# srqt02.f - Man Page

TESTING/LIN/srqt02.f

## Synopsis

### Functions/Subroutines

subroutine srqt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
SRQT02

## Function/Subroutine Documentation

### subroutine srqt02 (integer m, integer n, integer k, real, dimension( lda, * ) a, real, dimension( lda, * ) af, real, dimension( lda, * ) q, real, dimension( lda, * ) r, integer lda, real, dimension( * ) tau, real, dimension( lwork ) work, integer lwork, real, dimension( * ) rwork, real, dimension( * ) result)

SRQT02

Purpose:

``` SRQT02 tests SORGRQ, 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, SRQT02 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 REAL array, dimension (LDA,N)
The m-by-n matrix A which was factorized by SRQT01.```

AF

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

Q

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

R

`          R is REAL array, dimension (LDA,M)`

LDA

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

TAU

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

WORK

`          WORK is REAL 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( 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 srqt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page srqt02(3) is an alias of srqt02.f(3).

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