1032 lines
40 KiB
Fortran
1032 lines
40 KiB
Fortran
*> \brief \b SDRVGBX
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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 SDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
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* AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
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* RWORK, IWORK, NOUT )
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*
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* .. Scalar Arguments ..
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* LOGICAL TSTERR
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* INTEGER LA, LAFB, NN, NOUT, NRHS
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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 IWORK( * ), NVAL( * )
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* REAL A( * ), AFB( * ), ASAV( * ), B( * ), BSAV( * ),
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* $ RWORK( * ), S( * ), 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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*> SDRVGB tests the driver routines SGBSV, -SVX, and -SVXX.
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*>
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*> Note that this file is used only when the XBLAS are available,
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*> otherwise sdrvgb.f defines this subroutine.
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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] NRHS
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*> \verbatim
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*> NRHS is INTEGER
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*> The number of right hand side vectors to be generated for
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*> each linear system.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is 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 (LA)
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*> \endverbatim
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*>
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*> \param[in] LA
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*> \verbatim
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*> LA is INTEGER
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*> The length of the array A. LA >= (2*NMAX-1)*NMAX
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*> where NMAX is the largest entry in NVAL.
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*> \endverbatim
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*>
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*> \param[out] AFB
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*> \verbatim
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*> AFB is REAL array, dimension (LAFB)
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*> \endverbatim
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*>
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*> \param[in] LAFB
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*> \verbatim
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*> LAFB is INTEGER
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*> The length of the array AFB. LAFB >= (3*NMAX-2)*NMAX
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*> where NMAX is the largest entry in NVAL.
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*> \endverbatim
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*>
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*> \param[out] ASAV
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*> \verbatim
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*> ASAV is REAL array, dimension (LA)
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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*NRHS)
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*> \endverbatim
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*>
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*> \param[out] BSAV
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*> \verbatim
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*> BSAV is REAL array, dimension (NMAX*NRHS)
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is REAL array, dimension (NMAX*NRHS)
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*> \endverbatim
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*>
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*> \param[out] XACT
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*> \verbatim
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*> XACT is REAL array, dimension (NMAX*NRHS)
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*> \endverbatim
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*>
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*> \param[out] S
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*> \verbatim
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*> S is REAL array, dimension (2*NMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension
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*> (NMAX*max(3,NRHS,NMAX))
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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(2*NMAX,NMAX+2*NRHS))
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*> \endverbatim
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*>
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*> \param[out] IWORK
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*> \verbatim
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*> IWORK is INTEGER array, dimension (2*NMAX)
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*> \endverbatim
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*>
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*> \param[in] NOUT
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*> \verbatim
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*> NOUT is INTEGER
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*> The unit number for output.
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SDRVGB( DOTYPE, NN, NVAL, NRHS, THRESH, TSTERR, A, LA,
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$ AFB, LAFB, ASAV, B, BSAV, X, XACT, S, WORK,
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$ RWORK, IWORK, 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 LA, LAFB, NN, NOUT, NRHS
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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 IWORK( * ), NVAL( * )
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REAL A( * ), AFB( * ), ASAV( * ), B( * ), BSAV( * ),
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$ RWORK( * ), S( * ), 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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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 = 8 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 7 )
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INTEGER NTRAN
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PARAMETER ( NTRAN = 3 )
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* ..
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* .. Local Scalars ..
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LOGICAL EQUIL, NOFACT, PREFAC, TRFCON, ZEROT
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CHARACTER DIST, EQUED, FACT, TRANS, TYPE, XTYPE
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CHARACTER*3 PATH
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INTEGER I, I1, I2, IEQUED, IFACT, IKL, IKU, IMAT, IN,
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$ INFO, IOFF, ITRAN, IZERO, J, K, K1, KL, KU,
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$ LDA, LDAFB, LDB, MODE, N, NB, NBMIN, NERRS,
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$ NFACT, NFAIL, NIMAT, NKL, NKU, NRUN, NT,
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$ N_ERR_BNDS
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REAL AINVNM, AMAX, ANORM, ANORMI, ANORMO, ANRMPV,
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$ CNDNUM, COLCND, RCOND, RCONDC, RCONDI, RCONDO,
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$ ROLDC, ROLDI, ROLDO, ROWCND, RPVGRW,
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$ RPVGRW_SVXX
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* ..
