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annotate scripts/linear-algebra/rank.m @ 3372:f16c2ce14886

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[project @ 1999-11-23 19:07:09 by jwe]
author jwe
date Tue, 23 Nov 1999 19:07:18 +0000
parents 8b262e771614
children f8dde1807dee
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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} {} 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} 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 tolerance = max (size (A)) * sigma (1) * eps;
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43 elseif (nargin == 2)
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44 sigma = svd (A);
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45 tolerance = tol;
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46 else
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47 usage ("rank (A)");
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48 endif
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49 retval = sum (sigma > tolerance);
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50
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51 endfunction