zqrt02.f - Man Page

TESTING/LIN/zqrt02.f

Synopsis

Functions/Subroutines

subroutine zqrt02 (m, n, k, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZQRT02

Function/Subroutine Documentation

subroutine zqrt02 (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)

ZQRT02

Purpose:

``` ZQRT02 tests ZUNGQR, 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, ZQRT02 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 COMPLEX*16 array, dimension (LDA,N)
The m-by-n matrix A which was factorized by ZQRT01.```

AF

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

Q

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

R

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

LDA

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

TAU

```          TAU is COMPLEX*16 array, dimension (N)
The scalar factors of the elementary reflectors corresponding
to the QR 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 - 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 zqrt02.f.

Author

Generated automatically by Doxygen for LAPACK from the source code.

Referenced By

The man page zqrt02(3) is an alias of zqrt02.f(3).

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