# zgelq2.f man page

zgelq2.f —

## Synopsis

### Functions/Subroutines

subroutinezgelq2(M, N, A, LDA, TAU, WORK, INFO)ZGELQ2computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine zgelq2 (integerM, integerN, complex*16, dimension( lda, * )A, integerLDA, complex*16, dimension( * )TAU, complex*16, dimension( * )WORK, integerINFO)

**ZGELQ2** computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

**Purpose:**

```
ZGELQ2 computes an LQ factorization of a complex m by n matrix A:
A = L * Q.
```

**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*16 array, dimension (LDA,N)
On entry, the m by n matrix A.
On exit, the elements on and below the diagonal of the array
contain the m by min(m,n) lower trapezoidal matrix L (L is
lower triangular if m <= n); the elements above the diagonal,
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*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).
```

*WORK*

`WORK is COMPLEX*16 array, dimension (M)`

*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 . . . H(2)**H H(1)**H, 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(1:i-1) = 0 and v(i) = 1; conjg(v(i+1:n)) is stored on exit in
A(i,i+1:n), and tau in TAU(i).
```

Definition at line 122 of file zgelq2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

zgelq2(3) is an alias of zgelq2.f(3).