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*> \brief \b DLQT03
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
* Definition:
* ===========
*
* SUBROUTINE DLQT03( 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
*>
*> DLQT03 tests DORMLQ, which computes Q*C, Q'*C, C*Q or C*Q'.
*>
*> DLQT03 compares the results of a call to DORMLQ with the results of
*> forming Q explicitly by a call to DORGLQ and then performing matrix
*> multiplication by a call to DGEMM.
*> \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 DOUBLE PRECISION array, dimension (LDA,N)
*> Details of the LQ factorization of an m-by-n matrix, as
*> returned by DGELQF. See SGELQF 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,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 DOUBLE PRECISION array, dimension (min(M,N))
*> The scalar factors of the elementary reflectors corresponding
*> to the LQ 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 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 double_lin
*
* =====================================================================
SUBROUTINE DLQT03( 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, DORGLQ, DORMLQ
* ..
* .. 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 rows of the factorization to the array Q
*
CALL DLASET( 'Full', N, N, ROGUE, ROGUE, Q, LDA )
CALL DLACPY( 'Upper', K, N-1, AF( 1, 2 ), LDA, Q( 1, 2 ), LDA )
*
* Generate the n-by-n matrix Q
*
SRNAMT = 'DORGLQ'
CALL DORGLQ( N, N, K, Q, LDA, TAU, 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 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 = 'DORMLQ'
CALL DORMLQ( 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, N ) )*CNORM*EPS )
*
20 CONTINUE
30 CONTINUE
*
RETURN
*
* End of DLQT03
*
END
|