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* .. Local Arrays ..
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CHARACTER EQUEDS( 4 ), FACTS( 3 ), TRANSS( NTRAN )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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REAL RESULT( NTESTS ), BERR( NRHS ),
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$ ERRBNDS_N( NRHS, 3 ), ERRBNDS_C( NRHS, 3 )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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REAL SGET06, SLAMCH, SLANGB, SLANGE, SLANTB,
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$ SLA_GBRPVGRW
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EXTERNAL LSAME, SGET06, SLAMCH, SLANGB, SLANGE, SLANTB,
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$ SLA_GBRPVGRW
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* ..
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* .. External Subroutines ..
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EXTERNAL ALADHD, ALAERH, ALASVM, SERRVX, SGBEQU, SGBSV,
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$ SGBSVX, SGBT01, SGBT02, SGBT05, SGBTRF, SGBTRS,
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$ SGET04, SLACPY, SLAQGB, SLARHS, SLASET, SLATB4,
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$ SLATMS, XLAENV, SGBSVXX
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, 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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DATA TRANSS / 'N', 'T', 'C' /
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DATA FACTS / 'F', 'N', 'E' /
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DATA EQUEDS / 'N', 'R', 'C', 'B' /
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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 ) = 'Single precision'
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PATH( 2: 3 ) = 'GB'
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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 SERRVX( PATH, NOUT )
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INFOT = 0
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*
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* Set the block size and minimum block size for testing.
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*
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NB = 1
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NBMIN = 2
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CALL XLAENV( 1, NB )
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CALL XLAENV( 2, NBMIN )
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*
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* Do for each value of N in NVAL
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*
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DO 150 IN = 1, NN
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N = NVAL( IN )
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LDB = 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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NKL = MAX( 1, MIN( N, 4 ) )
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IF( N.EQ.0 )
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$ NKL = 1
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NKU = NKL
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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 140 IKL = 1, NKL
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*
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* Do for KL = 0, N-1, (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( IKL.EQ.1 ) THEN
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KL = 0
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ELSE IF( IKL.EQ.2 ) THEN
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KL = MAX( N-1, 0 )
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ELSE IF( IKL.EQ.3 ) THEN
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KL = ( 3*N-1 ) / 4
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ELSE IF( IKL.EQ.4 ) THEN
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KL = ( N+1 ) / 4
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END IF
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DO 130 IKU = 1, NKU
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*
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* Do for KU = 0, N-1, (3N-1)/4, and (N+1)/4. This order
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* makes it easier to skip redundant values for small
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* values of N.
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*
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IF( IKU.EQ.1 ) THEN
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KU = 0
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ELSE IF( IKU.EQ.2 ) THEN
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KU = MAX( N-1, 0 )
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ELSE IF( IKU.EQ.3 ) THEN
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KU = ( 3*N-1 ) / 4
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ELSE IF( IKU.EQ.4 ) THEN
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KU = ( N+1 ) / 4
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END IF
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*
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* Check that A and AFB are big enough to generate this
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* matrix.
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*
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LDA = KL + KU + 1
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LDAFB = 2*KL + KU + 1
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IF( LDA*N.GT.LA .OR. LDAFB*N.GT.LAFB ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALADHD( NOUT, PATH )
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IF( LDA*N.GT.LA ) THEN
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WRITE( NOUT, FMT = 9999 )LA, N, KL, KU,
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$ N*( KL+KU+1 )
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NERRS = NERRS + 1
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END IF
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IF( LDAFB*N.GT.LAFB ) THEN
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WRITE( NOUT, FMT = 9998 )LAFB, N, KL, KU,
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$ N*( 2*KL+KU+1 )
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NERRS = NERRS + 1
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END IF
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GO TO 130
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END IF
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*
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DO 120 IMAT = 1, NIMAT
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*
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* Do the tests only if DOTYPE( IMAT ) is true.
