Mercurial > octave
view scripts/general/trapz.m @ 12612:16cca721117b stable
doc: Update all documentation for chapter on Numerical Integration
* cumtrapz.m, dblquad.m, quadgk.m, quadl.m, quadv.m, trapz.m,
triplequad.m, quad.cc, quadcc.cc: Improve docstrings.
* Quad-opts.in: Keep code sample together on a single line.
* mk-opts.pl: Update quad-options function description
* octave.texi: Update order of detailmenu to match order in quad.texi.
* quad.txi: Add language about when to use each quad function,
add examples of using trapz.
* aspell-octave.en.pws: Add new spelling words from quad.texi chapter
author | Rik <octave@nomad.inbox5.com> |
---|---|
date | Sun, 17 Apr 2011 19:57:07 -0700 |
parents | c792872f8942 |
children | f96b9b9f141b |
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## Copyright (C) 2000-2011 Kai Habel ## ## This file is part of Octave. ## ## Octave is free software; you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation; either version 3 of the License, or (at ## your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU ## General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{q} =} trapz (@var{y}) ## @deftypefnx {Function File} {@var{q} =} trapz (@var{x}, @var{y}) ## @deftypefnx {Function File} {@var{q} =} trapz (@dots{}, @var{dim}) ## ## Numerically evaluate the integral of points @var{y} using the trapezoidal ## method. ## @w{@code{trapz (@var{y})}} computes the integral of @var{y} along the first ## non-singleton dimension. When the argument @var{x} is omitted an ## equally spaced @var{x} vector with unit spacing (1) is assumed. ## @code{trapz (@var{x}, @var{y})} evaluates the integral with respect ## to the spacing in @var{x} and the values in @var{y}. This is useful if ## the points in @var{y} have been sampled unevenly. ## If the optional @var{dim} argument is given, operate along this dimension. ## ## If @var{x} is not specified then unit spacing will be used. To scale ## the integral to the correct value you must multiply by the actual spacing ## value (deltaX). As an example, the integral of @math{x^3} over the range ## [0, 1] is @math{x^4/4} or 0.25. The following code uses @code{trapz} to ## calculate the integral in three different ways. ## ## @example ## @group ## x = 0:0.1:1; ## y = x.^3; ## q = trapz (y) ## @result{} q = 2.525 # No scaling ## q * 0.1 ## @result{} q = 0.2525 # Approximation to integral by scaling ## trapz (x, y) ## @result{} q = 0.2525 # Same result by specifying @var{x} ## @end group ## @end example ## ## @seealso{cumtrapz} ## @end deftypefn ## Author: Kai Habel <kai.habel@gmx.de> ## ## also: June 2000 - Paul Kienzle (fixes,suggestions) ## 2006-05-12 David Bateman - Modified for NDArrays function z = trapz (x, y, dim) if (nargin < 1) || (nargin > 3) print_usage (); endif nd = ndims (x); sz = size (x); have_x = false; have_dim = false; if (nargin == 3) have_x = true; have_dim = true; endif if (nargin == 2) if (! size_equal (x, y) && isscalar (y)) dim = y; have_dim = true; else have_x = true; endif endif if (! have_dim) ## Find the first non-singleton dimension. dim = find (sz > 1, 1); if (isempty (dim)) dim = 1; endif else dim = floor (dim); if (dim < 1 || dim > nd) error ("trapz: invalid dimension DIM along which to sort"); endif endif n = sz(dim); idx1 = cell (); for i = 1:nd idx1{i} = 1:sz(i); endfor idx2 = idx1; idx1{dim} = 2 : n; idx2{dim} = 1 : (n - 1); if (! have_x) z = 0.5 * sum (x(idx1{:}) + x(idx2{:}), dim); else if (! size_equal (x, y)) error ("trapz: X and Y must have same shape"); endif z = 0.5 * sum ((x(idx1{:}) - x(idx2{:})) .* (y(idx1{:}) + y(idx2{:})), dim); endif endfunction %!assert (trapz(1:5), 12) %!assert (trapz(0:0.5:2,1:5), 6) %!assert (trapz([1:5;1:5],2),[12;12]) %!assert (trapz([1:5;1:5].',1),[12,12]) %!assert (trapz([0:0.5:2;0:0.5:2],[1:5;1:5],2),[6;6]) %!assert (trapz([0:0.5:2;0:0.5:2].',[1:5;1:5].',1),[6,6])