*> \brief \b ZRQT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZRQT01( M, N, A, AF, Q, R, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION RESULT( * ), RWORK( * ) * COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), * \$ R( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZRQT01 tests ZGERQF, which computes the RQ factorization of an m-by-n *> matrix A, and partially tests ZUNGRQ which forms the n-by-n *> orthogonal matrix Q. *> *> ZRQT01 compares R with A*Q', 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*16 array, dimension (LDA,N) *> The m-by-n matrix A. *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is COMPLEX*16 array, dimension (LDA,N) *> Details of the RQ factorization of A, as returned by ZGERQF. *> See ZGERQF for further details. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDA,N) *> The n-by-n orthogonal matrix Q. *> \endverbatim *> *> \param[out] R *> \verbatim *> R is COMPLEX*16 array, dimension (LDA,max(M,N)) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the arrays A, AF, Q and L. *> LDA >= max(M,N). *> \endverbatim *> *> \param[out] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors, as returned *> by ZGERQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 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 (max(M,N)) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION 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 complex16_lin * * ===================================================================== SUBROUTINE ZRQT01( 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 .. DOUBLE PRECISION RESULT( * ), RWORK( * ) COMPLEX*16 A( LDA, * ), AF( LDA, * ), Q( LDA, * ), \$ R( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) COMPLEX*16 ROGUE PARAMETER ( ROGUE = ( -1.0D+10, -1.0D+10 ) ) * .. * .. Local Scalars .. INTEGER INFO, MINMN DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, ZLANGE, ZLANSY EXTERNAL DLAMCH, ZLANGE, ZLANSY * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZGERQF, ZHERK, ZLACPY, ZLASET, ZUNGRQ * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Executable Statements .. * MINMN = MIN( M, N ) EPS = DLAMCH( 'Epsilon' ) * * Copy the matrix A to the array AF. * CALL ZLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'ZGERQF' CALL ZGERQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( M.LE.N ) THEN IF( M.GT.0 .AND. M.LT.N ) \$ CALL ZLACPY( 'Full', M, N-M, AF, LDA, Q( N-M+1, 1 ), LDA ) IF( M.GT.1 ) \$ CALL ZLACPY( 'Lower', M-1, M-1, AF( 2, N-M+1 ), LDA, \$ Q( N-M+2, N-M+1 ), LDA ) ELSE IF( N.GT.1 ) \$ CALL ZLACPY( 'Lower', N-1, N-1, AF( M-N+2, 1 ), LDA, \$ Q( 2, 1 ), LDA ) END IF * * Generate the n-by-n matrix Q * SRNAMT = 'ZUNGRQ' CALL ZUNGRQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy R * CALL ZLASET( 'Full', M, N, DCMPLX( ZERO ), DCMPLX( ZERO ), R, \$ LDA ) IF( M.LE.N ) THEN IF( M.GT.0 ) \$ CALL ZLACPY( 'Upper', M, M, AF( 1, N-M+1 ), LDA, \$ R( 1, N-M+1 ), LDA ) ELSE IF( M.GT.N .AND. N.GT.0 ) \$ CALL ZLACPY( 'Full', M-N, N, AF, LDA, R, LDA ) IF( N.GT.0 ) \$ CALL ZLACPY( 'Upper', N, N, AF( M-N+1, 1 ), LDA, \$ R( M-N+1, 1 ), LDA ) END IF * * Compute R - A*Q' * CALL ZGEMM( 'No transpose', 'Conjugate transpose', M, N, N, \$ DCMPLX( -ONE ), A, LDA, Q, LDA, DCMPLX( ONE ), R, \$ LDA ) * * Compute norm( R - Q'*A ) / ( N * norm(A) * EPS ) . * ANORM = ZLANGE( '1', M, N, A, LDA, RWORK ) RESID = ZLANGE( '1', M, N, R, 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 ZLASET( 'Full', N, N, DCMPLX( ZERO ), DCMPLX( ONE ), R, LDA ) CALL ZHERK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, R, \$ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = ZLANSY( '1', 'Upper', N, R, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, N ) ) ) / EPS * RETURN * * End of ZRQT01 * END