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annotate scripts/linear-algebra/orth.m @ 14138:72c96de7a403 stable

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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 69a4609e61e2
children f3d52523cde1
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14138
72c96de7a403 maint: update copyright notices for 2012
John W. Eaton <jwe@octave.org>
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1 ## Copyright (C) 1994-2012 John W. Eaton
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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} {} orth (@var{A})
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21 ## @deftypefnx {Function File} {} orth (@var{A}, @var{tol})
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22 ## Return an orthonormal basis of the range space of @var{A}.
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23 ##
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24 ## The dimension of the range space is taken as the number of singular
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25 ## values of @var{A} greater than @var{tol}. If the argument @var{tol} is
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26 ## missing, it is computed as
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27 ##
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28 ## @example
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29 ## max (size (@var{A})) * max (svd (@var{A})) * eps
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30 ## @end example
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31 ## @seealso{null}
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32 ## @end deftypefn
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34 ## Author: KH <Kurt.Hornik@wu-wien.ac.at>
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35 ## Created: 24 December 1993.
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36 ## Adapted-By: jwe
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37
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38 function retval = orth (A, tol)
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39
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40 if (nargin == 1 || nargin == 2)
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41
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42 if (isempty (A))
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43 retval = [];
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44 return;
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45 endif
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46
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47 [U, S, V] = svd (A);
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48
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49 [rows, cols] = size (A);
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50
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51 [S_nr, S_nc] = size (S);
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52
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53 if (S_nr == 1 || S_nc == 1)
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54 s = S(1);
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55 else
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56 s = diag (S);
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57 endif
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59 if (nargin == 1)
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60 if (isa (A, "single"))
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61 tol = max (size (A)) * s (1) * eps ("single");
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62 else
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63 tol = max (size (A)) * s (1) * eps;
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64 endif
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65 endif
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66
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67 rank = sum (s > tol);
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69 if (rank > 0)
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70 retval = -U (:, 1:rank);
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71 else
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72 retval = zeros (rows, 0);
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73 endif
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75 else
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76
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77 print_usage ();
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78
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79 endif
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80
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81 endfunction
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83 %!test
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84 %! for ii=1:20
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85 %! A = rand (10, 10);
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86 %! V = orth (A);
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87 %! if (det (A) != 0)
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88 %! assert (V'*V, eye (10), 100*eps)
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89 %! endif
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90 %! endfor