DTZRQF - routine is deprecated and has been replaced by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This routine is deprecated and has been replaced by rou
tine 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.
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 ille
gal value
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 )', 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 ele
ments 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 ).
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