557 lines
		
	
	
		
			17 KiB
		
	
	
	
		
			Fortran
		
	
	
	
			
		
		
	
	
			557 lines
		
	
	
		
			17 KiB
		
	
	
	
		
			Fortran
		
	
	
	
*> \brief \b DCHKGT
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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 DCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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*                          A, AF, B, X, 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            NN, 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( * ), NSVAL( * ), NVAL( * )
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*       DOUBLE PRECISION   A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
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*      $                   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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*> DCHKGT tests DGTTRF, -TRS, -RFS, and -CON
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*> \endverbatim
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*
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*  Arguments:
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*  ==========
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*
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*> \param[in] DOTYPE
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*> \verbatim
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*>          DOTYPE is LOGICAL array, dimension (NTYPES)
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*>          The matrix types to be used for testing.  Matrices of type j
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*>          (for 1 <= j <= NTYPES) are used for testing if DOTYPE(j) =
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*>          .TRUE.; if DOTYPE(j) = .FALSE., then type j is not used.
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*> \endverbatim
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*>
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*> \param[in] NN
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*> \verbatim
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*>          NN is INTEGER
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*>          The number of values of N contained in the vector NVAL.
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*> \endverbatim
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*>
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*> \param[in] NVAL
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*> \verbatim
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*>          NVAL is INTEGER array, dimension (NN)
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*>          The values of the matrix dimension N.
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*> \endverbatim
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*>
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*> \param[in] NNS
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*> \verbatim
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*>          NNS is INTEGER
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*>          The number of values of NRHS contained in the vector NSVAL.
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*> \endverbatim
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*>
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*> \param[in] NSVAL
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*> \verbatim
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*>          NSVAL is INTEGER array, dimension (NNS)
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*>          The values of the number of right hand sides NRHS.
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*> \endverbatim
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*>
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*> \param[in] THRESH
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*> \verbatim
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*>          THRESH is 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[out] A
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*> \verbatim
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*>          A is DOUBLE PRECISION array, dimension (NMAX*4)
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*> \endverbatim
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*>
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*> \param[out] AF
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*> \verbatim
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*>          AF is DOUBLE PRECISION array, dimension (NMAX*4)
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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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 DOUBLE PRECISION 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 November 2011
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*
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*> \ingroup double_lin
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*
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*  =====================================================================
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      SUBROUTINE DCHKGT( DOTYPE, NN, NVAL, NNS, NSVAL, THRESH, TSTERR,
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     $                   A, AF, B, X, XACT, WORK, RWORK, IWORK, NOUT )
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*
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*  -- LAPACK test routine (version 3.4.0) --
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*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
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*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*     November 2011
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*
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*     .. Scalar Arguments ..
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      LOGICAL            TSTERR
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      INTEGER            NN, NNS, NOUT
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      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( * ), NSVAL( * ), NVAL( * )
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      DOUBLE PRECISION   A( * ), AF( * ), B( * ), RWORK( * ), WORK( * ),
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     $                   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   ONE, ZERO
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      PARAMETER          ( ONE = 1.0D+0, ZERO = 0.0D+0 )
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      INTEGER            NTYPES
