# dort01.f - Man Page

TESTING/EIG/dort01.f

## Synopsis

### Functions/Subroutines

subroutine dort01 (rowcol, m, n, u, ldu, work, lwork, resid)
DORT01

## Function/Subroutine Documentation

### subroutine dort01 (character rowcol, integer m, integer n, double precision, dimension( ldu, * ) u, integer ldu, double precision, dimension( * ) work, integer lwork, double precision resid)

DORT01

Purpose:

``` DORT01 checks that the matrix U is orthogonal by computing the ratio

RESID = norm( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = norm( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

Alternatively, if there isn't sufficient workspace to form
I - U*U' or I - U'*U, the ratio is computed as

RESID = abs( I - U*U' ) / ( n * EPS ), if ROWCOL = 'R',
or
RESID = abs( I - U'*U ) / ( m * EPS ), if ROWCOL = 'C'.

where EPS is the machine precision.  ROWCOL is used only if m = n;
if m > n, ROWCOL is assumed to be 'C', and if m < n, ROWCOL is
assumed to be 'R'.```
Parameters

ROWCOL

```          ROWCOL is CHARACTER
Specifies whether the rows or columns of U should be checked
for orthogonality.  Used only if M = N.
= 'R':  Check for orthogonal rows of U
= 'C':  Check for orthogonal columns of U```

M

```          M is INTEGER
The number of rows of the matrix U.```

N

```          N is INTEGER
The number of columns of the matrix U.```

U

```          U is DOUBLE PRECISION array, dimension (LDU,N)
The orthogonal matrix U.  U is checked for orthogonal columns
if m > n or if m = n and ROWCOL = 'C'.  U is checked for
orthogonal rows if m < n or if m = n and ROWCOL = 'R'.```

LDU

```          LDU is INTEGER
The leading dimension of the array U.  LDU >= max(1,M).```

WORK

`          WORK is DOUBLE PRECISION array, dimension (LWORK)`

LWORK

```          LWORK is INTEGER
The length of the array WORK.  For best performance, LWORK
should be at least N*(N+1) if ROWCOL = 'C' or M*(M+1) if
ROWCOL = 'R', but the test will be done even if LWORK is 0.```

RESID

```          RESID is DOUBLE PRECISION
RESID = norm( I - U * U' ) / ( n * EPS ), if ROWCOL = 'R', or
RESID = norm( I - U' * U ) / ( m * EPS ), if ROWCOL = 'C'.```
Author

Univ. of Tennessee

Univ. of California Berkeley

NAG Ltd.

Definition at line 115 of file dort01.f.

## Author

Generated automatically by Doxygen for LAPACK from the source code.

## Referenced By

The man page dort01(3) is an alias of dort01.f(3).

Tue Nov 28 2023 12:08:42 Version 3.12.0 LAPACK