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# zgeqlf

```
NAME
ZGEQLF - compute a QL factorization of a complex M-by-N
matrix A

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

INTEGER        INFO, LDA, LWORK, M, N

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

PURPOSE
ZGEQLF computes a QL factorization of a complex M-by-N
matrix A: A = Q * L.

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, if m >= n,
the lower triangle of the subarray A(m-n+1:m,1:n)
contains the N-by-N lower triangular matrix L; if m
<= n, the elements on and below the (n-m)-th super-
diagonal contain the M-by-N lower trapezoidal matrix
L; the remaining elements, with the array TAU,
represent the unitary matrix Q as a product of ele-
mentary reflectors (see Further Details).  LDA
(input) INTEGER The leading 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,N).
For optimum performance LWORK >= N*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(m-k+i+1:m) = 0 and v(m-k+i) = 1; v(1:m-k+i-1) is
stored on exit in A(1:m-k+i-1,n-k+i), and tau in TAU(i).
```