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annotate scripts/general/trapz.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
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rev   line source
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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} =} trapz (@var{y})
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21 ## @deftypefnx {Function File} {@var{q} =} trapz (@var{x}, @var{y})
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22 ## @deftypefnx {Function File} {@var{q} =} trapz (@dots{}, @var{dim})
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23 ##
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24 ## Numerically evaluate the integral of points @var{y} using the trapezoidal
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25 ## method.
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26 ##
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27 ## @w{@code{trapz (@var{y})}} computes the integral of @var{y} along the first
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28 ## non-singleton dimension. When the argument @var{x} is omitted an equally
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29 ## spaced @var{x} vector with unit spacing (1) is assumed.
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30 ## @code{trapz (@var{x}, @var{y})} evaluates the integral with respect to the
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31 ## spacing in @var{x} and the values in @var{y}. This is useful if the points
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32 ## in @var{y} have been sampled unevenly.
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33 ##
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34 ## If the optional @var{dim} argument is given, operate along this dimension.
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35 ##
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36 ## Application Note: If @var{x} is not specified then unit spacing will be
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37 ## used. To scale the integral to the correct value you must multiply by the
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38 ## actual spacing value (deltaX). As an example, the integral of @math{x^3}
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39 ## over the range [0, 1] is @math{x^4/4} or 0.25. The following code uses
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40 ## @code{trapz} to calculate the integral in three different ways.
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41 ##
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42 ## @example
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43 ## @group
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44 ## x = 0:0.1:1;
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45 ## y = x.^3;
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46 ## q = trapz (y)
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47 ## @result{} q = 2.525 # No scaling
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48 ## q * 0.1
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49 ## @result{} q = 0.2525 # Approximation to integral by scaling
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50 ## trapz (x, y)
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51 ## @result{} q = 0.2525 # Same result by specifying @var{x}
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52 ## @end group
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53 ## @end example
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54 ##
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55 ## @seealso{cumtrapz}
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56 ## @end deftypefn
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57
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58 ## Author: Kai Habel <kai.habel@gmx.de>
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59 ##
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60 ## also: June 2000 - Paul Kienzle (fixes,suggestions)
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61 ## 2006-05-12 David Bateman - Modified for NDArrays
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62
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63 function z = trapz (x, y, dim)
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64
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65 if (nargin < 1) || (nargin > 3)
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66 print_usage ();
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67 endif
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68
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69 have_xy = have_dim = false;
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70
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71 if (nargin == 3)
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72 have_xy = true;
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73 have_dim = true;
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74 elseif (nargin == 2)
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75 if (! size_equal (x, y) && isscalar (y))
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76 dim = y;
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77 have_dim = true;
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78 else
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79 have_xy = true;
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80 endif
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81 endif
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82
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83 if (have_xy)
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84 nd = ndims (y);
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85 sz = size (y);
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86 else
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87 nd = ndims (x);
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88 sz = size (x);
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89 endif
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90
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91 if (! have_dim)
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92 ## Find the first non-singleton dimension.
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93 (dim = find (sz > 1, 1)) || (dim = 1);
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94 else
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95 if (!(isscalar (dim) && dim == fix (dim))
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96 || !(1 <= dim && dim <= nd))
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97 error ("trapz: DIM must be an integer and a valid dimension");
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98 endif
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99 endif
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100
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101 n = sz(dim);
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102 idx1 = idx2 = repmat ({':'}, [nd, 1]);
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103 idx1{dim} = 2 : n;
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104 idx2{dim} = 1 : (n - 1);
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105
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106 if (! have_xy)
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107 z = 0.5 * sum (x(idx1{:}) + x(idx2{:}), dim);
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108 else
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109 if (isvector (x) && ! isvector (y))
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110 if (length (x) != sz(dim))
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111 error ("trapz: length of X and length of Y along DIM must match");
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112 endif
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113 ## Reshape vector to point along dimension DIM
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114 shape = ones (nd, 1);
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115 shape(dim) = sz(dim);
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116 x = reshape (x, shape);
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117 z = 0.5 * sum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim);
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118 else
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119 if (! size_equal (x, y))
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120 error ("trapz: X and Y must have same shape");
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121 endif
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122 z = 0.5 * sum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim);
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123 endif
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124 endif
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125 endfunction
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126
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127
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128 %!assert (trapz (1:5), 12)
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129 %!assert (trapz (0:0.5:2,1:5), 6)
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130 %!assert (trapz ([1:5;1:5].',1), [12,12])
f3d52523cde1 Use Octave coding conventions in all m-file %!test blocks
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131 %!assert (trapz ([1:5;1:5],2), [12;12])
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132 %!assert (trapz (repmat (reshape (1:5,1,1,5),2,2), 3), [12 12; 12 12])
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133 %!assert (trapz ([0:0.5:2;0:0.5:2].',[1:5;1:5].',1), [6, 6])
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134 %!assert (trapz ([0:0.5:2;0:0.5:2],[1:5;1:5],2), [6; 6])
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135 %!assert (trapz (repmat (reshape ([0:0.5:2],1,1,5),2,2), ...
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136 %! repmat (reshape (1:5,1,1,5),2,2), 3), [6 6; 6 6])
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137 %!assert (trapz (0:0.5:2,[(1:5)',(1:5)']), [6, 6])
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138 %!assert (trapz (0:0.5:2,[(1:5);(1:5)],2), [6; 6])
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139 %!assert (trapz (0:0.5:2,repmat (reshape (1:5,1,1,5),2,2),3), [6 6; 6 6])
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d8aff843a9e9 Accept input x vector with y matrix for trapz,cumtrapz (bug #33292).
Rik <octave@nomad.inbox5.com>
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140