numeric-linalg
Educational material on the SciPy implementation of numerical linear algebra algorithms
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| lapack/TESTING/LIN/slqt01.f | 6056B | -rw-r--r-- |
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*> \brief \b SLQT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE SLQT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * REAL A( LDA, * ), AF( LDA, * ), L( LDA, * ), * $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> SLQT01 tests SGELQF, which computes the LQ factorization of an m-by-n *> matrix A, and partially tests SORGLQ which forms the n-by-n *> orthogonal matrix Q. *> *> SLQT01 compares L 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 REAL array, dimension (LDA,N) *> The m-by-n matrix A. *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is REAL array, dimension (LDA,N) *> Details of the LQ factorization of A, as returned by SGELQF. *> See SGELQF for further details. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is REAL array, dimension (LDA,N) *> The n-by-n orthogonal matrix Q. *> \endverbatim *> *> \param[out] L *> \verbatim *> L is REAL 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 REAL array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors, as returned *> by SGELQF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is REAL 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 (max(M,N)) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is REAL array, dimension (2) *> The test ratios: *> RESULT(1) = norm( L - 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 single_lin * * ===================================================================== SUBROUTINE SLQT01( M, N, A, AF, Q, L, 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 A( LDA, * ), AF( LDA, * ), L( LDA, * ), $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. REAL ZERO, ONE PARAMETER ( ZERO = 0.0E+0, ONE = 1.0E+0 ) REAL ROGUE PARAMETER ( ROGUE = -1.0E+10 ) * .. * .. Local Scalars .. INTEGER INFO, MINMN REAL ANORM, EPS, RESID * .. * .. External Functions .. REAL SLAMCH, SLANGE, SLANSY EXTERNAL SLAMCH, SLANGE, SLANSY * .. * .. External Subroutines .. EXTERNAL SGELQF, SGEMM, SLACPY, SLASET, SORGLQ, SSYRK * .. * .. Intrinsic Functions .. INTRINSIC 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 SLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'SGELQF' CALL SGELQF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL SLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA ) IF( N.GT.1 ) $ CALL SLACPY( 'Upper', M, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA ) * * Generate the n-by-n matrix Q * SRNAMT = 'SORGLQ' CALL SORGLQ( N, N, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy L * CALL SLASET( 'Full', M, N, ZERO, ZERO, L, LDA ) CALL SLACPY( 'Lower', M, N, AF, LDA, L, LDA ) * * Compute L - A*Q' * CALL SGEMM( 'No transpose', 'Transpose', M, N, N, -ONE, A, LDA, Q, $ LDA, ONE, L, LDA ) * * Compute norm( L - Q'*A ) / ( N * norm(A) * EPS ) . * ANORM = SLANGE( '1', M, N, A, LDA, RWORK ) RESID = SLANGE( '1', M, N, L, 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 SLASET( 'Full', N, N, ZERO, ONE, L, LDA ) CALL SSYRK( 'Upper', 'No transpose', N, N, -ONE, Q, LDA, ONE, L, $ LDA ) * * Compute norm( I - Q*Q' ) / ( N * EPS ) . * RESID = SLANSY( '1', 'Upper', N, L, LDA, RWORK ) * RESULT( 2 ) = ( RESID / REAL( MAX( 1, N ) ) ) / EPS * RETURN * * End of SLQT01 * END