667 lines
22 KiB
Fortran
667 lines
22 KiB
Fortran
*> \brief \b SCHKSY
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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 SCHKSY( 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, IWORK, 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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* REAL THRESH
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* ..
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* .. Array Arguments ..
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* LOGICAL DOTYPE( * )
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* INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
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* REAL A( * ), AFAC( * ), AINV( * ), B( * ),
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* $ RWORK( * ), 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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*> SCHKSY tests SSYTRF, -TRI2, -TRS, -TRS2, -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 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[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 REAL 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 REAL 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 REAL 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 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[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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*> \date April 2012
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*
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*> \ingroup single_lin
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*
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* =====================================================================
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SUBROUTINE SCHKSY( 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, IWORK, NOUT )
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*
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* -- LAPACK test routine (version 3.4.1) --
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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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* April 2012
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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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REAL THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
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REAL A( * ), AFAC( * ), AINV( * ), B( * ),
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$ RWORK( * ), 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 ZERO
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PARAMETER ( ZERO = 0.0E+0 )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 10 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 9 )
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* ..
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* .. Local Scalars ..
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LOGICAL TRFCON, ZEROT
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CHARACTER DIST, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH
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INTEGER I, I1, I2, IMAT, IN, INB, INFO, IOFF, IRHS,
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$ IUPLO, IZERO, J, K, KL, KU, LDA, LWORK, MODE,
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$ N, NB, NERRS, NFAIL, NIMAT, NRHS, NRUN, NT
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REAL ANORM, CNDNUM, RCOND, RCONDC
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* ..
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* .. Local Arrays ..
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CHARACTER UPLOS( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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REAL RESULT( NTESTS )
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* ..
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* .. External Functions ..
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REAL SGET06, SLANSY
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EXTERNAL SGET06, SLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, SERRSY, SGET04, SLACPY,
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$ SLARHS, SLATB4, SLATMS, SPOT02, SPOT03, SPOT05,
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$ SSYCON, SSYCONV, SSYRFS, SSYT01, SSYTRF,
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$ SSYTRI2, SSYTRS, SSYTRS2, XLAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC 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 UPLOS / 'U', 'L' /
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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 ) = 'SY'
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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 SERRSY( PATH, NOUT )
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INFOT = 0
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*
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* Set the minimum block size for which the block routine should
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* be used, which will be later returned by ILAENV
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*
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CALL XLAENV( 2, 2 )
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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 180 IN = 1, NN
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N = NVAL( IN )
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LDA = MAX( N, 1 )
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XTYPE = 'N'
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NIMAT = NTYPES
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IF( N.LE.0 )
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$ NIMAT = 1
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*
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IZERO = 0
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*
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* Do for each value of matrix type IMAT
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*
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DO 170 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 170
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*
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* Skip types 3, 4, 5, or 6 if the matrix size is too small.
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*
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ZEROT = IMAT.GE.3 .AND. IMAT.LE.6
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IF( ZEROT .AND. N.LT.IMAT-2 )
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$ GO TO 170
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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 160 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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*
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* Begin generate the test matrix A.
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*
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* Set up parameters with SLATB4 for the matrix generator
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* based on the type of matrix to be generated.
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*
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CALL SLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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$ CNDNUM, DIST )
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*
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* Generate a matrix with SLATMS.
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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, UPLO, A, LDA, WORK,
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$ INFO )
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*
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* Check error code from SLATMS and handle error.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'SLATMS', INFO, 0, UPLO, N, N, -1,
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$ -1, -1, IMAT, NFAIL, NERRS, NOUT )
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GO TO 160
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END IF
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*
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* For matrix types 3-6, zero one or more rows and
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* columns of the matrix to test that INFO is returned
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* correctly.
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*
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IF( ZEROT ) THEN
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IF( IMAT.EQ.3 ) THEN
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IZERO = 1
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ELSE IF( IMAT.EQ.4 ) THEN
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IZERO = N
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ELSE
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IZERO = N / 2 + 1
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END IF
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*
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IF( IMAT.LT.6 ) THEN
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*
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* Set row and column IZERO to zero.
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*
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IF( IUPLO.EQ.1 ) THEN
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IOFF = ( IZERO-1 )*LDA
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DO 20 I = 1, IZERO - 1
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A( IOFF+I ) = ZERO
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20 CONTINUE
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IOFF = IOFF + IZERO
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DO 30 I = IZERO, N
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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30 CONTINUE
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ELSE
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IOFF = IZERO
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DO 40 I = 1, IZERO - 1
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A( IOFF ) = ZERO
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IOFF = IOFF + LDA
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40 CONTINUE
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IOFF = IOFF - IZERO
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DO 50 I = IZERO, N
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A( IOFF+I ) = ZERO
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50 CONTINUE
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END IF
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ELSE
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IOFF = 0
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IF( IUPLO.EQ.1 ) THEN
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*
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* Set the first IZERO rows and columns to zero.
