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