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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} {} hilb (@var{n}) |
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22 ## Return the Hilbert matrix of order @var{n}. The |
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23 ## @iftex |
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24 ## @tex |
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25 ## $i,\,j$ |
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26 ## @end tex |
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27 ## @end iftex |
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28 ## @ifinfo |
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29 ## i, j |
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30 ## @end ifinfo |
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31 ## element of a Hilbert matrix is defined as |
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32 ## @iftex |
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33 ## @tex |
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34 ## $$ |
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35 ## H (i, j) = {1 \over (i + j - 1)} |
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36 ## $$ |
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37 ## @end tex |
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38 ## @end iftex |
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39 ## @ifinfo |
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40 ## |
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41 ## @example |
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42 ## H (i, j) = 1 / (i + j - 1) |
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43 ## @end example |
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44 ## @end ifinfo |
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45 ## @end deftypefn |
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46 ## |
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47 ## @seealso{hankel, vander, sylvester_matrix, invhilb, and toeplitz} |
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48 |
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49 ## Author: jwe |
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50 |
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51 function retval = hilb (n) |
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52 |
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53 |
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54 if (nargin != 1) |
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55 usage ("hilb (n)"); |
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56 endif |
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57 |
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58 nmax = length (n); |
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59 if (nmax == 1) |
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60 retval = zeros (n); |
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61 tmp = 1:n; |
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62 for i = 1:n |
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63 retval (i, :) = 1.0 ./ (tmp + (i - 1)); |
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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 |