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*
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IF( .NOT.DOTYPE( IMAT ) )
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$ GO TO 120
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*
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* Skip types 2, 3, or 4 if the matrix 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 120
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*
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* Set up parameters with SLATB4 and generate a
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* test matrix with SLATMS.
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*
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CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM,
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$ MODE, CNDNUM, DIST )
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RCONDC = ONE / CNDNUM
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*
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SRNAMT = 'SLATMS'
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CALL SLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, 'Z', A, LDA, WORK,
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$ 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,
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$ KL, KU, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 120
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END IF
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*
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* For types 2, 3, and 4, zero one or more columns of
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* the matrix 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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IOFF = ( IZERO-1 )*LDA
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IF( IMAT.LT.4 ) THEN
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I1 = MAX( 1, KU+2-IZERO )
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I2 = MIN( KL+KU+1, KU+1+( N-IZERO ) )
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DO 20 I = I1, I2
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A( IOFF+I ) = ZERO
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20 CONTINUE
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ELSE
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DO 40 J = IZERO, N
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DO 30 I = MAX( 1, KU+2-J ),
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$ MIN( KL+KU+1, KU+1+( N-J ) )
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A( IOFF+I ) = ZERO
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30 CONTINUE
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IOFF = IOFF + LDA
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40 CONTINUE
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END IF
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END IF
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*
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* Save a copy of the matrix A in ASAV.
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*
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CALL SLACPY( 'Full', KL+KU+1, N, A, LDA, ASAV, LDA )
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*
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DO 110 IEQUED = 1, 4
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EQUED = EQUEDS( IEQUED )
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IF( IEQUED.EQ.1 ) THEN
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NFACT = 3
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ELSE
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NFACT = 1
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END IF
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*
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DO 100 IFACT = 1, NFACT
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FACT = FACTS( IFACT )
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PREFAC = LSAME( FACT, 'F' )
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NOFACT = LSAME( FACT, 'N' )
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EQUIL = LSAME( FACT, 'E' )
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*
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IF( ZEROT ) THEN
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IF( PREFAC )
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$ GO TO 100
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RCONDO = ZERO
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RCONDI = ZERO
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*
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ELSE IF( .NOT.NOFACT ) THEN
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*
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* Compute the condition number for comparison
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* with the value returned by SGESVX (FACT =
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* 'N' reuses the condition number from the
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* previous iteration with FACT = 'F').
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*
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CALL SLACPY( 'Full', KL+KU+1, N, ASAV, LDA,
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$ AFB( KL+1 ), LDAFB )
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IF( EQUIL .OR. IEQUED.GT.1 ) THEN
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*
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* Compute row and column scale factors to
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* equilibrate the matrix A.
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*
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CALL SGBEQU( N, N, KL, KU, AFB( KL+1 ),
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$ LDAFB, S, S( N+1 ), ROWCND,
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$ COLCND, AMAX, INFO )
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IF( INFO.EQ.0 .AND. N.GT.0 ) THEN
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IF( LSAME( EQUED, 'R' ) ) THEN
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ROWCND = ZERO
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COLCND = ONE
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ELSE IF( LSAME( EQUED, 'C' ) ) THEN
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ROWCND = ONE
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COLCND = ZERO
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ELSE IF( LSAME( EQUED, 'B' ) ) THEN
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ROWCND = ZERO
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COLCND = ZERO
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END IF
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*
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* Equilibrate the matrix.
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*
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CALL SLAQGB( N, N, KL, KU, AFB( KL+1 ),
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$ LDAFB, S, S( N+1 ),
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$ ROWCND, COLCND, AMAX,
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$ EQUED )
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END IF
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END IF
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*
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* Save the condition number of the
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* non-equilibrated system for use in SGET04.
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*
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IF( EQUIL ) THEN
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ROLDO = RCONDO
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ROLDI = RCONDI
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END IF
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*
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* Compute the 1-norm and infinity-norm of A.
