# cgelqt3.f man page

cgelqt3.f

## Synopsis

### Functions/Subroutines

recursive subroutine cgelqt3 (M, N, A, LDA, T, LDT, INFO)

## Function/Subroutine Documentation

### recursive subroutine cgelqt3 (integer M, integer N, complex, dimension( lda, * ) A, integer LDA, complex, dimension( ldt, * ) T, integer LDT, integer INFO)

Purpose:

CGELQT3 recursively computes a LQ factorization of a complex M-by-N matrix A, using the compact WY representation of Q.

Based on the algorithm of Elmroth and Gustavson, IBM J. Res. Develop. Vol 44 No. 4 July 2000.

Parameters:

M

```          M is INTEGER
The number of rows of the matrix A.  M =< N.```

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 real M-by-N matrix A.  On exit, the elements on and
below the diagonal contain the N-by-N lower triangular matrix L; the
elements above the diagonal are the rows of V.  See below for
further details.```

LDA

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

T

```          T is COMPLEX array, dimension (LDT,N)
The N-by-N upper triangular factor of the block reflector.
The elements on and above the diagonal contain the block
reflector T; the elements below the diagonal are not used.
See below for further details.```

LDT

```          LDT is INTEGER
The leading dimension of the array T.  LDT >= max(1,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:

November 2017

Further Details:

The matrix V stores the elementary reflectors H(i) in the i-th row above the diagonal. For example, if M=5 and N=3, the matrix V is

V = ( 1 v1 v1 v1 v1 ) ( 1 v2 v2 v2 ) ( 1 v3 v3 v3 )

where the vi's represent the vectors which define H(i), which are returned in the matrix A. The 1's along the diagonal of V are not stored in A. The block reflector H is then given by

H = I - V * T * V**T

where V**T is the transpose of V.

For details of the algorithm, see Elmroth and Gustavson (cited above).

Definition at line 116 of file cgelqt3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page cgelqt3(3) is an alias of cgelqt3.f(3).

Tue Nov 14 2017 Version 3.8.0 LAPACK