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[project @ 2007-10-12 21:27:11 by jwe]
author jwe
date Fri, 12 Oct 2007 21:27:37 +0000
parents 93c65f2a5668
children df9519e9990c
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1 ## Copyright (C) 1993, 1994, 1995, 1996, 1997, 1999, 2000, 2004, 2005,
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2 ## 2006, 2007 John W. Eaton
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Function File} {} rank (@var{a}, @var{tol})
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22 ## Compute the rank of @var{a}, using the singular value decomposition.
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23 ## The rank is taken to be the number of singular values of @var{a} that
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24 ## are greater than the specified tolerance @var{tol}. If the second
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25 ## argument is omitted, it is taken to be
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26 ##
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27 ## @example
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28 ## tol = max (size (@var{a})) * sigma(1) * eps;
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29 ## @end example
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30 ##
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31 ## @noindent
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32 ## where @code{eps} is machine precision and @code{sigma(1)} is the largest
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33 ## singular value of @var{a}.
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34 ## @end deftypefn
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36 ## Author: jwe
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37
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38 function retval = rank (A, tol)
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40 if (nargin == 1)
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41 sigma = svd (A);
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42 if (isempty (sigma))
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43 tolerance = 0;
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44 else
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45 tolerance = max (size (A)) * sigma (1) * eps;
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46 endif
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47 elseif (nargin == 2)
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48 sigma = svd (A);
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49 tolerance = tol;
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50 else
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51 print_usage ();
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52 endif
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53
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54 retval = sum (sigma > tolerance);
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56 endfunction