417 lines
14 KiB
Fortran
417 lines
14 KiB
Fortran
*> \brief \b ZDRVRF3
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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 ZDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
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* + D_WORK_ZLANGE, Z_WORK_ZGEQRF, TAU )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, NN, NOUT
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* DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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* INTEGER NVAL( NN )
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* DOUBLE PRECISION D_WORK_ZLANGE( * )
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* COMPLEX*16 A( LDA, * ), ARF( * ), B1( LDA, * ),
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* + B2( LDA, * )
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* COMPLEX*16 Z_WORK_ZGEQRF( * ), TAU( * )
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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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*> ZDRVRF3 tests the LAPACK RFP routines:
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*> ZTFSM
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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] 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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*> \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] 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[out] A
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*> \verbatim
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*> A is COMPLEX*16 array, dimension (LDA,NMAX)
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the array A. LDA >= max(1,NMAX).
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*> \endverbatim
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*>
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*> \param[out] ARF
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*> \verbatim
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*> ARF is COMPLEX*16 array, dimension ((NMAX*(NMAX+1))/2).
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*> \endverbatim
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*>
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*> \param[out] B1
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*> \verbatim
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*> B1 is COMPLEX*16 array, dimension (LDA,NMAX)
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*> \endverbatim
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*>
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*> \param[out] B2
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*> \verbatim
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*> B2 is COMPLEX*16 array, dimension (LDA,NMAX)
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*> \endverbatim
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*>
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*> \param[out] D_WORK_ZLANGE
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*> \verbatim
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*> D_WORK_ZLANGE is DOUBLE PRECISION array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] Z_WORK_ZGEQRF
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*> \verbatim
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*> Z_WORK_ZGEQRF is COMPLEX*16 array, dimension (NMAX)
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is COMPLEX*16 array, dimension (NMAX)
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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 ZDRVRF3( NOUT, NN, NVAL, THRESH, A, LDA, ARF, B1, B2,
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+ D_WORK_ZLANGE, Z_WORK_ZGEQRF, TAU )
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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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INTEGER LDA, NN, NOUT
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DOUBLE PRECISION THRESH
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* ..
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* .. Array Arguments ..
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INTEGER NVAL( NN )
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DOUBLE PRECISION D_WORK_ZLANGE( * )
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COMPLEX*16 A( LDA, * ), ARF( * ), B1( LDA, * ),
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+ B2( LDA, * )
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COMPLEX*16 Z_WORK_ZGEQRF( * ), TAU( * )
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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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COMPLEX*16 ZERO, ONE
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PARAMETER ( ZERO = ( 0.0D+0, 0.0D+0 ) ,
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+ ONE = ( 1.0D+0, 0.0D+0 ) )
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INTEGER NTESTS
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PARAMETER ( NTESTS = 1 )
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* ..
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* .. Local Scalars ..
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CHARACTER UPLO, CFORM, DIAG, TRANS, SIDE
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INTEGER I, IFORM, IIM, IIN, INFO, IUPLO, J, M, N, NA,
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+ NFAIL, NRUN, ISIDE, IDIAG, IALPHA, ITRANS
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COMPLEX*16 ALPHA
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DOUBLE PRECISION EPS
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* ..
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* .. Local Arrays ..
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CHARACTER UPLOS( 2 ), FORMS( 2 ), TRANSS( 2 ),
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+ DIAGS( 2 ), SIDES( 2 )
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INTEGER ISEED( 4 ), ISEEDY( 4 )
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DOUBLE PRECISION RESULT( NTESTS )
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, ZLANGE
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COMPLEX*16 ZLARND
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EXTERNAL DLAMCH, ZLARND, ZLANGE, LSAME
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* ..
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* .. External Subroutines ..
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EXTERNAL ZTRTTF, ZGEQRF, ZGEQLF, ZTFSM, ZTRSM
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC MAX, SQRT
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* ..
