*> \brief \b CRQT02 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CRQT02( 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 *> *> CRQT02 tests CUNGRQ, which generates an m-by-n matrix Q with *> orthonornmal rows that is defined as the product of k elementary *> reflectors. *> *> Given the RQ factorization of an m-by-n matrix A, CRQT02 generates *> the orthogonal matrix Q defined by the factorization of the last k *> rows of A; it compares R(m-k+1:m,n-m+1:n) with *> A(m-k+1:m,1:n)*Q(n-m+1:n,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 COMPLEX array, dimension (LDA,N) *> The m-by-n matrix A which was factorized by CRQT01. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is COMPLEX array, dimension (LDA,N) *> Details of the RQ factorization of A, as returned by CGERQF. *> See CGERQF 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,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 COMPLEX array, dimension (M) *> The scalar factors of the elementary reflectors corresponding *> to the RQ 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 - 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. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CRQT02( M, N, K, A, AF, Q, R, LDA, TAU, WORK, LWORK, \$ RWORK, RESULT ) * * -- LAPACK test routine -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. 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, CUNGRQ * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, REAL * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * * Quick return if possible * IF( M.EQ.0 .OR. N.EQ.0 .OR. K.EQ.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RETURN END IF * EPS = SLAMCH( 'Epsilon' ) * * Copy the last k rows of the factorization to the array Q * CALL CLASET( 'Full', M, N, ROGUE, ROGUE, Q, LDA ) IF( K.LT.N ) \$ CALL CLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, \$ Q( M-K+1, 1 ), LDA ) IF( K.GT.1 ) \$ CALL CLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, \$ Q( M-K+2, N-K+1 ), LDA ) * * Generate the last n rows of the matrix Q * SRNAMT = 'CUNGRQ' CALL CUNGRQ( M, N, K, Q, LDA, TAU( M-K+1 ), WORK, LWORK, INFO ) * * Copy R(m-k+1:m,n-m+1:n) * CALL CLASET( 'Full', K, M, CMPLX( ZERO ), CMPLX( ZERO ), \$ R( M-K+1, N-M+1 ), LDA ) CALL CLACPY( 'Upper', K, K, AF( M-K+1, N-K+1 ), LDA, \$ R( M-K+1, N-K+1 ), LDA ) * * Compute R(m-k+1:m,n-m+1:n) - A(m-k+1:m,1:n) * Q(n-m+1:n,1:n)' * CALL CGEMM( 'No transpose', 'Conjugate transpose', K, M, N, \$ CMPLX( -ONE ), A( M-K+1, 1 ), LDA, Q, LDA, \$ CMPLX( ONE ), R( M-K+1, N-M+1 ), LDA ) * * Compute norm( R - A*Q' ) / ( N * norm(A) * EPS ) . * ANORM = CLANGE( '1', K, N, A( M-K+1, 1 ), LDA, RWORK ) RESID = CLANGE( '1', K, M, R( M-K+1, N-M+1 ), LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / REAL( MAX( 1, N ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q*Q' * CALL CLASET( 'Full', M, M, CMPLX( ZERO ), CMPLX( ONE ), R, LDA ) CALL CHERK( 'Upper', 'No transpose', M, N, -ONE, Q, LDA, ONE, R, \$ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = CLANSY( '1', 'Upper', M, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS * RETURN * * End of CRQT02 * END