redhat man page for zlatrz

ZLATRZ(l)								 )								 ZLATRZ(l)

NAME
       ZLATRZ  -  factor the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of uni-
       tary transformations, where Z is an (M+L)-by-(M+L) unitary matrix and, R and A1 are M-by-M upper triangular matrices

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

	   INTEGER	  L, LDA, M, N

	   COMPLEX*16	  A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
       ZLATRZ factors the M-by-(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M) A(1:M,N-L+1:N) ] as ( R 0 ) * Z by means of unitary
       transformations, where Z is an (M+L)-by-(M+L) unitary 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) COMPLEX*16 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 unitary 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) COMPLEX*16 array, dimension (M)
	       The scalar factors of the elementary reflectors.

       WORK    (workspace) COMPLEX*16 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 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 							 ZLATRZ(l)