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853 lines
27 KiB
853 lines
27 KiB
2 years ago
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*> \brief \b ZCHKSY_ROOK
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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 ZCHKSY_ROOK( 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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* DOUBLE PRECISION 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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* DOUBLE PRECISION RWORK( * )
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* COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
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* $ WORK( * ), X( * ), XACT( * )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> ZCHKSY_ROOK tests ZSYTRF_ROOK, -TRI_ROOK, -TRS_ROOK,
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*> and -CON_ROOK.
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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 (NNB)
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*> The values of the blocksize NB.
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*> \endverbatim
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*>
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*> \param[in] NNS
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*> \verbatim
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*> NNS is INTEGER
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*> The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*> NSVAL is INTEGER array, dimension (NNS)
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*> The values of the number of right hand sides NRHS.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*> THRESH is DOUBLE PRECISION
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*> The threshold value for the test ratios. A result is
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*> included in the output file if RESULT >= THRESH. To have
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*> every test ratio printed, use THRESH = 0.
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*> \endverbatim
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*>
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*> \param[in] TSTERR
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*> \verbatim
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*> TSTERR is LOGICAL
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*> Flag that indicates whether error exits are to be tested.
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*> \endverbatim
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*>
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*> \param[in] NMAX
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*> \verbatim
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*> NMAX is INTEGER
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*> The maximum value permitted for N, used in dimensioning the
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*> work arrays.
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*> \endverbatim
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*>
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*> \param[out] A
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*> \verbatim
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*> A is COMPLEX*16 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 COMPLEX*16 array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] AINV
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*> \verbatim
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*> AINV is COMPLEX*16 array, dimension (NMAX*NMAX)
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*> \endverbatim
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*>
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*> \param[out] B
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*> \verbatim
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*> B is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> where NSMAX is the largest entry in NSVAL.
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] XACT
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*> \verbatim
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*> XACT is COMPLEX*16 array, dimension (NMAX*NSMAX)
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX*16 array, dimension (NMAX*max(3,NSMAX))
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (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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*> \ingroup complex16_lin
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*
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* =====================================================================
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SUBROUTINE ZCHKSY_ROOK( 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 --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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LOGICAL TSTERR
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INTEGER NMAX, NN, NNB, NNS, NOUT
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DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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LOGICAL DOTYPE( * )
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INTEGER IWORK( * ), NBVAL( * ), NSVAL( * ), NVAL( * )
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DOUBLE PRECISION RWORK( * )
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COMPLEX*16 A( * ), AFAC( * ), AINV( * ), B( * ),
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$ WORK( * ), X( * ), XACT( * )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 )
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DOUBLE PRECISION ONEHALF
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PARAMETER ( ONEHALF = 0.5D+0 )
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DOUBLE PRECISION EIGHT, SEVTEN
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PARAMETER ( EIGHT = 8.0D+0, SEVTEN = 17.0D+0 )
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COMPLEX*16 CZERO
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PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
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INTEGER NTYPES
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PARAMETER ( NTYPES = 11 )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 7 )
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* ..
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* .. Local Scalars ..
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LOGICAL TRFCON, ZEROT
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CHARACTER DIST, TYPE, UPLO, XTYPE
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CHARACTER*3 PATH, MATPATH
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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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DOUBLE PRECISION ALPHA, ANORM, CNDNUM, CONST, DTEMP, SING_MAX,
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$ SING_MIN, 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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DOUBLE PRECISION RESULT( NTESTS )
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COMPLEX*16 BLOCK( 2, 2 ), ZDUMMY( 1 )
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DGET06, ZLANGE, ZLANSY
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EXTERNAL DGET06, ZLANGE, ZLANSY
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* ..
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* .. External Subroutines ..
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EXTERNAL ALAERH, ALAHD, ALASUM, ZERRSY, ZGESVD, ZGET04,
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$ ZLACPY, ZLARHS, ZLATB4, ZLATMS, ZLATSY,ZSYT02,
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$ ZSYT03, ZSYCON_ROOK, ZSYT01_ROOK, ZSYTRF_ROOK,
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$ ZSYTRI_ROOK, ZSYTRS_ROOK, XLAENV
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, MIN, SQRT
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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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ALPHA = ( ONE+SQRT( SEVTEN ) ) / EIGHT
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*
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* Test path
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*
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PATH( 1: 1 ) = 'Zomplex precision'
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PATH( 2: 3 ) = 'SR'
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*
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* Path to generate matrices
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*
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MATPATH( 1: 1 ) = 'Zomplex precision'
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MATPATH( 2: 3 ) = 'SY'
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*
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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 ZERRSY( 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 270 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 260 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 260
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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 260
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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 250 IUPLO = 1, 2
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UPLO = UPLOS( IUPLO )
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*
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* Begin generate test matrix A.
