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annotate scripts/general/cumtrapz.m @ 20652:a3b9ee5c040a

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Replace bsxfun with broadcasting for performance with complex inputs (bug #38628). cumtrapz.m, quadgk.m, trapz.m, center.m, zscore.m: Replace bsxfun with broadcasting for performance where inputs might be complex.
author Rik <rik@octave.org>
date Mon, 12 Oct 2015 21:28:32 -0700
parents 7503499a252b
children
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
rev   line source
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4197fc428c7d maint: Update copyright notices for 2015.
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1 ## Copyright (C) 2000-2015 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 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{q} =} cumtrapz (@var{y})
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21 ## @deftypefnx {Function File} {@var{q} =} cumtrapz (@var{x}, @var{y})
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22 ## @deftypefnx {Function File} {@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 unevenly.
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35 ##
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36 ## If the optional @var{dim} argument is given, operate along this dimension.
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37 ##
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38 ## Application Note: If @var{x} is not specified then unit spacing will be
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39 ## used. To scale the integral to the correct value you must multiply by the
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40 ## actual spacing value (deltaX).
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41 ## @seealso{trapz, cumsum}
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42 ## @end deftypefn
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43
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44 ## Author: Kai Habel <kai.habel@gmx.de>
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45 ##
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46 ## also: June 2000 Paul Kienzle (fixes,suggestions)
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47 ## 2006-05-12 David Bateman - Modified for NDArrays
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48
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49 function z = cumtrapz (x, y, dim)
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50
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51 if (nargin < 1) || (nargin > 3)
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52 print_usage ();
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53 endif
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54
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55 have_xy = have_dim = false;
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56
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57 if (nargin == 3)
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58 have_xy = true;
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59 have_dim = true;
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60 elseif (nargin == 2)
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61 if (! size_equal (x, y) && isscalar (y))
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62 dim = y;
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63 have_dim = true;
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64 else
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65 have_xy = true;
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66 endif
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67 endif
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68
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69 if (have_xy)
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70 nd = ndims (y);
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71 sz = size (y);
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72 else
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73 nd = ndims (x);
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74 sz = size (x);
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75 endif
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76
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77 if (! have_dim)
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78 ## Find the first non-singleton dimension.
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79 (dim = find (sz > 1, 1)) || (dim = 1);
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80 else
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81 if (!(isscalar (dim) && dim == fix (dim))
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82 || !(1 <= dim && dim <= nd))
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83 error ("trapz: DIM must be an integer and a valid dimension");
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84 endif
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85 endif
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86
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87 n = sz(dim);
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88 idx1 = idx2 = repmat ({':'}, [nd, 1]);
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89 idx1{dim} = 2 : n;
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90 idx2{dim} = 1 : (n - 1);
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91
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92 if (! have_xy)
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93 z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim);
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94 else
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95 if (isvector (x) && ! isvector (y))
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96 if (length (x) != sz(dim))
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97 error ("cumtrapz: length of X and length of Y along DIM must match");
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98 endif
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99 ## Reshape vector to point along dimension DIM
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100 shape = ones (nd, 1);
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101 shape(dim) = sz(dim);
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102 x = reshape (x, shape);
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103 z = 0.5 * cumsum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim);
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104 else
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105 if (! size_equal (x, y))
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106 error ("cumtrapz: X and Y must have same shape");
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107 endif
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108 z = 0.5 * cumsum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim);
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109 endif
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110 endif
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111
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112 sz(dim) = 1;
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113 z = cat (dim, zeros (sz), z);
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114
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115 endfunction
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116
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117
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118 %!shared x1,x2,y
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119 %! x1 = [0,0,0;2,2,2];
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120 %! x2 = [0,2,4;0,2,4];
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121 %! y = [1,2,3;4,5,6];
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122 %!
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123 %!assert (cumtrapz (y), [0,0,0;2.5,3.5,4.5])
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124 %!assert (cumtrapz (x1,y), [0,0,0;5,7,9])
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125 %!assert (cumtrapz (y,1), [0,0,0;2.5,3.5,4.5])
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126 %!assert (cumtrapz (x1,y,1), [0,0,0;5,7,9])
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127 %!assert (cumtrapz (y,2), [0,1.5,4;0,4.5,10])
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128 %!assert (cumtrapz (x2,y,2), [0,3,8;0,9,20])
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129
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130 ## Test ND-array implementation
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parents: 12642
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131 %!shared x1,x2,y
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parents: 12642
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132 %! x1 = 1:3;
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parents: 12642
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133 %! x2 = reshape ([0,2,4;0,2,4], [1 2 3]);
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parents: 12642
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134 %! y = reshape ([1,2,3;4,5,6], [1 2 3]);
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parents: 19731
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135 %!
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parents: 14138
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136 %!assert (cumtrapz (y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3]))
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parents: 14138
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137 %!assert (cumtrapz (x1,y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3]))
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parents: 14138
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138 %!assert (cumtrapz (x2,y,3), reshape ([0,3,8;0,9,20],[1 2 3]))
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parents: 12642
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139