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---
:name: dlatrz
:md5sum: 29240b38847f5fec70a609188c5ec3c5
:category: :subroutine
:arguments:
- m:
:type: integer
:intent: input
- n:
:type: integer
:intent: input
- l:
:type: integer
:intent: input
- a:
:type: doublereal
:intent: input/output
:dims:
- lda
- n
- lda:
:type: integer
:intent: input
- tau:
:type: doublereal
:intent: output
:dims:
- m
- work:
:type: doublereal
:intent: workspace
:dims:
- m
:substitutions:
m: lda
:fortran_help: " SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )\n\n\
* Purpose\n\
* =======\n\
*\n\
* DLATRZ factors the M-by-(M+L) real upper trapezoidal matrix\n\
* [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z, by means\n\
* of orthogonal transformations. Z is an (M+L)-by-(M+L) orthogonal\n\
* matrix and, R and A1 are M-by-M upper triangular matrices.\n\
*\n\n\
* Arguments\n\
* =========\n\
*\n\
* M (input) INTEGER\n\
* The number of rows of the matrix A. M >= 0.\n\
*\n\
* N (input) INTEGER\n\
* The number of columns of the matrix A. N >= 0.\n\
*\n\
* L (input) INTEGER\n\
* The number of columns of the matrix A containing the\n\
* meaningful part of the Householder vectors. N-M >= L >= 0.\n\
*\n\
* A (input/output) DOUBLE PRECISION array, dimension (LDA,N)\n\
* On entry, the leading M-by-N upper trapezoidal part of the\n\
* array A must contain the matrix to be factorized.\n\
* On exit, the leading M-by-M upper triangular part of A\n\
* contains the upper triangular matrix R, and elements N-L+1 to\n\
* N of the first M rows of A, with the array TAU, represent the\n\
* orthogonal matrix Z as a product of M elementary reflectors.\n\
*\n\
* LDA (input) INTEGER\n\
* The leading dimension of the array A. LDA >= max(1,M).\n\
*\n\
* TAU (output) DOUBLE PRECISION array, dimension (M)\n\
* The scalar factors of the elementary reflectors.\n\
*\n\
* WORK (workspace) DOUBLE PRECISION array, dimension (M)\n\
*\n\n\
* Further Details\n\
* ===============\n\
*\n\
* Based on contributions by\n\
* A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA\n\
*\n\
* The factorization is obtained by Householder's method. The kth\n\
* transformation matrix, Z( k ), which is used to introduce zeros into\n\
* the ( m - k + 1 )th row of A, is given in the form\n\
*\n\
* Z( k ) = ( I 0 ),\n\
* ( 0 T( k ) )\n\
*\n\
* where\n\
*\n\
* T( k ) = I - tau*u( k )*u( k )', u( k ) = ( 1 ),\n\
* ( 0 )\n\
* ( z( k ) )\n\
*\n\
* tau is a scalar and z( k ) is an l element vector. tau and z( k )\n\
* are chosen to annihilate the elements of the kth row of A2.\n\
*\n\
* The scalar tau is returned in the kth element of TAU and the vector\n\
* u( k ) in the kth row of A2, such that the elements of z( k ) are\n\
* in a( k, l + 1 ), ..., a( k, n ). The elements of R are returned in\n\
* the upper triangular part of A1.\n\
*\n\
* Z is given by\n\
*\n\
* Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).\n\
*\n\
* =====================================================================\n\
*\n"
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