*> \brief \b DQLT01 * * =========== DOCUMENTATION =========== * * Online html documentation available at * http://www.netlib.org/lapack/explore-html/ * * Definition: * =========== * * SUBROUTINE DQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, * RWORK, RESULT ) * * .. Scalar Arguments .. * INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. * DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ), * $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), * $ WORK( LWORK ) * .. * * *> \par Purpose: * ============= *> *> \verbatim *> *> DQLT01 tests DGEQLF, which computes the QL factorization of an m-by-n *> matrix A, and partially tests DORGQL which forms the m-by-m *> orthogonal matrix Q. *> *> DQLT01 compares L 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 DOUBLE PRECISION array, dimension (LDA,N) *> The m-by-n matrix A. *> \endverbatim *> *> \param[out] AF *> \verbatim *> AF is DOUBLE PRECISION array, dimension (LDA,N) *> Details of the QL factorization of A, as returned by DGEQLF. *> See DGEQLF for further details. *> \endverbatim *> *> \param[out] Q *> \verbatim *> Q is DOUBLE PRECISION array, dimension (LDA,M) *> The m-by-m orthogonal matrix Q. *> \endverbatim *> *> \param[out] L *> \verbatim *> L is DOUBLE PRECISION 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 DOUBLE PRECISION array, dimension (min(M,N)) *> The scalar factors of the elementary reflectors, as returned *> by DGEQLF. *> \endverbatim *> *> \param[out] WORK *> \verbatim *> WORK is DOUBLE PRECISION 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 (M) *> \endverbatim *> *> \param[out] RESULT *> \verbatim *> RESULT is DOUBLE PRECISION array, dimension (2) *> The test ratios: *> RESULT(1) = norm( L - 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. * *> \date November 2011 * *> \ingroup double_lin * * ===================================================================== SUBROUTINE DQLT01( M, N, A, AF, Q, L, LDA, TAU, WORK, LWORK, $ RWORK, RESULT ) * * -- LAPACK test routine (version 3.4.0) -- * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * November 2011 * * .. Scalar Arguments .. INTEGER LDA, LWORK, M, N * .. * .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), AF( LDA, * ), L( LDA, * ), $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ), $ WORK( LWORK ) * .. * * ===================================================================== * * .. Parameters .. DOUBLE PRECISION ZERO, ONE PARAMETER ( ZERO = 0.0D+0, ONE = 1.0D+0 ) DOUBLE PRECISION ROGUE PARAMETER ( ROGUE = -1.0D+10 ) * .. * .. Local Scalars .. INTEGER INFO, MINMN DOUBLE PRECISION ANORM, EPS, RESID * .. * .. External Functions .. DOUBLE PRECISION DLAMCH, DLANGE, DLANSY EXTERNAL DLAMCH, DLANGE, DLANSY * .. * .. External Subroutines .. EXTERNAL DGEMM, DGEQLF, DLACPY, DLASET, DORGQL, DSYRK * .. * .. Intrinsic Functions .. INTRINSIC DBLE, 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 DLACPY( 'Full', M, N, A, LDA, AF, LDA ) * * Factorize the matrix A in the array AF. * SRNAMT = 'DGEQLF' CALL DGEQLF( M, N, AF, LDA, TAU, WORK, LWORK, INFO ) * * Copy details of Q * CALL DLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA ) IF( M.GE.N ) THEN IF( N.LT.M .AND. N.GT.0 ) $ CALL DLACPY( 'Full', M-N, N, AF, LDA, Q( 1, M-N+1 ), LDA ) IF( N.GT.1 ) $ CALL DLACPY( 'Upper', N-1, N-1, AF( M-N+1, 2 ), LDA, $ Q( M-N+1, M-N+2 ), LDA ) ELSE IF( M.GT.1 ) $ CALL DLACPY( 'Upper', M-1, M-1, AF( 1, N-M+2 ), LDA, $ Q( 1, 2 ), LDA ) END IF * * Generate the m-by-m matrix Q * SRNAMT = 'DORGQL' CALL DORGQL( M, M, MINMN, Q, LDA, TAU, WORK, LWORK, INFO ) * * Copy L * CALL DLASET( 'Full', M, N, ZERO, ZERO, L, LDA ) IF( M.GE.N ) THEN IF( N.GT.0 ) $ CALL DLACPY( 'Lower', N, N, AF( M-N+1, 1 ), LDA, $ L( M-N+1, 1 ), LDA ) ELSE IF( N.GT.M .AND. M.GT.0 ) $ CALL DLACPY( 'Full', M, N-M, AF, LDA, L, LDA ) IF( M.GT.0 ) $ CALL DLACPY( 'Lower', M, M, AF( 1, N-M+1 ), LDA, $ L( 1, N-M+1 ), LDA ) END IF * * Compute L - Q'*A * CALL DGEMM( 'Transpose', 'No transpose', M, N, M, -ONE, Q, LDA, A, $ LDA, ONE, L, LDA ) * * Compute norm( L - Q'*A ) / ( M * norm(A) * EPS ) . * ANORM = DLANGE( '1', M, N, A, LDA, RWORK ) RESID = DLANGE( '1', M, N, L, LDA, RWORK ) IF( ANORM.GT.ZERO ) THEN RESULT( 1 ) = ( ( RESID / DBLE( MAX( 1, M ) ) ) / ANORM ) / EPS ELSE RESULT( 1 ) = ZERO END IF * * Compute I - Q'*Q * CALL DLASET( 'Full', M, M, ZERO, ONE, L, LDA ) CALL DSYRK( 'Upper', 'Transpose', M, M, -ONE, Q, LDA, ONE, L, $ LDA ) * * Compute norm( I - Q'*Q ) / ( M * EPS ) . * RESID = DLANSY( '1', 'Upper', M, L, LDA, RWORK ) * RESULT( 2 ) = ( RESID / DBLE( MAX( 1, M ) ) ) / EPS * RETURN * * End of DQLT01 * END