changelog shortlog tags changeset files revisions annotate raw

scripts/general/dblquad.m

changeset 10289: 4b124317dc38
parent:eb63fbe60fab
author: John W. Eaton <jwe@octave.org>
date: Tue Feb 09 20:58:55 2010 -0500 (44 minutes ago)
permissions: -rw-r--r--
description: base_properties::set_children: account for hidden children 
     1## Copyright (C) 2008, 2009 David Bateman

     2##

     3## This file is part of Octave.

     4##

     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.

     9##

    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.

    14##

    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/>.

    18

    19## -*- texinfo -*-

    20## @deftypefn {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})

    21## Numerically evaluate a double integral.  The function over with to

    22## integrate is defined by @code{@var{f}}, and the interval for the

    23## integration is defined by @code{[@var{xa}, @var{xb}, @var{ya},

    24## @var{yb}]}.  The function @var{f} must accept a vector @var{x} and a

    25## scalar @var{y}, and return a vector of the same length as @var{x}. 

    26##

    27## If defined, @var{tol} defines the absolute tolerance to which to

    28## which to integrate each sub-integral.

    29##

    30## Additional arguments, are passed directly to @var{f}.  To use the default

    31## value for @var{tol} one may pass an empty matrix.

    32## @seealso{triplequad, quad, quadv, quadl, quadgk, trapz}

    33## @end deftypefn

    34

    35function q = dblquad(f, xa, xb, ya, yb, tol, quadf, varargin) 

    36  if (nargin < 5)

    37    print_usage ();

    38  endif

    39  if (nargin < 6 || isempty (tol))

    40    tol = 1e-6; 

    41  endif

    42  if (nargin < 7 || isempty (quadf))

    43    quadf = @quadgk; 

    44  endif

    45

    46  inner = @__dblquad_inner__;

    47  if (ischar (f))

    48    f = @(x,y) feval (f, x, y, varargin{:});

    49    varargin = {};

    50  endif

    51

    52  q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,

    53				varargin{:}), ya, yb, tol);

    54endfunction

    55

    56function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)

    57  q = zeros (size(y));

    58  for i = 1 : length (y)

    59    q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);

    60  endfor

    61endfunction

    62

    63%% Nasty integrand to show quadgk off

    64%!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log(2), 1e-6)

    65

    66%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [],  @quadgk), pi * erf(1).^2, 1e-6)

    67%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [],  @quadl), pi * erf(1).^2, 1e-6)

    68%!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [],  @quadv), pi * erf(1).^2, 1e-6)