# dtzrqf.f man page

dtzrqf.f —

## Synopsis

### Functions/Subroutines

subroutine dtzrqf (M, N, A, LDA, TAU, INFO)
DTZRQF

## Function/Subroutine Documentation

### subroutine dtzrqf (integerM, integerN, double precision, dimension( lda, * )A, integerLDA, double precision, dimension( * )TAU, integerINFO)

DTZRQF

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``````This routine is deprecated and has been replaced by routine DTZRZF.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
triangular matrix.``````

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 >= M.``````

A

``````A is 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

``````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.``````

INFO

``````INFO is INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal value``````

Author:

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Date:

November 2011

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 ( 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 ).``````

Definition at line 139 of file dtzrqf.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

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

LAPACK Version 3.4.2 Sat Nov 16 2013