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annotate scripts/linear-algebra/orth.m @ 2303:5cffc4b8de57

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[project @ 1996-06-24 09:15:24 by jwe]
author jwe
date Mon, 24 Jun 1996 09:15:24 +0000
parents 5d29638dd524
children 2b5788792cad
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2303
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1 ### Copyright (C) 1996 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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19
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20 function retval = orth (A, tol)
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21
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22 ## usage: orth (A, tol)
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23 ## orth (A)
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24 ##
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25 ## Returns an orthonormal basis of the range of A.
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26 ##
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27 ## The dimension of the range space is taken as the number of singular
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28 ## values of A greater than tol; the default for tol is
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29 ## max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the
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30 ## maximal singular value of A.
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31
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32 ## Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 24, 1993.
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33
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34 [U, S, V] = svd (A);
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35
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36 [rows, cols] = size (A);
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37
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38 [S_nr, S_nc] = size (S);
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39
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40 if (S_nr == 1 || S_nc == 1)
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41 s = S(1);
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42 else
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43 s = diag (S);
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44 endif
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45
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46 if (nargin == 1)
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47 tol = max (size (A)) * s (1) * eps;
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48 elseif (nargin != 2)
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49 usage ("orth (A [, tol])");
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50 endif
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51
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52 rank = sum (s > tol);
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53
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54 if (rank > 0)
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55 retval = -U (:, 1:rank);
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56 else
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57 retval = zeros (rows, 0);
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58 endif
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59
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60 endfunction