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annotate scripts/special-matrix/invhilb.m @ 2303:5cffc4b8de57

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[project @ 1996-06-24 09:15:24 by jwe]
author jwe
date Mon, 24 Jun 1996 09:15:24 +0000
parents 5d29638dd524
children 2b5788792cad
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2303
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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
4
b4df021f796c [project @ 1993-08-08 01:26:08 by jwe]
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20 function retval = invhilb (n)
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21
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22 ## usage: invhilb (n)
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23 ##
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24 ## Return the inverse of a Hilbert matrix of order n. This is slow but
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25 ## exact. Compare with inv (hilb (n)).
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26 ##
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27 ## See also: hankel, vander, hadamard, hilb, toeplitz
4
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28
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29 if (nargin != 1)
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30 usage ("invhilb (n)");
4
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31 endif
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32
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33 nmax = length (n);
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34 if (nmax == 1)
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35 retval = zeros (n);
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36 for l = 1:n
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37 for k = l:n
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38 tmp = 1;
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39 for i = 1:n
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40 tmp = tmp * (i + k - 1);
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41 endfor
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42 for i = 1:n
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43 if (i != k)
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44 tmp = tmp * (l + i - 1);
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45 endif
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46 endfor
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47 for i = 1:n
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48 if (i != l)
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49 tmp = tmp / (i - l);
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50 endif
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51 endfor
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52 for i = 1:n
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53 if (i != k)
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54 tmp = tmp / (i - k);
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55 endif
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56 endfor
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57 retval (k, l) = tmp;
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58 retval (l, k) = tmp;
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59 endfor
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60 endfor
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61 else
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62 error ("hilb: expecting scalar argument, found something else");
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63 endif
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64
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65 endfunction