DTZRQF(l) ) DTZRQF(l)NAME
DTZRQF - routine is deprecated and has been replaced by routine DTZRZF
SYNOPSIS
SUBROUTINE DTZRQF( M, N, A, LDA, TAU, INFO )
INTEGER INFO, LDA, M, N
DOUBLE PRECISION A( LDA, * ), TAU( * )
PURPOSE
This routine is deprecated and has been replaced by routine DTZRZF.
DTZRQF reduces the M-by-N ( M<=N ) real upper trapezoidal matrix A to
upper triangular form by means of orthogonal transformations.
The upper trapezoidal matrix A is factored as
A = ( R 0 ) * Z,
where Z is an N-by-N orthogonal matrix and R is an M-by-M upper trian‐
gular matrix.
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 >= M.
A (input/output) DOUBLE PRECISION 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 M+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 (input) INTEGER
The leading dimension of the array A. LDA >= max(1,M).
TAU (output) DOUBLE PRECISION array, dimension (M)
The scalar factors of the elementary reflectors.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value
FURTHER DETAILS
The factorization is obtained by Householder's method. The kth trans‐
formation 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 )', u( k ) = ( 1 ),
( 0 )
( z( k ) )
tau is a scalar and z( k ) is an ( n - m ) element vector. tau and z(
k ) are chosen to annihilate the elements of the kth row of X.
The scalar tau is returned in the kth element of TAU and the vector u(
k ) in the kth row of A, such that the elements of z( k ) are in a( k,
m + 1 ), ..., a( k, n ). The elements of R are returned in the upper
triangular part of A.
Z is given by
Z = Z( 1 ) * Z( 2 ) * ... * Z( m ).
LAPACK version 3.0 15 June 2000 DTZRQF(l)