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*
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ANORMO = SLANGB( '1', N, KL, KU, AFB( KL+1 ),
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$ LDAFB, RWORK )
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ANORMI = SLANGB( 'I', N, KL, KU, AFB( KL+1 ),
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$ LDAFB, RWORK )
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*
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* Factor the matrix A.
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*
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CALL SGBTRF( N, N, KL, KU, AFB, LDAFB, IWORK,
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$ INFO )
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*
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* Form the inverse of A.
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*
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CALL SLASET( 'Full', N, N, ZERO, ONE, WORK,
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$ LDB )
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SRNAMT = 'SGBTRS'
|
|
CALL SGBTRS( 'No transpose', N, KL, KU, N,
|
|
$ AFB, LDAFB, IWORK, WORK, LDB,
|
|
$ INFO )
|
|
*
|
|
* Compute the 1-norm condition number of A.
|
|
*
|
|
AINVNM = SLANGE( '1', N, N, WORK, LDB,
|
|
$ RWORK )
|
|
IF( ANORMO.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
|
|
RCONDO = ONE
|
|
ELSE
|
|
RCONDO = ( ONE / ANORMO ) / AINVNM
|
|
END IF
|
|
*
|
|
* Compute the infinity-norm condition number
|
|
* of A.
|
|
*
|
|
AINVNM = SLANGE( 'I', N, N, WORK, LDB,
|
|
$ RWORK )
|
|
IF( ANORMI.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
|
|
RCONDI = ONE
|
|
ELSE
|
|
RCONDI = ( ONE / ANORMI ) / AINVNM
|
|
END IF
|
|
END IF
|
|
*
|
|
DO 90 ITRAN = 1, NTRAN
|
|
*
|
|
* Do for each value of TRANS.
|
|
*
|
|
TRANS = TRANSS( ITRAN )
|
|
IF( ITRAN.EQ.1 ) THEN
|
|
RCONDC = RCONDO
|
|
ELSE
|
|
RCONDC = RCONDI
|
|
END IF
|
|
*
|
|
* Restore the matrix A.
|
|
*
|
|
CALL SLACPY( 'Full', KL+KU+1, N, ASAV, LDA,
|
|
$ A, LDA )
|
|
*
|
|
* Form an exact solution and set the right hand
|
|
* side.
|
|
*
|
|
SRNAMT = 'SLARHS'
|
|
CALL SLARHS( PATH, XTYPE, 'Full', TRANS, N,
|
|
$ N, KL, KU, NRHS, A, LDA, XACT,
|
|
$ LDB, B, LDB, ISEED, INFO )
|
|
XTYPE = 'C'
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDB, BSAV,
|
|
$ LDB )
|
|
*
|
|
IF( NOFACT .AND. ITRAN.EQ.1 ) THEN
|
|
*
|
|
* --- Test SGBSV ---
|
|
*
|
|
* Compute the LU factorization of the matrix
|
|
* and solve the system.
|
|
*
|
|
CALL SLACPY( 'Full', KL+KU+1, N, A, LDA,
|
|
$ AFB( KL+1 ), LDAFB )
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDB, X,
|
|
$ LDB )
|
|
*
|
|
SRNAMT = 'SGBSV '
|
|
CALL SGBSV( N, KL, KU, NRHS, AFB, LDAFB,
|
|
$ IWORK, X, LDB, INFO )
|
|
*
|
|
* Check error code from SGBSV .
|
|
*
|
|
IF( INFO.NE.IZERO )
|
|
$ CALL ALAERH( PATH, 'SGBSV ', INFO,
|
|
$ IZERO, ' ', N, N, KL, KU,
|
|
$ NRHS, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
* Reconstruct matrix from factors and
|
|
* compute residual.
|
|
*
|
|
CALL SGBT01( N, N, KL, KU, A, LDA, AFB,
|
|
$ LDAFB, IWORK, WORK,
|
|
$ RESULT( 1 ) )
|
|
NT = 1
|
|
IF( IZERO.EQ.0 ) THEN
|
|
*
|
|
* Compute residual of the computed
|
|
* solution.
