# zqrt01.f - Man Page

TESTING/LIN/zqrt01.f

## Synopsis

### Functions/Subroutines

subroutine zqrt01 (m, n, a, af, q, r, lda, tau, work, lwork, rwork, result)
ZQRT01

## Function/Subroutine Documentation

### subroutine zqrt01 (integer m, integer n, 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)

ZQRT01

Purpose:

``` ZQRT01 tests ZGEQRF, which computes the QR factorization of an m-by-n
matrix A, and partially tests ZUNGQR which forms the m-by-m
orthogonal matrix Q.

ZQRT01 compares R with Q'*A, and checks that Q is orthogonal.```
Parameters

M

```          M is INTEGER
The number of rows of the matrix A.  M >= 0.```

N

```          N is INTEGER
The number of columns of the matrix A.  N >= 0.```

A

```          A is COMPLEX*16 array, dimension (LDA,N)
The m-by-n matrix A.```

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,M)
The m-by-m orthogonal matrix Q.```

R

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

LDA

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

TAU

```          TAU is COMPLEX*16 array, dimension (min(M,N))
The scalar factors of the elementary reflectors, as returned
by ZGEQRF.```

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 124 of file zqrt01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page zqrt01(3) is an alias of zqrt01.f(3).

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