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*
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DO 70 J = 1, N
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I2 = MIN( J, IZERO )
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DO 60 I = 1, I2
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A( IOFF+I ) = ZERO
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60 CONTINUE
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IOFF = IOFF + LDA
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70 CONTINUE
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ELSE
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*
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* Set the last IZERO rows and columns to zero.
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*
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DO 90 J = 1, N
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I1 = MAX( J, IZERO )
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DO 80 I = I1, N
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A( IOFF+I ) = ZERO
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80 CONTINUE
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IOFF = IOFF + LDA
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90 CONTINUE
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END IF
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END IF
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ELSE
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IZERO = 0
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END IF
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*
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* End generate the test matrix A.
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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 150 INB = 1, NNB
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*
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* Set the optimal blocksize, which will be later
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* returned by ILAENV.
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*
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NB = NBVAL( INB )
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CALL XLAENV( 1, NB )
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*
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* Copy the test matrix A into matrix AFAC which
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* will be factorized in place. This is needed to
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* preserve the test matrix A for subsequent tests.
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*
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CALL SLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
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*
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* Compute the L*D*L**T or U*D*U**T factorization of the
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* matrix. IWORK stores details of the interchanges and
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* the block structure of D. AINV is a work array for
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* block factorization, LWORK is the length of AINV.
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*
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LWORK = MAX( 2, NB )*LDA
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SRNAMT = 'SSYTRF'
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CALL SSYTRF( UPLO, N, AFAC, LDA, IWORK, AINV, LWORK,
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$ INFO )
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*
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* Adjust the expected value of INFO to account for
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* pivoting.
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*
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K = IZERO
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IF( K.GT.0 ) THEN
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100 CONTINUE
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IF( IWORK( K ).LT.0 ) THEN
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IF( IWORK( K ).NE.-K ) THEN
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K = -IWORK( K )
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GO TO 100
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END IF
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ELSE IF( IWORK( K ).NE.K ) THEN
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K = IWORK( K )
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GO TO 100
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END IF
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END IF
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*
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* Check error code from SSYTRF and handle error.
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*
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IF( INFO.NE.K )
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$ CALL ALAERH( PATH, 'SSYTRF', INFO, K, UPLO, N, N,
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$ -1, -1, NB, IMAT, NFAIL, NERRS, NOUT )
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*
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* Set the condition estimate flag if the INFO is not 0.
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*
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IF( INFO.NE.0 ) THEN
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TRFCON = .TRUE.
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ELSE
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TRFCON = .FALSE.
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END IF
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*
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*+ TEST 1
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* Reconstruct matrix from factors and compute residual.
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*
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CALL SSYT01( UPLO, N, A, LDA, AFAC, LDA, IWORK, AINV,
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$ LDA, RWORK, RESULT( 1 ) )
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NT = 1
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*
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*+ TEST 2
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* Form the inverse and compute the residual,
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* if the factorization was competed without INFO > 0
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* (i.e. there is no zero rows and columns).
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* Do it only for the first block size.
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*
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IF( INB.EQ.1 .AND. .NOT.TRFCON ) THEN
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CALL SLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
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SRNAMT = 'SSYTRI2'
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LWORK = (N+NB+1)*(NB+3)
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CALL SSYTRI2( UPLO, N, AINV, LDA, IWORK, WORK,
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$ LWORK, INFO )
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*
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* Check error code from SSYTRI2 and handle error.
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*
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IF( INFO.NE.0 )
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$ CALL ALAERH( PATH, 'SSYTRI2', INFO, -1, UPLO, N,
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$ N, -1, -1, -1, IMAT, NFAIL, NERRS,
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$ NOUT )
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*
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* Compute the residual for a symmetric matrix times
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* its inverse.
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*
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CALL SPOT03( UPLO, N, A, LDA, AINV, LDA, WORK, LDA,
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$ RWORK, RCONDC, RESULT( 2 ) )
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NT = 2
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END IF
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*
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* Print information about the tests that did not pass
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* the threshold.
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*
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DO 110 K = 1, NT
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IF( RESULT( K ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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$ CALL ALAHD( NOUT, PATH )
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WRITE( NOUT, FMT = 9999 )UPLO, N, NB, 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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110 CONTINUE
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NRUN = NRUN + NT
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*
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* Skip the other tests if this is not the first block
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* size.
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*
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IF( INB.GT.1 )
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$ GO TO 150
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*
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* Do only the condition estimate if INFO is not 0.
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*
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IF( TRFCON ) THEN
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RCONDC = ZERO
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GO TO 140
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END IF
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*
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DO 130 IRHS = 1, NNS
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NRHS = NSVAL( IRHS )
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*
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*+ TEST 3 (Using DSYTRS)
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* Solve and compute residual for A * X = B.
