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*> \brief \b ZGLMTS
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE ZGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF, X, U,
* WORK, LWORK, RWORK, RESULT )
*
* .. Scalar Arguments ..
* INTEGER LDA, LDB, LWORK, M, N, P
* DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> ZGLMTS tests ZGGGLM - a subroutine for solving the generalized
*> linear model problem.
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] N
*> \verbatim
*> N is INTEGER
*> The number of rows of the matrices A and B. N >= 0.
*> \endverbatim
*>
*> \param[in] M
*> \verbatim
*> M is INTEGER
*> The number of columns of the matrix A. M >= 0.
*> \endverbatim
*>
*> \param[in] P
*> \verbatim
*> P is INTEGER
*> The number of columns of the matrix B. P >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*> A is COMPLEX*16 array, dimension (LDA,M)
*> The N-by-M matrix A.
*> \endverbatim
*>
*> \param[out] AF
*> \verbatim
*> AF is COMPLEX*16 array, dimension (LDA,M)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*> LDA is INTEGER
*> The leading dimension of the arrays A, AF. LDA >= max(M,N).
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is COMPLEX*16 array, dimension (LDB,P)
*> The N-by-P matrix A.
*> \endverbatim
*>
*> \param[out] BF
*> \verbatim
*> BF is COMPLEX*16 array, dimension (LDB,P)
*> \endverbatim
*>
*> \param[in] LDB
*> \verbatim
*> LDB is INTEGER
*> The leading dimension of the arrays B, BF. LDB >= max(P,N).
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is COMPLEX*16 array, dimension( N )
*> On input, the left hand side of the GLM.
*> \endverbatim
*>
*> \param[out] DF
*> \verbatim
*> DF is COMPLEX*16 array, dimension( N )
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*> X is COMPLEX*16 array, dimension( M )
*> solution vector X in the GLM problem.
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*> U is COMPLEX*16 array, dimension( P )
*> solution vector U in the GLM problem.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*> WORK is COMPLEX*16 array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*> LWORK is INTEGER
*> The dimension of the array WORK.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*> RWORK is DOUBLE PRECISION array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*> RESULT is DOUBLE PRECISION
*> The test ratio:
*> norm( d - A*x - B*u )
*> RESULT = -----------------------------------------
*> (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date November 2011
*
*> \ingroup complex16_eig
*
* =====================================================================
SUBROUTINE ZGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF, X, U,
$ WORK, LWORK, RWORK, RESULT )
*
* -- LAPACK test routine (version 3.4.0) --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
* November 2011
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LWORK, M, N, P
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
*
* ====================================================================
*
DOUBLE PRECISION RWORK( * )
COMPLEX*16 A( LDA, * ), AF( LDA, * ), B( LDB, * ),
$ BF( LDB, * ), D( * ), DF( * ), U( * ),
$ WORK( LWORK ), X( * )
* ..
* .. Parameters ..
DOUBLE PRECISION ZERO
PARAMETER ( ZERO = 0.0D+0 )
COMPLEX*16 CONE
PARAMETER ( CONE = 1.0D+0 )
* ..
* .. Local Scalars ..
INTEGER INFO
DOUBLE PRECISION ANORM, BNORM, DNORM, EPS, UNFL, XNORM, YNORM
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DZASUM, ZLANGE
EXTERNAL DLAMCH, DZASUM, ZLANGE
* ..
* .. External Subroutines ..
*
EXTERNAL ZCOPY, ZGEMV, ZGGGLM, ZLACPY
* ..
* .. Intrinsic Functions ..
INTRINSIC MAX
* ..
* .. Executable Statements ..
*
EPS = DLAMCH( 'Epsilon' )
UNFL = DLAMCH( 'Safe minimum' )
ANORM = MAX( ZLANGE( '1', N, M, A, LDA, RWORK ), UNFL )
BNORM = MAX( ZLANGE( '1', N, P, B, LDB, RWORK ), UNFL )
*
* Copy the matrices A and B to the arrays AF and BF,
* and the vector D the array DF.
*
CALL ZLACPY( 'Full', N, M, A, LDA, AF, LDA )
CALL ZLACPY( 'Full', N, P, B, LDB, BF, LDB )
CALL ZCOPY( N, D, 1, DF, 1 )
*
* Solve GLM problem
*
CALL ZGGGLM( N, M, P, AF, LDA, BF, LDB, DF, X, U, WORK, LWORK,
$ INFO )
*
* Test the residual for the solution of LSE
*
* norm( d - A*x - B*u )
* RESULT = -----------------------------------------
* (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*
CALL ZCOPY( N, D, 1, DF, 1 )
CALL ZGEMV( 'No transpose', N, M, -CONE, A, LDA, X, 1, CONE, DF,
$ 1 )
*
CALL ZGEMV( 'No transpose', N, P, -CONE, B, LDB, U, 1, CONE, DF,
$ 1 )
*
DNORM = DZASUM( N, DF, 1 )
XNORM = DZASUM( M, X, 1 ) + DZASUM( P, U, 1 )
YNORM = ANORM + BNORM
*
IF( XNORM.LE.ZERO ) THEN
RESULT = ZERO
ELSE
RESULT = ( ( DNORM / YNORM ) / XNORM ) / EPS
END IF
*
RETURN
*
* End of ZGLMTS
*
END
|
