dlqt02.f

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*> \brief \b DLQT02
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE DLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
*                          RWORK, RESULT )
*
*       .. Scalar Arguments ..
*       INTEGER            K, LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       DOUBLE PRECISION   A( LDA, * ), AF( LDA, * ), L( LDA, * ),
*      $                   Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
*      $                   WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> DLQT02 tests DORGLQ, which generates an m-by-n matrix Q with
*> orthonornmal rows that is defined as the product of k elementary
*> reflectors.
*>
*> Given the LQ factorization of an m-by-n matrix A, DLQT02 generates
*> the orthogonal matrix Q defined by the factorization of the first k
*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
*> checks that the rows of Q are orthonormal.
*> \endverbatim
*
*  Arguments:
*  ==========
*
*> \param[in] M
*> \verbatim
*>          M is INTEGER
*>          The number of rows of the matrix Q to be generated.  M >= 0.
*> \endverbatim
*>
*> \param[in] N
*> \verbatim
*>          N is INTEGER
*>          The number of columns of the matrix Q to be generated.
*>          N >= M >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines the
*>          matrix Q. M >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is DOUBLE PRECISION array, dimension (LDA,N)
*>          The m-by-n matrix A which was factorized by DLQT01.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is DOUBLE PRECISION array, dimension (LDA,N)
*>          Details of the LQ factorization of A, as returned by DGELQF.
*>          See DGELQF for further details.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is DOUBLE PRECISION array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] L
*> \verbatim
*>          L is DOUBLE PRECISION array, dimension (LDA,M)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the arrays A, AF, Q and L. LDA >= N.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is DOUBLE PRECISION array, dimension (M)
*>          The scalar factors of the elementary reflectors corresponding
*>          to the LQ factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is DOUBLE PRECISION 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 array, dimension (2)
*>          The test ratios:
*>          RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
*>          RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup double_lin
*
*  =====================================================================
      SUBROUTINE dlqt02( M, N, K, A, AF, Q, L, LDA, TAU, 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            K, LDA, LWORK, M, N
*     ..
*     .. Array Arguments ..
      DOUBLE PRECISION   A( LDA, * ), AF( LDA, * ), L( LDA, * ),
     $                   q( lda, * ), result( * ), rwork( * ), tau( * ),
     $                   work( lwork )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      DOUBLE PRECISION   ZERO, ONE
      parameter( zero = 0.0d+0, one = 1.0d+0 )
      DOUBLE PRECISION   ROGUE
      parameter( rogue = -1.0d+10 )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO
      DOUBLE PRECISION   ANORM, EPS, RESID
*     ..
*     .. External Functions ..
      DOUBLE PRECISION   DLAMCH, DLANGE, DLANSY
      EXTERNAL           dlamch, dlange, dlansy
*     ..
*     .. External Subroutines ..
      EXTERNAL           dgemm, dlacpy, dlaset, dorglq, dsyrk
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          dble, max
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Executable Statements ..
*
      eps = dlamch( 'Epsilon' )
*
*     Copy the first k rows of the factorization to the array Q
*
      CALL dlaset( 'Full', m, n, rogue, rogue, q, lda )
      CALL dlacpy( 'Upper', k, n-1, af( 1, 2 ), lda, q( 1, 2 ), lda )
*
*     Generate the first n columns of the matrix Q
*
      srnamt = 'DORGLQ'
      CALL dorglq( m, n, k, q, lda, tau, work, lwork, info )
*
*     Copy L(1:k,1:m)
*
      CALL dlaset( 'Full', k, m, zero, zero, l, lda )
      CALL dlacpy( 'Lower', k, m, af, lda, l, lda )
*
*     Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
*
      CALL dgemm( 'No transpose', 'Transpose', k, m, n, -one, a, lda, q,
     $            lda, one, l, lda )
*
*     Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
*
      anorm = dlange( '1', k, n, a, lda, rwork )
      resid = dlange( '1', k, m, l, lda, rwork )
      IF( anorm.GT.zero ) THEN
         result( 1 ) = ( ( resid / dble( max( 1, n ) ) ) / anorm ) / eps
      ELSE
         result( 1 ) = zero
      END IF
*
*     Compute I - Q*Q'
*
      CALL dlaset( 'Full', m, m, zero, one, l, lda )
      CALL dsyrk( 'Upper', 'No transpose', m, n, -one, q, lda, one, l,
     $            lda )
*
*     Compute norm( I - Q*Q' ) / ( N * EPS ) .
*
      resid = dlansy( '1', 'Upper', m, l, lda, rwork )
*
      result( 2 ) = ( resid / dble( max( 1, n ) ) ) / eps
*
      RETURN
*
*     End of DLQT02
*
      END