Mercurial > octave
annotate scripts/general/cumtrapz.m @ 26376:00f796120a6d stable
maint: Update copyright dates in all source files.
author | John W. Eaton <jwe@octave.org> |
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date | Wed, 02 Jan 2019 16:32:43 -0500 |
parents | 7d7970c7b3e8 |
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1 ## Copyright (C) 2000-2019 Kai Habel |
5820 | 2 ## |
3 ## This file is part of Octave. | |
4 ## | |
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5 ## Octave is free software: you can redistribute it and/or modify it |
5820 | 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 |
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8 ## (at your option) any later version. |
5820 | 9 ## |
10 ## Octave is distributed in the hope that it will be useful, but | |
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
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13 ## GNU General Public License for more details. |
5820 | 14 ## |
15 ## You should have received a copy of the GNU General Public License | |
7016 | 16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <https://www.gnu.org/licenses/>. |
5820 | 18 |
19 ## -*- texinfo -*- | |
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20 ## @deftypefn {} {@var{q} =} cumtrapz (@var{y}) |
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21 ## @deftypefnx {} {@var{q} =} cumtrapz (@var{x}, @var{y}) |
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22 ## @deftypefnx {} {@var{q} =} cumtrapz (@dots{}, @var{dim}) |
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23 ## Cumulative numerical integration of points @var{y} using the trapezoidal |
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24 ## method. |
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25 ## |
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26 ## @w{@code{cumtrapz (@var{y})}} computes the cumulative integral of @var{y} |
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27 ## along the first non-singleton dimension. Where @code{trapz} reports only |
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28 ## the overall integral sum, @code{cumtrapz} reports the current partial sum |
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29 ## value at each point of @var{y}. |
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30 ## |
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31 ## When the argument @var{x} is omitted an equally spaced @var{x} vector with |
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32 ## unit spacing (1) is assumed. @code{cumtrapz (@var{x}, @var{y})} evaluates |
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33 ## the integral with respect to the spacing in @var{x} and the values in |
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34 ## @var{y}. This is useful if the points in @var{y} have been sampled |
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35 ## unevenly. |
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36 ## |
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37 ## If the optional @var{dim} argument is given, operate along this dimension. |
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38 ## |
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39 ## Application Note: If @var{x} is not specified then unit spacing will be |
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40 ## used. To scale the integral to the correct value you must multiply by the |
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41 ## actual spacing value (deltaX). |
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42 ## @seealso{trapz, cumsum} |
5820 | 43 ## @end deftypefn |
44 | |
10549 | 45 ## Author: Kai Habel <kai.habel@gmx.de> |
5820 | 46 ## |
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47 ## also: June 2000 Paul Kienzle (fixes,suggestions) |
5820 | 48 ## 2006-05-12 David Bateman - Modified for NDArrays |
49 | |
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50 function z = cumtrapz (x, y, dim) |
5820 | 51 |
52 if (nargin < 1) || (nargin > 3) | |
6046 | 53 print_usage (); |
5820 | 54 endif |
55 | |
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56 have_xy = have_dim = false; |
5820 | 57 |
58 if (nargin == 3) | |
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59 have_xy = true; |
5820 | 60 have_dim = true; |
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61 elseif (nargin == 2) |
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62 if (isscalar (y) && ! isscalar (x)) |
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63 have_dim = true; |
5820 | 64 dim = y; |
65 else | |
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66 have_xy = true; |
5820 | 67 endif |
68 endif | |
69 | |
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70 if (have_xy) |
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71 nd = ndims (y); |
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72 sz = size (y); |
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73 else |
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74 nd = ndims (x); |
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75 sz = size (x); |
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76 endif |
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77 |
5820 | 78 if (! have_dim) |
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79 ## Find the first non-singleton dimension. |
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80 (dim = find (sz > 1, 1)) || (dim = 1); |
5820 | 81 else |
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82 if (!(isscalar (dim) && dim == fix (dim)) |
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83 || !(1 <= dim && dim <= nd)) |
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84 error ("trapz: DIM must be an integer and a valid dimension"); |
5820 | 85 endif |
86 endif | |
87 | |
88 n = sz(dim); | |
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89 idx1 = idx2 = {':'}(ones (nd, 1)); # repmat ({':'}, [nd, 1]), but faster |
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90 idx1{dim} = 2 : n; |
5820 | 91 idx2{dim} = 1 : (n - 1); |
