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