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annotate scripts/special-matrix/invhilb.m @ 2314:949ab8eba8bc

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[project @ 1996-07-12 03:58:02 by jwe]
author jwe
date Fri, 12 Jul 1996 03:58:02 +0000
parents 5ca126254d15
children 8b262e771614
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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: invhilb (n)
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21 ##
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22 ## Return the inverse of a Hilbert matrix of order n. This is slow but
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23 ## exact. Compare with inv (hilb (n)).
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24 ##
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25 ## See also: hankel, vander, hadamard, hilb, toeplitz
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26
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27 ## Author: jwe
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28
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29 function retval = invhilb (n)
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30
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31 if (nargin != 1)
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32 usage ("invhilb (n)");
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33 endif
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34
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35 nmax = length (n);
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36 if (nmax == 1)
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37 retval = zeros (n);
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38 for l = 1:n
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39 for k = l:n
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40 tmp = 1;
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41 for i = 1:n
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42 tmp = tmp * (i + k - 1);
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43 endfor
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44 for i = 1:n
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45 if (i != k)
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46 tmp = tmp * (l + i - 1);
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47 endif
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48 endfor
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49 for i = 1:n
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50 if (i != l)
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51 tmp = tmp / (i - l);
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52 endif
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53 endfor
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54 for i = 1:n
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55 if (i != k)
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56 tmp = tmp / (i - k);
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57 endif
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58 endfor
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59 retval (k, l) = tmp;
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60 retval (l, k) = tmp;
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61 endfor
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62 endfor
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63 else
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64 error ("hilb: expecting scalar argument, found something else");
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65 endif
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66
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67 endfunction