Mercurial > hg > octave-lyh

comparison scripts/general/triplequad.m @ 12612:16cca721117b stable

Find changesets by keywords (author, files, the commit message), revision number or hash, or revset expression.
doc: Update all documentation for chapter on Numerical Integration * cumtrapz.m, dblquad.m, quadgk.m, quadl.m, quadv.m, trapz.m, triplequad.m, quad.cc, quadcc.cc: Improve docstrings. * Quad-opts.in: Keep code sample together on a single line. * mk-opts.pl: Update quad-options function description * octave.texi: Update order of detailmenu to match order in quad.texi. * quad.txi: Add language about when to use each quad function, add examples of using trapz. * aspell-octave.en.pws: Add new spelling words from quad.texi chapter
author Rik <octave@nomad.inbox5.com>
date Sun, 17 Apr 2011 19:57:07 -0700
parents d0b799dafede
children 0713ad019e53 f96b9b9f141b
comparison
equal deleted inserted replaced
12607:2846ea58b288 12612:16cca721117b
15 ## You should have received a copy of the GNU General Public License 15 ## You should have received a copy of the GNU General Public License
16 ## along with Octave; see the file COPYING. If not, see 16 ## along with Octave; see the file COPYING. If not, see
17 ## <http://www.gnu.org/licenses/>. 17 ## <http://www.gnu.org/licenses/>.
18 18
19 ## -*- texinfo -*- 19 ## -*- texinfo -*-
20 ## @deftypefn {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{}) 20 ## @deftypefn {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
21 ## Numerically evaluate a triple integral. The function over which to 21 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol})
22 ## integrate is defined by @code{@var{f}}, and the interval for the 22 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf})
23 ## integration is defined by @code{[@var{xa}, @var{xb}, @var{ya}, 23 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{})
24 ## @var{yb}, @var{za}, @var{zb}]}. The function @var{f} must accept a 24 ## Numerically evaluate the triple integral of @var{f}.
25 ## vector @var{x} and a scalar @var{y}, and return a vector of the same 25 ## @var{f} is a function handle, inline function, or string
26 ## length as @var{x}. 26 ## containing the name of the function to evaluate. The function @var{f} must
27 ## have the form @math{w = f(x,y,z)} where either @var{x} or @var{y} is a
28 ## vector and the remaining inputs are scalars. It should return a vector of
29 ## the same length and orientation as @var{x} or @var{y}.
27 ## 30 ##
28 ## If defined, @var{tol} defines the absolute tolerance to which to 31 ## @var{xa}, @var{ya}, @var{za} and @var{xb}, @var{yb}, @var{zb} are the lower
29 ## which to integrate each sub-integral. 32 ## and upper limits of integration for x, y, and z respectively. The
33 ## underlying integrator determines whether infinite bounds are accepted.
34 ##
35 ## The optional argument @var{tol} defines the absolute tolerance used to
36 ## integrate each sub-integral. The default value is @math{1e^{-6}}.
37 ##
38 ## The optional argument @var{quadf} specifies which underlying integrator
39 ## function to use. Any choice but @code{quad} is available and the default
40 ## is @code{quadgk}.
30 ## 41 ##
31 ## Additional arguments, are passed directly to @var{f}. To use the default 42 ## Additional arguments, are passed directly to @var{f}. To use the default
32 ## value for @var{tol} one may pass an empty matrix. 43 ## value for @var{tol} or @var{quadf} one may pass an empty matrix ([]).
33 ## @seealso{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz} 44 ## @seealso{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz}
34 ## @end deftypefn 45 ## @end deftypefn
35 46
36 function Q = triplequad(f, xa, xb, ya, yb, za, zb, tol, quadf, varargin) 47 function q = triplequad(f, xa, xb, ya, yb, za, zb, tol, quadf, varargin)
37 if (nargin < 7) 48 if (nargin < 7)
38 print_usage (); 49 print_usage ();
39 endif 50 endif
40 if (nargin < 8 || isempty (tol)) 51 if (nargin < 8 || isempty (tol))
41 tol = 1e-6; 52 tol = 1e-6;
48 if (ischar (f)) 59 if (ischar (f))
49 f = @(x,y,z) feval (f, x, y, z, varargin{:}); 60 f = @(x,y,z) feval (f, x, y, z, varargin{:});
50 varargin = {}; 61 varargin = {};
51 endif 62 endif
52 63
53 Q = dblquad(@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}),ya, yb, za, zb, tol); 64 q = dblquad(@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}),ya, yb, za, zb, tol);
54 endfunction 65 endfunction
55 66
56 function Q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin) 67 function q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin)
57 Q = zeros (size(y)); 68 q = zeros (size(y));
58 for i = 1 : length (y) 69 for i = 1 : length (y)
59 Q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol); 70 q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol);
60 endfor 71 endfor
61 endfunction 72 endfunction
62 73
63 %% These tests are too expensive to run normally. Disable them 74 %% These tests are too expensive to run normally. Disable them
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) 75 % !#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)
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) 76 % !#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)
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) 77 % !#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)
78