#include "ESMF_LapackBlas.inc" !> \brief \b DLATRZ ! ! =========== DOCUMENTATION =========== ! ! Online html documentation available at ! http://www.netlib.org/lapack/explore-html/ ! !> \htmlonly !> Download DLATRZ + dependencies !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlatrz.f"> !> [TGZ]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlatrz.f"> !> [ZIP]</a> !> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlatrz.f"> !> [TXT]</a> !> \endhtmlonly ! ! Definition: ! =========== ! ! SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK ) ! ! .. Scalar Arguments .. ! INTEGER L, LDA, M, N ! .. ! .. Array Arguments .. ! DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! !> \par Purpose: ! ============= !> !> \verbatim !> !> DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix !> [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means !> of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal !> matrix and, R and A1 are M-by-M upper triangular matrices. !> \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] L !> \verbatim !> L is INTEGER !> The number of columns of the matrix A containing the !> meaningful part of the Householder vectors. N-M >= L >= 0. !> \endverbatim !> !> \param[in,out] A !> \verbatim !> A is DOUBLE PRECISION array, dimension (LDA,N) !> On entry, the leading M-by-N upper trapezoidal part of the !> array A must contain the matrix to be factorized. !> On exit, the leading M-by-M upper triangular part of A !> contains the upper triangular matrix R, and elements N-L+1 to !> N of the first M rows of A, with the array TAU, represent the !> orthogonal matrix Z as a product of M elementary reflectors. !> \endverbatim !> !> \param[in] LDA !> \verbatim !> LDA is INTEGER !> The leading dimension of the array A. LDA >= max(1,M). !> \endverbatim !> !> \param[out] TAU !> \verbatim !> TAU is DOUBLE PRECISION array, dimension (M) !> The scalar factors of the elementary reflectors. !> \endverbatim !> !> \param[out] WORK !> \verbatim !> WORK is DOUBLE PRECISION array, dimension (M) !> \endverbatim ! ! Authors: ! ======== ! !> \author Univ. of Tennessee !> \author Univ. of California Berkeley !> \author Univ. of Colorado Denver !> \author NAG Ltd. ! !> \date November 2011 ! !> \ingroup doubleOTHERcomputational ! !> \par Contributors: ! ================== !> !> A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA ! !> \par Further Details: ! ===================== !> !> \verbatim !> !> The factorization is obtained by Householder's method. The kth !> transformation matrix, Z( k ), which is used to introduce zeros into !> the ( m - k + 1 )th row of A, is given in the form !> !> Z( k ) = ( I 0 ), !> ( 0 T( k ) ) !> !> where !> !> T( k ) = I - tau*u( k )*u( k )**T, u( k ) = ( 1 ), !> ( 0 ) !> ( z( k ) ) !> !> tau is a scalar and z( k ) is an l element vector. tau and z( k ) !> are chosen to annihilate the elements of the kth row of A2. !> !> The scalar tau is returned in the kth element of TAU and the vector !> u( k ) in the kth row of A2, such that the elements of z( k ) are !> in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in !> the upper triangular part of A1. !> !> Z is given by !> !> Z = Z( 1 ) * Z( 2 ) * ... * Z( m ). !> \endverbatim !> ! ===================================================================== SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK ) ! ! -- LAPACK computational 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 L, LDA, M, N ! .. ! .. Array Arguments .. DOUBLE PRECISION A( LDA, * ), TAU( * ), WORK( * ) ! .. ! ! ===================================================================== ! ! .. Parameters .. DOUBLE PRECISION ZERO PARAMETER ( ZERO = 0.0D+0 ) ! .. ! .. Local Scalars .. INTEGER I ! .. ! .. External Subroutines .. EXTERNAL DLARFG, DLARZ ! .. ! .. Executable Statements .. ! ! Test the input arguments ! ! Quick return if possible ! IF( M.EQ.0 ) THEN RETURN ELSE IF( M.EQ.N ) THEN DO 10 I = 1, N TAU( I ) = ZERO 10 CONTINUE RETURN END IF ! DO 20 I = M, 1, -1 ! ! Generate elementary reflector H(i) to annihilate ! [ A(i,i) A(i,n-l+1:n) ] ! CALL DLARFG( L+1, A( I, I ), A( I, N-L+1 ), LDA, TAU( I ) ) ! ! Apply H(i) to A(1:i-1,i:n) from the right ! CALL DLARZ( 'Right', I-1, N-I+1, L, A( I, N-L+1 ), LDA, & & TAU( I ), A( 1, I ), LDA, WORK ) ! 20 CONTINUE ! RETURN ! ! End of DLATRZ ! END