1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
|
########################################################################
##
## Copyright (C) 2008-2024 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################
## -*- texinfo -*-
## @deftypefn {} {@var{q} =} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
## @deftypefnx {} {@var{q} =} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
## @deftypefnx {} {@var{q} =} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
## @deftypefnx {} {@var{q} =} 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 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 @qcode{':'} or an empty
## matrix ([]).
## @seealso{integral2, integral3, 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)
|
