scripts/general/triplequad.m

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author	Rik <octave@nomad.inbox5.com>
date	Mon, 04 Apr 2011 15:33:46 -0700
parents	c792872f8942
children	16cca721117b
rev	line source
11523 fd0a3ac60b0e update copyright notices John W. Eaton <jwe@octave.org> parents: 9245 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 --
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	20 ## @deftypefn {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{})
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 7771 diff changeset	21 ## Numerically evaluate a triple integral. The function over which to
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	22 ## integrate is defined by @code{@var{f}}, and the interval for the
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	23 ## integration is defined by @code{[@var{xa}, @var{xb}, @var{ya},
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 7771 diff changeset	24 ## @var{yb}, @var{za}, @var{zb}]}. The function @var{f} must accept a
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	25 ## vector @var{x} and a scalar @var{y}, and return a vector of the same
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	26 ## length as @var{x}.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	27 ##
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	28 ## If defined, @var{tol} defines the absolute tolerance to which to
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	29 ## which to integrate each sub-integral.
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	30 ##
9051 1bf0ce0930be Grammar check TexInfo in all .m files Rik <rdrider0-list@yahoo.com> parents: 7771 diff changeset	31 ## Additional arguments, are passed directly to @var{f}. To use the default
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	32 ## value for @var{tol} one may pass an empty matrix.
12575 d0b799dafede Grammarcheck files for 3.4.1 release. Rik <octave@nomad.inbox5.com> parents: 11587 diff changeset	33 ## @seealso{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz}
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	34 ## @end deftypefn
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	35
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	36 function Q = triplequad(f, xa, xb, ya, yb, za, zb, tol, quadf, varargin)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	37 if (nargin < 7)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	38 print_usage ();
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	39 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	40 if (nargin < 8 \|\| isempty (tol))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	41 tol = 1e-6;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	42 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	43 if (nargin < 9 \|\| isempty (quadf))
11587 c792872f8942 all script files: untabify and strip trailing whitespace John W. Eaton <jwe@octave.org> parents: 11562 diff changeset	44 quadf = @quadgk;
7771 680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	45 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	46
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	47 inner = @__triplequad_inner__;
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	48 if (ischar (f))
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	49 f = @(x,y,z) feval (f, x, y, z, varargin{:});
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	50 varargin = {};
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	51 endif
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	52
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	53 Q = dblquad(@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}),ya, yb, za, zb, tol);
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	54 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	55
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	56 function Q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	57 Q = zeros (size(y));
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	58 for i = 1 : length (y)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	59 Q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol);
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	60 endfor
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	61 endfunction
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	62
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	63 %% These tests are too expensive to run normally. Disable them
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	64 % !#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)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	65 % !#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)
680631e787aa Add quadv, quadgk, dblquad and triplequad functions David Bateman <dbateman@free.fr> parents: diff changeset	66 % !#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)