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maint: update copyright notices for 2012
author John W. Eaton <jwe@octave.org>
date Mon, 02 Jan 2012 14:25:41 -0500
parents 614505385171
children 11949c9795a0
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1 ## Copyright (C) 2000-2012 Paul Kienzle
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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 3 of the License, or (at
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8 ## your option) 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, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {@var{pp} =} mkpp (@var{breaks}, @var{coefs})
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21 ## @deftypefnx {Function File} {@var{pp} =} mkpp (@var{breaks}, @var{coefs}, @var{d})
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22 ##
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23 ## Construct a piecewise polynomial (pp) structure from sample points
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24 ## @var{breaks} and coefficients @var{coefs}. @var{breaks} must be a vector of
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25 ## strictly increasing values. The number of intervals is given by
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26 ## @code{@var{ni} = length (@var{breaks}) - 1}.
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27 ## When @var{m} is the polynomial order @var{coefs} must be of
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28 ## size: @var{ni} x @var{m} + 1.
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29 ##
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30 ## The i-th row of @var{coefs},
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31 ## @code{@var{coefs} (@var{i},:)}, contains the coefficients for the polynomial
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32 ## over the @var{i}-th interval, ordered from highest (@var{m}) to
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33 ## lowest (@var{0}).
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34 ##
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35 ## @var{coefs} may also be a multi-dimensional array, specifying a vector-valued
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36 ## or array-valued polynomial. In that case the polynomial order is defined
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37 ## by the length of the last dimension of @var{coefs}.
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38 ## The size of first dimension(s) are given by the scalar or
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39 ## vector @var{d}. If @var{d} is not given it is set to @code{1}.
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40 ## In any case @var{coefs} is reshaped to a 2-D matrix of
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41 ## size @code{[@var{ni}*prod(@var{d} @var{m})] }
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42 ##
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43 ## @seealso{unmkpp, ppval, spline, pchip, ppder, ppint, ppjumps}
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44 ## @end deftypefn
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45
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46 function pp = mkpp (x, P, d)
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47
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48 # check number of arguments
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49 if (nargin < 2 || nargin > 3)
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50 print_usage ();
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51 endif
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52
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53 # check x
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54 if (length (x) < 2)
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55 error ("mkpp: at least one interval is needed");
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56 endif
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57
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58 if (!isvector (x))
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59 error ("mkpp: x must be a vector");
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60 endif
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61
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62 len = length (x) - 1;
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63 dP = length (size (P));
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64
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65 pp = struct ("form", "pp",
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66 "breaks", x(:).',
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67 "coefs", [],
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68 "pieces", len,
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69 "order", prod (size (P)) / len,
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70 "dim", 1);
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71
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72 if (nargin == 3)
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73 pp.dim = d;
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74 pp.order /= prod (d);
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75 endif
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76
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77 dim_vec = [pp.pieces * prod(pp.dim), pp.order];
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78 pp.coefs = reshape (P, dim_vec);
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79
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80 endfunction
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81
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82 %!demo # linear interpolation
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83 %! x=linspace(0,pi,5)';
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84 %! t=[sin(x),cos(x)];
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85 %! m=diff(t)./(x(2)-x(1));
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86 %! b=t(1:4,:);
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87 %! pp = mkpp(x, [m(:),b(:)]);
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88 %! xi=linspace(0,pi,50);
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89 %! plot(x,t,"x",xi,ppval(pp,xi));
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90 %! legend("control","interp");
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91
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92 %!shared b,c,pp
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93 %! b = 1:3; c = 1:24; pp=mkpp(b,c);
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94 %!assert (pp.pieces,2);
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95 %!assert (pp.order,12);
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96 %!assert (pp.dim,1);
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97 %!assert (size(pp.coefs),[2,12]);
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98 %! pp=mkpp(b,c,2);
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99 %!assert (pp.pieces,2);
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100 %!assert (pp.order,6);
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101 %!assert (pp.dim,2);
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102 %!assert (size(pp.coefs),[4,6]);
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103 %! pp=mkpp(b,c,3);
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104 %!assert (pp.pieces,2);
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105 %!assert (pp.order,4);
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106 %!assert (pp.dim,3);
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107 %!assert (size(pp.coefs),[6,4]);
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108 %! pp=mkpp(b,c,[2,3]);
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109 %!assert (pp.pieces,2);
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110 %!assert (pp.order,2);
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111 %!assert (pp.dim,[2,3]);
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112 %!assert (size(pp.coefs),[12,2]);