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reimplement polyvalm using Horner
author Jaroslav Hajek <highegg@gmail.com>
date Tue, 03 Mar 2009 11:56:51 +0100
parents 6f2d95255911
children eb63fbe60fab
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1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004,
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2 ## 2005, 2006, 2007 John W. Eaton
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3 ## Copyright (C) 2009 Jaroslav Hajek
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4 ##
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5 ## This file is part of Octave.
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6 ##
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7 ## Octave is free software; you can redistribute it and/or modify it
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8 ## under the terms of the GNU General Public License as published by
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9 ## the Free Software Foundation; either version 3 of the License, or (at
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10 ## your option) any later version.
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11 ##
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12 ## Octave is distributed in the hope that it will be useful, but
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13 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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14 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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15 ## General Public License for more details.
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16 ##
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17 ## You should have received a copy of the GNU General Public License
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18 ## along with Octave; see the file COPYING. If not, see
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19 ## <http://www.gnu.org/licenses/>.
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20
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21 ## -*- texinfo -*-
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22 ## @deftypefn {Function File} {} polyvalm (@var{c}, @var{x})
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23 ## Evaluate a polynomial in the matrix sense.
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24 ##
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25 ## @code{polyvalm (@var{c}, @var{x})} will evaluate the polynomial in the
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26 ## matrix sense, i.e. matrix multiplication is used instead of element by
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27 ## element multiplication as is used in polyval.
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28 ##
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29 ## The argument @var{x} must be a square matrix.
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30 ## @seealso{polyval, poly, roots, conv, deconv, residue, filter,
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31 ## polyderiv, polyinteg}
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32 ## @end deftypefn
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33
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34 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
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35 ## Created: June 1994
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36 ## Adapted-By: jwe
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37
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38 function y = polyvalm (c, x)
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39
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40 if (nargin != 2)
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41 print_usage ();
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42 endif
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43
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44 if (! (isvector (c) || isempty (c)))
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45 error ("polyvalm: first argument must be a vector");
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46 endif
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47
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48 if (! issquare (x))
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49 error ("polyvalm: second argument must be a square matrix");
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50 endif
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51
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52 n = length (c);
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53 if (n == 0)
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54 y = zeros (rows (x), class (x));
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55 else
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56 id = eye (rows (x), class (x));
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57 y = c(1) * id;
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58 for i = 2:n
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59 y = y * x + c(i) * id;
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60 endfor
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61 endif
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63 endfunction
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64
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66 %!assert(! any (polyvalm ([], [1, 2; 3, 4]))(:));
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67 %!assert(polyvalm ([1, 2, 3, 4], [3, -4, 1; -2, 0, 2; -1, 4, -3]), [117, -124, 11; -70, 36, 38; -43, 92, -45])
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69 %!error polyvalm ([1, 1, 1], [1, 2; 3, 4; 5, 6]);
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