# sgeql2.f man page

sgeql2.f —

## Synopsis

### Functions/Subroutines

subroutinesgeql2(M, N, A, LDA, TAU, WORK, INFO)SGEQL2computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine sgeql2 (integerM, integerN, real, dimension( lda, * )A, integerLDA, real, dimension( * )TAU, real, dimension( * )WORK, integerINFO)

**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

Univ. of Colorado Denver

NAG Ltd.

**Date:**

September 2012

**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 124 of file sgeql2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

sgeql2(3) is an alias of sgeql2.f(3).