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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} {} invhilb (@var{n}) |
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22 ## Return the inverse of a Hilbert matrix of order @var{n}. This is exact. |
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23 ## Compare with the numerical calculation of @code{inverse (hilb (n))}, |
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24 ## which suffers from the ill-conditioning of the Hilbert matrix, and the |
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25 ## finite precision of your computer's floating point arithmetic. |
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26 ## @end deftypefn |
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27 ## @seealso{hankel, vander, sylvester_matrix, hilb, and toeplitz} |
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28 |
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29 ## Author: jwe |
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30 |
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31 function retval = invhilb (n) |
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32 |
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33 if (nargin != 1) |
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34 usage ("invhilb (n)"); |
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35 endif |
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36 |
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37 nmax = length (n); |
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38 if (nmax == 1) |
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39 retval = zeros (n); |
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40 for l = 1:n |
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41 for k = l:n |
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42 tmp = 1; |
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43 for i = 1:n |
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44 tmp = tmp * (i + k - 1); |
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45 endfor |
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46 for i = 1:n |
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47 if (i != k) |
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48 tmp = tmp * (l + i - 1); |
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49 endif |
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50 endfor |
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51 for i = 1:n |
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52 if (i != l) |
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53 tmp = tmp / (i - l); |
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54 endif |
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55 endfor |
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56 for i = 1:n |
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57 if (i != k) |
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58 tmp = tmp / (i - k); |
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59 endif |
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60 endfor |
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61 retval (k, l) = tmp; |
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62 retval (l, k) = tmp; |
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63 endfor |
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64 endfor |
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65 else |
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66 error ("hilb: expecting scalar argument, found something else"); |
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67 endif |
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68 |
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69 endfunction |
