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# zgelqf

```
NAME
ZGELQF - compute an LQ factorization of a complex M-by-N
matrix A

SYNOPSIS
SUBROUTINE ZGELQF( M, N, A, LDA, TAU, WORK, LWORK, INFO )

INTEGER        INFO, LDA, LWORK, M, N

COMPLEX*16     A( LDA, * ), TAU( * ), WORK( LWORK )

PURPOSE
ZGELQF computes an LQ factorization of a complex M-by-N
matrix A: A = L * Q.

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 >= 0.

A       (input/output) COMPLEX*16 array, dimension (LDA,N)
On entry, the M-by-N matrix A.  On exit, the ele-
ments on and below the diagonal of the array contain
the m-by-min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the
diagonal, with the array TAU, represent the unitary
matrix Q as a product of elementary reflectors (see
Further Details).  LDA     (input) INTEGER The lead-
ing dimension of the array A.  LDA >= max(1,M).

TAU     (output) COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see
Further Details).

WORK    (workspace) COMPLEX*16 array, dimension (LWORK)
On exit, if INFO = 0, WORK(1) returns the optimal
LWORK.

LWORK   (input) INTEGER
The dimension of the array WORK.  LWORK >= max(1,M).
For optimum performance LWORK >= M*NB, where NB is
the optimal blocksize.

INFO    (output) INTEGER
= 0:  successful exit
< 0:  if INFO = -i, the i-th argument had an illegal
value

FURTHER DETAILS
The matrix Q is represented as a product of elementary
reflectors

Q = H(k)' . . . H(2)' H(1)', where k = min(m,n).

Each H(i) has the form

H(i) = I - tau * v * v'

where tau is a complex scalar, and v is a complex vector
with v(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on
exit in A(i,i+1:n), and tau in TAU(i).
```