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDB,
|
|
$ WORK, LDB )
|
|
CALL SGBT02( 'No transpose', N, N, KL,
|
|
$ KU, NRHS, A, LDA, X, LDB,
|
|
$ WORK, LDB, RWORK,
|
|
$ RESULT( 2 ) )
|
|
*
|
|
* Check solution from generated exact
|
|
* solution.
|
|
*
|
|
CALL SGET04( N, NRHS, X, LDB, XACT,
|
|
$ LDB, RCONDC, RESULT( 3 ) )
|
|
NT = 3
|
|
END IF
|
|
*
|
|
* Print information about the tests that did
|
|
* not pass the threshold.
|
|
*
|
|
DO 50 K = 1, NT
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )'SGBSV ',
|
|
$ N, KL, KU, IMAT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
50 CONTINUE
|
|
NRUN = NRUN + NT
|
|
END IF
|
|
*
|
|
* --- Test SGBSVX ---
|
|
*
|
|
IF( .NOT.PREFAC )
|
|
$ CALL SLASET( 'Full', 2*KL+KU+1, N, ZERO,
|
|
$ ZERO, AFB, LDAFB )
|
|
CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X,
|
|
$ LDB )
|
|
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
|
|
*
|
|
* Equilibrate the matrix if FACT = 'F' and
|
|
* EQUED = 'R', 'C', or 'B'.
|
|
*
|
|
CALL SLAQGB( N, N, KL, KU, A, LDA, S,
|
|
$ S( N+1 ), ROWCND, COLCND,
|
|
$ AMAX, EQUED )
|
|
END IF
|
|
*
|
|
* Solve the system and compute the condition
|
|
* number and error bounds using SGBSVX.
|
|
*
|
|
SRNAMT = 'SGBSVX'
|
|
CALL SGBSVX( FACT, TRANS, N, KL, KU, NRHS, A,
|
|
$ LDA, AFB, LDAFB, IWORK, EQUED,
|
|
$ S, S( N+1 ), B, LDB, X, LDB,
|
|
$ RCOND, RWORK, RWORK( NRHS+1 ),
|
|
$ WORK, IWORK( N+1 ), INFO )
|
|
*
|
|
* Check the error code from SGBSVX.
|
|
*
|
|
IF( INFO.NE.IZERO )
|
|
$ CALL ALAERH( PATH, 'SGBSVX', INFO, IZERO,
|
|
$ FACT // TRANS, N, N, KL, KU,
|
|
$ NRHS, IMAT, NFAIL, NERRS,
|
|
$ NOUT )
|
|
*
|
|
* Compare WORK(1) from SGBSVX with the computed
|
|
* reciprocal pivot growth factor RPVGRW
|
|
*
|
|
IF( INFO.NE.0 ) THEN
|
|
ANRMPV = ZERO
|
|
DO 70 J = 1, INFO
|
|
DO 60 I = MAX( KU+2-J, 1 ),
|
|
$ MIN( N+KU+1-J, KL+KU+1 )
|
|
ANRMPV = MAX( ANRMPV,
|
|
$ ABS( A( I+( J-1 )*LDA ) ) )
|
|
60 CONTINUE
|
|
70 CONTINUE
|
|
RPVGRW = SLANTB( 'M', 'U', 'N', INFO,
|
|
$ MIN( INFO-1, KL+KU ),
|
|
$ AFB( MAX( 1, KL+KU+2-INFO ) ),
|
|
$ LDAFB, WORK )
|
|
IF( RPVGRW.EQ.ZERO ) THEN
|
|
RPVGRW = ONE
|
|
ELSE
|
|
RPVGRW = ANRMPV / RPVGRW
|
|
END IF
|
|
ELSE
|
|
RPVGRW = SLANTB( 'M', 'U', 'N', N, KL+KU,
|
|
$ AFB, LDAFB, WORK )
|
|
IF( RPVGRW.EQ.ZERO ) THEN
|
|
RPVGRW = ONE
|
|
ELSE
|
|
RPVGRW = SLANGB( 'M', N, KL, KU, A,
|
|
$ LDA, WORK ) / RPVGRW
|
|
END IF
|
|
END IF
|
|
RESULT( 7 ) = ABS( RPVGRW-WORK( 1 ) ) /
|
|
$ MAX( WORK( 1 ), RPVGRW ) /
|
|
$ SLAMCH( 'E' )
|
|
*
|
|
IF( .NOT.PREFAC ) THEN
|
|
*
|
|
* Reconstruct matrix from factors and
|
|
* compute residual.
