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doc: Match docstring variable names to function variable names for linear-algebra m-files. * isbanded.m, isdefinite.m, isdiag.m, ishermitian.m, issymmetric.m, istril.m, istriu.m: Use 'A' for input matrix in linear algebra routines. Change docstrings from 'x' to 'A'.
author Rik <rik@octave.org>
date Mon, 14 Jul 2014 08:54:45 -0700
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John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1996-2013 John W. Eaton
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2 ## Copyright (C) 2009 VZLU Prague
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} ishermitian (@var{A})
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22 ## @deftypefnx {Function File} {} ishermitian (@var{A}, @var{tol})
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23 ## Return true if @var{A} is Hermitian within the tolerance specified by
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24 ## @var{tol}.
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25 ##
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26 ## The default tolerance is zero (uses faster code).
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27 ## Matrix @var{A} is considered symmetric if
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28 ## @code{norm (@var{A} - @var{A}', Inf) / norm (@var{A}, Inf) < @var{tol}}.
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29 ## @seealso{issymmetric, isdefinite}
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30 ## @end deftypefn
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31
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32 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
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33 ## Created: August 1993
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34 ## Adapted-By: jwe
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35
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36 function retval = ishermitian (A, tol = 0)
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37
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38 if (nargin < 1 || nargin > 2)
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39 print_usage ();
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40 endif
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41
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42 retval = isnumeric (A) && issquare (A);
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43 if (retval)
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44 if (tol == 0)
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45 retval = all ((A == A')(:));
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46 else
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47 norm_x = norm (A, inf);
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48 retval = norm_x == 0 || norm (A - A', inf) / norm_x <= tol;
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49 endif
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50 endif
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51
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52 endfunction
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53
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54
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55 %!assert (ishermitian (1))
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56 %!assert (! ishermitian ([1, 2]))
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57 %!assert (ishermitian ([]))
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58 %!assert (ishermitian ([1, 2; 2, 1]))
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59 %!assert (! ishermitian ("test"))
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60 %!assert (ishermitian ([1, 2.1; 2, 1.1], 0.2))
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61 %!assert (ishermitian ([1, -2i; 2i, 1]))
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62 %!assert (! ishermitian ("t"))
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63 %!assert (! ishermitian (["te"; "et"]))
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64
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65 %!test
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66 %! s.a = 1;
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67 %! assert (! ishermitian (s));
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68
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69 %!error ishermitian ([1, 2; 2, 1], 0, 0)
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70 %!error ishermitian ()
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71