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      PARAMETER          ( NTYPES = 12 )
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      INTEGER            NTESTS
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      PARAMETER          ( NTESTS = 7 )
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*     ..
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*     .. Local Scalars ..
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      LOGICAL            TRFCON, ZEROT
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      CHARACTER          DIST, NORM, TRANS, TYPE
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      CHARACTER*3        PATH
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      INTEGER            I, IMAT, IN, INFO, IRHS, ITRAN, IX, IZERO, J,
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     $                   K, KL, KOFF, KU, LDA, M, MODE, N, NERRS, NFAIL,
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     $                   NIMAT, NRHS, NRUN
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      DOUBLE PRECISION   AINVNM, ANORM, COND, RCOND, RCONDC, RCONDI,
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     $                   RCONDO
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*     ..
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*     .. Local Arrays ..
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      CHARACTER          TRANSS( 3 )
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      INTEGER            ISEED( 4 ), ISEEDY( 4 )
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      DOUBLE PRECISION   RESULT( NTESTS ), Z( 3 )
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*     ..
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*     .. External Functions ..
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      DOUBLE PRECISION   DASUM, DGET06, DLANGT
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      EXTERNAL           DASUM, DGET06, DLANGT
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*     ..
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*     .. External Subroutines ..
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      EXTERNAL           ALAERH, ALAHD, ALASUM, DCOPY, DERRGE, DGET04,
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     $                   DGTCON, DGTRFS, DGTT01, DGTT02, DGTT05, DGTTRF,
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     $                   DGTTRS, DLACPY, DLAGTM, DLARNV, DLATB4, DLATMS,
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     $                   DSCAL
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*     ..
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*     .. Intrinsic Functions ..
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      INTRINSIC          MAX
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*     ..
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*     .. Scalars in Common ..
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      LOGICAL            LERR, OK
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      CHARACTER*32       SRNAMT
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      INTEGER            INFOT, NUNIT
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*     ..
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*     .. Common blocks ..
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      COMMON             / INFOC / INFOT, NUNIT, OK, LERR
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      COMMON             / SRNAMC / SRNAMT
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*     ..
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*     .. Data statements ..
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      DATA               ISEEDY / 0, 0, 0, 1 / , TRANSS / 'N', 'T',
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     $                   'C' /
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*     ..
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*     .. Executable Statements ..
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*
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      PATH( 1: 1 ) = 'Double precision'
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      PATH( 2: 3 ) = 'GT'
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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 DERRGE( PATH, NOUT )
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      INFOT = 0
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*
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      DO 110 IN = 1, NN
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*
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*        Do for each value of N in NVAL.
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*
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         N = NVAL( IN )
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         M = MAX( N-1, 0 )
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         LDA = MAX( 1, N )
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         NIMAT = NTYPES
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         IF( N.LE.0 )
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     $      NIMAT = 1
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*
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         DO 100 IMAT = 1, NIMAT
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*
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*           Do the tests only if DOTYPE( IMAT ) is true.
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*
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            IF( .NOT.DOTYPE( IMAT ) )
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     $         GO TO 100
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*
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*           Set up parameters with DLATB4.
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*
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            CALL DLATB4( PATH, IMAT, N, N, TYPE, KL, KU, ANORM, MODE,
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     $                   COND, DIST )
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*
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            ZEROT = IMAT.GE.8 .AND. IMAT.LE.10
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            IF( IMAT.LE.6 ) THEN
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*
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*              Types 1-6:  generate matrices of known condition number.
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*
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               KOFF = MAX( 2-KU, 3-MAX( 1, N ) )
