*> \brief \b ZRQT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE ZRQT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER K, LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION RESULT( * ), RWORK( * ) * COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), * \$ Q( LDA, * ), TAU( * ), WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> ZRQT03 tests ZUNMRQ, which computes Q*C, Q'*C, C*Q or C*Q'. *> *> ZRQT03 compares the results of a call to ZUNMRQ with the results of *> forming Q explicitly by a call to ZUNGRQ and then performing matrix *> multiplication by a call to ZGEMM. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The number of rows or columns of the matrix C; C is n-by-m if *> Q is applied from the left, or m-by-n if Q is applied from *> the right. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The order of the orthogonal matrix Q. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> orthogonal matrix Q. N >= K >= 0. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is COMPLEX*16 array, dimension (LDA,N) *> Details of the RQ factorization of an m-by-n matrix, as *> returned by ZGERQF. See CGERQF for further details. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is COMPLEX*16 array, dimension (LDA,N) *> \endverbatim *> *> \param[out] CC *> \verbatim *> CC is COMPLEX*16 array, dimension (LDA,N) *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is COMPLEX*16 array, dimension (LDA,N) *> \endverbatim *> *> \param[in] LDA *> \verbatim *> LDA is INTEGER *> The leading dimension of the arrays AF, C, CC, and Q. *> \endverbatim *> *> \param[in] TAU *> \verbatim *> TAU is COMPLEX*16 array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors corresponding *> to the RQ factorization in AF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is COMPLEX*16 array, dimension (LWORK) *> \endverbatim *> *> \param[in] LWORK *> \verbatim *> LWORK is INTEGER *> The length of WORK. LWORK must be at least M, and should be *> M*NB, where NB is the blocksize for this environment. *> \endverbatim *> *> \param[out] RWORK *> \verbatim *> RWORK is DOUBLE PRECISION array, dimension (M) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (4) *> The test ratios compare two techniques for multiplying a *> random matrix C by an n-by-n orthogonal matrix Q. *> RESULT(1) = norm( Q*C - Q*C ) / ( N * norm(C) * EPS ) *> RESULT(2) = norm( C*Q - C*Q ) / ( N * norm(C) * EPS ) *> RESULT(3) = norm( Q'*C - Q'*C )/ ( N * norm(C) * EPS ) *> RESULT(4) = norm( C*Q' - C*Q' )/ ( N * norm(C) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup complex16_lin * * ===================================================================== SUBROUTINE ZRQT03( M, N, K, AF, C, CC, Q, 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 .. DOUBLE PRECISION RESULT( * ), RWORK( * ) COMPLEX*16 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), \$ Q( 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 .. CHARACTER SIDE, TRANS INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC DOUBLE PRECISION CNORM, EPS, RESID * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, ZLANGE EXTERNAL LSAME, DLAMCH, ZLANGE * .. * .. External Subroutines .. EXTERNAL ZGEMM, ZLACPY, ZLARNV, ZLASET, ZUNGRQ, ZUNMRQ * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC DBLE, DCMPLX, MAX, MIN * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * EPS = DLAMCH( 'Epsilon' ) MINMN = MIN( M, N ) * * Quick return if possible * IF( MINMN.EQ.0 ) THEN RESULT( 1 ) = ZERO RESULT( 2 ) = ZERO RESULT( 3 ) = ZERO RESULT( 4 ) = ZERO RETURN END IF * * Copy the last k rows of the factorization to the array Q * CALL ZLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( K.GT.0 .AND. N.GT.K ) \$ CALL ZLACPY( 'Full', K, N-K, AF( M-K+1, 1 ), LDA, \$ Q( N-K+1, 1 ), LDA ) IF( K.GT.1 ) \$ CALL ZLACPY( 'Lower', K-1, K-1, AF( M-K+2, N-K+1 ), LDA, \$ Q( N-K+2, N-K+1 ), LDA ) * * Generate the n-by-n matrix Q * SRNAMT = 'ZUNGRQ' CALL ZUNGRQ( N, N, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK, \$ INFO ) * DO 30 ISIDE = 1, 2 IF( ISIDE.EQ.1 ) THEN SIDE = 'L' MC = N NC = M ELSE SIDE = 'R' MC = M NC = N END IF * * Generate MC by NC matrix C * DO 10 J = 1, NC CALL ZLARNV( 2, ISEED, MC, C( 1, J ) ) 10 CONTINUE CNORM = ZLANGE( '1', MC, NC, C, LDA, RWORK ) IF( CNORM.EQ.ZERO ) \$ CNORM = ONE * DO 20 ITRANS = 1, 2 IF( ITRANS.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'C' END IF * * Copy C * CALL ZLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) * * Apply Q or Q' to C * SRNAMT = 'ZUNMRQ' IF( K.GT.0 ) \$ CALL ZUNMRQ( SIDE, TRANS, MC, NC, K, AF( M-K+1, 1 ), LDA, \$ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK, \$ INFO ) * * Form explicit product and subtract * IF( LSAME( SIDE, 'L' ) ) THEN CALL ZGEMM( TRANS, 'No transpose', MC, NC, MC, \$ DCMPLX( -ONE ), Q, LDA, C, LDA, \$ DCMPLX( ONE ), CC, LDA ) ELSE CALL ZGEMM( 'No transpose', TRANS, MC, NC, NC, \$ DCMPLX( -ONE ), C, LDA, Q, LDA, \$ DCMPLX( ONE ), CC, LDA ) END IF * * Compute error in the difference * RESID = ZLANGE( '1', MC, NC, CC, LDA, RWORK ) RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / \$ ( DBLE( MAX( 1, N ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of ZRQT03 * END