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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {[@var{p}, @var{s}] =} polyfit (@var{x}, @var{y}, @var{n}) |
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22 ## Return the coefficients of a polynomial @var{p}(@var{x}) of degree |
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23 ## @var{n} that minimizes |
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24 ## @iftex |
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25 ## @tex |
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26 ## $$ |
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27 ## \sum_{i=1}^N (p(x_i) - y_i)^2 |
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28 ## $$ |
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29 ## @end tex |
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30 ## @end iftex |
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31 ## @ifinfo |
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32 ## @code{sumsq (p(x(i)) - y(i))}, |
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33 ## @end ifinfo |
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34 ## to best fit the data in the least squares sense. |
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35 ## |
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36 ## The polynomial coefficients are returned in a row vector. |
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37 ## |
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38 ## If two output arguments are requested, the second is a structure |
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39 ## containing the following fields: |
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40 ## |
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41 ## @table @code |
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42 ## @item R |
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43 ## The Cholesky factor of the Vandermonde matrix used to compute the |
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44 ## polynomial coefficients. |
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45 ## @item X |
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46 ## The Vandermonde matrix used to compute the polynomial coefficients. |
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47 ## @item df |
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48 ## The degrees of freedom. |
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49 ## @item normr |
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50 ## The norm of the residuals. |
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51 ## @item yf |
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52 ## The values of the polynomial for each value of @var{x}. |
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53 ## @end table |
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54 ## @end deftypefn |
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55 |
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56 ## Author: KH <Kurt.Hornik@wu-wien.ac.at> |
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57 ## Created: 13 December 1994 |
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58 ## Adapted-By: jwe |
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59 |
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60 function [p, s, mu] = polyfit (x, y, n) |
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61 |
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62 |
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63 if (nargin != 3) |
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64 print_usage (); |
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65 endif |
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66 |
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67 if (! (isvector (x) && isvector (y) && size (x) == size (y))) |
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68 error ("polyfit: x and y must be vectors of the same size"); |
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69 endif |
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70 |
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71 if (! (isscalar (n) && n >= 0 && ! isinf (n) && n == round (n))) |
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72 error ("polyfit: n must be a nonnegative integer"); |
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73 endif |
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74 |
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75 y_is_row_vector = (rows (y) == 1); |
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76 |
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77 l = length (x); |
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78 x = reshape (x, l, 1); |
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79 y = reshape (y, l, 1); |
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80 |
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81 X = (x * ones (1, n+1)) .^ (ones (l, 1) * (n : -1 : 0)); |
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82 |
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83 p = X \ y; |
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84 |
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85 if (nargout > 1) |
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86 |
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87 yf = X*p; |
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88 |
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89 if (y_is_row_vector) |
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90 s.yf = yf.'; |
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91 else |
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92 s.yf = yf; |
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93 endif |
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94 |
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95 [s.R, dummy] = chol (X'*X); |
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96 s.X = X; |
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97 s.df = l - n - 1; |
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98 s.normr = norm (yf - y); |
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99 |
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100 endif |
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101 |
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102 ## Return value should be a row vector. |
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103 |
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104 p = p.'; |
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105 |
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106 endfunction |
