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annotate scripts/linear-algebra/null.m @ 3456:434790acb067

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[project @ 2000-01-19 06:58:51 by jwe]
author jwe
date Wed, 19 Jan 2000 06:59:23 +0000
parents f8dde1807dee
children c14ec945fabb
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1 ## Copyright (C) 1996, 1997 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 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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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} null (@var{a}, @var{tol})
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22 ## Return an orthonormal basis of the null space of @var{a}.
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23 ##
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24 ## The dimension of the null space is taken as the number of singular
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25 ## values of @var{a} not greater than @var{tol}. If the argument @var{tol}
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26 ## is 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 ## @end deftypefn
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32
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33 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at>
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34 ## Created: 24 December 1993.
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35 ## Adapted-By: jwe
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36
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37 function retval = null (A, tol)
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39 [U, S, V] = svd (A);
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41 [rows, cols] = size (A);
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42
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43 [S_nr, S_nc] = size (S);
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44
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45 if (S_nr == 1 || S_nc == 1)
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46 s = S(1);
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47 else
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48 s = diag (S);
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49 endif
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51 if (nargin == 1)
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52 tol = max (size (A)) * s (1) * eps;
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53 elseif (nargin != 2)
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54 usage ("null (A, tol)");
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55 endif
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56
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57 rank = sum (s > tol);
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58
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59 if (rank < cols)
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60 retval = V (:, rank+1:cols);
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61 else
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62 retval = zeros (cols, 0);
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63 endif
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64
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65 endfunction