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maint: Merge default to bytecode-interpreter.
author Markus Mützel <markus.muetzel@gmx.de>
date Tue, 21 May 2024 18:29:03 +0200
parents 2e484f9f1f18
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ########################################################################
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2 ##
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3 ## Copyright (C) 2000-2024 The Octave Project Developers
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4 ##
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5 ## See the file COPYRIGHT.md in the top-level directory of this
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6 ## distribution or <https://octave.org/copyright/>.
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7 ##
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8 ## This file is part of Octave.
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9 ##
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10 ## Octave is free software: you can redistribute it and/or modify it
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11 ## under the terms of the GNU General Public License as published by
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12 ## the Free Software Foundation, either version 3 of the License, or
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13 ## (at your option) any later version.
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14 ##
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15 ## Octave is distributed in the hope that it will be useful, but
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16 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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17 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
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18 ## GNU General Public License for more details.
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19 ##
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20 ## You should have received a copy of the GNU General Public License
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21 ## along with Octave; see the file COPYING. If not, see
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22 ## <https://www.gnu.org/licenses/>.
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23 ##
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24 ########################################################################
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25
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26 ## -*- texinfo -*-
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27 ## @deftypefn {} {@var{q} =} cumtrapz (@var{y})
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28 ## @deftypefnx {} {@var{q} =} cumtrapz (@var{x}, @var{y})
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29 ## @deftypefnx {} {@var{q} =} cumtrapz (@dots{}, @var{dim})
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30 ## Cumulative numerical integration of points @var{y} using the trapezoidal
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31 ## method.
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32 ##
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33 ## @w{@code{cumtrapz (@var{y})}} computes the cumulative integral of @var{y}
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34 ## along the first non-singleton dimension. Where @code{trapz} reports only
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35 ## the overall integral sum, @code{cumtrapz} reports the current partial sum
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36 ## value at each point of @var{y}.
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37 ##
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38 ## When the argument @var{x} is omitted an equally spaced @var{x} vector with
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39 ## unit spacing (1) is assumed. @code{cumtrapz (@var{x}, @var{y})} evaluates
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40 ## the integral with respect to the spacing in @var{x} and the values in
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41 ## @var{y}. This is useful if the points in @var{y} have been sampled
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42 ## unevenly.
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43 ##
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44 ## If the optional @var{dim} argument is given, operate along this dimension.
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45 ##
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46 ## Application Note: If @var{x} is not specified then unit spacing will be
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47 ## used. To scale the integral to the correct value you must multiply by the
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48 ## actual spacing value (deltaX).
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49 ## @seealso{trapz, cumsum}
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50 ## @end deftypefn
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51
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52 function z = cumtrapz (x, y, dim)
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53
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54 if (nargin < 1)
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55 print_usage ();
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56 endif
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57
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58 have_xy = have_dim = false;
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59
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60 if (nargin == 3)
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61 have_xy = true;
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62 have_dim = true;
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63 elseif (nargin == 2)
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64 if (isscalar (y) && ! isscalar (x))
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65 have_dim = true;
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66 dim = y;
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67 else
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68 have_xy = true;
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69 endif
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70 endif
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71
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72 if (have_xy)
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73 nd = ndims (y);
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74 sz = size (y);
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75 else
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76 nd = ndims (x);
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77 sz = size (x);
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78 endif
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79
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80 if (! have_dim)
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81 ## Find the first non-singleton dimension.