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*
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IF( IMAT.NE.NTYPES ) THEN
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*
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* Set up parameters with ZLATB4 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 ZLATB4( MATPATH, IMAT, N, N, TYPE, KL, KU, ANORM,
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$ MODE, CNDNUM, DIST )
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*
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* Generate a matrix with ZLATMS.
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*
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SRNAMT = 'ZLATMS'
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CALL ZLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE,
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$ CNDNUM, ANORM, KL, KU, UPLO, A, LDA,
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$ WORK, INFO )
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*
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* Check error code from ZLATMS and handle error.
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*
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IF( INFO.NE.0 ) THEN
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CALL ALAERH( PATH, 'ZLATMS', INFO, 0, UPLO, N, N,
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$ -1, -1, -1, IMAT, NFAIL, NERRS, NOUT )
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*
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* Skip all tests for this generated matrix
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*
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GO TO 250
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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 ) = CZERO
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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 ) = CZERO
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IOFF = IOFF + LDA
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30 CONTINUE
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ELSE
|
||
|
|
IOFF = IZERO
|
||
|
|
DO 40 I = 1, IZERO - 1
|
||
|
|
A( IOFF ) = CZERO
|
||
|
|
IOFF = IOFF + LDA
|
||
|
|
40 CONTINUE
|
||
|
|
IOFF = IOFF - IZERO
|
||
|
|
DO 50 I = IZERO, N
|
||
|
|
A( IOFF+I ) = CZERO
|
||
|
|
50 CONTINUE
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
IF( IUPLO.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Set the first IZERO rows and columns to zero.
|
||
|
|
*
|
||
|
|
IOFF = 0
|
||
|
|
DO 70 J = 1, N
|
||
|
|
I2 = MIN( J, IZERO )
|
||
|
|
DO 60 I = 1, I2
|
||
|
|
A( IOFF+I ) = CZERO
|
||
|
|
60 CONTINUE
|
||
|
|
IOFF = IOFF + LDA
|
||
|
|
70 CONTINUE
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Set the last IZERO rows and columns to zero.
|
||
|
|
*
|
||
|
|
IOFF = 0
|
||
|
|
DO 90 J = 1, N
|
||
|
|
I1 = MAX( J, IZERO )
|
||
|
|
DO 80 I = I1, N
|
||
|
|
A( IOFF+I ) = CZERO
|
||
|
|
80 CONTINUE
|
||
|
|
IOFF = IOFF + LDA
|
||
|
|
90 CONTINUE
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
ELSE
|
||
|
|
IZERO = 0
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* For matrix kind IMAT = 11, generate special block
|
||
|
|
* diagonal matrix to test alternate code
|
||
|
|
* for the 2 x 2 blocks.
|
||
|
|
*
|
||
|
|
CALL ZLATSY( UPLO, N, A, LDA, ISEED )
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* End generate test matrix A.
|
||
|
|
*
|
||
|
|
*
|
||
|
|
* Do for each value of NB in NBVAL
|
||
|
|
*
|
||
|
|
DO 240 INB = 1, NNB
|
||
|
|
*
|
||
|
|
* Set the optimal blocksize, which will be later
|
||
|
|
* returned by ILAENV.
|
||
|
|
*
|
||
|
|
NB = NBVAL( INB )
|
||
|
|
CALL XLAENV( 1, NB )
|
||
|
|
*
|
||
|
|
* Copy the test matrix A into matrix AFAC which
|
||
|
|
* will be factorized in place. This is needed to
|
||
|
|
* preserve the test matrix A for subsequent tests.
