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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: 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 ## Author: KH <Kurt.Hornik@ci.tuwien.ac.at> |
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27 ## Created: 13 December 1994 |
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28 ## Adapted-By: jwe |
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29 |
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30 function p = polyfit (x, y, n) |
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31 |
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32 |
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33 if (nargin != 3) |
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34 usage ("polyfit (x, y, n)"); |
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35 endif |
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36 |
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37 if (! (is_vector (x) && is_vector (y) && size (x) == size (y))) |
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38 error ("polyfit: x and y must be vectors of the same size"); |
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39 endif |
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40 |
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41 if (! (is_scalar (n) && n >= 0 && ! isinf (n) && n == round (n))) |
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42 error ("polyfit: n must be a nonnegative integer"); |
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43 endif |
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44 |
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45 l = length (x); |
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46 x = reshape (x, l, 1); |
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47 y = reshape (y, l, 1); |
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48 |
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49 X = ones (l, 1); |
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50 |
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51 if (n > 0) |
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52 tmp = (x * ones (1, n)) .^ (ones (l, 1) * (1 : n)); |
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53 X = [X, tmp]; |
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54 endif |
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55 |
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56 ## Compute polynomial coeffients, making returned value compatible |
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57 ## with Matlab. |
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58 |
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59 [Q, R] = qr (X, 0); |
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60 |
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61 p = flipud (R \ (Q' * y)); |
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62 |
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63 if (! prefer_column_vectors) |
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64 p = p'; |
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65 endif |
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66 |
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67 endfunction |