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               SRNAMT = 'DLATMS'
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               CALL DLATMS( N, N, DIST, ISEED, TYPE, RWORK, MODE, COND,
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     $                      ANORM, KL, KU, 'Z', AF( KOFF ), 3, WORK,
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     $                      INFO )
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*
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*              Check the error code from DLATMS.
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*
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               IF( INFO.NE.0 ) THEN
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                  CALL ALAERH( PATH, 'DLATMS', INFO, 0, ' ', N, N, KL,
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     $                         KU, -1, IMAT, NFAIL, NERRS, NOUT )
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                  GO TO 100
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               END IF
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               IZERO = 0
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*
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               IF( N.GT.1 ) THEN
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                  CALL DCOPY( N-1, AF( 4 ), 3, A, 1 )
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                  CALL DCOPY( N-1, AF( 3 ), 3, A( N+M+1 ), 1 )
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               END IF
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               CALL DCOPY( N, AF( 2 ), 3, A( M+1 ), 1 )
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            ELSE
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*
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*              Types 7-12:  generate tridiagonal matrices with
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*              unknown condition numbers.
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*
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               IF( .NOT.ZEROT .OR. .NOT.DOTYPE( 7 ) ) THEN
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*
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*                 Generate a matrix with elements from [-1,1].
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*
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                  CALL DLARNV( 2, ISEED, N+2*M, A )
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                  IF( ANORM.NE.ONE )
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     $               CALL DSCAL( N+2*M, ANORM, A, 1 )
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               ELSE IF( IZERO.GT.0 ) THEN
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*
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*                 Reuse the last matrix by copying back the zeroed out
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*                 elements.
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*
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                  IF( IZERO.EQ.1 ) THEN
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                     A( N ) = Z( 2 )
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                     IF( N.GT.1 )
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     $                  A( 1 ) = Z( 3 )
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                  ELSE IF( IZERO.EQ.N ) THEN
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                     A( 3*N-2 ) = Z( 1 )
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                     A( 2*N-1 ) = Z( 2 )
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                  ELSE
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                     A( 2*N-2+IZERO ) = Z( 1 )
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                     A( N-1+IZERO ) = Z( 2 )
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                     A( IZERO ) = Z( 3 )
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                  END IF
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               END IF
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*
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*              If IMAT > 7, set one column of the matrix to 0.
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*
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               IF( .NOT.ZEROT ) THEN
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                  IZERO = 0
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               ELSE IF( IMAT.EQ.8 ) THEN
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                  IZERO = 1
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                  Z( 2 ) = A( N )
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                  A( N ) = ZERO
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                  IF( N.GT.1 ) THEN
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                     Z( 3 ) = A( 1 )
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                     A( 1 ) = ZERO
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                  END IF
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               ELSE IF( IMAT.EQ.9 ) THEN
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                  IZERO = N
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                  Z( 1 ) = A( 3*N-2 )
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                  Z( 2 ) = A( 2*N-1 )
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                  A( 3*N-2 ) = ZERO
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                  A( 2*N-1 ) = ZERO
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               ELSE
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                  IZERO = ( N+1 ) / 2
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                  DO 20 I = IZERO, N - 1
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                     A( 2*N-2+I ) = ZERO
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                     A( N-1+I ) = ZERO
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                     A( I ) = ZERO
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   20             CONTINUE
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                  A( 3*N-2 ) = ZERO
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                  A( 2*N-1 ) = ZERO
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               END IF
