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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents b2e9c4b0c4f8
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2003-2012 Gabriele Pannocchia
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} isdefinite (@var{x})
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21 ## @deftypefnx {Function File} {} isdefinite (@var{x}, @var{tol})
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22 ## Return 1 if @var{x} is symmetric positive definite within the
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23 ## tolerance specified by @var{tol} or 0 if @var{x} is symmetric
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24 ## positive semidefinite. Otherwise, return -1. If @var{tol}
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25 ## is omitted, use a tolerance of
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26 ## @code{100 * eps * norm (@var{x}, "fro")}
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27 ## @seealso{issymmetric, ishermitian}
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28 ## @end deftypefn
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29
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30 ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
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31 ## Created: November 2003
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32 ## Adapted-By: jwe
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33
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34 function retval = isdefinite (x, tol)
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35
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36 if (nargin < 1 || nargin > 2)
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37 print_usage ();
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38 endif
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39
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40 if (! isfloat (x))
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41 x = double (x);
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42 endif
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43
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44 if (nargin == 1)
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45 tol = 100 * eps (class (x)) * norm (x, "fro");
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46 endif
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47
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48 if (! ishermitian (x, tol))
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49 error ("isdefinite: X must be a Hermitian matrix");
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50 endif
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51
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52 e = tol * eye (rows (x));
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53 [r, p] = chol (x - e);
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54 if (p == 0)
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55 retval = 1;
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56 else
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57 [r, p] = chol (x + e);
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58 if (p == 0)
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59 retval = 0;
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60 else
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61 retval = -1;
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62 endif
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63 endif
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64
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65 endfunction
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66
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68 %!test
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69 %! A = [-1 0; 0 -1];
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70 %! assert (isdefinite (A), -1)
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72 %!test
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73 %! A = [1 0; 0 1];
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74 %! assert (isdefinite (A), 1)
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75
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76 %!test
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77 %! A = [2 -1 0; -1 2 -1; 0 -1 2];
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78 %! assert (isdefinite (A), 1)
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79
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80 %!test
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81 %! A = [1 0; 0 0];
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82 %! assert (isdefinite (A), 0)
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83
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84 %!error isdefinite ()
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85 %!error isdefinite (1,2,3)
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86 %!error <X must be a Hermitian matrix> isdefinite ([1 2; 3 4])
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87