|
|
*
|
|
CALL SGBT01( N, N, KL, KU, A, LDA, AFB,
|
|
$ LDAFB, IWORK, WORK,
|
|
$ RESULT( 1 ) )
|
|
K1 = 1
|
|
ELSE
|
|
K1 = 2
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
TRFCON = .FALSE.
|
|
*
|
|
* Compute residual of the computed solution.
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, BSAV, LDB,
|
|
$ WORK, LDB )
|
|
CALL SGBT02( TRANS, N, N, KL, KU, NRHS,
|
|
$ ASAV, LDA, X, LDB, WORK, LDB,
|
|
$ RWORK( 2*NRHS+1 ),
|
|
$ RESULT( 2 ) )
|
|
*
|
|
* Check solution from generated exact
|
|
* solution.
|
|
*
|
|
IF( NOFACT .OR. ( PREFAC .AND.
|
|
$ LSAME( EQUED, 'N' ) ) ) THEN
|
|
CALL SGET04( N, NRHS, X, LDB, XACT,
|
|
$ LDB, RCONDC, RESULT( 3 ) )
|
|
ELSE
|
|
IF( ITRAN.EQ.1 ) THEN
|
|
ROLDC = ROLDO
|
|
ELSE
|
|
ROLDC = ROLDI
|
|
END IF
|
|
CALL SGET04( N, NRHS, X, LDB, XACT,
|
|
$ LDB, ROLDC, RESULT( 3 ) )
|
|
END IF
|
|
*
|
|
* Check the error bounds from iterative
|
|
* refinement.
|
|
*
|
|
CALL SGBT05( TRANS, N, KL, KU, NRHS, ASAV,
|
|
$ LDA, B, LDB, X, LDB, XACT,
|
|
$ LDB, RWORK, RWORK( NRHS+1 ),
|
|
$ RESULT( 4 ) )
|
|
ELSE
|
|
TRFCON = .TRUE.
|
|
END IF
|
|
*
|
|
* Compare RCOND from SGBSVX with the computed
|
|
* value in RCONDC.
|
|
*
|
|
RESULT( 6 ) = SGET06( RCOND, RCONDC )
|
|
*
|
|
* Print information about the tests that did
|
|
* not pass the threshold.
|
|
*
|
|
IF( .NOT.TRFCON ) THEN
|
|
DO 80 K = K1, NTESTS
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )
|
|
$ 'SGBSVX', FACT, TRANS, N, KL,
|
|
$ KU, EQUED, IMAT, K,
|
|
$ RESULT( K )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )
|
|
$ 'SGBSVX', FACT, TRANS, N, KL,
|
|
$ KU, IMAT, K, RESULT( K )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
80 CONTINUE
|
|
NRUN = NRUN + 7 - K1
|
|
ELSE
|
|
IF( RESULT( 1 ).GE.THRESH .AND. .NOT.
|
|
$ PREFAC ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, EQUED,
|
|
$ IMAT, 1, RESULT( 1 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, IMAT, 1,
|
|
$ RESULT( 1 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
IF( RESULT( 6 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, EQUED,
|
|
$ IMAT, 6, RESULT( 6 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, IMAT, 6,
|
|
$ RESULT( 6 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, EQUED,
|
|
$ IMAT, 7, RESULT( 7 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVX',
|
|
$ FACT, TRANS, N, KL, KU, IMAT, 7,
|
|
$ RESULT( 7 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
*
|
|
END IF
|
|
*
|
|
* --- Test SGBSVXX ---
|
|
*
|
|
* Restore the matrices A and B.
