# clqt02.f - Man Page

TESTING/LIN/clqt02.f

## Synopsis

### Functions/Subroutines

subroutine clqt02 (m, n, k, a, af, q, l, lda, tau, work, lwork, rwork, result)
CLQT02

## Function/Subroutine Documentation

### subroutine clqt02 (integer m, integer n, integer k, complex, dimension( lda, * ) a, complex, dimension( lda, * ) af, complex, dimension( lda, * ) q, complex, dimension( lda, * ) l, integer lda, complex, dimension( * ) tau, complex, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

CLQT02

Purpose:

``` CLQT02 tests CUNGLQ, which generates an m-by-n matrix Q with
orthonormal rows that is defined as the product of k elementary
reflectors.

Given the LQ factorization of an m-by-n matrix A, CLQT02 generates
the orthogonal matrix Q defined by the factorization of the first k
rows of A; it compares L(1:k,1:m) with A(1:k,1:n)*Q(1:m,1:n)', and
checks that the rows of Q are orthonormal.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix Q to be generated.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix Q to be generated.
N >= M >= 0.```

K

```          K is INTEGER
The number of elementary reflectors whose product defines the
matrix Q. M >= K >= 0.```

A

```          A is COMPLEX array, dimension (LDA,N)
The m-by-n matrix A which was factorized by CLQT01.```

AF

```          AF is COMPLEX array, dimension (LDA,N)
Details of the LQ factorization of A, as returned by CGELQF.
See CGELQF for further details.```

Q

`          Q is COMPLEX array, dimension (LDA,N)`

L

`          L is COMPLEX array, dimension (LDA,M)`

LDA

```          LDA is INTEGER
The leading dimension of the arrays A, AF, Q and L. LDA >= N.```

TAU

```          TAU is COMPLEX array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the LQ factorization in AF.```

WORK

`          WORK is COMPLEX array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The dimension of the array WORK.```

RWORK

`          RWORK is REAL array, dimension (M)`

RESULT

```          RESULT is REAL array, dimension (2)
The test ratios:
RESULT(1) = norm( L - A*Q' ) / ( N * norm(A) * EPS )
RESULT(2) = norm( I - Q*Q' ) / ( N * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

Univ. of Colorado Denver

NAG Ltd.

Definition at line 133 of file clqt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page clqt02(3) is an alias of clqt02.f(3).

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