# dqrt02.f - Man Page

TESTING/LIN/dqrt02.f

## Synopsis

### Functions/Subroutines

subroutine dqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
DQRT02

## Function/Subroutine Documentation

### subroutine dqrt02 (integer m, integer n, integer k, double precision, dimension( lda, * ) a, double precision, dimension( lda, * ) af, double precision, dimension( lda, * ) q, double precision, dimension( lda, * ) r, integer lda, double precision, dimension( * ) tau, double precision, dimension( lwork ) work, integer lwork, double precision, dimension( * ) rwork, double precision, dimension( * ) result)

DQRT02

Purpose:

``` DQRT02 tests DORGQR, which generates an m-by-n matrix Q with
orthonormal columns that is defined as the product of k elementary
reflectors.

Given the QR factorization of an m-by-n matrix A, DQRT02 generates
the orthogonal matrix Q defined by the factorization of the first k
columns of A; it compares R(1:n,1:k) with Q(1:m,1:n)'*A(1:m,1:k),
and checks that the columns 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.
M >= N >= 0.```

K

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

A

```          A is DOUBLE PRECISION array, dimension (LDA,N)
The m-by-n matrix A which was factorized by DQRT01.```

AF

```          AF is DOUBLE PRECISION array, dimension (LDA,N)
Details of the QR factorization of A, as returned by DGEQRF.
See DGEQRF for further details.```

Q

`          Q is DOUBLE PRECISION array, dimension (LDA,N)`

R

`          R is DOUBLE PRECISION array, dimension (LDA,N)`

LDA

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

TAU

```          TAU is DOUBLE PRECISION array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QR factorization in AF.```

WORK

`          WORK is DOUBLE PRECISION 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 - Q'*A ) / ( M * norm(A) * EPS )
RESULT(2) = norm( I - Q'*Q ) / ( M * EPS )```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 133 of file dqrt02.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dqrt02(3) is an alias of dqrt02.f(3).

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