
dlatrz.f(3) LAPACK dlatrz.f(3)
NAME
dlatrz.f 
SYNOPSIS
Functions/Subroutines
subroutine dlatrz (M, N, L, A, LDA, TAU, WORK)
DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
Function/Subroutine Documentation
subroutine dlatrz (integerM, integerN, integerL, double precision, dimension( lda, * )A,
integerLDA, double precision, dimension( * )TAU, double precision, dimension( * )WORK)
DLATRZ factors an upper trapezoidal matrix by means of orthogonal transformations.
Purpose:
DLATRZ factors the Mby(M+L) real upper trapezoidal matrix
[ A1 A2 ] = [ A(1:M,1:M) A(1:M,NL+1:N) ] as ( R 0 ) * Z, by means
of orthogonal transformations. Z is an (M+L)by(M+L) orthogonal
matrix and, R and A1 are MbyM 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. NM >= L >= 0.
A
A is DOUBLE PRECISION array, dimension (LDA,N)
On entry, the leading MbyN upper trapezoidal part of the
array A must contain the matrix to be factorized.
On exit, the leading MbyM upper triangular part of A
contains the upper triangular matrix R, and elements NL+1 to
N of the first M rows of A, with the array TAU, represent the
orthogonal 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 DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors.
WORK
WORK is DOUBLE PRECISION 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 )**T, 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 dlatrz.f.
Author
Generated automatically by Doxygen for LAPACK from the source code.
Version 3.4.2 Tue Sep 25 2012 dlatrz.f(3) 
