# cgeql2.f

Section: LAPACK (3)
Updated: Tue Nov 14 2017
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cgeql2.f

## SYNOPSIS

### Functions/Subroutines

subroutine cgeql2 (M, N, A, LDA, TAU, WORK, INFO)
CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgeql2 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( * ) TAU, complex, dimension( * ) WORK, integer INFO)

CGEQL2 computes the QL factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` CGEQL2 computes a QL factorization of a complex 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 COMPLEX 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

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

TAU

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

WORK

```          WORK is COMPLEX 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.

Date:

December 2016

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**H

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).
```

Definition at line 125 of file cgeql2.f.

## Author

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