numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/dqrt03.f | 7321B | -rw-r--r-- |
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*> \brief \b DQRT03 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DQRT03( 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 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), * $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DQRT03 tests DORMQR, which computes Q*C, Q'*C, C*Q or C*Q'. *> *> DQRT03 compares the results of a call to DORMQR with the results of *> forming Q explicitly by a call to DORGQR and then performing matrix *> multiplication by a call to DGEMM. *> \endverbatim * * Arguments: * ========== * *> \param[in] M *> \verbatim *> M is INTEGER *> The order of the orthogonal matrix Q. M >= 0. *> \endverbatim *> *> \param[in] N *> \verbatim *> N is INTEGER *> The number of rows or columns of the matrix C; C is m-by-n if *> Q is applied from the left, or n-by-m if Q is applied from *> the right. N >= 0. *> \endverbatim *> *> \param[in] K *> \verbatim *> K is INTEGER *> The number of elementary reflectors whose product defines the *> orthogonal matrix Q. M >= K >= 0. *> \endverbatim *> *> \param[in] AF *> \verbatim *> AF is DOUBLE PRECISION array, dimension (LDA,N) *> Details of the QR factorization of an m-by-n matrix, as *> returned by DGEQRF. See DGEQRF for further details. *> \endverbatim *> *> \param[out] C *> \verbatim *> C is DOUBLE PRECISION array, dimension (LDA,N) *> \endverbatim *> *> \param[out] CC *> \verbatim *> CC is DOUBLE PRECISION array, dimension (LDA,N) *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDA,M) *> \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 DOUBLE PRECISION array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors corresponding *> to the QR factorization in AF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION 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 m-by-m orthogonal matrix Q. *> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS ) *> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS ) *> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS ) *> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS ) *> \endverbatim * * Authors: * ======== * *> \author Univ. of Tennessee *> \author Univ. of California Berkeley *> \author Univ. of Colorado Denver *> \author NAG Ltd. * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DQRT03( 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 AF( LDA, * ), C( LDA, * ), CC( LDA, * ), $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ONE PARAMETER ( ONE = 1.0D0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. CHARACTER SIDE, TRANS INTEGER INFO, ISIDE, ITRANS, J, MC, NC DOUBLE PRECISION CNORM, EPS, RESID * .. * .. External Functions .. LOGICAL LSAME DOUBLE PRECISION DLAMCH, DLANGE EXTERNAL LSAME, DLAMCH, DLANGE * .. * .. External Subroutines .. EXTERNAL DGEMM, DLACPY, DLARNV, DLASET, DORGQR, DORMQR * .. * .. Local Arrays .. INTEGER ISEED( 4 ) * .. * .. Intrinsic Functions .. INTRINSIC DBLE, MAX * .. * .. Scalars in Common .. CHARACTER*32 SRNAMT * .. * .. Common blocks .. COMMON / SRNAMC / SRNAMT * .. * .. Data statements .. DATA ISEED / 1988, 1989, 1990, 1991 / * .. * .. Executable Statements .. * EPS = DLAMCH( 'Epsilon' ) * * Copy the first k columns of the factorization to the array Q * CALL DLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) CALL DLACPY( 'Lower', M-1, K, AF( 2, 1 ), LDA, Q( 2, 1 ), LDA ) * * Generate the m-by-m matrix Q * SRNAMT = 'DORGQR' CALL DORGQR( M, M, K, Q, LDA, TAU, WORK, LWORK, INFO ) * DO 30 ISIDE = 1, 2 IF( ISIDE.EQ.1 ) THEN SIDE = 'L' MC = M NC = N ELSE SIDE = 'R' MC = N NC = M END IF * * Generate MC by NC matrix C * DO 10 J = 1, NC CALL DLARNV( 2, ISEED, MC, C( 1, J ) ) 10 CONTINUE CNORM = DLANGE( '1', MC, NC, C, LDA, RWORK ) IF( CNORM.EQ.0.0D0 ) $ CNORM = ONE * DO 20 ITRANS = 1, 2 IF( ITRANS.EQ.1 ) THEN TRANS = 'N' ELSE TRANS = 'T' END IF * * Copy C * CALL DLACPY( 'Full', MC, NC, C, LDA, CC, LDA ) * * Apply Q or Q' to C * SRNAMT = 'DORMQR' CALL DORMQR( SIDE, TRANS, MC, NC, K, AF, LDA, TAU, CC, LDA, $ WORK, LWORK, INFO ) * * Form explicit product and subtract * IF( LSAME( SIDE, 'L' ) ) THEN CALL DGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q, $ LDA, C, LDA, ONE, CC, LDA ) ELSE CALL DGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C, $ LDA, Q, LDA, ONE, CC, LDA ) END IF * * Compute error in the difference * RESID = DLANGE( '1', MC, NC, CC, LDA, RWORK ) RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID / $ ( DBLE( MAX( 1, M ) )*CNORM*EPS ) * 20 CONTINUE 30 CONTINUE * RETURN * * End of DQRT03 * END