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            END IF
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*
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*+    TEST 1
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*           Factor A as L*U and compute the ratio
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*              norm(L*U - A) / (n * norm(A) * EPS )
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*
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            CALL DCOPY( N+2*M, A, 1, AF, 1 )
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            SRNAMT = 'DGTTRF'
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            CALL DGTTRF( N, AF, AF( M+1 ), AF( N+M+1 ), AF( N+2*M+1 ),
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     $                   IWORK, INFO )
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*
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*           Check error code from DGTTRF.
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*
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            IF( INFO.NE.IZERO )
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     $         CALL ALAERH( PATH, 'DGTTRF', INFO, IZERO, ' ', N, N, 1,
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     $                      1, -1, IMAT, NFAIL, NERRS, NOUT )
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            TRFCON = INFO.NE.0
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*
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            CALL DGTT01( N, A, A( M+1 ), A( N+M+1 ), AF, AF( M+1 ),
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     $                   AF( N+M+1 ), AF( N+2*M+1 ), IWORK, WORK, LDA,
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     $                   RWORK, RESULT( 1 ) )
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*
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*           Print the test ratio if it is .GE. THRESH.
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*
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            IF( RESULT( 1 ).GE.THRESH ) THEN
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               IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
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     $            CALL ALAHD( NOUT, PATH )
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               WRITE( NOUT, FMT = 9999 )N, IMAT, 1, RESULT( 1 )
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               NFAIL = NFAIL + 1
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            END IF
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            NRUN = NRUN + 1
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*
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            DO 50 ITRAN = 1, 2
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               TRANS = TRANSS( ITRAN )
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               IF( ITRAN.EQ.1 ) THEN
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                  NORM = 'O'
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               ELSE
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                  NORM = 'I'
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               END IF
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               ANORM = DLANGT( NORM, N, A, A( M+1 ), A( N+M+1 ) )
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*
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               IF( .NOT.TRFCON ) THEN
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*
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*                 Use DGTTRS to solve for one column at a time of inv(A)
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*                 or inv(A^T), computing the maximum column sum as we
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*                 go.
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*
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                  AINVNM = ZERO
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                  DO 40 I = 1, N
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                     DO 30 J = 1, N
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                        X( J ) = ZERO
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   30                CONTINUE
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                     X( I ) = ONE
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                     CALL DGTTRS( TRANS, N, 1, AF, AF( M+1 ),
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     $                            AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
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     $                            LDA, INFO )
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                     AINVNM = MAX( AINVNM, DASUM( N, X, 1 ) )
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   40             CONTINUE
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*
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*                 Compute RCONDC = 1 / (norm(A) * norm(inv(A))
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*
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                  IF( ANORM.LE.ZERO .OR. AINVNM.LE.ZERO ) THEN
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                     RCONDC = ONE
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                  ELSE
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                     RCONDC = ( ONE / ANORM ) / AINVNM
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                  END IF
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                  IF( ITRAN.EQ.1 ) THEN
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                     RCONDO = RCONDC
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                  ELSE
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                     RCONDI = RCONDC
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                  END IF
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               ELSE
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                  RCONDC = ZERO
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               END IF
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*
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*+    TEST 7
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*              Estimate the reciprocal of the condition number of the
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*              matrix.
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*
