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1 ## Copyright (C) 1994, 1995, 1996, 1997, 1998, 1999, 2000, 2002, 2004, |
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2 ## 2005, 2006, 2007, 2008 John W. Eaton |
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3 ## |
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4 ## This file is part of Octave. |
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5 ## |
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6 ## Octave is free software; you can redistribute it and/or modify it |
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7 ## under the terms of the GNU General Public License as published by |
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8 ## the Free Software Foundation; either version 3 of the License, or (at |
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9 ## your option) any later version. |
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10 ## |
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11 ## Octave is distributed in the hope that it will be useful, but |
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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14 ## General Public License for more details. |
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15 ## |
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16 ## You should have received a copy of the GNU General Public License |
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17 ## along with Octave; see the file COPYING. If not, see |
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18 ## <http://www.gnu.org/licenses/>. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {} polyderiv (@var{c}) |
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22 ## @deftypefnx {Function File} {[@var{q}] =} polyderiv (@var{b}, @var{a}) |
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23 ## @deftypefnx {Function File} {[@var{q}, @var{r}] =} polyderiv (@var{b}, @var{a}) |
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24 ## Return the coefficients of the derivative of the polynomial whose |
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25 ## coefficients are given by vector @var{c}. If a pair of polynomials |
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26 ## is given @var{b} and @var{a}, the derivative of the product is |
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27 ## returned in @var{q}, or the quotient numerator in @var{q} and the |
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28 ## quotient denominator in @var{r}. |
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29 ## @seealso{poly, polyinteg, polyreduce, roots, conv, deconv, residue, |
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30 ## filter, polygcd, polyval, polyvalm} |
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31 ## @end deftypefn |
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32 |
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33 ## Author: Tony Richardson <arichard@stark.cc.oh.us> |
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34 ## Created: June 1994 |
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35 ## Adapted-By: jwe |
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36 |
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37 function [q, r] = polyderiv (p, a) |
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38 |
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39 if (nargin == 1 || nargin == 2) |
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40 if (! isvector (p)) |
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41 error ("polyderiv: argument must be a vector"); |
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42 endif |
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43 if (nargin == 2) |
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44 if (! isvector (a)) |
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45 error ("polyderiv: argument must be a vector"); |
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46 endif |
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47 if (nargout == 1) |
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48 ## derivative of p*a returns a single polynomial |
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49 q = polyderiv (conv (p, a)); |
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50 else |
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51 ## derivative of p/a returns numerator and denominator |
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52 r = conv (a, a); |
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53 if (numel (p) == 1) |
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54 q = -p * polyderiv (a); |
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55 elseif (numel (a) == 1) |
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56 q = a * polyderiv (p); |
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57 else |
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58 q = conv (polyderiv (p), a) - conv (p, polyderiv (a)); |
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59 q = polyreduce (q); |
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60 endif |
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61 |
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62 ## remove common factors from numerator and denominator |
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63 x = polygcd (q, r); |
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64 if (length(x) != 1) |
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65 q = deconv (q, x); |
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66 r = deconv (r, x); |
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67 endif |
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68 |
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69 ## move all the gain into the numerator |
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70 q = q/r(1); |
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71 r = r/r(1); |
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72 endif |
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73 else |
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74 lp = numel (p); |
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75 if (lp == 1) |
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76 q = 0; |
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77 return; |
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78 elseif (lp == 0) |
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79 q = []; |
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80 return; |
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81 endif |
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82 |
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83 ## Force P to be a row vector. |
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84 p = p(:).'; |
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85 |
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86 q = p(1:(lp-1)) .* [(lp-1):-1:1]; |
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87 endif |
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88 else |
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89 print_usage (); |
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90 endif |
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91 |
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92 endfunction |
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93 |
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94 %!assert(all (all (polyderiv ([1, 2, 3]) == [2, 2]))); |
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95 |
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96 %!assert(polyderiv (13) == 0); |
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97 |
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98 %!error polyderiv ([]); |
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99 |
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100 %!error polyderiv ([1, 2; 3, 4]); |
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101 |
