# zgelqt3.f - Man Page

SRC/zgelqt3.f

## Synopsis

### Functions/Subroutines

recursive subroutine zgelqt3 (m, n, a, lda, t, ldt, info)
ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

## Function/Subroutine Documentation

### recursive subroutine zgelqt3 (integer m, integer n, complex*16, dimension( lda, * ) a, integer lda, complex*16, dimension( ldt, * ) t, integer ldt, integer info)

ZGELQT3 recursively computes a LQ factorization of a general real or complex matrix using the compact WY representation of Q.

Purpose:

``` ZGELQT3 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*16 array, dimension (LDA,N)
On entry, the complex 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*16 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.

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 130 of file zgelqt3.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zgelqt3(3) is an alias of zgelqt3.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK