update packages

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

diff --git a/octave_packages/m/general/dblquad.m b/octave_packages/m/general/dblquad.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} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
+## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
+## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
+## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})
+## Numerically evaluate the double 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{z = f(x,y)} where @var{x} is a vector and @var{y} is a
+## scalar.  It should return a vector of the same length and orientation as
+## @var{x}.
+##
+## @var{xa}, @var{ya} and @var{xb}, @var{yb} are the lower and upper limits of
+## integration for x and y 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{triplequad, quad, quadv, quadl, quadgk, quadcc, trapz}
+## @end deftypefn
+
+function q = dblquad (f, xa, xb, ya, yb, tol = 1e-6, quadf = @quadcc, varargin)
+
+  if (nargin < 5)
+    print_usage ();
+  endif
+  if (isempty (tol))
+    tol = 1e-6;
+  endif
+  if (isempty (quadf))
+    quadf = @quadcc;
+  endif
+
+  inner = @__dblquad_inner__;
+  if (ischar (f))
+    f = @(x,y) feval (f, x, y, varargin{:});
+    varargin = {};
+  endif
+
+  q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
+                                varargin{:}), ya, yb, tol);
+endfunction
+
+function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
+  q = zeros (size(y));
+  for i = 1 : length (y)
+    q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
+  endfor
+endfunction
+
+%% Nasty integrand to show quadcc off
+%!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log(2), 1e-6)
+
+%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadgk), pi * erf(1).^2, 1e-6)
+%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadl), pi * erf(1).^2, 1e-6)
+%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadv), pi * erf(1).^2, 1e-6)
+