536 lines
16 KiB
Fortran
536 lines
16 KiB
Fortran
*> \brief \b SCHKPT
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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 SCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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* A, D, E, 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 NN, NNS, NOUT
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* REAL 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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* REAL A( * ), B( * ), D( * ), E( * ), RWORK( * ),
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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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*> SCHKPT tests SPTTRF, -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] 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 REAL
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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[out] A
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*> \verbatim
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*> A is REAL array, dimension (NMAX*2)
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*> \endverbatim
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*>
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*> \param[out] D
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*> \verbatim
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*> D is REAL array, dimension (NMAX*2)
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*> \endverbatim
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*>
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*> \param[out] E
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*> \verbatim
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*> E is REAL array, dimension (NMAX*2)
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is REAL 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 REAL 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 REAL 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 REAL 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 REAL 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 single_lin
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*
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* =====================================================================
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SUBROUTINE SCHKPT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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$ A, D, E, B, X, 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 NN, NNS, NOUT
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REAL 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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REAL A( * ), B( * ), D( * ), E( * ), RWORK( * ),
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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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REAL ONE, ZERO
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PARAMETER ( ONE = 1.0E+0, ZERO = 0.0E+0 )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 12 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 7 )
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* ..
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* .. Local Scalars ..
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LOGICAL ZEROT
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CHARACTER DIST, TYPE
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CHARACTER*3 PATH
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INTEGER I, IA, IMAT, IN, INFO, IRHS, IX, IZERO, J, K,
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$ KL, KU, LDA, MODE, N, NERRS, NFAIL, NIMAT,
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$ NRHS, NRUN
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REAL AINVNM, ANORM, COND, DMAX, RCOND, RCONDC
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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REAL RESULT( NTESTS ), Z( 3 )
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* ..
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* .. External Functions ..
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INTEGER ISAMAX
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REAL SASUM, SGET06, SLANST
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EXTERNAL ISAMAX, SASUM, SGET06, SLANST
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, SCOPY, SERRGT, SGET04,
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$ SLACPY, SLAPTM, SLARNV, SLATB4, SLATMS, SPTCON,
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$ SPTRFS, SPTT01, SPTT02, SPTT05, SPTTRF, SPTTRS,
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$ SSCAL
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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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 / 0, 0, 0, 1 /
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* ..
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* .. Executable Statements ..
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*
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PATH( 1: 1 ) = 'Single precision'
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PATH( 2: 3 ) = 'PT'
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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 SERRGT( PATH, NOUT )
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INFOT = 0
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*
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DO 110 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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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 100 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( N.GT.0 .AND. .NOT.DOTYPE( IMAT ) )
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$ GO TO 100
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*
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* Set up parameters with SLATB4.
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*
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CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ COND, DIST )
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*
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ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
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IF( IMAT.LE.6 ) THEN
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*
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* Type 1-6: generate a symmetric tridiagonal matrix of
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* known condition number in lower triangular band storage.
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*
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SRNAMT = 'SLATMS'
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CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
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$ ANORM, KL, KU, 'B', A, 2, WORK, INFO )
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*
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* Check the error code from SLATMS.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'SLATMS', INFO, 0, ' ', N, N, KL,
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$ KU, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 100
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END IF
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IZERO = 0
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*
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* Copy the matrix to D and E.
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*
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IA = 1
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DO 20 I = 1, N - 1
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D( I ) = A( IA )
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E( I ) = A( IA+1 )
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IA = IA + 2
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20 CONTINUE
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IF( N.GT.0 )
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$ D( N ) = A( IA )
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ELSE
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*
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* Type 7-12: generate a diagonally dominant matrix with
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* unknown condition number in the vectors D and E.
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*
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IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
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*
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* Let D and E have values from [-1,1].
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*
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CALL SLARNV( 2, ISEED, N, D )
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CALL SLARNV( 2, ISEED, N-1, E )
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*
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* Make the tridiagonal matrix diagonally dominant.
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*
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IF( N.EQ.1 ) THEN
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D( 1 ) = ABS( D( 1 ) )
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ELSE
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D( 1 ) = ABS( D( 1 ) ) + ABS( E( 1 ) )
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D( N ) = ABS( D( N ) ) + ABS( E( N-1 ) )
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DO 30 I = 2, N - 1
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D( I ) = ABS( D( I ) ) + ABS( E( I ) ) +
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$ ABS( E( I-1 ) )
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30 CONTINUE
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END IF
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*
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* Scale D and E so the maximum element is ANORM.
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*
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IX = ISAMAX( N, D, 1 )
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DMAX = D( IX )
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CALL SSCAL( N, ANORM / DMAX, D, 1 )
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CALL SSCAL( N-1, ANORM / DMAX, E, 1 )
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*
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ELSE IF( IZERO.GT.0 ) THEN
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*
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* Reuse the last matrix by copying back the zeroed out
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* elements.
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*
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IF( IZERO.EQ.1 ) THEN
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D( 1 ) = Z( 2 )
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IF( N.GT.1 )
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$ E( 1 ) = Z( 3 )
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ELSE IF( IZERO.EQ.N ) THEN
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E( N-1 ) = Z( 1 )
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D( N ) = Z( 2 )
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ELSE
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E( IZERO-1 ) = Z( 1 )
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D( IZERO ) = Z( 2 )
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E( IZERO ) = Z( 3 )
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END IF
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END IF
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*
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* For types 8-10, set one row and column of the matrix to
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* zero.