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               SRNAMT = 'DGTCON'
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               CALL DGTCON( NORM, N, AF, AF( M+1 ), AF( N+M+1 ),
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     $                      AF( N+2*M+1 ), IWORK, ANORM, RCOND, WORK,
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     $                      IWORK( N+1 ), INFO )
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*
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*              Check error code from DGTCON.
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*
 | 
						|
               IF( INFO.NE.0 )
 | 
						|
     $            CALL ALAERH( PATH, 'DGTCON', INFO, 0, NORM, N, N, -1,
 | 
						|
     $                         -1, -1, IMAT, NFAIL, NERRS, NOUT )
 | 
						|
*
 | 
						|
               RESULT( 7 ) = DGET06( RCOND, RCONDC )
 | 
						|
*
 | 
						|
*              Print the test ratio if it is .GE. THRESH.
 | 
						|
*
 | 
						|
               IF( RESULT( 7 ).GE.THRESH ) THEN
 | 
						|
                  IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
 | 
						|
     $               CALL ALAHD( NOUT, PATH )
 | 
						|
                  WRITE( NOUT, FMT = 9997 )NORM, N, IMAT, 7,
 | 
						|
     $               RESULT( 7 )
 | 
						|
                  NFAIL = NFAIL + 1
 | 
						|
               END IF
 | 
						|
               NRUN = NRUN + 1
 | 
						|
   50       CONTINUE
 | 
						|
*
 | 
						|
*           Skip the remaining tests if the matrix is singular.
 | 
						|
*
 | 
						|
            IF( TRFCON )
 | 
						|
     $         GO TO 100
 | 
						|
*
 | 
						|
            DO 90 IRHS = 1, NNS
 | 
						|
               NRHS = NSVAL( IRHS )
 | 
						|
*
 | 
						|
*              Generate NRHS random solution vectors.
 | 
						|
*
 | 
						|
               IX = 1
 | 
						|
               DO 60 J = 1, NRHS
 | 
						|
                  CALL DLARNV( 2, ISEED, N, XACT( IX ) )
 | 
						|
                  IX = IX + LDA
 | 
						|
   60          CONTINUE
 | 
						|
*
 | 
						|
               DO 80 ITRAN = 1, 3
 | 
						|
                  TRANS = TRANSS( ITRAN )
 | 
						|
                  IF( ITRAN.EQ.1 ) THEN
 | 
						|
                     RCONDC = RCONDO
 | 
						|
                  ELSE
 | 
						|
                     RCONDC = RCONDI
 | 
						|
                  END IF
 | 
						|
*
 | 
						|
*                 Set the right hand side.
 | 
						|
*
 | 
						|
                  CALL DLAGTM( TRANS, N, NRHS, ONE, A, A( M+1 ),
 | 
						|
     $                         A( N+M+1 ), XACT, LDA, ZERO, B, LDA )
 | 
						|
*
 | 
						|
*+    TEST 2
 | 
						|
*                 Solve op(A) * X = B and compute the residual.
 | 
						|
*
 | 
						|
                  CALL DLACPY( 'Full', N, NRHS, B, LDA, X, LDA )
 | 
						|
                  SRNAMT = 'DGTTRS'
 | 
						|
                  CALL DGTTRS( TRANS, N, NRHS, AF, AF( M+1 ),
 | 
						|
     $                         AF( N+M+1 ), AF( N+2*M+1 ), IWORK, X,
 | 
						|
     $                         LDA, INFO )
 | 
						|
*
 | 
						|
*                 Check error code from DGTTRS.
 | 
						|
*
 | 
						|
                  IF( INFO.NE.0 )
 | 
						|
     $               CALL ALAERH( PATH, 'DGTTRS', INFO, 0, TRANS, N, N,
 | 
						|
     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
 | 
						|
     $                            NOUT )
 | 
						|
*
 | 
						|
                  CALL DLACPY( 'Full', N, NRHS, B, LDA, WORK, LDA )
 | 
						|
                  CALL DGTT02( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
 | 
						|
     $                         X, LDA, WORK, LDA, RESULT( 2 ) )
 | 
						|
*
 | 
						|
*+    TEST 3
 | 
						|
*                 Check solution from generated exact solution.
 | 
						|
*
 | 
						|
                  CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
 | 
						|
     $                         RESULT( 3 ) )
 | 
						|
*
 | 
						|
*+    TESTS 4, 5, and 6
 | 
						|
*                 Use iterative refinement to improve the solution.
 | 
						|
*
 | 
						|
                  SRNAMT = 'DGTRFS'
 | 
						|
                  CALL DGTRFS( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
 | 
						|
     $                         AF, AF( M+1 ), AF( N+M+1 ),
 | 
						|
     $                         AF( N+2*M+1 ), IWORK, B, LDA, X, LDA,
 | 
						|
     $                         RWORK, RWORK( NRHS+1 ), WORK,
 | 
						|
     $                         IWORK( N+1 ), INFO )
 | 
						|
*
 | 
						|
*                 Check error code from DGTRFS.
 | 
						|
*
 | 
						|
                  IF( INFO.NE.0 )
 | 
						|
     $               CALL ALAERH( PATH, 'DGTRFS', INFO, 0, TRANS, N, N,
 | 
						|
     $                            -1, -1, NRHS, IMAT, NFAIL, NERRS,
 | 
						|
     $                            NOUT )
 | 
						|
*
 | 
						|
                  CALL DGET04( N, NRHS, X, LDA, XACT, LDA, RCONDC,
 | 
						|
     $                         RESULT( 4 ) )
 | 
						|
                  CALL DGTT05( TRANS, N, NRHS, A, A( M+1 ), A( N+M+1 ),
 | 
						|
     $                         B, LDA, X, LDA, XACT, LDA, RWORK,
 | 
						|
     $                         RWORK( NRHS+1 ), RESULT( 5 ) )
 | 
						|
*
 | 
						|
*                 Print information about the tests that did not pass
 | 
						|
*                 the threshold.
 | 
						|
*
 | 
						|
                  DO 70 K = 2, 6
 | 
						|
                     IF( RESULT( K ).GE.THRESH ) THEN
 | 
						|
                        IF( NFAIL.EQ.0 .AND. NERRS.EQ.0 )
 | 
						|
     $                     CALL ALAHD( NOUT, PATH )
 | 
						|
                        WRITE( NOUT, FMT = 9998 )TRANS, N, NRHS, IMAT,
 | 
						|
     $                     K, RESULT( K )
 | 
						|
                        NFAIL = NFAIL + 1
 | 
						|
                     END IF
 | 
						|
   70             CONTINUE
 | 
						|
                  NRUN = NRUN + 5
 | 
						|
   80          CONTINUE
 | 
						|
   90       CONTINUE
 | 
						|
*
 | 
						|
  100    CONTINUE
 | 
						|
  110 CONTINUE
 | 
						|
*
 | 
						|
*     Print a summary of the results.
 | 
						|
*
 | 
						|
      CALL ALASUM( PATH, NOUT, NFAIL, NRUN, NERRS )
 | 
						|
*
 | 
						|
 9999 FORMAT( 12X, 'N =', I5, ',', 10X, ' type ', I2, ', test(', I2,
 | 
						|
     $      ') = ', G12.5 )
 | 
						|
 9998 FORMAT( ' TRANS=''', A1, ''', N =', I5, ', NRHS=', I3, ', type ',
 | 
						|
     $      I2, ', test(', I2, ') = ', G12.5 )
 | 
						|
 9997 FORMAT( ' NORM =''', A1, ''', N =', I5, ',', 10X, ' type ', I2,
 | 
						|
     $      ', test(', I2, ') = ', G12.5 )
 | 
						|
      RETURN
 | 
						|
*
 | 
						|
*     End of DCHKGT
 | 
						|
*
 | 
						|
      END
 |