|
||
|
|
*
|
||
|
|
CALL ZLACPY( UPLO, N, N, A, LDA, AFAC, LDA )
|
||
|
|
*
|
||
|
|
* Compute the L*D*L**T or U*D*U**T factorization of the
|
||
|
|
* matrix. IWORK stores details of the interchanges and
|
||
|
|
* the block structure of D. AINV is a work array for
|
||
|
|
* block factorization, LWORK is the length of AINV.
|
||
|
|
*
|
||
|
|
LWORK = MAX( 2, NB )*LDA
|
||
|
|
SRNAMT = 'ZSYTRF_ROOK'
|
||
|
|
CALL ZSYTRF_ROOK( UPLO, N, AFAC, LDA, IWORK, AINV,
|
||
|
|
$ LWORK, INFO )
|
||
|
|
*
|
||
|
|
* Adjust the expected value of INFO to account for
|
||
|
|
* pivoting.
|
||
|
|
*
|
||
|
|
K = IZERO
|
||
|
|
IF( K.GT.0 ) THEN
|
||
|
|
100 CONTINUE
|
||
|
|
IF( IWORK( K ).LT.0 ) THEN
|
||
|
|
IF( IWORK( K ).NE.-K ) THEN
|
||
|
|
K = -IWORK( K )
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
ELSE IF( IWORK( K ).NE.K ) THEN
|
||
|
|
K = IWORK( K )
|
||
|
|
GO TO 100
|
||
|
|
END IF
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Check error code from ZSYTRF_ROOK and handle error.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.K)
|
||
|
|
$ CALL ALAERH( PATH, 'ZSYTRF_ROOK', INFO, K,
|
||
|
|
$ UPLO, N, N, -1, -1, NB, IMAT,
|
||
|
|
$ NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Set the condition estimate flag if the INFO is not 0.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 ) THEN
|
||
|
|
TRFCON = .TRUE.
|
||
|
|
ELSE
|
||
|
|
TRFCON = .FALSE.
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
*+ TEST 1
|
||
|
|
* Reconstruct matrix from factors and compute residual.
|
||
|
|
*
|
||
|
|
CALL ZSYT01_ROOK( UPLO, N, A, LDA, AFAC, LDA, IWORK,
|
||
|
|
$ AINV, LDA, RWORK, RESULT( 1 ) )
|
||
|
|
NT = 1
|
||
|
|
*
|
||
|
|
*+ TEST 2
|
||
|
|
* Form the inverse and compute the residual,
|
||
|
|
* if the factorization was competed without INFO > 0
|
||
|
|
* (i.e. there is no zero rows and columns).
|
||
|
|
* Do it only for the first block size.
|
||
|
|
*
|
||
|
|
IF( INB.EQ.1 .AND. .NOT.TRFCON ) THEN
|
||
|
|
CALL ZLACPY( UPLO, N, N, AFAC, LDA, AINV, LDA )
|
||
|
|
SRNAMT = 'ZSYTRI_ROOK'
|
||
|
|
CALL ZSYTRI_ROOK( UPLO, N, AINV, LDA, IWORK, WORK,
|
||
|
|
$ INFO )
|
||
|
|
*
|
||
|
|
* Check error code from ZSYTRI_ROOK and handle error.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'ZSYTRI_ROOK', INFO, -1,
|
||
|
|
$ UPLO, N, N, -1, -1, -1, IMAT,
|
||
|
|
$ NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Compute the residual for a symmetric matrix times
|
||
|
|
* its inverse.
