
ZLATRZ(l) ) ZLATRZ(l)
NAME
ZLATRZ  factor the Mby(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M)
A(1:M,NL+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 MbyM 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 Mby(M+L) complex upper trapezoidal matrix [ A1 A2 ] = [ A(1:M,1:M)
A(1:M,NL+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 MbyM 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. NM >= L >= 0.
A (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the leading MbyN upper trapezoidal part of the array A must contain
the matrix to be factorized. On exit, the leading MbyM upper triangular part of
A contains the upper triangular matrix R, and elements NL+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 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 ZLATRZ(l) 
