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annotate scripts/linear-algebra/subspace.m @ 17692:38cf56b77274

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Overhaul image, imagesc to use newplot and support low-level invocation form. * scripts/image/image.m: New variable do_new indicates high-level calling form. For high-level invocation, call newplot before __img__. Correct linearity check if vectors are reversed (high-to-low values). Only apply image properties to axes if doing a high-level invocation. * scripts/image/imagesc.m: New variable do_new indicates high-level calling form. Delete subfunction __imagesc__ and incorporate minimal amount of code into imagesc. Only apply climits for high-level invocation.
author Rik <rik@octave.org>
date Fri, 18 Oct 2013 16:27:44 -0700
parents 1c89599167a6
children d63878346099
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72c96de7a403 maint: update copyright notices for 2012
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1 ## Copyright (C) 2008-2012 VZLU Prague, a.s., Czech Republic
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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} {@var{angle} =} subspace (@var{A}, @var{B})
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21 ## Determine the largest principal angle between two subspaces
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22 ## spanned by the columns of matrices @var{A} and @var{B}.
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23 ## @end deftypefn
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24
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25 ## Author: Jaroslav Hajek <highegg@gmail.com>
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26
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27 ## reference:
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28 ## [1] Andrew V. Knyazev, Merico E. Argentati:
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29 ## Principal Angles between Subspaces in an A-Based Scalar Product:
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30 ## Algorithms and Perturbation Estimates.
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31 ## SIAM Journal on Scientific Computing, Vol. 23 no. 6, pp. 2008-2040
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32 ##
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33 ## other texts are also around...
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34
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35 function ang = subspace (A, B)
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36
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37 if (nargin != 2)
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38 print_usage ();
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39 elseif (ndims (A) != 2 || ndims (B) != 2)
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40 error ("subspace: expecting A and B to be 2-dimensional arrays");
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41 elseif (rows (A) != rows (B))
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42 error ("subspace: column dimensions of A and B must match");
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43 endif
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44
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45 A = orth (A);
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46 B = orth (B);
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47 c = A'*B;
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48 scos = min (svd (c));
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49 if (scos^2 > 1/2)
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50 if (columns (A) >= columns (B))
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51 c = B - A*c;
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52 else
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53 c = A - B*c';
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54 endif
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55 ssin = max (svd (c));
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56 ang = asin (min (ssin, 1));
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57 else
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58 ang = acos (scos);
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59 endif
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60
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61 endfunction
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