201 lines
5.5 KiB
Fortran
201 lines
5.5 KiB
Fortran
*> \brief \b DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
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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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*> \htmlonly
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*> Download DLATRZ + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrz.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrz.f">
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*> [ZIP]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrz.f">
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*> [TXT]</a>
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*> \endhtmlonly
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*
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* Definition:
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* ===========
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*
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* SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
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*
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* .. Scalar Arguments ..
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* INTEGER L, LDA, M, N
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* ..
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* .. Array Arguments ..
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* DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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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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*> DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix
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*> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means
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*> of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal
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*> matrix and, R and A1 are M-by-M upper triangular matrices.
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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 number of rows of the matrix A. 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 columns of the matrix A. N >= 0.
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*> \endverbatim
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*>
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*> \param[in] L
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*> \verbatim
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*> L is INTEGER
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*> The number of columns of the matrix A containing the
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*> meaningful part of the Householder vectors. N-M >= L >= 0.
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*> \endverbatim
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*>
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*> \param[in,out] A
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*> \verbatim
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*> A is DOUBLE PRECISION array, dimension (LDA,N)
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*> On entry, the leading M-by-N upper trapezoidal part of the
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*> array A must contain the matrix to be factorized.
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*> On exit, the leading M-by-M upper triangular part of A
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*> contains the upper triangular matrix R, and elements N-L+1 to
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*> N of the first M rows of A, with the array TAU, represent the
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*> orthogonal matrix Z as a product of M elementary reflectors.
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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 array A. LDA >= max(1,M).
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*> \endverbatim
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*>
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*> \param[out] TAU
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*> \verbatim
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*> TAU is DOUBLE PRECISION array, dimension (M)
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*> The scalar factors of the elementary reflectors.
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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 (M)
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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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*> \date September 2012
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*
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*> \ingroup doubleOTHERcomputational
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*
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*> \par Contributors:
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* ==================
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*>
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*> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA
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*
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*> \par Further Details:
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* =====================
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*>
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*> \verbatim
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*>
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*> The factorization is obtained by Householder's method. The kth
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*> transformation matrix, Z( k ), which is used to introduce zeros into
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*> the ( m - k + 1 )th row of A, is given in the form
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*>
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*> Z( k ) = ( I 0 ),
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*> ( 0 T( k ) )
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*>
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*> where
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*>
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*> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ),
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*> ( 0 )
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*> ( z( k ) )
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*>
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*> tau is a scalar and z( k ) is an l element vector. tau and z( k )
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*> are chosen to annihilate the elements of the kth row of A2.
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*>
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*> The scalar tau is returned in the kth element of TAU and the vector
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*> u( k ) in the kth row of A2, such that the elements of z( k ) are
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*> in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in
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*> the upper triangular part of A1.
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*>
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*> Z is given by
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*>
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*> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
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*> \endverbatim
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*>
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* =====================================================================
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SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )
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*
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* -- LAPACK computational routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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INTEGER L, LDA, M, N
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* ..
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* .. Array Arguments ..
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DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * )
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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
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PARAMETER ( ZERO = 0.0D+0 )
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* ..
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* .. Local Scalars ..
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INTEGER I
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* ..
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* .. External Subroutines ..
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EXTERNAL DLARFG, DLARZ
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* ..
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* .. Executable Statements ..
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*
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* Test the input arguments
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*
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* Quick return if possible
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*
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IF( M.EQ.0 ) THEN
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RETURN
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ELSE IF( M.EQ.N ) THEN
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DO 10 I = 1, N
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TAU( I ) = ZERO
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10 CONTINUE
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RETURN
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END IF
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*
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DO 20 I = M, 1, -1
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*
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* Generate elementary reflector H(i) to annihilate
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* [ A(i,i) A(i,n-l+1:n) ]
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*
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CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) )
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*
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* Apply H(i) to A(1:i-1,i:n) from the right
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*
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CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA,
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$ TAU( I ), A( 1, I ), LDA, WORK )
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*
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20 CONTINUE
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*
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RETURN
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*
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* End of DLATRZ
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*
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END
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