sglmts.f

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*> \brief \b SGLMTS
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at 
*            http://www.netlib.org/lapack/explore-html/ 
*
*  Definition:
*  ===========
*
*       SUBROUTINE SGLMTS( N, M, P, A, AF, LDA, B, BF, LDB, D, DF,
*                          X, U, WORK, LWORK, RWORK, RESULT )
* 
*       .. Scalar Arguments ..
*       INTEGER            LDA, LDB, LWORK, M, P, N
*       REAL               RESULT
*       ..
*       .. Array Arguments ..
*       REAL               A( LDA, * ), AF( LDA, * ), B( LDB, * ),
*      $                   BF( LDB, * ), RWORK( * ), D( * ), DF( * ),
*      $                   U( * ), WORK( LWORK ), X( * )
*  
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> SGLMTS tests SGGGLM - 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 REAL array, dimension (LDA,M)
*>          The N-by-M matrix A.
*> \endverbatim
*>
*> \param[out] AF
*> \verbatim
*>          AF is REAL 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 REAL array, dimension (LDB,P)
*>          The N-by-P matrix A.
*> \endverbatim
*>
*> \param[out] BF
*> \verbatim
*>          BF is REAL 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 REAL array, dimension( N )
*>          On input, the left hand side of the GLM.
*> \endverbatim
*>
*> \param[out] DF
*> \verbatim
*>          DF is REAL array, dimension( N )
*> \endverbatim
*>
*> \param[out] X
*> \verbatim
*>          X is REAL array, dimension( M )
*>          solution vector X in the GLM problem.
*> \endverbatim
*>
*> \param[out] U
*> \verbatim
*>          U is REAL array, dimension( P )
*>          solution vector U in the GLM problem.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is REAL array, dimension (LWORK)
*> \endverbatim
*>
*> \param[in] LWORK
*> \verbatim
*>          LWORK is INTEGER
*>          The dimension of the array WORK.
*> \endverbatim
*>
*> \param[out] RWORK
*> \verbatim
*>          RWORK is REAL array, dimension (M)
*> \endverbatim
*>
*> \param[out] RESULT
*> \verbatim
*>          RESULT is REAL
*>          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 single_eig
*
*  =====================================================================
      SUBROUTINE sglmts( 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, P, N
      REAL               RESULT
*     ..
*     .. Array Arguments ..
      REAL               A( lda, * ), AF( lda, * ), B( ldb, * ),
     $                   bf( ldb, * ), rwork( * ), d( * ), df( * ),
     $                   u( * ), work( lwork ), x( * )
*
*  ====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter                ( zero = 0.0e+0, one = 1.0e+0 )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO
      REAL               ANORM, BNORM, EPS, XNORM, YNORM, DNORM, UNFL
*     ..
*     .. External Functions ..
      REAL               SASUM, SLAMCH, SLANGE
      EXTERNAL           sasum, slamch, slange
*     ..
*     .. External Subroutines ..
      EXTERNAL           slacpy
*
*     .. Intrinsic Functions ..
      INTRINSIC          max
*     ..
*     .. Executable Statements ..
*
      eps = slamch( 'Epsilon' )
      unfl = slamch( 'Safe minimum' )
      anorm = max( slange( '1', n, m, a, lda, rwork ), unfl )
      bnorm = max( slange( '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 slacpy( 'Full', n, m, a, lda, af, lda )
      CALL slacpy( 'Full', n, p, b, ldb, bf, ldb )
      CALL scopy( n, d, 1, df, 1 )
*
*     Solve GLM problem
*
      CALL sggglm( 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 scopy( n, d, 1, df, 1 )
      CALL sgemv( 'No transpose', n, m, -one, a, lda, x, 1,
     $             one, df, 1 )
*
      CALL sgemv( 'No transpose', n, p, -one, b, ldb, u, 1,
     $             one, df, 1 )
*
      dnorm = sasum( n, df, 1 )
      xnorm = sasum( m, x, 1 ) + sasum( p, u, 1 )
      ynorm = anorm + bnorm
*
      IF( xnorm.LE.zero ) THEN
         result = zero
      ELSE
         result =  ( ( dnorm / ynorm ) / xnorm ) /eps
      END IF
*
      RETURN
*
*     End of SGLMTS
*
      END