dtzrqf.f(3) LAPACK dtzrqf.f(3)
NAME
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This routine is deprecated and has been replaced by routine DTZRZF.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
Univ. of Colorado Denver
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
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Version 3.4.2 Tue Sep 25 2012 dtzrqf.f(3)
