# sgeql2.f - Man Page

SRC/sgeql2.f

## Synopsis

### Functions/Subroutines

subroutine sgeql2 (m, n, a, lda, tau, work, info)
SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine sgeql2 (integer m, integer n, real, dimension( lda, * ) a, integer lda, real, dimension( * ) tau, real, dimension( * ) work, integer info)

SGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` SGEQL2 computes a QL factorization of a real m by n matrix A:
A = Q * L.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.```

A

```          A is 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
superdiagonal 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

```          LDA is INTEGER
The leading dimension of the array A.  LDA >= max(1,M).```

TAU

```          TAU is REAL array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).```

WORK

`          WORK is REAL array, dimension (N)`

INFO

```          INFO is INTEGER
= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

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**T

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).```

Definition at line 122 of file sgeql2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page sgeql2(3) is an alias of sgeql2.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK