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# sgeql2

```
NAME
SGEQL2 - compute a QL factorization of a real m by n matrix
A

SYNOPSIS
SUBROUTINE SGEQL2( M, N, A, LDA, TAU, WORK, INFO )

INTEGER        INFO, LDA, M, N

REAL           A( LDA, * ), TAU( * ), WORK( * )

PURPOSE
SGEQL2 computes a QL factorization of a real 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) REAL 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 orthogonal 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) REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see
Further Details).

WORK    (workspace) REAL 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 real scalar, and v is a real 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).
```