|
|
*
|
|
CALL SLACPY( 'Full', KL+KU+1, N, ASAV, LDA, A,
|
|
$ LDA )
|
|
CALL SLACPY( 'Full', N, NRHS, BSAV, LDB, B, LDB )
|
|
|
|
IF( .NOT.PREFAC )
|
|
$ CALL SLASET( 'Full', 2*KL+KU+1, N, ZERO, ZERO,
|
|
$ AFB, LDAFB )
|
|
CALL SLASET( 'Full', N, NRHS, ZERO, ZERO, X, LDB )
|
|
IF( IEQUED.GT.1 .AND. N.GT.0 ) THEN
|
|
*
|
|
* Equilibrate the matrix if FACT = 'F' and
|
|
* EQUED = 'R', 'C', or 'B'.
|
|
*
|
|
CALL SLAQGB( N, N, KL, KU, A, LDA, S,
|
|
$ S( N+1 ), ROWCND, COLCND, AMAX, EQUED )
|
|
END IF
|
|
*
|
|
* Solve the system and compute the condition number
|
|
* and error bounds using SGBSVXX.
|
|
*
|
|
SRNAMT = 'SGBSVXX'
|
|
N_ERR_BNDS = 3
|
|
CALL SGBSVXX( FACT, TRANS, N, KL, KU, NRHS, A, LDA,
|
|
$ AFB, LDAFB, IWORK, EQUED, S, S( N+1 ), B, LDB,
|
|
$ X, LDB, RCOND, RPVGRW_SVXX, BERR, N_ERR_BNDS,
|
|
$ ERRBNDS_N, ERRBNDS_C, 0, ZERO, WORK,
|
|
$ IWORK( N+1 ), INFO )
|
|
|
|
* Check the error code from SGBSVXX.
|
|
*
|
|
IF( INFO.EQ.N+1 ) GOTO 90
|
|
IF( INFO.NE.IZERO ) THEN
|
|
CALL ALAERH( PATH, 'SGBSVXX', INFO, IZERO,
|
|
$ FACT // TRANS, N, N, -1, -1, NRHS,
|
|
$ IMAT, NFAIL, NERRS, NOUT )
|
|
GOTO 90
|
|
END IF
|
|
*
|
|
* Compare rpvgrw_svxx from SGBSVXX with the computed
|
|
* reciprocal pivot growth factor RPVGRW
|
|
*
|
|
|
|
IF ( INFO .GT. 0 .AND. INFO .LT. N+1 ) THEN
|
|
RPVGRW = SLA_GBRPVGRW(N, KL, KU, INFO, A, LDA,
|
|
$ AFB, LDAFB )
|
|
ELSE
|
|
RPVGRW = SLA_GBRPVGRW(N, KL, KU, N, A, LDA,
|
|
$ AFB, LDAFB )
|
|
ENDIF
|
|
|
|
RESULT( 7 ) = ABS( RPVGRW-rpvgrw_svxx ) /
|
|
$ MAX( rpvgrw_svxx, RPVGRW ) /
|
|
$ SLAMCH( 'E' )
|
|
*
|
|
IF( .NOT.PREFAC ) THEN
|
|
*
|
|
* Reconstruct matrix from factors and compute
|
|
* residual.
|
|
*
|
|
CALL SGBT01( N, N, KL, KU, A, LDA, AFB, LDAFB,
|
|
$ IWORK, WORK,
|
|
$ RESULT( 1 ) )
|
|
K1 = 1
|
|
ELSE
|
|
K1 = 2
|
|
END IF
|
|
*
|
|
IF( INFO.EQ.0 ) THEN
|
|
TRFCON = .FALSE.
|
|
*
|
|
* Compute residual of the computed solution.
