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1 # Copyright (C) 1993 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 the |
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7 # Free Software Foundation; either version 2, or (at your option) any |
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8 # later version. |
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9 # |
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10 # Octave is distributed in the hope that it will be useful, but WITHOUT |
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11 # ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or |
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12 # FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License |
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13 # 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, 675 Mass Ave, Cambridge, MA 02139, USA. |
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18 |
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4
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19 function retval = invhilb (n) |
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20 |
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21 # usage: invhilb (n) |
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22 # |
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23 # Return the inverse of a Hilbert matrix of order n. This is slow but |
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24 # exact. Compare with inv (hilb (n)). |
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25 # |
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26 # See also: hankel, vander, hadamard, hilb, toeplitz |
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27 |
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28 if (nargin != 1) |
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29 error ("usage: invhilb (n)"); |
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30 endif |
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31 |
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32 nmax = length (n); |
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33 if (nmax == 1) |
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34 retval = zeros (n); |
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35 for l = 1:n |
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36 for k = l:n |
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37 tmp = 1; |
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38 for i = 1:n |
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39 tmp = tmp * (i + k - 1); |
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40 endfor |
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41 for i = 1:n |
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42 if (i != k) |
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43 tmp = tmp * (l + i - 1); |
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44 endif |
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45 endfor |
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46 for i = 1:n |
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47 if (i != l) |
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48 tmp = tmp / (i - l); |
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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 != k) |
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53 tmp = tmp / (i - k); |
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54 endif |
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55 endfor |
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56 retval (k, l) = tmp; |
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57 retval (l, k) = tmp; |
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58 endfor |
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59 endfor |
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60 else |
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61 error ("hilb: expecting scalar argument, found something else"); |
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62 endif |
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63 |
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64 endfunction |