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*
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* Choose a set of NRHS random solution vectors
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* stored in XACT and set up the right hand side B
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*
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SRNAMT = 'SLARHS'
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CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
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$ NRHS, A, LDA, XACT, LDA, B, LDA,
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$ ISEED, INFO )
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CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
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*
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|
SRNAMT = 'SSYTRS'
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|
CALL SSYTRS( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
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|
$ LDA, INFO )
|
|
*
|
|
* Check error code from SSYTRS and handle error.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SSYTRS', INFO, 0, UPLO, N,
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|
$ N, -1, -1, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
|
*
|
|
* Compute the residual for the solution
|
|
*
|
|
CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
|
|
$ LDA, RWORK, RESULT( 3 ) )
|
|
*
|
|
*+ TEST 4 (Using DSYTRS2)
|
|
* Solve and compute residual for A * X = B.
|
|
*
|
|
* Choose a set of NRHS random solution vectors
|
|
* stored in XACT and set up the right hand side B
|
|
*
|
|
SRNAMT = 'SLARHS'
|
|
CALL SLARHS( PATH, XTYPE, UPLO, ' ', N, N, KL, KU,
|
|
$ NRHS, A, LDA, XACT, LDA, B, LDA,
|
|
$ ISEED, INFO )
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
|
*
|
|
SRNAMT = 'DSYTRS2'
|
|
CALL SSYTRS2( UPLO, N, NRHS, AFAC, LDA, IWORK, X,
|
|
$ LDA, WORK, INFO )
|
|
*
|
|
* Check error code from SSYTRS2 and handle error.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SSYTRS2', INFO, 0, UPLO, N,
|
|
$ N, -1, -1, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
*
|
|
CALL SLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
|
*
|
|
* Compute the residual for the solution
|
|
*
|
|
CALL SPOT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
|
|
$ LDA, RWORK, RESULT( 4 ) )
|
|
*
|
|
*+ TEST 5
|
|
* Check solution from generated exact solution.
|
|
*
|
|
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 5 ) )
|
|
*
|
|
*+ TESTS 6, 7, and 8
|
|
* Use iterative refinement to improve the solution.
|
|
*
|
|
SRNAMT = 'SSYRFS'
|
|
CALL SSYRFS( UPLO, N, NRHS, A, LDA, AFAC, LDA,
|
|
$ IWORK, B, LDA, X, LDA, RWORK,
|
|
$ RWORK( NRHS+1 ), WORK, IWORK( N+1 ),
|
|
$ INFO )
|
|
*
|
|
* Check error code from SSYRFS.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SSYRFS', INFO, 0, UPLO, N,
|
|
$ N, -1, -1, NRHS, IMAT, NFAIL,
|
|
$ NERRS, NOUT )
|
|
*
|
|
CALL SGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
|
$ RESULT( 6 ) )
|
|
CALL SPOT05( UPLO, N, NRHS, A, LDA, B, LDA, X, LDA,
|
|
$ XACT, LDA, RWORK, RWORK( NRHS+1 ),
|
|
$ RESULT( 7 ) )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
DO 120 K = 3, 8
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
|
|
$ IMAT, K, RESULT( K )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
120 CONTINUE
|
|
NRUN = NRUN + 6
|
|
130 CONTINUE
|
|
*
|
|
*+ TEST 9
|
|
* Get an estimate of RCOND = 1/CNDNUM.
|
|
*
|
|
140 CONTINUE
|
|
ANORM = SLANSY( '1', UPLO, N, A, LDA, RWORK )
|
|
SRNAMT = 'SSYCON'
|
|
CALL SSYCON( UPLO, N, AFAC, LDA, IWORK, ANORM, RCOND,
|
|
$ WORK, IWORK( N+1 ), INFO )
|
|
*
|
|
* Check error code from SSYCON and handle error.
|
|
*
|
|
IF( INFO.NE.0 )
|
|
$ CALL ALAERH( PATH, 'SSYCON', INFO, 0, UPLO, N, N,
|
|
$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
|
|
*
|
|
* Compute the test ratio to compare to values of RCOND
|
|
*
|
|
RESULT( 9 ) = SGET06( RCOND, RCONDC )
|
|
*
|
|
* Print information about the tests that did not pass
|
|
* the threshold.
|
|
*
|
|
IF( RESULT( 9 ).GE.THRESH ) THEN
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
|
$ CALL ALAHD( NOUT, PATH )
|
|
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 9,
|
|
$ RESULT( 9 )
|
|
NFAIL = NFAIL + 1
|
|
END IF
|
|
NRUN = NRUN + 1
|
|
150 CONTINUE
|
|
*
|
|
160 CONTINUE
|
|
170 CONTINUE
|
|
180 CONTINUE
|
|
*
|
|
* Print a summary of the results.
|
|
*
|
|
CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
|
|
*
|
|
9999 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NB =', I4, ', type ',
|
|
$ I2, ', test ', I2, ', ratio =', G12.5 )
|
|
9998 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
|
|
$ I2, ', test(', I2, ') =', G12.5 )
|
|
9997 FORMAT( ' UPLO = ''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
|
|
$ ', test(', I2, ') =', G12.5 )
|
|
RETURN
|
|
*
|
|
* End of SCHKSY
|
|
*
|
|
END
|