Use the same matrix for types 3 and 4 as for type
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* 2 by copying back the zeroed out column,
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*
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IW = 2*LDA + 1
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IF( IUPLO.EQ.1 ) THEN
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IOFF = ( IZERO-1 )*LDAB + KD + 1
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CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
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$ A( IOFF-IZERO+I1 ), 1 )
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IW = IW + IZERO - I1
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CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
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$ A( IOFF ), MAX( LDAB-1, 1 ) )
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ELSE
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IOFF = ( I1-1 )*LDAB + 1
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CALL ZCOPY( IZERO-I1, WORK( IW ), 1,
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$ A( IOFF+IZERO-I1 ),
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$ MAX( LDAB-1, 1 ) )
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IOFF = ( IZERO-1 )*LDAB + 1
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IW = IW + IZERO - I1
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CALL ZCOPY( I2-IZERO+1, WORK( IW ), 1,
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$ A( IOFF ), 1 )
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END IF
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END IF
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*
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* For types 2-4, zero one row and column of the matrix
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* to test that INFO is returned correctly.
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*
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IZERO = 0
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IF( ZEROT ) THEN
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IF( IMAT.EQ.2 ) THEN
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IZERO = 1
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ELSE IF( IMAT.EQ.3 ) 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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* Save the zeroed out row and column in WORK(*,3)
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*
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IW = 2*LDA
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DO 20 I = 1, MIN( 2*KD+1, N )
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WORK( IW+I ) = ZERO
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20 CONTINUE
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IW = IW + 1
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I1 = MAX( IZERO-KD, 1 )
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I2 = MIN( IZERO+KD, N )
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*
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IF( IUPLO.EQ.1 ) THEN
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IOFF = ( IZERO-1 )*LDAB + KD + 1
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CALL ZSWAP( IZERO-I1, A( IOFF-IZERO+I1 ), 1,
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$ WORK( IW ), 1 )
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IW = IW + IZERO - I1
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CALL ZSWAP( I2-IZERO+1, A( IOFF ),
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$ MAX( LDAB-1, 1 ), WORK( IW ), 1 )
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ELSE
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IOFF = ( I1-1 )*LDAB + 1
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CALL ZSWAP( IZERO-I1, A( IOFF+IZERO-I1 ),
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$ MAX( LDAB-1, 1 ), WORK( IW ), 1 )
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IOFF = ( IZERO-1 )*LDAB + 1
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IW = IW + IZERO - I1
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CALL ZSWAP( I2-IZERO+1, A( IOFF ), 1,
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$ WORK( IW ), 1 )
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END IF
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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( KD+1 ), LDAB, 0 )
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ELSE
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CALL ZLAIPD( N, A( 1 ), LDAB, 0 )
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END IF
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*
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* Do for each value of NB in NBVAL
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*
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DO 50 INB = 1, NNB
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NB = NBVAL( INB )
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CALL XLAENV( 1, NB )
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*
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* Compute the L*L' or U'*U factorization of the band
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* matrix.
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*
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CALL ZLACPY( 'Full', KD+1, N, A, LDAB, AFAC, LDAB )
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SRNAMT = 'ZPBTRF'
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CALL ZPBTRF( UPLO, N, KD, AFAC, LDAB, INFO )
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*
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* Check error code from ZPBTRF.
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*
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IF( INFO.NE.IZERO ) THEN
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CALL ALAERH( PATH, 'ZPBTRF', INFO, IZERO, UPLO,
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$ N, N, KD, KD, NB, IMAT, NFAIL,
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$ NERRS, NOUT )
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GO TO 50
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END IF
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*
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* Skip the tests if INFO is not 0.
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*
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IF( INFO.NE.0 )
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$ GO TO 50
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*
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*+ TEST 1
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* Reconstruct matrix from factors and compute
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* residual.
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*
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CALL ZLACPY( 'Full', KD+1, N, AFAC, LDAB, AINV,
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$ LDAB )
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CALL ZPBT01( UPLO, N, KD, A, LDAB, AINV, LDAB,
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$ RWORK, RESULT( 1 ) )
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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( 1 ).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, N, KD, NB, IMAT,
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$ 1, RESULT( 1 )
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NFAIL = NFAIL + 1
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END IF
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NRUN = NRUN + 1
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*
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* Only do other tests if this is the first blocksize.