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* .. Scalars in Common ..
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CHARACTER*32 SRNAMT
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* ..
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* .. Common blocks ..
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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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DATA FORMS / 'N', 'C' /
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DATA SIDES / 'L', 'R' /
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DATA TRANSS / 'N', 'C' /
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DATA DIAGS / 'N', 'U' /
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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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NRUN = 0
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NFAIL = 0
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INFO = 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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EPS = DLAMCH( 'Precision' )
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*
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DO 170 IIM = 1, NN
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*
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M = NVAL( IIM )
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*
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DO 160 IIN = 1, NN
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*
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N = NVAL( IIN )
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*
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DO 150 IFORM = 1, 2
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*
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CFORM = FORMS( IFORM )
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*
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DO 140 IUPLO = 1, 2
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*
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UPLO = UPLOS( IUPLO )
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*
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DO 130 ISIDE = 1, 2
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*
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SIDE = SIDES( ISIDE )
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*
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DO 120 ITRANS = 1, 2
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*
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TRANS = TRANSS( ITRANS )
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*
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DO 110 IDIAG = 1, 2
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*
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DIAG = DIAGS( IDIAG )
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*
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DO 100 IALPHA = 1, 3
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*
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IF ( IALPHA.EQ.1 ) THEN
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ALPHA = ZERO
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ELSE IF ( IALPHA.EQ.2 ) THEN
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ALPHA = ONE
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ELSE
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ALPHA = ZLARND( 4, ISEED )
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END IF
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*
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* All the parameters are set:
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* CFORM, SIDE, UPLO, TRANS, DIAG, M, N,
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* and ALPHA
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* READY TO TEST!
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*
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NRUN = NRUN + 1
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*
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IF ( ISIDE.EQ.1 ) THEN
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*
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* The case ISIDE.EQ.1 is when SIDE.EQ.'L'
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* -> A is M-by-M ( B is M-by-N )
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*
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NA = M
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*
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ELSE
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*
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* The case ISIDE.EQ.2 is when SIDE.EQ.'R'
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* -> A is N-by-N ( B is M-by-N )
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*
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NA = N
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*
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END IF
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*
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* Generate A our NA--by--NA triangular
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* matrix.
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* Our test is based on forward error so we
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* do want A to be well conditioned! To get
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* a well-conditioned triangular matrix, we
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* take the R factor of the QR/LQ factorization
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* of a random matrix.
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*
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DO J = 1, NA
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DO I = 1, NA
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A( I, J ) = ZLARND( 4, ISEED )
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END DO
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END DO
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*
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IF ( IUPLO.EQ.1 ) THEN
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*
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* The case IUPLO.EQ.1 is when SIDE.EQ.'U'
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* -> QR factorization.
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*
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SRNAMT = 'ZGEQRF'
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CALL ZGEQRF( NA, NA, A, LDA, TAU,
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+ Z_WORK_ZGEQRF, LDA,
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+ INFO )
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*
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* Forcing main diagonal of test matrix to
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* be unit makes it ill-conditioned for
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* some test cases
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*
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IF ( LSAME( DIAG, 'U' ) ) THEN
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DO J = 1, NA
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DO I = 1, J
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A( I, J ) = A( I, J ) /
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+ ( 2.0 * A( J, J ) )
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END DO
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END DO
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END IF
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*
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ELSE
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*
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* The case IUPLO.EQ.2 is when SIDE.EQ.'L'
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* -> QL factorization.
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*
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SRNAMT = 'ZGELQF'
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CALL ZGELQF( NA, NA, A, LDA, TAU,
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+ Z_WORK_ZGEQRF, LDA,
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+ INFO )
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*
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* Forcing main diagonal of test matrix to
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* be unit makes it ill-conditioned for
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* some test cases
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*
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IF ( LSAME( DIAG, 'U' ) ) THEN
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DO I = 1, NA
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DO J = 1, I
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A( I, J ) = A( I, J ) /
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+ ( 2.0 * A( I, I ) )
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END DO
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END DO
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END IF
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*
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END IF
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*
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* After the QR factorization, the diagonal
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* of A is made of real numbers, we multiply
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* by a random complex number of absolute
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* value 1.0E+00.
