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1 ## Copyright (C) 2000 Kai Habel |
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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, Inc., 51 Franklin Street, Fifth Floor, Boston, MA |
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18 ## 02110-1301, USA. |
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19 |
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20 ## -*- texinfo -*- |
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21 ## @deftypefn {Function File} {@var{z} =} cumtrapz (@var{y}) |
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22 ## @deftypefnx {Function File} {@var{z} =} cumtrapz (@var{x}, @var{y}) |
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23 ## @deftypefnx {Function File} {@var{z} =} cumtrapz (@dots{}, @var{dim}) |
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24 ## |
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25 ## Cumulative numerical integration using trapezoidal method. |
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26 ## @code{cumtrapz (@var{y})} computes the cumulative integral of the |
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27 ## @var{y} along the first non singleton dimension. If the argument |
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28 ## @var{x} is omitted a equally spaced vector is assumed. @code{cumtrapz |
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29 ## (@var{x}, @var{y})} evaluates the cumulative integral with respect |
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30 ## to @var{x}. |
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31 ## |
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32 ## @seealso{trapz,cumsum} |
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33 ## @end deftypefn |
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34 |
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35 ## Author: Kai Habel <kai.habel@gmx.de> |
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36 ## |
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37 ## also: June 2000 Paul Kienzle (fixes,suggestions) |
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38 ## 2006-05-12 David Bateman - Modified for NDArrays |
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39 |
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40 function z = cumtrapz (x, y, dim) |
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41 |
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42 if (nargin < 1) || (nargin > 3) |
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43 print_usage (); |
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44 endif |
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45 |
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46 nd = ndims (x); |
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47 sz = size (x); |
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48 |
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49 have_x = false; |
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50 have_dim = false; |
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51 if (nargin == 3) |
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52 have_x = true; |
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53 have_dim = true; |
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54 endif |
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55 if (nargin == 2) |
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56 if (! size_equal (x, y) && isscalar (y)) |
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57 dim = y; |
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58 have_dim = true; |
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59 else |
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60 have_x = true; |
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61 endif |
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62 endif |
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63 |
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64 if (! have_dim) |
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65 ## Find the first singleton dimension. |
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66 dim = 0; |
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67 while (dim < nd && sz(dim+1) == 1) |
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68 dim++; |
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69 endwhile |
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70 dim++; |
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71 if (dim > nd) |
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72 dim = 1; |
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73 endif |
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74 else |
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75 dim = floor (dim); |
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76 if (dim < 1 || dim > nd) |
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77 error ("cumtrapz: invalid dimension along which to sort"); |
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78 endif |
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79 endif |
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80 |
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81 n = sz(dim); |
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82 idx1 = cell (); |
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83 for i = 1:nd |
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84 idx1{i} = 1:sz(i); |
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85 endfor |
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86 idx2 = idx1; |
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87 idx1{dim} = 2 : n; |
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88 idx2{dim} = 1 : (n - 1); |
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89 |
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90 if (! have_x) |
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91 z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim); |
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92 else |
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93 if (! size_equal (x, y)) |
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94 error ("cumtrapz: x and y must have same shape"); |
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95 endif |
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96 z = 0.5 * cumsum ((x(idx1{:}) - x(idx2{:})) .* |
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97 (y(idx1{:}) + y(idx2{:})), dim); |
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98 endif |
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99 |
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100 sz(dim) = 1; |
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101 z = cat (dim, zeros (sz), z); |
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102 |
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103 endfunction |
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104 |
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105 %!shared x1,x2,y |
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106 %! x1 = [0,0,0;2,2,2]; |
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107 %! x2 = [0,2,4;0,2,4]; |
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108 %! y = [1,2,3;4,5,6]; |
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109 %!assert (cumtrapz(y),[0,0,0;2.5,3.5,4.5]) |
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110 %!assert (cumtrapz(x1,y),[0,0,0;5,7,9]) |
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111 %!assert (cumtrapz(y,1),[0,0,0;2.5,3.5,4.5]) |
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112 %!assert (cumtrapz(x1,y,1),[0,0,0;5,7,9]) |
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113 %!assert (cumtrapz(y,2),[0,1.5,4;0,4.5,10]) |
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114 %!assert (cumtrapz(x2,y,2),[0,3,8;0,9,20]) |
