280 lines
7.7 KiB
Fortran
280 lines
7.7 KiB
Fortran
*> \brief \b DQLT03
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
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* RWORK, RESULT )
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*
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* .. Scalar Arguments ..
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* INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
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* $ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
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* $ WORK( LWORK )
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* ..
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*
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*
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*> \par Purpose:
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* =============
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*>
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*> \verbatim
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*>
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*> DQLT03 tests DORMQL, which computes Q*C, Q'*C, C*Q or C*Q'.
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*>
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*> DQLT03 compares the results of a call to DORMQL with the results of
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*> forming Q explicitly by a call to DORGQL and then performing matrix
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*> multiplication by a call to DGEMM.
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*> \endverbatim
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*
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* Arguments:
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* ==========
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*
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*> \param[in] M
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*> \verbatim
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*> M is INTEGER
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*> The order of the orthogonal matrix Q. M >= 0.
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*> \endverbatim
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*>
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*> \param[in] N
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*> \verbatim
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*> N is INTEGER
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*> The number of rows or columns of the matrix C; C is m-by-n if
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*> Q is applied from the left, or n-by-m if Q is applied from
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*> the right. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] K
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*> \verbatim
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*> K is INTEGER
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*> The number of elementary reflectors whose product defines the
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*> orthogonal matrix Q. M >= K >= 0.
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*> \endverbatim
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*>
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*> \param[in] AF
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*> \verbatim
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*> AF is DOUBLE PRECISION array, dimension (LDA,N)
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*> Details of the QL factorization of an m-by-n matrix, as
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*> returned by DGEQLF. See SGEQLF for further details.
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*> \endverbatim
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*>
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*> \param[out] C
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*> \verbatim
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*> C is DOUBLE PRECISION array, dimension (LDA,N)
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*> \endverbatim
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*>
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*> \param[out] CC
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*> \verbatim
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*> CC is DOUBLE PRECISION array, dimension (LDA,N)
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is DOUBLE PRECISION array, dimension (LDA,M)
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*> \endverbatim
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*>
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*> \param[in] LDA
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*> \verbatim
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*> LDA is INTEGER
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*> The leading dimension of the arrays AF, C, CC, and Q.
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*> \endverbatim
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*>
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*> \param[in] TAU
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*> \verbatim
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*> TAU is DOUBLE PRECISION array, dimension (min(M,N))
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*> The scalar factors of the elementary reflectors corresponding
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*> to the QL factorization in AF.
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*> \endverbatim
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*>
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*> \param[out] WORK
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*> \verbatim
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*> WORK is DOUBLE PRECISION array, dimension (LWORK)
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*> \endverbatim
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*>
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*> \param[in] LWORK
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*> \verbatim
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*> LWORK is INTEGER
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*> The length of WORK. LWORK must be at least M, and should be
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*> M*NB, where NB is the blocksize for this environment.
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*> \endverbatim
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*>
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*> \param[out] RWORK
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*> \verbatim
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*> RWORK is DOUBLE PRECISION array, dimension (M)
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*> \endverbatim
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*>
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*> \param[out] RESULT
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*> \verbatim
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*> RESULT is DOUBLE PRECISION array, dimension (4)
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*> The test ratios compare two techniques for multiplying a
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*> random matrix C by an m-by-m orthogonal matrix Q.
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*> RESULT(1) = norm( Q*C - Q*C ) / ( M * norm(C) * EPS )
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*> RESULT(2) = norm( C*Q - C*Q ) / ( M * norm(C) * EPS )
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*> RESULT(3) = norm( Q'*C - Q'*C )/ ( M * norm(C) * EPS )
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*> RESULT(4) = norm( C*Q' - C*Q' )/ ( M * norm(C) * EPS )
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*> \endverbatim
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*
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* Authors:
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* ========
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*
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*> \author Univ. of Tennessee
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*> \author Univ. of California Berkeley
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*> \author Univ. of Colorado Denver
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*> \author NAG Ltd.
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*
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*> \ingroup double_lin
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*
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* =====================================================================
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SUBROUTINE DQLT03( M, N, K, AF, C, CC, Q, LDA, TAU, WORK, LWORK,
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$ RWORK, RESULT )
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*
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* -- LAPACK test routine --
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* -- LAPACK is a software package provided by Univ. of Tennessee, --
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
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*
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* .. Scalar Arguments ..
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INTEGER K, LDA, LWORK, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION AF( LDA, * ), C( LDA, * ), CC( LDA, * ),
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$ Q( LDA, * ), RESULT( * ), RWORK( * ), TAU( * ),
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$ WORK( LWORK )
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO, ONE
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PARAMETER ( ZERO = 0.0D0, ONE = 1.0D0 )
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DOUBLE PRECISION ROGUE
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PARAMETER ( ROGUE = -1.0D+10 )
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* ..
