233 lines
5.9 KiB
Fortran
233 lines
5.9 KiB
Fortran
*> \brief \b SGLMTS
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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 SGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF,
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* X, U, WORK, LWORK, RWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER LDA, LDB, LWORK, M, P, N
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* REAL RESULT
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* ..
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* .. Array Arguments ..
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* REAL A( LDA, * ), AF( LDA, * ), B( LDB, * ),
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* $ BF( LDB, * ), RWORK( * ), D( * ), DF( * ),
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* $ U( * ), WORK( LWORK ), X( * )
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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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*> SGLMTS tests SGGGLM - a subroutine for solving the generalized
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*> linear model problem.
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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] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows of the matrices A and B. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of columns of the matrix A. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] P
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*> \verbatim
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*> P is INTEGER
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*> The number of columns of the matrix B. P >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is REAL array, dimension (LDA,M)
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*> The N-by-M matrix A.
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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 REAL array, dimension (LDA,M)
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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 arrays A, AF. LDA >= max(M,N).
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is REAL array, dimension (LDB,P)
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*> The N-by-P matrix A.
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*> \endverbatim
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*>
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*> \param[out] BF
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*> \verbatim
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*> BF is REAL array, dimension (LDB,P)
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*> \endverbatim
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*>
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*> \param[in] LDB
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*> \verbatim
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*> LDB is INTEGER
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*> The leading dimension of the arrays B, BF. LDB >= max(P,N).
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is REAL array, dimension( N )
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*> On input, the left hand side of the GLM.
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*> \endverbatim
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*>
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*> \param[out] DF
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*> \verbatim
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*> DF is REAL array, dimension( N )
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*> \endverbatim
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*>
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*> \param[out] X
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*> \verbatim
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*> X is REAL array, dimension( M )
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*> solution vector X in the GLM problem.
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*> \endverbatim
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*>
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*> \param[out] U
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*> \verbatim
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*> U is REAL array, dimension( P )
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*> solution vector U in the GLM problem.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is REAL array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (M)
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL
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*> The test ratio:
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*> norm( d - A*x - B*u )
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*> RESULT = -----------------------------------------
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*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
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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 single_eig
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*
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* =====================================================================
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SUBROUTINE SGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF,
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$ X, U, WORK, LWORK, RWORK, RESULT )
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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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INTEGER LDA, LDB, LWORK, M, P, N
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REAL RESULT
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* ..
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* .. Array Arguments ..
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REAL A( LDA, * ), AF( LDA, * ), B( LDB, * ),
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$ BF( LDB, * ), RWORK( * ), D( * ), DF( * ),
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$ U( * ), WORK( LWORK ), X( * )
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*
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* ====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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* ..
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* .. Local Scalars ..
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INTEGER INFO
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REAL ANORM, BNORM, EPS, XNORM, YNORM, DNORM, UNFL
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* ..
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* .. External Functions ..
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REAL SASUM, SLAMCH, SLANGE
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EXTERNAL SASUM, SLAMCH, SLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL SLACPY
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*
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* .. Intrinsic Functions ..
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INTRINSIC MAX
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'Epsilon' )
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UNFL = SLAMCH( 'Safe minimum' )
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ANORM = MAX( SLANGE( '1', N, M, A, LDA, RWORK ), UNFL )
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BNORM = MAX( SLANGE( '1', N, P, B, LDB, RWORK ), UNFL )
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*
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* Copy the matrices A and B to the arrays AF and BF,
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* and the vector D the array DF.
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*
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CALL SLACPY( 'Full', N, M, A, LDA, AF, LDA )
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CALL SLACPY( 'Full', N, P, B, LDB, BF, LDB )
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CALL SCOPY( N, D, 1, DF, 1 )
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*
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* Solve GLM problem
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*
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CALL SGGGLM( N, M, P, AF, LDA, BF, LDB, DF, X, U, WORK, LWORK,
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$ INFO )
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*
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* Test the residual for the solution of LSE
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*
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* norm( d - A*x - B*u )
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* RESULT = -----------------------------------------
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* (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
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*
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CALL SCOPY( N, D, 1, DF, 1 )
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CALL SGEMV( 'No transpose', N, M, -ONE, A, LDA, X, 1,
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$ ONE, DF, 1 )
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*
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CALL SGEMV( 'No transpose', N, P, -ONE, B, LDB, U, 1,
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$ ONE, DF, 1 )
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*
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DNORM = SASUM( N, DF, 1 )
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XNORM = SASUM( M, X, 1 ) + SASUM( P, U, 1 )
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YNORM = ANORM + BNORM
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*
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IF( XNORM.LE.ZERO ) THEN
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RESULT = ZERO
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ELSE
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RESULT = ( ( DNORM / YNORM ) / XNORM ) /EPS
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END IF
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*
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RETURN
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*
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* End of SGLMTS
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*
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END
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