zglmts.f

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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 December 2016
*
*> \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 3.7.0) --
*  -- LAPACK is a software package provided by Univ. of Tennessee,    --
*  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*     December 2016
*
*     .. 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