update packages

[CreaPhase.git] / octave_packages / m / general / triplequad.m

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+## Copyright (C) 2008-2012 David Bateman
+##
+## 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} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
+## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol})
+## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf})
+## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{})
+## Numerically evaluate the triple integral of @var{f}.
+## @var{f} is a function handle, inline function, or string
+## containing the name of the function to evaluate.  The function @var{f} must
+## have the form @math{w = f(x,y,z)} where either @var{x} or @var{y} is a
+## vector and the remaining inputs are scalars.  It should return a vector of
+## the same length and orientation as @var{x} or @var{y}.
+##
+## @var{xa}, @var{ya}, @var{za} and @var{xb}, @var{yb}, @var{zb} are the lower
+## and upper limits of integration for x, y, and z respectively.  The
+## underlying integrator determines whether infinite bounds are accepted.
+##
+## The optional argument @var{tol} defines the absolute tolerance used to
+## integrate each sub-integral.  The default value is @math{1e^{-6}}.
+##
+## The optional argument @var{quadf} specifies which underlying integrator
+## function to use.  Any choice but @code{quad} is available and the default
+## is @code{quadcc}.
+##
+## Additional arguments, are passed directly to @var{f}.  To use the default
+## value for @var{tol} or @var{quadf} one may pass ':' or an empty matrix ([]).
+## @seealso{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz}
+## @end deftypefn
+
+function q = triplequad (f, xa, xb, ya, yb, za, zb, tol = 1e-6, quadf = @quadcc, varargin)
+
+  if (nargin < 7)
+    print_usage ();
+  endif
+
+  ## Allow use of empty matrix ([]) to indicate default
+  if (isempty (tol))
+    tol = 1e-6;
+  endif
+  if (isempty (quadf))
+    quadf = @quadcc;
+  endif
+
+  inner = @__triplequad_inner__;
+  if (ischar (f))
+    f = @(x,y,z) feval (f, x, y, z, varargin{:});
+    varargin = {};
+  endif
+
+  q = dblquad (@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}), ya, yb, za, zb, tol);
+
+endfunction
+
+function q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin)
+  q = zeros (size(y));
+  for i = 1 : length (y)
+    q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol);
+  endfor
+endfunction
+
+
+%!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)
+
+%% These tests are too expensive to run normally (~30 sec each).  Disable them
+#%!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)
+#%!#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)
+#%!#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)
+