1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
|
## Copyright (C) 1996-2013 John W. Eaton
## Copyright (C) 2009 VZLU Prague
##
## This file is part of Octave.
##
## Octave is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or (at
## your option) any later version.
##
## Octave is distributed in the hope that it will be useful, but
## WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
## General Public License for more details.
##
## You should have received a copy of the GNU General Public License
## along with Octave; see the file COPYING. If not, see
## <http://www.gnu.org/licenses/>.
## -*- texinfo -*-
## @deftypefn {Function File} {} ishermitian (@var{x})
## @deftypefnx {Function File} {} ishermitian (@var{x}, @var{tol})
## Return true if @var{x} is Hermitian within the tolerance specified by
## @var{tol}.
## The default tolerance is zero (uses faster code).
## Matrix @var{x} is considered symmetric if
## @code{norm (@var{x} - @var{x}', Inf) / norm (@var{x}, Inf) < @var{tol}}.
## @seealso{issymmetric, isdefinite}
## @end deftypefn
## Author: A. S. Hodel <scotte@eng.auburn.edu>
## Created: August 1993
## Adapted-By: jwe
function retval = ishermitian (x, tol = 0)
if (nargin < 1 || nargin > 2)
print_usage ();
endif
retval = isnumeric (x) && issquare (x);
if (retval)
if (tol == 0)
retval = all ((x == x')(:));
else
norm_x = norm (x, inf);
retval = norm_x == 0 || norm (x - x', inf) / norm_x <= tol;
endif
endif
endfunction
%!assert (ishermitian (1))
%!assert (! ishermitian ([1, 2]))
%!assert (ishermitian ([]))
%!assert (ishermitian ([1, 2; 2, 1]))
%!assert (! ishermitian ("test"))
%!assert (ishermitian ([1, 2.1; 2, 1.1], 0.2))
%!assert (ishermitian ([1, -2i; 2i, 1]))
%!assert (! ishermitian ("t"))
%!assert (! ishermitian (["te"; "et"]))
%!test
%! s.a = 1;
%! assert (! ishermitian (s));
%!error ishermitian ([1, 2; 2, 1], 0, 0)
%!error ishermitian ()
|