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*
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IF( INB.GT.1 )
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$ GO TO 50
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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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SRNAMT = 'ZPBTRS'
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CALL ZPBTRS( UPLO, N, KD, N, AFAC, LDAB, AINV, LDA,
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$ INFO )
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*
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* Compute RCONDC = 1/(norm(A) * norm(inv(A))).
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*
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ANORM = ZLANHB( '1', UPLO, N, KD, A, LDAB, RWORK )
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AINVNM = ZLANGE( '1', N, N, AINV, 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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*
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DO 40 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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*
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*+ TEST 2
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* Solve and compute residual for A * X = B.
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*
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SRNAMT = 'ZLARHS'
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CALL ZLARHS( PATH, XTYPE, UPLO, ' ', N, N, KD,
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$ KD, NRHS, A, LDAB, XACT, LDA, B,
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$ LDA, ISEED, INFO )
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CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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*
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SRNAMT = 'ZPBTRS'
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CALL ZPBTRS( UPLO, N, KD, NRHS, AFAC, LDAB, X,
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$ LDA, INFO )
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*
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* Check error code from ZPBTRS.
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|
*
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|
IF( INFO.NE.0 )
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|
$ CALL ALAERH( PATH, 'ZPBTRS', INFO, 0, UPLO,
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|
$ N, N, KD, KD, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
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|
*
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|
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK,
|
|
$ LDA )
|
|
CALL ZPBT02( UPLO, N, KD, NRHS, A, LDAB, X, LDA,
|
|
$ WORK, LDA, RWORK, RESULT( 2 ) )
|
|
*
|
|
*+ TEST 3
|
|
* Check solution from generated exact solution.
|
|
*
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 3 ) )
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|
*
|
|
*+ TESTS 4, 5, and 6
|
|
* Use iterative refinement to improve the solution.
|
|
*
|
|
SRNAMT = 'ZPBRFS'
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|
CALL ZPBRFS( UPLO, N, KD, NRHS, A, LDAB, AFAC,
|
|
$ LDAB, B, LDA, X, LDA, RWORK,
|
|
$ RWORK( NRHS+1 ), WORK,
|
|
$ RWORK( 2*NRHS+1 ), INFO )
|
|
*
|
|
* Check error code from ZPBRFS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZPBRFS', INFO, 0, UPLO,
|
|
$ N, N, KD, KD, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
*
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 4 ) )
|
|
CALL ZPBT05( UPLO, N, KD, NRHS, A, LDAB, B, LDA,
|
|
$ X, LDA, XACT, LDA, RWORK,
|
|
$ RWORK( NRHS+1 ), RESULT( 5 ) )
|
|
*
|
|
* Print information about the tests that did not
|
|
* pass the threshold.
|
|
*
|
|
DO 30 K = 2, 6
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9998 )UPLO, N, KD,
|
|
$ NRHS, IMAT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
30 CONTINUE
|
|
NRUN = NRUN + 5
|
|
40 CONTINUE
|
|
*
|
|
*+ TEST 7
|
|
* Get an estimate of RCOND = 1/CNDNUM.
|
|
*
|
|
SRNAMT = 'ZPBCON'
|
|
CALL ZPBCON( UPLO, N, KD, AFAC, LDAB, ANORM, RCOND,
|
|
$ WORK, RWORK, INFO )
|
|
*
|
|
* Check error code from ZPBCON.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'ZPBCON', INFO, 0, UPLO, N,
|
|
$ N, KD, KD, -1, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
RESULT( 7 ) = DGET06( RCOND, RCONDC )
|
|
*
|
|
* Print the test ratio if it is .GE. THRESH.
|
|
*
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )UPLO, N, KD, IMAT, 7,
|
|
$ RESULT( 7 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
50 CONTINUE
|
|
60 CONTINUE
|
|
70 CONTINUE
|
|
80 CONTINUE
|
|
90 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NB=', I4,
|
|
$ ', type ', I2, ', test ', I2, ', ratio= ', G12.5 )
|
|
9998 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ', NRHS=', I3,
|
|
$ ', type ', I2, ', test(', I2, ') = ', G12.5 )
|
|
9997 FORMAT( ' UPLO=''', A1, ''', N=', I5, ', KD=', I5, ',', 10X,
|
|
$ ' type ', I2, ', test(', I2, ') = ', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of ZCHKPB
|
|
*
|
|
END
|