92 | |
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93 if (! have_xy) |
5820 | 94 z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim); |
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95 elseif (isscalar (x)) |
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96 z = x * 0.5 * cumsum (y(idx1{:}) + y(idx2{:}), dim); |
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97 elseif (isvector (x)) |
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98 if (length (x) != n) |
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99 error ("cumtrapz: length of X and length of Y along DIM must match"); |
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100 endif |
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101 ## Reshape vector to point along dimension DIM |
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102 shape = ones (nd, 1); |
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103 shape(dim) = n; |
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104 x = reshape (x, shape); |
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105 z = 0.5 * cumsum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim); |
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106 else |
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107 if (! size_equal (x, y)) |
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108 error ("cumtrapz: X and Y must have same shape"); |
5820 | 109 endif |
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110 z = 0.5 * cumsum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim); |
5820 | 111 endif |
112 | |
113 sz(dim) = 1; | |
114 z = cat (dim, zeros (sz), z); | |
115 | |
116 endfunction | |
117 | |
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118 |
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119 %!shared x1, x2, y |
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120 %! x1 = [1:5]; |
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121 %! x2 = [2:2:10]; |
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122 %! y = [1:5]; |
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123 %! |
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124 %!assert (cumtrapz (y), [0, 1.5, 4, 7.5, 12]) |
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125 %!assert (cumtrapz (y'), [0, 1.5, 4, 7.5, 12]') |
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126 %!assert (cumtrapz (1, y), [0, 1.5, 4, 7.5, 12]) |
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127 %!assert (cumtrapz (2, y), [0, 3, 8, 15, 24]) |
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128 %!assert (cumtrapz (x1, y),[0, 1.5, 4, 7.5, 12]) |
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129 %!assert (cumtrapz (x2, y),[0, 3, 8, 15, 24]) |
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130 %!assert (cumtrapz (2, y, 2), [0, 3, 8, 15, 24]) |
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131 %!assert (cumtrapz (x2, y, 2), [0, 3, 8, 15, 24]) |
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132 %!assert (cumtrapz (y, 1), [0, 0, 0, 0, 0]) |
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133 %!assert (cumtrapz (2, y, 1), [0, 0, 0, 0, 0]) |
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134 %!assert (cumtrapz (y', 2), [0, 0, 0, 0, 0]') |
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135 |
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136 %!shared x1, x2, y |
5820 | 137 %! x1 = [0,0,0;2,2,2]; |
138 %! x2 = [0,2,4;0,2,4]; | |
139 %! y = [1,2,3;4,5,6]; | |
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140 %! |
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141 %!assert (cumtrapz (y), [0,0,0;2.5,3.5,4.5]) |
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142 %!assert (cumtrapz (x1, y), [0,0,0;5,7,9]) |
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143 %!assert (cumtrapz (y, 1), [0,0,0;2.5,3.5,4.5]) |
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144 %!assert (cumtrapz (x1, y, 1), [0,0,0;5,7,9]) |
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145 %!assert (cumtrapz (y, 2), [0,1.5,4;0,4.5,10]) |
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146 %!assert (cumtrapz (x2, y, 2), [0,3,8;0,9,20]) |
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147 |
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148 ## Test ND-array implementation |
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149 %!shared x1,x2,y |
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150 %! x1 = 1:3; |
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151 %! x2 = reshape ([0,2,4;0,2,4], [1 2 3]); |
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152 %! y = reshape ([1,2,3;4,5,6], [1 2 3]); |
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153 %! |
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154 %!assert (cumtrapz (y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3])) |
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155 %!assert (cumtrapz (x1,y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3])) |
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156 %!assert (cumtrapz (x2,y,3), reshape ([0,3,8;0,9,20],[1 2 3])) |
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157 |
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158 ## Test input validation |
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159 %!error cumtrapz () |
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160 %!error cumtrapz (1,2,3,4) |
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161 %!error <DIM must be an integer> cumtrapz (1, 2, [1 2]) |
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162 %!error <DIM must be an integer> cumtrapz (1, 2, 1.5) |
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163 %!error <DIM must be .* a valid dimension> cumtrapz (1, 2, 0) |
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164 %!error <length of X and length of Y.*must match> cumtrapz ([1 2], [1 2 3]) |
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165 %!error <X and Y must have same shape> cumtrapz (ones (2,3), ones (2,4)) |
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166 |