*> \brief \b CQRT01P * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE CQRT01P( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * REAL RESULT( * ), RWORK( * ) * COMPLEX A( LDA, * ), AF( LDA, * ), Q( LDA, * ), * \$ R( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> CQRT01P tests CGEQRFP, which computes the QR factorization of an m-by-n *> matrix A, and partially tests CUNGQR which forms the m-by-m *> orthogonal matrix Q. *> *> CQRT01P compares R with Q'*A, and checks that Q is orthogonal. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows of the matrix A. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of columns of the matrix A. N >= 0. *> \endverbatim *> *> \param[in] A *> \verbatim *> A is COMPLEX array, dimension (LDA,N) *> The m-by-n matrix A. *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is COMPLEX array, dimension (LDA,N) *> Details of the QR factorization of A, as returned by CGEQRFP. *> See CGEQRFP for further details. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX array, dimension (LDA,M) *> The m-by-m orthogonal matrix Q. *> \endverbatim *> *> \param[out] R *> \verbatim *> R is COMPLEX array, dimension (LDA,max(M,N)) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the arrays A, AF, Q and R. *> LDA >= max(M,N). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors, as returned *> by CGEQRFP. *> \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. * *> \ingroup complex_lin * * ===================================================================== SUBROUTINE CQRT01P( M, N, 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 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, MINMN REAL ANORM, EPS, RESID * .. * .. External Functions .. REAL CLANGE, CLANSY, SLAMCH EXTERNAL CLANGE, CLANSY, SLAMCH * .. * .. External Subroutines .. EXTERNAL CGEMM, CGEQRFP, CHERK, CLACPY, CLASET, CUNGQR * .. * .. Intrinsic Functions .. INTRINSIC CMPLX, MAX, MIN, REAL * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * MINMN = MIN( M, N ) EPS = SLAMCH( 'Epsilon' ) * * Copy the matrix A to the array AF. * CALL CLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'CGEQRFP' CALL CGEQRFP( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL CLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) CALL CLACPY( 'Lower', M-1, N, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) * * Generate the m-by-m matrix Q * SRNAMT = 'CUNGQR' CALL CUNGQR( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy R * CALL CLASET( 'Full', M, N, CMPLX( ZERO ), CMPLX( ZERO ), R, LDA ) CALL CLACPY( 'Upper', M, N, AF, LDA, R, LDA ) * * Compute R - Q'*A * CALL CGEMM( 'Conjugate transpose', 'No transpose', M, N, M, \$ CMPLX( -ONE ), Q, LDA, A, LDA, CMPLX( ONE ), R, LDA ) * * Compute norm( R - Q'*A ) / ( M * norm(A) * EPS ) . * ANORM = CLANGE( '1', M, N, A, LDA, RWORK ) RESID = CLANGE( '1', M, N, 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', M, M, CMPLX( ZERO ), CMPLX( ONE ), R, LDA ) CALL CHERK( 'Upper', 'Conjugate transpose', M, M, -ONE, Q, LDA, \$ ONE, R, LDA ) * * Compute norm( I - Q'*Q ) / ( M * EPS ) . * RESID = CLANSY( '1', 'Upper', M, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, M ) ) ) / EPS * RETURN * * End of CQRT01P * END