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, BSAV, LDB, WORK,
|
|
$ LDB )
|
|
CALL SGBT02( TRANS, N, N, KL, KU, NRHS, ASAV,
|
|
$ LDA, X, LDB, WORK, LDB, RWORK,
|
|
$ RESULT( 2 ) )
|
|
*
|
|
* Check solution from generated exact solution.
|
|
*
|
|
IF( NOFACT .OR. ( PREFAC .AND. LSAME( EQUED,
|
|
$ 'N' ) ) ) THEN
|
|
CALL SGET04( N, NRHS, X, LDB, XACT, LDB,
|
|
$ RCONDC, RESULT( 3 ) )
|
|
ELSE
|
|
IF( ITRAN.EQ.1 ) THEN
|
|
ROLDC = ROLDO
|
|
ELSE
|
|
ROLDC = ROLDI
|
|
END IF
|
|
CALL SGET04( N, NRHS, X, LDB, XACT, LDB,
|
|
$ ROLDC, RESULT( 3 ) )
|
|
END IF
|
|
ELSE
|
|
TRFCON = .TRUE.
|
|
END IF
|
|
*
|
|
* Compare RCOND from SGBSVXX with the computed value
|
|
* in RCONDC.
|
|
*
|
|
RESULT( 6 ) = SGET06( RCOND, RCONDC )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
IF( .NOT.TRFCON ) THEN
|
|
DO 45 K = K1, NTESTS
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVXX',
|
|
$ FACT, TRANS, N, KL, KU, EQUED,
|
|
$ IMAT, K, RESULT( K )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVXX',
|
|
$ FACT, TRANS, N, KL, KU, IMAT, K,
|
|
$ RESULT( K )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
45 CONTINUE
|
|
NRUN = NRUN + 7 - K1
|
|
ELSE
|
|
IF( RESULT( 1 ).GE.THRESH .AND. .NOT.PREFAC )
|
|
$ THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, EQUED, IMAT, 1,
|
|
$ RESULT( 1 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, IMAT, 1,
|
|
$ RESULT( 1 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
IF( RESULT( 6 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, EQUED, IMAT, 6,
|
|
$ RESULT( 6 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, IMAT, 6,
|
|
$ RESULT( 6 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALADHD( NOUT, PATH )
|
|
IF( PREFAC ) THEN
|
|
WRITE( NOUT, FMT = 9995 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, EQUED, IMAT, 7,
|
|
$ RESULT( 7 )
|
|
ELSE
|
|
WRITE( NOUT, FMT = 9996 )'SGBSVXX', FACT,
|
|
$ TRANS, N, KL, KU, IMAT, 7,
|
|
$ RESULT( 7 )
|
|
END IF
|
|
NFAIL = NFAIL + 1
|
|
NRUN = NRUN + 1
|
|
END IF
|
|
|
|
END IF
|
|
*
|
|
90 CONTINUE
|
|
100 CONTINUE
|
|
110 CONTINUE
|
|
120 CONTINUE
|
|
130 CONTINUE
|
|
140 CONTINUE
|
|
150 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASVM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
|
|
* Test Error Bounds from SGBSVXX
|
|
|
|
CALL SEBCHVXX(THRESH, PATH)
|
|
|
|
9999 FORMAT( ' *** In SDRVGB, LA=', I5, ' is too small for N=', I5,
|
|
$ ', KU=', I5, ', KL=', I5, / ' ==> Increase LA to at least ',
|
|
$ I5 )
|
|
9998 FORMAT( ' *** In SDRVGB, LAFB=', I5, ' is too small for N=', I5,
|
|
$ ', KU=', I5, ', KL=', I5, /
|
|
$ ' ==> Increase LAFB to at least ', I5 )
|
|
9997 FORMAT( 1X, A, ', N=', I5, ', KL=', I5, ', KU=', I5, ', type ',
|
|
$ I1, ', test(', I1, ')=', G12.5 )
|
|
9996 FORMAT( 1X, A, '( ''', A1, ''',''', A1, ''',', I5, ',', I5, ',',
|
|
$ I5, ',...), type ', I1, ', test(', I1, ')=', G12.5 )
|
|
9995 FORMAT( 1X, A, '( ''', A1, ''',''', A1, ''',', I5, ',', I5, ',',
|
|
$ I5, ',...), EQUED=''', A1, ''', type ', I1, ', test(', I1,
|
|
$ ')=', G12.5 )
|
|
*
|
|
RETURN
|
|
*
|
|
* End of SDRVGBX
|
|
*
|
|
END
|