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1 # Copyright (C) 1993 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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4
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19 function retval = rank (A, tol) |
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20 |
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21 # usage: rank (a, tol) |
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4
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22 # |
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23 # Return the rank of the matrix a. The rank is taken to be the number |
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24 # of singular values of a that are greater than tol. |
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25 # |
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26 # If the second argument is omitted, it is taken to be |
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27 # |
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28 # tol = max (size (a)) * sigma (1) * eps; |
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29 # |
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30 # where eps is machine precision and sigma is the largest singular |
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31 # value of a. |
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32 |
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33 if (nargin == 1) |
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34 sigma = svd (A); |
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35 tolerance = max (size (A)) * sigma (1) * eps; |
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36 elseif (nargin == 2) |
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37 sigma = svd (A); |
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38 tolerance = tol; |
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39 else |
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40 error ("usage: rank (A)"); |
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41 endif |
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42 retval = sum (sigma > tolerance); |
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43 |
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44 endfunction |