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82 (dim = find (sz > 1, 1)) || (dim = 1);
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83 else
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84 if (!(isscalar (dim) && dim == fix (dim))
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85 || !(1 <= dim && dim <= nd))
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86 error ("trapz: DIM must be an integer and a valid dimension");
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87 endif
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88 endif
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89
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90 n = sz(dim);
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91 idx1 = idx2 = {':'}(ones (nd, 1)); # repmat ({':'}, [nd, 1]), but faster
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92 idx1{dim} = 2 : n;
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93 idx2{dim} = 1 : (n - 1);
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94
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95 if (! have_xy)
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96 z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim);
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97 elseif (isscalar (x))
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98 z = x * 0.5 * cumsum (y(idx1{:}) + y(idx2{:}), dim);
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99 elseif (isvector (x))
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100 if (length (x) != n)
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101 error ("cumtrapz: length of X and length of Y along DIM must match");
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102 endif
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103 ## Reshape vector to point along dimension DIM
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104 shape = ones (nd, 1);
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105 shape(dim) = n;
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106 x = reshape (x, shape);
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107 z = 0.5 * cumsum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim);
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108 else
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109 if (! size_equal (x, y))
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110 error ("cumtrapz: X and Y must have same shape");
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111 endif
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112 z = 0.5 * cumsum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim);
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113 endif
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114
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115 sz(dim) = 1;
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116 z = cat (dim, zeros (sz), z);
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117
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118 endfunction
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119
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120
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121 %!shared x1, x2, y
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122 %! x1 = [1:5];
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123 %! x2 = [2:2:10];
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124 %! y = [1:5];
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125 %!
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126 %!assert (cumtrapz (y), [0, 1.5, 4, 7.5, 12])
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127 %!assert (cumtrapz (y'), [0, 1.5, 4, 7.5, 12]')
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128 %!assert (cumtrapz (1, y), [0, 1.5, 4, 7.5, 12])
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129 %!assert (cumtrapz (2, y), [0, 3, 8, 15, 24])
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130 %!assert (cumtrapz (x1, y),[0, 1.5, 4, 7.5, 12])
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131 %!assert (cumtrapz (x2, y),[0, 3, 8, 15, 24])
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132 %!assert (cumtrapz (2, y, 2), [0, 3, 8, 15, 24])
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133 %!assert (cumtrapz (x2, y, 2), [0, 3, 8, 15, 24])
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134 %!assert (cumtrapz (y, 1), [0, 0, 0, 0, 0])
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135 %!assert (cumtrapz (2, y, 1), [0, 0, 0, 0, 0])
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136 %!assert (cumtrapz (y', 2), [0, 0, 0, 0, 0]')
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137
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138 %!shared x1, x2, y
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139 %! x1 = [0,0,0;2,2,2];
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140 %! x2 = [0,2,4;0,2,4];
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141 %! y = [1,2,3;4,5,6];
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142 %!
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143 %!assert (cumtrapz (y), [0,0,0;2.5,3.5,4.5])
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144 %!assert (cumtrapz (x1, y), [0,0,0;5,7,9])
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145 %!assert (cumtrapz (y, 1), [0,0,0;2.5,3.5,4.5])
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146 %!assert (cumtrapz (x1, y, 1), [0,0,0;5,7,9])
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147 %!assert (cumtrapz (y, 2), [0,1.5,4;0,4.5,10])
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148 %!assert (cumtrapz (x2, y, 2), [0,3,8;0,9,20])
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149
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150 ## Test ND-array implementation
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151 %!shared x1,x2,y
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152 %! x1 = 1:3;
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153 %! x2 = reshape ([0,2,4;0,2,4], [1 2 3]);
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154 %! y = reshape ([1,2,3;4,5,6], [1 2 3]);
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155 %!
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156 %!assert (cumtrapz (y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3]))
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157 %!assert (cumtrapz (x1,y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3]))
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158 %!assert (cumtrapz (x2,y,3), reshape ([0,3,8;0,9,20],[1 2 3]))
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159
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160 ## Test input validation
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161 %!error <Invalid call> cumtrapz ()
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162 %!error <DIM must be an integer> cumtrapz (1, 2, [1 2])
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163 %!error <DIM must be an integer> cumtrapz (1, 2, 1.5)
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164 %!error <DIM must be .* a valid dimension> cumtrapz (1, 2, 0)
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165 %!error <length of X and length of Y.*must match> cumtrapz ([1 2], [1 2 3])
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166 %!error <X and Y must have same shape> cumtrapz (ones (2,3), ones (2,4))