# cgelq2.f - Man Page

SRC/cgelq2.f

## Synopsis

### Functions/Subroutines

subroutine cgelq2 (m, n, a, lda, tau, work, info)
CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

## Function/Subroutine Documentation

### subroutine cgelq2 (integer m, integer n, complex, dimension( lda, * ) a, integer lda, complex, dimension( * ) tau, complex, dimension( * ) work, integer info)

CGELQ2 computes the LQ factorization of a general rectangular matrix using an unblocked algorithm.

Purpose:

``` CGELQ2 computes an LQ factorization of a complex m-by-n matrix A:

A = ( L 0 ) *  Q

where:

Q is a n-by-n orthogonal matrix;
L is a lower-triangular m-by-m matrix;
0 is a m-by-(n-m) zero matrix, if m < n.```
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, 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 array, dimension (min(M,N))
The scalar factors of the elementary reflectors (see Further
Details).```

WORK

`          WORK is COMPLEX 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

NAG Ltd.

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 128 of file cgelq2.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgelq2(3) is an alias of cgelq2.f(3).

Tue Nov 28 2023 12:08:41 Version 3.12.0 LAPACK