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# LAPACK-3

## man page of LAPACK-3

### LAPACK-3: computes a QL factorization of a complex m by n matrix A

```NAME
LAPACK-3 - computes a QL factorization of a complex m by n matrix A

SYNOPSIS
SUBROUTINE ZGEQL2( M, N, A, LDA, TAU, WORK, INFO )

INTEGER        INFO, LDA, M, N

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

PURPOSE
ZGEQL2 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
superdiagonal 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 elementary 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 (N)

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).

LAPACK routine (version 3.2.2)   March 2011                       LAPACK-3(3)
```