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*
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DO J = 1, NA
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A( J, J ) = A( J, J ) *
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+ ZLARND( 5, ISEED )
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END DO
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*
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* Store a copy of A in RFP format (in ARF).
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*
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SRNAMT = 'ZTRTTF'
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CALL ZTRTTF( CFORM, UPLO, NA, A, LDA, ARF,
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+ INFO )
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*
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* Generate B1 our M--by--N right-hand side
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* and store a copy in B2.
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*
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DO J = 1, N
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DO I = 1, M
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B1( I, J ) = ZLARND( 4, ISEED )
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B2( I, J ) = B1( I, J )
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END DO
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END DO
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*
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* Solve op( A ) X = B or X op( A ) = B
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* with ZTRSM
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*
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SRNAMT = 'ZTRSM'
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CALL ZTRSM( SIDE, UPLO, TRANS, DIAG, M, N,
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+ ALPHA, A, LDA, B1, LDA )
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*
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* Solve op( A ) X = B or X op( A ) = B
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* with ZTFSM
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*
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SRNAMT = 'ZTFSM'
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CALL ZTFSM( CFORM, SIDE, UPLO, TRANS,
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+ DIAG, M, N, ALPHA, ARF, B2,
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+ LDA )
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*
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* Check that the result agrees.
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*
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DO J = 1, N
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DO I = 1, M
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B1( I, J ) = B2( I, J ) - B1( I, J )
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END DO
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END DO
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*
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RESULT( 1 ) = ZLANGE( 'I', M, N, B1, LDA,
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+ D_WORK_ZLANGE )
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*
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RESULT( 1 ) = RESULT( 1 ) / SQRT( EPS )
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+ / MAX ( MAX( M, N ), 1 )
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*
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IF( RESULT( 1 ).GE.THRESH ) THEN
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IF( NFAIL.EQ.0 ) THEN
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WRITE( NOUT, * )
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WRITE( NOUT, FMT = 9999 )
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END IF
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WRITE( NOUT, FMT = 9997 ) 'ZTFSM',
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+ CFORM, SIDE, UPLO, TRANS, DIAG, M,
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+ N, RESULT( 1 )
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NFAIL = NFAIL + 1
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END IF
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*
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100 CONTINUE
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110 CONTINUE
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120 CONTINUE
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130 CONTINUE
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140 CONTINUE
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150 CONTINUE
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160 CONTINUE
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170 CONTINUE
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*
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* Print a summary of the results.
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*
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IF ( NFAIL.EQ.0 ) THEN
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WRITE( NOUT, FMT = 9996 ) 'ZTFSM', NRUN
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ELSE
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WRITE( NOUT, FMT = 9995 ) 'ZTFSM', NFAIL, NRUN
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END IF
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*
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9999 FORMAT( 1X, ' *** Error(s) or Failure(s) while testing ZTFSM
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+ ***')
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9997 FORMAT( 1X, ' Failure in ',A5,', CFORM=''',A1,''',',
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+ ' SIDE=''',A1,''',',' UPLO=''',A1,''',',' TRANS=''',A1,''',',
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+ ' DIAG=''',A1,''',',' M=',I3,', N =', I3,', test=',G12.5)
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9996 FORMAT( 1X, 'All tests for ',A5,' auxiliary routine passed the ',
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+ 'threshold ( ',I5,' tests run)')
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9995 FORMAT( 1X, A6, ' auxiliary routine:',I5,' out of ',I5,
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+ ' tests failed to pass the threshold')
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*
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RETURN
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*
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* End of ZDRVRF3
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*
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END
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