# clatrz.f - Man Page

SRC/clatrz.f

## Synopsis

### Functions/Subroutines

subroutine clatrz (m, n, l, a, lda, tau, work)
CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

## Function/Subroutine Documentation

### subroutine clatrz (integer m, integer n, integer l, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work)

CLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Purpose:

CLATRZ 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.
Parameters

M

M is INTEGER
The number of rows of the matrix A.  M >= 0.

N

N is INTEGER
The number of columns of the matrix A.  N >= 0.

L

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

A

A is COMPLEX 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

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

TAU

TAU is COMPLEX array, dimension (M)
The scalar factors of the elementary reflectors.

WORK

WORK is COMPLEX array, dimension (M)
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Contributors:

A. Petitet, Computer Science Dept., Univ. of Tenn., Knoxville, USA

Further Details:

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 )**H,   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 ).

Definition at line 139 of file clatrz.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clatrz(3) is an alias of clatrz.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK