Provided by: liblapack-doc_3.3.1-1_all #### NAME

```       LAPACK-3 - routine i deprecated and has been replaced by routine CTZRZF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```       This routine is deprecated and has been replaced by routine CTZRZF.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-by-N ( M<=N ) complex upper trapezoidal matrix A
to upper triangular form by means of unitary transformations.
The upper trapezoidal matrix A is factored as
A = ( R  0 ) * Z,
where Z is an N-by-N unitary 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) COMPLEX 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
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 i-th argument had an illegal value

```

#### FURTHERDETAILS

```        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 )**H,   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 routine (version 3.3.1)             April 2011                            CTZRQF(3lapack)
```