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[project @ 2004-04-07 02:41:22 by jwe]
author jwe
date Wed, 07 Apr 2004 02:41:22 +0000
parents 02d2fcf835fc
children c08cb1098afc
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1 ## Copyright (C) 2003 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 2, or (at your option)
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8 ## 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, write to the Free
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17 ## Software Foundation, 59 Temple Place - Suite 330, Boston, MA
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18 ## 02111-1307, USA.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {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 equal to 100 times the machine precision.
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26 ## @end deftypefn
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27 ## @seealso{issymmetric}
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28
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29 ## Author: Gabriele Pannocchia <g.pannocchia@ing.unipi.it>
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30 ## Created: November 2003
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31 ## Adapted-By: jwe
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32
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33 function retval = isdefinite (x, tol)
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34
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35 if (nargin == 1 || nargin == 2)
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36 if (nargin == 1)
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37 tol = 100*eps;
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38 endif
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39 sym = issymmetric (x, tol);
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40 if (sym > 0)
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41 ## Matrix is symmetric, check eigenvalues.
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42 mineig = min (eig (x));
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43 if (mineig > tol)
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44 retval = 1;
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45 elseif (mineig > -tol)
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46 retval = 0;
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47 else
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48 retval = -1;
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49 end
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50 else
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51 error ("isdefinite: matrix x must be symmetric");
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52 endif
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53 else
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54 usage ("isdefinite (x,tol)");
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55 endif
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56
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57 endfunction