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228 lines
6.2 KiB
228 lines
6.2 KiB
2 years ago
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*> \brief \b CLQT02
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE CLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
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* RWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* REAL RESULT( * ), RWORK( * )
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* COMPLEX A( LDA, * ), AF( LDA, * ), L( LDA, * ),
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* $ Q( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> CLQT02 tests CUNGLQ, which generates an m-by-n matrix Q with
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*> orthonormal rows that is defined as the product of k elementary
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*> reflectors.
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*>
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*> Given the LQ factorization of an m-by-n matrix A, CLQT02 generates
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*> the orthogonal matrix Q defined by the factorization of the first k
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*> rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
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*> checks that the rows of Q are orthonormal.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The number of rows of the matrix Q to be generated. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of columns of the matrix Q to be generated.
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*> N >= M >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines the
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*> matrix Q. M >= K >= 0.
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*> \endverbatim
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*>
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*> \param[in] A
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*> \verbatim
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*> A is COMPLEX array, dimension (LDA,N)
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*> The m-by-n matrix A which was factorized by CLQT01.
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is COMPLEX array, dimension (LDA,N)
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*> Details of the LQ factorization of A, as returned by CGELQF.
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*> See CGELQF for further details.
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is COMPLEX array, dimension (LDA,N)
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*> \endverbatim
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*>
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*> \param[out] L
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*> \verbatim
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*> L is COMPLEX array, dimension (LDA,M)
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the arrays A, AF, Q and L. LDA >= N.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is COMPLEX array, dimension (M)
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*> The scalar factors of the elementary reflectors corresponding
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*> to the LQ factorization in AF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is COMPLEX array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The dimension of the array WORK.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is REAL array, dimension (M)
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is REAL array, dimension (2)
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*> The test ratios:
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*> RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
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*> RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup complex_lin
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*
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* =====================================================================
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SUBROUTINE CLQT02( M, N, K, A, AF, Q, L, LDA, TAU, WORK, LWORK,
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$ RWORK, RESULT )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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REAL RESULT( * ), RWORK( * )
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COMPLEX A( LDA, * ), AF( LDA, * ), L( LDA, * ),
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$ Q( LDA, * ), TAU( * ), WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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REAL ZERO, ONE
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PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 )
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COMPLEX ROGUE
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PARAMETER ( ROGUE = ( -1.0E+10, -1.0E+10 ) )
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* ..
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* .. Local Scalars ..
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INTEGER INFO
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REAL ANORM, EPS, RESID
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* ..
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* .. External Functions ..
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REAL CLANGE, CLANSY, SLAMCH
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EXTERNAL CLANGE, CLANSY, SLAMCH
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* ..
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* .. External Subroutines ..
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EXTERNAL CGEMM, CHERK, CLACPY, CLASET, CUNGLQ
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC CMPLX, MAX, REAL
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* ..
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* .. Scalars in Common ..
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CHARACTER*32 SRNAMT
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* ..
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* .. Common blocks ..
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Executable Statements ..
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*
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EPS = SLAMCH( 'Epsilon' )
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*
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* Copy the first k rows of the factorization to the array Q
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*
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CALL CLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA )
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CALL CLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA )
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*
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* Generate the first n columns of the matrix Q
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*
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SRNAMT = 'CUNGLQ'
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CALL CUNGLQ( M, N, K, Q, LDA, TAU, WORK, LWORK, INFO )
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*
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* Copy L(1:k,1:m)
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*
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CALL CLASET( 'Full', K, M, CMPLX( ZERO ), CMPLX( ZERO ), L, LDA )
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CALL CLACPY( 'Lower', K, M, AF, LDA, L, LDA )
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*
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* Compute L(1:k,1:m) - A(1:k,1:n) * Q(1:m,1:n)'
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*
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CALL CGEMM( 'No transpose', 'Conjugate transpose', K, M, N,
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$ CMPLX( -ONE ), A, LDA, Q, LDA, CMPLX( ONE ), L, LDA )
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*
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* Compute norm( L - A*Q' ) / ( N * norm(A) * EPS ) .
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*
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ANORM = CLANGE( '1', K, N, A, LDA, RWORK )
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RESID = CLANGE( '1', K, M, L, LDA, RWORK )
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IF( ANORM.GT.ZERO ) THEN
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RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS
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ELSE
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RESULT( 1 ) = ZERO
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END IF
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*
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* Compute I - Q*Q'
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*
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CALL CLASET( 'Full', M, M, CMPLX( ZERO ), CMPLX( ONE ), L, LDA )
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CALL CHERK( 'Upper', 'No transpose', M, N, -ONE, Q, LDA, ONE, L,
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$ LDA )
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*
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* Compute norm( I - Q*Q' ) / ( N * EPS ) .
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*
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RESID = CLANSY( '1', 'Upper', M, L, LDA, RWORK )
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*
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RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS
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*
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RETURN
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*
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* End of CLQT02
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*
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END
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