# 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

Univ. of Colorado Denver

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