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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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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} cond (@var{a}) |
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22 ## Compute the (two-norm) condition number of a matrix. @code{cond (a)} is |
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23 ## defined as @code{norm (a) * norm (inv (a))}, and is computed via a |
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24 ## singular value decomposition. |
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25 ## @end deftypefn |
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26 ## @seealso{norm, svd, and rank} |
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27 |
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28 ## Author: jwe |
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29 |
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30 function retval = cond (a) |
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31 |
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32 if (nargin == 1) |
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33 [nr, nc] = size (a); |
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34 if (nr == 0 && nc == 0) |
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35 if (! propagate_empty_matrices) |
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36 error ("cond: empty matrix is invalid as argument"); |
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37 endif |
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38 if (strcmp (propagate_empty_matrices, "warn")) |
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39 warning ("cond: argument is empty matrix\n"); |
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40 endif |
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41 retval = 0.0; |
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42 endif |
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43 if (any (any (isinf (a) | isnan (a)))) |
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44 error ("cond: argument must not contain Inf or NaN values"); |
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45 else |
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46 sigma = svd (a); |
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47 sigma_1 = sigma(1); |
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48 sigma_n = sigma(length (sigma)); |
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49 if (sigma_1 == 0 || sigma_n == 0) |
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50 retval = Inf; |
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51 else |
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52 retval = sigma_1 / sigma_n; |
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53 endif |
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54 endif |
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55 else |
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56 usage ("cond (a)"); |
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57 endif |
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58 |
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59 endfunction |
