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SUBROUTINE ZGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF, X, U,
$ WORK, LWORK, RWORK, RESULT )
*
* -- LAPACK test routine (version 3.0) --
* Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd.,
* Courant Institute, Argonne National Lab, and Rice University
* March 31, 1993
*
* .. Scalar Arguments ..
INTEGER LDA, LDB, LWORK, M, N, P
DOUBLE PRECISION RESULT
* ..
* .. Array Arguments ..
*
* Purpose
* =======
*
* ZGLMTS tests ZGGGLM - a subroutine for solving the generalized
* linear model problem.
*
* Arguments
* =========
*
* N (input) INTEGER
* The number of rows of the matrices A and B. N >= 0.
*
* M (input) INTEGER
* The number of columns of the matrix A. M >= 0.
*
* P (input) INTEGER
* The number of columns of the matrix B. P >= 0.
*
* A (input) COMPLEX*16 array, dimension (LDA,M)
* The N-by-M matrix A.
*
* AF (workspace) COMPLEX*16 array, dimension (LDA,M)
*
* LDA (input) INTEGER
* The leading dimension of the arrays A, AF. LDA >= max(M,N).
*
* B (input) COMPLEX*16 array, dimension (LDB,P)
* The N-by-P matrix A.
*
* BF (workspace) COMPLEX*16 array, dimension (LDB,P)
*
* LDB (input) INTEGER
* The leading dimension of the arrays B, BF. LDB >= max(P,N).
*
* D (input) COMPLEX*16 array, dimension( N )
* On input, the left hand side of the GLM.
*
* DF (workspace) COMPLEX*16 array, dimension( N )
*
* X (output) COMPLEX*16 array, dimension( M )
* solution vector X in the GLM problem.
*
* U (output) COMPLEX*16 array, dimension( P )
* solution vector U in the GLM problem.
*
* WORK (workspace) COMPLEX*16 array, dimension (LWORK)
*
* LWORK (input) INTEGER
* The dimension of the array WORK.
*
* RWORK (workspace) DOUBLE PRECISION array, dimension (M)
*
* RESULT (output) DOUBLE PRECISION
* The test ratio:
* norm( d - A*x - B*u )
* RESULT = -----------------------------------------
* (norm(A)+norm(B))*(norm(x)+norm(u))*EPS
*
* ====================================================================
*
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
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