# zrqt02.f - Man Page

TESTING/LIN/zrqt02.f

## Synopsis

### Functions/Subroutines

subroutine zrqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZRQT02

## Function/Subroutine Documentation

### subroutine zrqt02 (integer m, integer n, integer k, complex*16, dimension( lda, * ) a, complex*16, dimension( lda, * ) af, complex*16, dimension( lda, * ) q, complex*16, dimension( lda, * ) r, integer lda, complex*16, dimension( * ) tau, complex*16, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

ZRQT02

Purpose:

``` ZRQT02 tests ZUNGRQ, which generates an m-by-n matrix Q with
orthonormal rows that is defined as the product of k elementary
reflectors.

Given the RQ factorization of an m-by-n matrix A, ZRQT02 generates
the orthogonal matrix Q defined by the factorization of the last k
rows of A; it compares R(m-k+1:m,n-m+1:n) with
A(m-k+1:m,1:n)*Q(n-m+1:n,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*16 array, dimension (LDA,N)
The m-by-n matrix A which was factorized by ZRQT01.```

AF

```          AF is COMPLEX*16 array, dimension (LDA,N)
Details of the RQ factorization of A, as returned by ZGERQF.
See ZGERQF for further details.```

Q

`          Q is COMPLEX*16 array, dimension (LDA,N)`

R

`          R is COMPLEX*16 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*16 array, dimension (M)
The scalar factors of the elementary reflectors corresponding
to the RQ factorization in AF.```

WORK

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

LWORK

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

RWORK

`          RWORK is DOUBLE PRECISION array, dimension (M)`

RESULT

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

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 134 of file zrqt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zrqt02(3) is an alias of zrqt02.f(3).

Tue Nov 28 2023 12:08:43 Version 3.12.0 LAPACK