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move issymmetric & isdefinite to linear-algebra, create ishermitian
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 24 Nov 2009 15:02:04 +0100
parents
children 73fc43e01f4c
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9869
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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1 ## Copyright (C) 1996, 1997, 2002, 2003, 2004, 2005, 2006, 2007, 2008
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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2 ## John W. Eaton
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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3 ## Copyright (C) 2009 VZLU Prague
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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4 ##
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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5 ## This file is part of Octave.
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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6 ##
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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7 ## Octave is free software; you can redistribute it and/or modify it
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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8 ## under the terms of the GNU General Public License as published by
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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9 ## the Free Software Foundation; either version 3 of the License, or (at
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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10 ## your option) any later version.
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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11 ##
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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12 ## Octave is distributed in the hope that it will be useful, but
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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15 ## General Public License for more details.
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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16 ##
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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17 ## You should have received a copy of the GNU General Public License
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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18 ## along with Octave; see the file COPYING. If not, see
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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19 ## <http://www.gnu.org/licenses/>.
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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20
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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21 ## -*- texinfo -*-
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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22 ## @deftypefn {Function File} {} ishermitian (@var{x}, @var{tol})
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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23 ## Return true if @var{x} is symmetric within the tolerance specified by @var{tol},
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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24 ## otherwise return false. The default tolerance is zero (uses faster code).
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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25 ## Matrix @var{x} is considered symmetric if
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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26 ## @code{norm (@var{x} - @var{x}.', inf) / norm (@var{x}, inf) < @var{tol}}.
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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27 ## @seealso{size, rows, columns, length, ismatrix, isscalar,
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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28 ## issquare, isvector}
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29 ## @end deftypefn
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30
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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31 ## Author: A. S. Hodel <scotte@eng.auburn.edu>
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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32 ## Created: August 1993
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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33 ## Adapted-By: jwe
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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34
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35 function retval = ishermitian (x, tol = 0)
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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36
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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37 if (nargin < 1 || nargin > 2)
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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38 print_usage ();
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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39 endif
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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40
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41 retval = issquare (x);
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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42 if (retval)
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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43 if (tol == 0)
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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44 retval = all ((x == x')(:));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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45 else
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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46 norm_x = norm (x, inf);
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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47 retval = norm_x == 0 || norm (x - x', inf) / norm_x <= tol;
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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48 endif
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49 endif
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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50
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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51 endfunction
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52
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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53 %!assert(ishermitian (1));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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54 %!assert(!(ishermitian ([1, 2])));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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55 %!assert(ishermitian ([]));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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56 %!assert(ishermitian ([1, 2; 2, 1]));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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57 %!assert(!(ishermitian ("test")));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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58 %!assert(ishermitian ([1, 2.1; 2, 1.1], 0.2));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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59 %!assert(ishermitian ([1, -2i; 2i, 1]));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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60 %!assert(!(ishermitian ("t")));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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61 %!assert(!(ishermitian (["te"; "et"])));
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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62 %!error ishermitian ([1, 2; 2, 1], 0, 0);
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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63 %!error ishermitian ();
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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64
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
Jaroslav Hajek <highegg@gmail.com>
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65 %!test
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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66 %! s.a = 1;
ecd750d1eabd move issymmetric & isdefinite to linear-algebra, create ishermitian
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67 %! assert(!(ishermitian (s)));