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annotate scripts/linear-algebra/orth.m @ 1065:5eeb61cac52e

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[project @ 1995-01-25 14:04:13 by jwe]
author jwe
date Wed, 25 Jan 1995 14:06:23 +0000
parents 9fc405c8c06c
children 611d403c7f3d
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1 # Copyright (C) 1995 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 the
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7 # Free Software Foundation; either version 2, or (at your option) any
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8 # later version.
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9 #
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License
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13 # 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, 675 Mass Ave, Cambridge, MA 02139, USA.
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18
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e6ae50d8d4eb [project @ 1994-07-25 20:23:22 by jwe]
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19 function retval = orth (A, tol)
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20
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21 # usage: orth (A, tol)
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22 # orth (A)
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23 #
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24 # Returns an orthonormal basis of the range of A.
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25 #
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26 # The dimension of the range space is taken as the number of singular
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27 # values of A greater than tol; the default for tol is
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28 # max (size (A)) * sigma_max (A) * eps, where sigma_max (A) is the
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29 # maximal singular value of A.
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30
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31 # Written by KH (Kurt.Hornik@ci.tuwien.ac.at) on Dec 24, 1993.
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32
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33 [U, S, V] = svd (A);
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34
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35 [rows, cols] = size (A);
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36
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37 [S_nr, S_nc] = size (S);
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38
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39 if (S_nr == 1 || S_nc == 1)
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40 s = S(1);
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41 else
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42 s = diag (S);
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43 endif
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44
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45 if (nargin == 1)
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46 tol = max (size (A)) * s (1) * eps;
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47 elseif (nargin != 2)
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48 usage ("orth (A [, tol])");
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49 endif
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50
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51 rank = sum (s > tol);
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52
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53 if (rank > 0)
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54 retval = -U (:, 1:rank);
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55 else
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56 retval = zeros (rows, 0);
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57 endif
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58
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59 endfunction