|
||
|
|
*
|
||
|
|
CALL ZSYT03( UPLO, N, A, LDA, AINV, LDA, WORK, LDA,
|
||
|
|
$ RWORK, RCONDC, RESULT( 2 ) )
|
||
|
|
NT = 2
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 110 K = 1, NT
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
|
||
|
|
$ RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
110 CONTINUE
|
||
|
|
NRUN = NRUN + NT
|
||
|
|
*
|
||
|
|
*+ TEST 3
|
||
|
|
* Compute largest element in U or L
|
||
|
|
*
|
||
|
|
RESULT( 3 ) = ZERO
|
||
|
|
DTEMP = ZERO
|
||
|
|
*
|
||
|
|
CONST = ( ( ALPHA**2-ONE ) / ( ALPHA**2-ONEHALF ) ) /
|
||
|
|
$ ( ONE-ALPHA )
|
||
|
|
*
|
||
|
|
IF( IUPLO.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Compute largest element in U
|
||
|
|
*
|
||
|
|
K = N
|
||
|
|
120 CONTINUE
|
||
|
|
IF( K.LE.1 )
|
||
|
|
$ GO TO 130
|
||
|
|
*
|
||
|
|
IF( IWORK( K ).GT.ZERO ) THEN
|
||
|
|
*
|
||
|
|
* Get max absolute value from elements
|
||
|
|
* in column k in in U
|
||
|
|
*
|
||
|
|
DTEMP = ZLANGE( 'M', K-1, 1,
|
||
|
|
$ AFAC( ( K-1 )*LDA+1 ), LDA, RWORK )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Get max absolute value from elements
|
||
|
|
* in columns k and k-1 in U
|
||
|
|
*
|
||
|
|
DTEMP = ZLANGE( 'M', K-2, 2,
|
||
|
|
$ AFAC( ( K-2 )*LDA+1 ), LDA, RWORK )
|
||
|
|
K = K - 1
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* DTEMP should be bounded by CONST
|
||
|
|
*
|
||
|
|
DTEMP = DTEMP - CONST + THRESH
|
||
|
|
IF( DTEMP.GT.RESULT( 3 ) )
|
||
|
|
$ RESULT( 3 ) = DTEMP
|
||
|
|
*
|
||
|
|
K = K - 1
|
||
|
|
*
|
||
|
|
GO TO 120
|
||
|
|
130 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Compute largest element in L
|
||
|
|
*
|
||
|
|
K = 1
|
||
|
|
140 CONTINUE
|
||
|
|
IF( K.GE.N )
|
||
|
|
$ GO TO 150
|
||
|
|
*
|
||
|
|
IF( IWORK( K ).GT.ZERO ) THEN
|
||
|
|
*
|
||
|
|
* Get max absolute value from elements
|
||
|
|
* in column k in in L
|
||
|
|
*
|
||
|
|
DTEMP = ZLANGE( 'M', N-K, 1,
|
||
|
|
$ AFAC( ( K-1 )*LDA+K+1 ), LDA, RWORK )
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Get max absolute value from elements
|
||
|
|
* in columns k and k+1 in L
|
||
|
|
*
|
||
|
|
DTEMP = ZLANGE( 'M', N-K-1, 2,
|
||
|
|
$ AFAC( ( K-1 )*LDA+K+2 ), LDA, RWORK )
|
||
|
|
K = K + 1
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* DTEMP should be bounded by CONST
|
||
|
|
*
|
||
|
|
DTEMP = DTEMP - CONST + THRESH
|
||
|
|
IF( DTEMP.GT.RESULT( 3 ) )
|
||
|
|
$ RESULT( 3 ) = DTEMP
|
||
|
|
*
|
||
|
|
K = K + 1
|
||
|
|
*
|
||
|
|
GO TO 140
|
||
|
|
150 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
*
|
||
|
|
*+ TEST 4
|
||
|
|
* Compute largest 2-Norm (condition number)
|
||
|
|
* of 2-by-2 diag blocks
|
||
|
|
*
|
||
|
|
RESULT( 4 ) = ZERO
|
||
|
|
DTEMP = ZERO
|
||
|
|
*
|
||
|
|
CONST = ( ( ALPHA**2-ONE ) / ( ALPHA**2-ONEHALF ) )*
|
||
|
|
$ ( ( ONE + ALPHA ) / ( ONE - ALPHA ) )
|
||
|
|
*
|
||
|
|