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*
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IZERO = 0
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IF( IMAT.EQ.8 ) THEN
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IZERO = 1
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Z( 2 ) = D( 1 )
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D( 1 ) = ZERO
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IF( N.GT.1 ) THEN
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Z( 3 ) = E( 1 )
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E( 1 ) = ZERO
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END IF
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ELSE IF( IMAT.EQ.9 ) THEN
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IZERO = N
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IF( N.GT.1 ) THEN
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Z( 1 ) = E( N-1 )
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E( N-1 ) = ZERO
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END IF
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Z( 2 ) = D( N )
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D( N ) = ZERO
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ELSE IF( IMAT.EQ.10 ) THEN
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IZERO = ( N+1 ) / 2
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IF( IZERO.GT.1 ) THEN
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Z( 1 ) = E( IZERO-1 )
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E( IZERO-1 ) = ZERO
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Z( 3 ) = E( IZERO )
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E( IZERO ) = ZERO
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END IF
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Z( 2 ) = D( IZERO )
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D( IZERO ) = ZERO
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END IF
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END IF
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*
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CALL SCOPY( N, D, 1, D( N+1 ), 1 )
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IF( N.GT.1 )
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$ CALL SCOPY( N-1, E, 1, E( N+1 ), 1 )
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*
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*+ TEST 1
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* Factor A as L*D*L' and compute the ratio
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* norm(L*D*L' - A) / (n * norm(A) * EPS )
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*
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CALL SPTTRF( N, D( N+1 ), E( N+1 ), INFO )
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*
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* Check error code from SPTTRF.
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*
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IF( INFO.NE.IZERO ) THEN
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CALL ALAERH( PATH, 'SPTTRF', INFO, IZERO, ' ', N, N, -1,
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$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 100
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END IF
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*
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IF( INFO.GT.0 ) THEN
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RCONDC = ZERO
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GO TO 90
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END IF
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*
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CALL SPTT01( N, D, E, D( N+1 ), E( N+1 ), WORK,
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$ RESULT( 1 ) )
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*
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* Print the test ratio if greater than or equal to 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 )N, IMAT, 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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* Compute RCONDC = 1 / (norm(A) * norm(inv(A))
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*
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* Compute norm(A).
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*
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ANORM = SLANST( '1', N, D, E )
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*
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* Use SPTTRS to solve for one column at a time of inv(A),
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* computing the maximum column sum as we go.
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*
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AINVNM = ZERO
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DO 50 I = 1, N
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DO 40 J = 1, N
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X( J ) = ZERO
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40 CONTINUE
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X( I ) = ONE
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CALL SPTTRS( N, 1, D( N+1 ), E( N+1 ), X, LDA, INFO )
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AINVNM = MAX( AINVNM, SASUM( N, X, 1 ) )
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50 CONTINUE
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RCONDC = ONE / MAX( ONE, ANORM*AINVNM )
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*
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DO 80 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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*
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* Generate NRHS random solution vectors.
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*
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IX = 1
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DO 60 J = 1, NRHS
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CALL SLARNV( 2, ISEED, N, XACT( IX ) )
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IX = IX + LDA
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60 CONTINUE
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*
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* Set the right hand side.
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*
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CALL SLAPTM( N, NRHS, ONE, D, E, XACT, LDA, ZERO, B,
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$ LDA )
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*
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*+ TEST 2
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* Solve A*x = b and compute the residual.
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*
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CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
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CALL SPTTRS( N, NRHS, D( N+1 ), E( N+1 ), X, LDA, INFO )
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*
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* Check error code from SPTTRS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'SPTTRS', INFO, 0, ' ', N, N, -1,
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$ -1, NRHS, IMAT, NFAIL, NERRS, NOUT )
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*
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CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
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CALL SPTT02( N, NRHS, D, E, X, LDA, WORK, LDA,
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$ RESULT( 2 ) )
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*
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*+ TEST 3
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* Check solution from generated exact solution.
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*
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CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 3 ) )
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*
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*+ TESTS 4, 5, and 6
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* Use iterative refinement to improve the solution.
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*
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SRNAMT = 'SPTRFS'
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CALL SPTRFS( N, NRHS, D, E, D( N+1 ), E( N+1 ), B, LDA,
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$ X, LDA, RWORK, RWORK( NRHS+1 ), WORK, INFO )
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*
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* Check error code from SPTRFS.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'SPTRFS', INFO, 0, ' ', N, N, -1,
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$ -1, NRHS, IMAT, NFAIL, NERRS, NOUT )
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*
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CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
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$ RESULT( 4 ) )
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CALL SPTT05( N, NRHS, D, E, B, LDA, X, LDA, XACT, LDA,
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$ RWORK, RWORK( NRHS+1 ), RESULT( 5 ) )
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*
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* Print information about the tests that did not pass the
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* threshold.
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*
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DO 70 K = 2, 6
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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 = 9998 )N, NRHS, IMAT, K,
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$ RESULT( K )
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NFAIL = NFAIL + 1
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END IF
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70 CONTINUE
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NRUN = NRUN + 5
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80 CONTINUE
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*
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*+ TEST 7
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* Estimate the reciprocal of the condition number of the
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* matrix.
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*
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90 CONTINUE
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SRNAMT = 'SPTCON'
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CALL SPTCON( N, D( N+1 ), E( N+1 ), ANORM, RCOND, RWORK,
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$ INFO )
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*
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* Check error code from SPTCON.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'SPTCON', INFO, 0, ' ', N, N, -1, -1,
|
|
$ -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
RESULT( 7 ) = SGET06( RCOND, RCONDC )
|
|
*
|
|
* Print the test ratio if greater than or equal to THRESH.
|
|
*
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9999 )N, IMAT, 7, RESULT( 7 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' N =', I5, ', type ', I2, ', test ', I2, ', ratio = ',
|
|
$ G12.5 )
|
|
9998 FORMAT( ' N =', I5, ', NRHS=', I3, ', type ', I2, ', test(', I2,
|
|
$ ') = ', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of SCHKPT
|
|
*
|
|
END
|