zlatrz.f man page

zlatrz.f —

Synopsis

Functions/Subroutines

subroutine zlatrz (M, N, L, A, LDA, TAU, WORK)
ZLATRZ factors an upper trapezoidal matrix by means of unitary transformations.

Function/Subroutine Documentation

subroutine zlatrz (integerM, integerN, integerL, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK)

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

Purpose:

ZLATRZ 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*16 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*16 array, dimension (M)
The scalar factors of the elementary reflectors.

WORK

WORK is COMPLEX*16 array, dimension (M)

Author:

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Date:

September 2012

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 141 of file zlatrz.f.

Author

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Referenced By

zlatrz(3) is an alias of zlatrz.f(3).

Sat Nov 16 2013 Version 3.4.2 LAPACK