scripts/general/dblquad.m

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author	Rik <octave@nomad.inbox5.com>
date	Sun, 01 May 2011 11:39:50 -0700
parents	16cca721117b
children	25d4e163ee38
rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 10549 diff changeset	1 ## Copyright (C) 2008-2011 David Bateman
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	2 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	3 ## This file is part of Octave.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	4 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	5 ## Octave is free software; you can redistribute it and/or modify it
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	6 ## under the terms of the GNU General Public License as published by
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	7 ## the Free Software Foundation; either version 3 of the License, or (at
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	8 ## your option) any later version.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	9 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	10 ## Octave is distributed in the hope that it will be useful, but
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	13 ## General Public License for more details.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	14 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	15 ## You should have received a copy of the GNU General Public License
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	16 ## along with Octave; see the file COPYING. If not, see
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	17 ## <http://www.gnu.org/licenses/>.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	18
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	19 ## -- texinfo --
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	20 ## @deftypefn {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	21 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	22 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	23 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	24 ## Numerically evaluate the double integral of @var{f}.
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	25 ## @var{f} is a function handle, inline function, or string
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	26 ## containing the name of the function to evaluate. The function @var{f} must
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	27 ## have the form @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	28 ## scalar. It should return a vector of the same length and orientation as
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	29 ## @var{x}.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	30 ##
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	31 ## @var{xa}, @var{ya} and @var{xb}, @var{yb} are the lower and upper limits of
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	32 ## integration for x and y respectively. The underlying integrator determines
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	33 ## whether infinite bounds are accepted.
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	34 ##
12642 f96b9b9f141b doc: Periodic grammarcheck and spellcheck of documentation. Rik <octave@nomad.inbox5.com> parents: 12612 diff changeset	35 ## The optional argument @var{tol} defines the absolute tolerance used to
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	36 ## integrate each sub-integral. The default value is @math{1e^{-6}}.
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	37 ##
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	38 ## The optional argument @var{quadf} specifies which underlying integrator
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	39 ## function to use. Any choice but @code{quad} is available and the default
16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	40 ## is @code{quadgk}.
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	41 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 8920 diff changeset	42 ## Additional arguments, are passed directly to @var{f}. To use the default
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	43 ## value for @var{tol} or @var{quadf} one may pass an empty matrix ([]).
12575 d0b799dafede Grammarcheck files for 3.4.1 release. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	44 ## @seealso{triplequad, quad, quadv, quadl, quadgk, quadcc, trapz}
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	45 ## @end deftypefn
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	46
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	47 function q = dblquad(f, xa, xb, ya, yb, tol, quadf, varargin)
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	48 if (nargin < 5)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	49 print_usage ();
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	50 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	51 if (nargin < 6 \|\| isempty (tol))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	52 tol = 1e-6;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	53 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	54 if (nargin < 7 \|\| isempty (quadf))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	55 quadf = @quadgk;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	56 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	57
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	58 inner = @__dblquad_inner__;
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	59 if (ischar (f))
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	60 f = @(x,y) feval (f, x, y, varargin{:});
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	61 varargin = {};
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	62 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	63
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	64 q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
10549 95c3e38098bf Untabify .m scripts Rik <code@nomad.inbox5.com> parents: 9051 diff changeset	65 varargin{:}), ya, yb, tol);
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	66 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	67
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	68 function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	69 q = zeros (size(y));
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	70 for i = 1 : length (y)
8507 cadc73247d65 style fixes John W. Eaton <jwe@octave.org> parents: 7771 diff changeset	71 q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	72 endfor
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	73 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	74
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	75 %% Nasty integrand to show quadgk off
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	76 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log(2), 1e-6)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	77
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	78 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadgk), pi * erf(1).^2, 1e-6)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	79 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadl), pi * erf(1).^2, 1e-6)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	80 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadv), pi * erf(1).^2, 1e-6)
12612 16cca721117b doc: Update all documentation for chapter on Numerical Integration Rik <octave@nomad.inbox5.com> parents: 12575 diff changeset	81