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* .. Local Scalars ..
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CHARACTER SIDE, TRANS
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INTEGER INFO, ISIDE, ITRANS, J, MC, MINMN, NC
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DOUBLE PRECISION CNORM, EPS, RESID
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* ..
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* .. External Functions ..
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LOGICAL LSAME
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DOUBLE PRECISION DLAMCH, DLANGE
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EXTERNAL LSAME, DLAMCH, DLANGE
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* ..
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* .. External Subroutines ..
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EXTERNAL DGEMM, DLACPY, DLARNV, DLASET, DORGQL, DORMQL
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* ..
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* .. Local Arrays ..
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INTEGER ISEED( 4 )
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC DBLE, MAX, MIN
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* ..
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* .. Scalars in Common ..
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CHARACTER*32 SRNAMT
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* ..
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* .. Common blocks ..
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COMMON / SRNAMC / SRNAMT
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* ..
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* .. Data statements ..
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DATA ISEED / 1988, 1989, 1990, 1991 /
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* ..
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* .. Executable Statements ..
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*
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EPS = DLAMCH( 'Epsilon' )
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MINMN = MIN( M, N )
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*
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* Quick return if possible
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*
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IF( MINMN.EQ.0 ) THEN
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RESULT( 1 ) = ZERO
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RESULT( 2 ) = ZERO
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RESULT( 3 ) = ZERO
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RESULT( 4 ) = ZERO
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RETURN
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END IF
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*
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* Copy the last k columns of the factorization to the array Q
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*
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CALL DLASET( 'Full', M, M, ROGUE, ROGUE, Q, LDA )
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IF( K.GT.0 .AND. M.GT.K )
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$ CALL DLACPY( 'Full', M-K, K, AF( 1, N-K+1 ), LDA,
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$ Q( 1, M-K+1 ), LDA )
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IF( K.GT.1 )
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$ CALL DLACPY( 'Upper', K-1, K-1, AF( M-K+1, N-K+2 ), LDA,
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$ Q( M-K+1, M-K+2 ), LDA )
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*
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* Generate the m-by-m matrix Q
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*
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SRNAMT = 'DORGQL'
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CALL DORGQL( M, M, K, Q, LDA, TAU( MINMN-K+1 ), WORK, LWORK,
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$ INFO )
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*
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DO 30 ISIDE = 1, 2
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IF( ISIDE.EQ.1 ) THEN
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SIDE = 'L'
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MC = M
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NC = N
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ELSE
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SIDE = 'R'
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MC = N
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NC = M
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END IF
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*
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* Generate MC by NC matrix C
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*
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DO 10 J = 1, NC
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CALL DLARNV( 2, ISEED, MC, C( 1, J ) )
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10 CONTINUE
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CNORM = DLANGE( '1', MC, NC, C, LDA, RWORK )
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IF( CNORM.EQ.0.0D0 )
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$ CNORM = ONE
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*
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DO 20 ITRANS = 1, 2
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IF( ITRANS.EQ.1 ) THEN
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TRANS = 'N'
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ELSE
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TRANS = 'T'
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END IF
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*
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* Copy C
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*
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CALL DLACPY( 'Full', MC, NC, C, LDA, CC, LDA )
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*
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* Apply Q or Q' to C
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*
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SRNAMT = 'DORMQL'
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IF( K.GT.0 )
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$ CALL DORMQL( SIDE, TRANS, MC, NC, K, AF( 1, N-K+1 ), LDA,
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$ TAU( MINMN-K+1 ), CC, LDA, WORK, LWORK,
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$ INFO )
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*
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* Form explicit product and subtract
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*
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IF( LSAME( SIDE, 'L' ) ) THEN
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CALL DGEMM( TRANS, 'No transpose', MC, NC, MC, -ONE, Q,
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$ LDA, C, LDA, ONE, CC, LDA )
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ELSE
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CALL DGEMM( 'No transpose', TRANS, MC, NC, NC, -ONE, C,
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$ LDA, Q, LDA, ONE, CC, LDA )
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END IF
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*
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* Compute error in the difference
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*
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RESID = DLANGE( '1', MC, NC, CC, LDA, RWORK )
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RESULT( ( ISIDE-1 )*2+ITRANS ) = RESID /
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$ ( DBLE( MAX( 1, M ) )*CNORM*EPS )
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*
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20 CONTINUE
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30 CONTINUE
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*
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RETURN
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*
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* End of DQLT03
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*
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END
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