
CTZRQF(l) ) CTZRQF(l)
NAME
CTZRQF  routine is deprecated and has been replaced by routine CTZRZF
SYNOPSIS
SUBROUTINE CTZRQF( M, N, A, LDA, TAU, INFO )
INTEGER INFO, LDA, M, N
COMPLEX A( LDA, * ), TAU( * )
PURPOSE
This routine is deprecated and has been replaced by routine CTZRZF. CTZRQF reduces the M
byN ( M<=N ) complex upper trapezoidal matrix A to upper triangular form by means of uni
tary transformations.
The upper trapezoidal matrix A is factored as
A = ( R 0 ) * Z,
where Z is an NbyN unitary matrix and R is an MbyM 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) COMPLEX array, dimension (LDA,N)
On entry, the leading MbyN upper trapezoidal part of the array A must contain
the matrix to be factorized. On exit, the leading MbyM 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 unitary 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) COMPLEX array, dimension (M)
The scalar factors of the elementary reflectors.
INFO (output) INTEGER
= 0: successful exit
< 0: if INFO = i, the ith argument had an illegal value
FURTHER DETAILS
The factorization is obtained by Householder's method. The kth transformation matrix, Z(
k ), whose conjugate transpose 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 CTZRQF(l) 
