# clatrz (l) - Linux Manuals

## 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

## NAME

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## SYNOPSIS

- SUBROUTINE CLATRZ(
- M, N, L, A, LDA, TAU, WORK )

- INTEGER L, LDA, M, N

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

## 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.## 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 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 array, dimension (M)
- The scalar factors of the elementary reflectors.
- WORK (workspace) COMPLEX array, dimension (M)

## FURTHER DETAILS

Based on contributions byZ(

where

T(

Z is given by

Z