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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 ## usage: [p, yf] = polyfit (x, y, n) |
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21 ## |
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22 ## Returns the coefficients of a polynomial p(x) of degree n that |
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23 ## minimizes sumsq (p(x(i)) - y(i)), i.e., that best fits the data |
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24 ## in the least squares sense. |
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25 ## |
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26 ## If two outputs are requested, also return the values of the |
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27 ## polynomial for each value of x. |
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28 |
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29 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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30 ## Created: 13 December 1994 |
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31 ## Adapted-By: jwe |
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32 |
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33 function [p, yf] = polyfit (x, y, n) |
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34 |
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35 |
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36 if (nargin != 3) |
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37 usage ("polyfit (x, y, n)"); |
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38 endif |
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39 |
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40 if (! (is_vector (x) && is_vector (y) && size (x) == size (y))) |
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41 error ("polyfit: x and y must be vectors of the same size"); |
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42 endif |
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43 |
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44 if (! (is_scalar (n) && n >= 0 && ! isinf (n) && n == round (n))) |
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45 error ("polyfit: n must be a nonnegative integer"); |
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46 endif |
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47 |
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48 y_is_row_vector = (rows (y) == 1); |
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49 |
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50 l = length (x); |
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51 x = reshape (x, l, 1); |
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52 y = reshape (y, l, 1); |
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53 |
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54 ## Unfortunately, the economy QR factorization doesn't really save |
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55 ## memory doing the computation -- the returned values are just |
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56 ## smaller. |
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57 |
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58 ## [Q, R] = qr (X, 0); |
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59 ## p = flipud (R \ (Q' * y)); |
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60 |
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61 ## XXX FIXME XXX -- this is probably not so good for extreme values of |
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62 ## N or X... |
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63 |
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64 X = (x * ones (1, n+1)) .^ (ones (l, 1) * (0 : n)); |
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65 |
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66 p = (X' * X) \ (X' * y); |
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67 |
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68 if (nargout == 2) |
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69 yf = X * p; |
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70 endif |
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71 |
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72 p = flipud (p); |
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73 |
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74 if (! prefer_column_vectors) |
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75 p = p'; |
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76 endif |
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77 |
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78 if (y_is_row_vector) |
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79 yf = yf'; |
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80 endif |
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81 |
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82 endfunction |
