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1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2003, 2004, |
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2 ## 2005, 2006, 2007, 2008 John W. Eaton |
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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} {} cond (@var{a},@var{p}) |
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22 ## Compute the @var{p}-norm condition number of a matrix. @code{cond (@var{a})} is |
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23 ## defined as @code{norm (@var{a}, @var{p}) * norm (inv (@var{a}), @var{p})}. |
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24 ## By default @code{@var{p}=2} is used which implies a (relatively slow) |
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25 ## singular value decomposition. Other possible selections are |
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26 ## @code{@var{p}= 1, Inf, inf, 'Inf', 'fro'} which are generally faster. |
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27 ## @seealso{norm, inv, det, svd, rank} |
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28 ## @end deftypefn |
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29 |
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30 ## Author: jwe |
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31 |
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32 function retval = cond (a, p) |
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33 |
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34 if (nargin && nargin < 3) |
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35 if (ndims (a) > 2) |
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36 error ("cond: only valid on 2-D objects") |
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37 endif |
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38 |
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39 if (nargin <2) |
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40 p = 2; |
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41 endif |
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42 |
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43 if (! isstr (p) && p == 2) |
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44 [nr, nc] = size (a); |
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45 if (nr == 0 || nc == 0) |
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46 retval = 0.0; |
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47 elseif (any (any (isinf (a) | isnan (a)))) |
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48 error ("cond: argument must not contain Inf or NaN values"); |
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49 else |
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50 sigma = svd (a); |
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51 sigma_1 = sigma(1); |
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52 sigma_n = sigma(end); |
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53 if (sigma_1 == 0 || sigma_n == 0) |
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54 retval = Inf; |
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55 else |
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56 retval = sigma_1 / sigma_n; |
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57 endif |
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58 endif |
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59 else |
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60 retval = norm (a, p) * norm (inv (a), p); |
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61 endif |
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62 else |
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63 print_usage (); |
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64 endif |
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65 |
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66 endfunction |
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67 |
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68 %!test |
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69 %! y= [7, 2, 3; 1, 3, 4; 6, 4, 5]; |
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70 %! tol = 1e-6; |
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71 %! type = {1, 2, 'fro', 'inf', inf}; |
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72 %! for n = 1:numel(type) |
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73 %! rcondition(n) = 1 / cond (y, type{n}); |
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74 %! endfor |
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75 %! assert (rcondition, [0.017460, 0.019597, 0.018714, 0.012022, 0.012022], tol); |
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76 |
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77 %!assert (abs (cond ([1, 2; 2, 1]) - 3) < sqrt (eps)); |
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78 |
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79 %!assert (cond ([1, 2, 3; 4, 5, 6; 7, 8, 9]) > 1.0e+16); |
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80 |
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81 %!error cond (); |
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82 |
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83 %!error cond (1, 2, 3); |
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84 |