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RedHat 9 (Linux i386) - man page for slatrz (redhat section l)

SLATRZ(l)					)					SLATRZ(l)

NAME
       SLATRZ  -  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 SLATRZ( M, N, L, A, LDA, TAU, WORK )

	   INTEGER	  L, LDA, M, N

	   REAL 	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       SLATRZ 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 House-
	       holder vectors. N-M >= L >= 0.

       A       (input/output) REAL 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) REAL array, dimension (M)
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) REAL 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 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 )',   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 ele-
       ments 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 				SLATRZ(l)


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