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DLATRZ(l)			       )			     DLATRZ(l)

NAME
       DLATRZ  - factor 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

SYNOPSIS
       SUBROUTINE DLATRZ( M, N, L, A, LDA, TAU, WORK )

	   INTEGER	  L, LDA, M, N

	   DOUBLE	  PRECISION A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       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.

ARGUMENTS
       M       (input) INTEGER
	       The number of rows of the matrix A.  M >= 0.

       N       (input) INTEGER
	       The number of columns of the matrix A.  N >= 0.

       L       (input) INTEGER
	       The number of columns of the matrix A containing the meaningful
	       part of the Householder vectors. N-M >= L >= 0.

       A       (input/output) 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.

       LDA     (input) INTEGER
	       The leading dimension of the array A.  LDA >= max(1,M).

       TAU     (output) DOUBLE PRECISION array, dimension (M)
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) DOUBLE PRECISION array, dimension (M)

FURTHER DETAILS
       Based on contributions by
	 A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

       The factorization is obtained by Householder's method.  The kth	transā€
       formation 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 )',   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 ).

LAPACK version 3.0		 15 June 2000			     DLATRZ(l)
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