cqrt02.f

Go to the documentation of this file.

*> \brief \b CQRT02
*
*  =========== DOCUMENTATION ===========
*
* Online html documentation available at
*            http://www.netlib.org/lapack/explore-html/
*
*  Definition:
*  ===========
*
*       SUBROUTINE CQRT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK,
*                          RWORK, RESULT )
*
*       .. Scalar Arguments ..
*       INTEGER            K, LDA, LWORK, M, N
*       ..
*       .. Array Arguments ..
*       REAL               RESULT( * ), RWORK( * )
*       COMPLEX            A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
*      $                   R( LDA, * ), TAU( * ), WORK( LWORK )
*       ..
*
*
*> \par Purpose:
*  =============
*>
*> \verbatim
*>
*> CQRT02 tests CUNGQR, which generates an m-by-n matrix Q with
*> orthonornmal columns that is defined as the product of k elementary
*> reflectors.
*>
*> Given the QR factorization of an m-by-n matrix A, CQRT02 generates
*> the orthogonal matrix Q defined by the factorization of the first k
*> columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
*> and checks that the columns 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.
*>          M >= N >= 0.
*> \endverbatim
*>
*> \param[in] K
*> \verbatim
*>          K is INTEGER
*>          The number of elementary reflectors whose product defines the
*>          matrix Q. N >= K >= 0.
*> \endverbatim
*>
*> \param[in] A
*> \verbatim
*>          A is COMPLEX array, dimension (LDA,N)
*>          The m-by-n matrix A which was factorized by CQRT01.
*> \endverbatim
*>
*> \param[in] AF
*> \verbatim
*>          AF is COMPLEX array, dimension (LDA,N)
*>          Details of the QR factorization of A, as returned by CGEQRF.
*>          See CGEQRF for further details.
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*>          Q is COMPLEX array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[out] R
*> \verbatim
*>          R is COMPLEX array, dimension (LDA,N)
*> \endverbatim
*>
*> \param[in] LDA
*> \verbatim
*>          LDA is INTEGER
*>          The leading dimension of the arrays A, AF, Q and R. LDA >= M.
*> \endverbatim
*>
*> \param[in] TAU
*> \verbatim
*>          TAU is COMPLEX array, dimension (N)
*>          The scalar factors of the elementary reflectors corresponding
*>          to the QR factorization in AF.
*> \endverbatim
*>
*> \param[out] WORK
*> \verbatim
*>          WORK is COMPLEX 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 array, dimension (2)
*>          The test ratios:
*>          RESULT(1) = norm( R - Q'*A ) / ( M * norm(A) * EPS )
*>          RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )
*> \endverbatim
*
*  Authors:
*  ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \date December 2016
*
*> \ingroup complex_lin
*
*  =====================================================================
      SUBROUTINE cqrt02( M, N, K, A, AF, Q, R, 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 ..
      REAL               RESULT( * ), RWORK( * )
      COMPLEX            A( LDA, * ), AF( LDA, * ), Q( LDA, * ),
     $                   r( lda, * ), tau( * ), work( lwork )
*     ..
*
*  =====================================================================
*
*     .. Parameters ..
      REAL               ZERO, ONE
      parameter( zero = 0.0e+0, one = 1.0e+0 )
      COMPLEX            ROGUE
      parameter( rogue = ( -1.0e+10, -1.0e+10 ) )
*     ..
*     .. Local Scalars ..
      INTEGER            INFO
      REAL               ANORM, EPS, RESID
*     ..
*     .. External Functions ..
      REAL               CLANGE, CLANSY, SLAMCH
      EXTERNAL           clange, clansy, slamch
*     ..
*     .. External Subroutines ..
      EXTERNAL           cgemm, cherk, clacpy, claset, cungqr
*     ..
*     .. Intrinsic Functions ..
      INTRINSIC          cmplx, max, real
*     ..
*     .. Scalars in Common ..
      CHARACTER*32       SRNAMT
*     ..
*     .. Common blocks ..
      COMMON             / srnamc / srnamt
*     ..
*     .. Executable Statements ..
*
      eps = slamch( 'Epsilon' )
*
*     Copy the first k columns of the factorization to the array Q
*
      CALL claset( 'Full', m, n, rogue, rogue, q, lda )
      CALL clacpy( 'Lower', m-1, k, af( 2, 1 ), lda, q( 2, 1 ), lda )
*
*     Generate the first n columns of the matrix Q
*
      srnamt = 'CUNGQR'
      CALL cungqr( m, n, k, q, lda, tau, work, lwork, info )
*
*     Copy R(1:n,1:k)
*
      CALL claset( 'Full', n, k, cmplx( zero ), cmplx( zero ), r, lda )
      CALL clacpy( 'Upper', n, k, af, lda, r, lda )
*
*     Compute R(1:n,1:k) - Q(1:m,1:n)' * A(1:m,1:k)
*
      CALL cgemm( 'Conjugate transpose', 'No transpose', n, k, m,
     $            cmplx( -one ), q, lda, a, lda, cmplx( one ), r, lda )
*
*     Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) .
*
      anorm = clange( '1', m, k, a, lda, rwork )
      resid = clange( '1', n, k, r, lda, rwork )
      IF( anorm.GT.zero ) THEN
         result( 1 ) = ( ( resid / real( max( 1, m ) ) ) / anorm ) / eps
      ELSE
         result( 1 ) = zero
      END IF
*
*     Compute I - Q'*Q
*
      CALL claset( 'Full', n, n, cmplx( zero ), cmplx( one ), r, lda )
      CALL cherk( 'Upper', 'Conjugate transpose', n, m, -one, q, lda,
     $            one, r, lda )
*
*     Compute norm( I - Q'*Q ) / ( M * EPS ) .
*
      resid = clansy( '1', 'Upper', n, r, lda, rwork )
*
      result( 2 ) = ( resid / real( max( 1, m ) ) ) / eps
*
      RETURN
*
*     End of CQRT02
*
      END