1 ## Copyright (C) 2008-2012 David Bateman
3 ## This file is part of Octave.
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6 ## under the terms of the GNU General Public License as published by
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13 ## General Public License for more details.
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20 ## @deftypefn {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
21 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol})
22 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf})
23 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{})
24 ## Numerically evaluate the triple 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{w = f(x,y,z)} where either @var{x} or @var{y} is a
28 ## vector and the remaining inputs are scalars. It should return a vector of
29 ## the same length and orientation as @var{x} or @var{y}.
31 ## @var{xa}, @var{ya}, @var{za} and @var{xb}, @var{yb}, @var{zb} are the lower
32 ## and upper limits of integration for x, y, and z respectively. The
33 ## underlying integrator determines 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{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz}
47 function q = triplequad (f, xa, xb, ya, yb, za, zb, tol = 1e-6, quadf = @quadcc, varargin)
53 ## Allow use of empty matrix ([]) to indicate default
61 inner = @__triplequad_inner__;
63 f = @(x,y,z) feval (f, x, y, z, varargin{:});
67 q = dblquad (@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}), ya, yb, za, zb, tol);
71 function q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin)
73 for i = 1 : length (y)
74 q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol);
79 %!assert (triplequad (@(x,y,z) exp(-x.^2 - y.^2 - z.^2) , -1, 1, -1, 1, -1, 1, [], @quadcc), pi ^ (3/2) * erf(1).^3, 1e-6)
81 %% These tests are too expensive to run normally (~30 sec each). Disable them
82 #%!assert (triplequad (@(x,y,z) exp(-x.^2 - y.^2 - z.^2) , -1, 1, -1, 1, -1, 1, [], @quadgk), pi ^ (3/2) * erf(1).^3, 1e-6)
83 #%!#assert (triplequad (@(x,y,z) exp(-x.^2 - y.^2 - z.^2) , -1, 1, -1, 1, -1, 1, [], @quadl), pi ^ (3/2) * erf(1).^3, 1e-6)
84 #%!#assert (triplequad (@(x,y,z) exp(-x.^2 - y.^2 - z.^2) , -1, 1, -1, 1, -1, 1, [], @quadv), pi ^ (3/2) * erf(1).^3, 1e-6)