IF( IUPLO.EQ.1 ) THEN
|
||
|
|
*
|
||
|
|
* Loop backward for UPLO = 'U'
|
||
|
|
*
|
||
|
|
K = N
|
||
|
|
160 CONTINUE
|
||
|
|
IF( K.LE.1 )
|
||
|
|
$ GO TO 170
|
||
|
|
*
|
||
|
|
IF( IWORK( K ).LT.ZERO ) THEN
|
||
|
|
*
|
||
|
|
* Get the two singular values
|
||
|
|
* (real and non-negative) of a 2-by-2 block,
|
||
|
|
* store them in RWORK array
|
||
|
|
*
|
||
|
|
BLOCK( 1, 1 ) = AFAC( ( K-2 )*LDA+K-1 )
|
||
|
|
BLOCK( 1, 2 ) = AFAC( (K-1)*LDA+K-1 )
|
||
|
|
BLOCK( 2, 1 ) = BLOCK( 1, 2 )
|
||
|
|
BLOCK( 2, 2 ) = AFAC( (K-1)*LDA+K )
|
||
|
|
*
|
||
|
|
CALL ZGESVD( 'N', 'N', 2, 2, BLOCK, 2, RWORK,
|
||
|
|
$ ZDUMMY, 1, ZDUMMY, 1,
|
||
|
|
$ WORK, 6, RWORK( 3 ), INFO )
|
||
|
|
*
|
||
|
|
*
|
||
|
|
SING_MAX = RWORK( 1 )
|
||
|
|
SING_MIN = RWORK( 2 )
|
||
|
|
*
|
||
|
|
DTEMP = SING_MAX / SING_MIN
|
||
|
|
*
|
||
|
|
* DTEMP should be bounded by CONST
|
||
|
|
*
|
||
|
|
DTEMP = DTEMP - CONST + THRESH
|
||
|
|
IF( DTEMP.GT.RESULT( 4 ) )
|
||
|
|
$ RESULT( 4 ) = DTEMP
|
||
|
|
K = K - 1
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
K = K - 1
|
||
|
|
*
|
||
|
|
GO TO 160
|
||
|
|
170 CONTINUE
|
||
|
|
*
|
||
|
|
ELSE
|
||
|
|
*
|
||
|
|
* Loop forward for UPLO = 'L'
|
||
|
|
*
|
||
|
|
K = 1
|
||
|
|
180 CONTINUE
|
||
|
|
IF( K.GE.N )
|
||
|
|
$ GO TO 190
|
||
|
|
*
|
||
|
|
IF( IWORK( K ).LT.ZERO ) THEN
|
||
|
|
*
|
||
|
|
* Get the two singular values
|
||
|
|
* (real and non-negative) of a 2-by-2 block,
|
||
|
|
* store them in RWORK array
|
||
|
|
*
|
||
|
|
BLOCK( 1, 1 ) = AFAC( ( K-1 )*LDA+K )
|
||
|
|
BLOCK( 2, 1 ) = AFAC( ( K-1 )*LDA+K+1 )
|
||
|
|
BLOCK( 1, 2 ) = BLOCK( 2, 1 )
|
||
|
|
BLOCK( 2, 2 ) = AFAC( K*LDA+K+1 )
|
||
|
|
*
|
||
|
|
CALL ZGESVD( 'N', 'N', 2, 2, BLOCK, 2, RWORK,
|
||
|
|
$ ZDUMMY, 1, ZDUMMY, 1,
|
||
|
|
$ WORK, 6, RWORK(3), INFO )
|
||
|
|
*
|
||
|
|
SING_MAX = RWORK( 1 )
|
||
|
|
SING_MIN = RWORK( 2 )
|
||
|
|
*
|
||
|
|
DTEMP = SING_MAX / SING_MIN
|
||
|
|
*
|
||
|
|
* DTEMP should be bounded by CONST
|
||
|
|
*
|
||
|
|
DTEMP = DTEMP - CONST + THRESH
|
||
|
|
IF( DTEMP.GT.RESULT( 4 ) )
|
||
|
|
$ RESULT( 4 ) = DTEMP
|
||
|
|
K = K + 1
|
||
|
|
*
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
K = K + 1
|
||
|
|
*
|
||
|
|
GO TO 180
|
||
|
|
190 CONTINUE
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 200 K = 3, 4
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9999 )UPLO, N, NB, IMAT, K,
|
||
|
|
$ RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
200 CONTINUE
|
||
|
|
NRUN = NRUN + 2
|
||
|
|
*
|
||
|
|
* Skip the other tests if this is not the first block
|
||
|
|
* size.
|
||
|
|
*
|
||
|
|
IF( INB.GT.1 )
|
||
|
|
$ GO TO 240
|
||
|
|
*
|
||
|
|
* Do only the condition estimate if INFO is not 0.
|
||
|
|
*
|
||
|
|
IF( TRFCON ) THEN
|
||
|
|
RCONDC = ZERO
|
||
|
|
GO TO 230
|
||
|
|
END IF
|
||
|
|
*
|
||
|
|
* Do for each value of NRHS in NSVAL.
