DTZRQF(3f)

NAME
DTZRQF - i deprecated and has been replaced by routine DTZRZF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This routine is deprecated and has been replaced by routine DTZRZF.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 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 illegal value

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 )', 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 ).