# clatrz.f man page

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.

Date:

December 2016

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 142 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 14 2017 Version 3.8.0 LAPACK