|
||
|
|
*
|
||
|
|
DO 220 IRHS = 1, NNS
|
||
|
|
NRHS = NSVAL( IRHS )
|
||
|
|
*
|
||
|
|
*+ TEST 5 ( Using TRS_ROOK)
|
||
|
|
* 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 = 'ZLARHS'
|
||
|
|
CALL ZLARHS( MATPATH, XTYPE, UPLO, ' ', N, N,
|
||
|
|
$ KL, KU, NRHS, A, LDA, XACT, LDA,
|
||
|
|
$ B, LDA, ISEED, INFO )
|
||
|
|
CALL ZLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
|
||
|
|
*
|
||
|
|
SRNAMT = 'ZSYTRS_ROOK'
|
||
|
|
CALL ZSYTRS_ROOK( UPLO, N, NRHS, AFAC, LDA, IWORK,
|
||
|
|
$ X, LDA, INFO )
|
||
|
|
*
|
||
|
|
* Check error code from ZSYTRS_ROOK and handle error.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'ZSYTRS_ROOK', INFO, 0,
|
||
|
|
$ UPLO, N, N, -1, -1, NRHS, IMAT,
|
||
|
|
$ NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
CALL ZLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
|
||
|
|
*
|
||
|
|
* Compute the residual for the solution
|
||
|
|
*
|
||
|
|
CALL ZSYT02( UPLO, N, NRHS, A, LDA, X, LDA, WORK,
|
||
|
|
$ LDA, RWORK, RESULT( 5 ) )
|
||
|
|
*
|
||
|
|
*+ TEST 6
|
||
|
|
* Check solution from generated exact solution.
|
||
|
|
*
|
||
|
|
CALL ZGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
|
||
|
|
$ RESULT( 6 ) )
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
DO 210 K = 5, 6
|
||
|
|
IF( RESULT( K ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9998 )UPLO, N, NRHS,
|
||
|
|
$ IMAT, K, RESULT( K )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
210 CONTINUE
|
||
|
|
NRUN = NRUN + 2
|
||
|
|
*
|
||
|
|
* End do for each value of NRHS in NSVAL.
|
||
|
|
*
|
||
|
|
220 CONTINUE
|
||
|
|
*
|
||
|
|
*+ TEST 7
|
||
|
|
* Get an estimate of RCOND = 1/CNDNUM.
|
||
|
|
*
|
||
|
|
230 CONTINUE
|
||
|
|
ANORM = ZLANSY( '1', UPLO, N, A, LDA, RWORK )
|
||
|
|
SRNAMT = 'ZSYCON_ROOK'
|
||
|
|
CALL ZSYCON_ROOK( UPLO, N, AFAC, LDA, IWORK, ANORM,
|
||
|
|
$ RCOND, WORK, INFO )
|
||
|
|
*
|
||
|
|
* Check error code from ZSYCON_ROOK and handle error.
|
||
|
|
*
|
||
|
|
IF( INFO.NE.0 )
|
||
|
|
$ CALL ALAERH( PATH, 'ZSYCON_ROOK', INFO, 0,
|
||
|
|
$ UPLO, N, N, -1, -1, -1, IMAT,
|
||
|
|
$ NFAIL, NERRS, NOUT )
|
||
|
|
*
|
||
|
|
* Compute the test ratio to compare values of RCOND
|
||
|
|
*
|
||
|
|
RESULT( 7 ) = DGET06( RCOND, RCONDC )
|
||
|
|
*
|
||
|
|
* Print information about the tests that did not pass
|
||
|
|
* the threshold.
|
||
|
|
*
|
||
|
|
IF( RESULT( 7 ).GE.THRESH ) THEN
|
||
|
|
IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
|
||
|
|
$ CALL ALAHD( NOUT, PATH )
|
||
|
|
WRITE( NOUT, FMT = 9997 )UPLO, N, IMAT, 7,
|
||
|
|
$ RESULT( 7 )
|
||
|
|
NFAIL = NFAIL + 1
|
||
|
|
END IF
|
||
|
|
NRUN = NRUN + 1
|
||
|
|
240 CONTINUE
|
||
|
|
*
|
||
|
|
250 CONTINUE
|
||
|
|
260 CONTINUE
|
||
|
|
270 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 ZCHKSY_ROOK
|
||
|
|
*
|
||
|
|
END
|