1 ## Copyright (C) 2008-2012 David Bateman
3 ## This file is part of Octave.
5 ## Octave is free software; you can redistribute it and/or modify it
6 ## under the terms of the GNU General Public License as published by
7 ## the Free Software Foundation; either version 3 of the License, or (at
8 ## your option) any later version.
10 ## Octave is distributed in the hope that it will be useful, but
11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
13 ## General Public License for more details.
15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>.
20 ## @deftypefn {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
21 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
22 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
23 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})
24 ## Numerically evaluate the double integral of @var{f}.
25 ## @var{f} is a function handle, inline function, or string
26 ## containing the name of the function to evaluate. The function @var{f} must
27 ## have the form @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a
28 ## scalar. It should return a vector of the same length and orientation as
31 ## @var{xa}, @var{ya} and @var{xb}, @var{yb} are the lower and upper limits of
32 ## integration for x and y respectively. The underlying integrator determines
33 ## whether infinite bounds are accepted.
35 ## The optional argument @var{tol} defines the absolute tolerance used to
36 ## integrate each sub-integral. The default value is @math{1e^{-6}}.
38 ## The optional argument @var{quadf} specifies which underlying integrator
39 ## function to use. Any choice but @code{quad} is available and the default
42 ## Additional arguments, are passed directly to @var{f}. To use the default
43 ## value for @var{tol} or @var{quadf} one may pass ':' or an empty matrix ([]).
44 ## @seealso{triplequad, quad, quadv, quadl, quadgk, quadcc, trapz}
47 function q = dblquad (f, xa, xb, ya, yb, tol = 1e-6, quadf = @quadcc, varargin)
59 inner = @__dblquad_inner__;
61 f = @(x,y) feval (f, x, y, varargin{:});
65 q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
66 varargin{:}), ya, yb, tol);
69 function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
71 for i = 1 : length (y)
72 q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
76 %% Nasty integrand to show quadcc off
77 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log(2), 1e-6)
79 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadgk), pi * erf(1).^2, 1e-6)
80 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadl), pi * erf(1).^2, 1e-6)
81 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadv), pi * erf(1).^2, 1e-6)