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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
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1 ## Copyright (C) 2008-2011 David Bateman
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
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21 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
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22 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
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23 ## @deftypefnx {Function File} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf}, @dots{})
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24 ## Numerically evaluate the double integral of @var{f}.
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25 ## @var{f} is a function handle, inline function, or string
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26 ## containing the name of the function to evaluate. The function @var{f} must
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27 ## have the form @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a
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28 ## scalar. It should return a vector of the same length and orientation as
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29 ## @var{x}.
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30 ##
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31 ## @var{xa}, @var{ya} and @var{xb}, @var{yb} are the lower and upper limits of
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32 ## integration for x and y respectively. The underlying integrator determines
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33 ## whether infinite bounds are accepted.
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34 ##
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35 ## The optional argument @var{tol} defines the absolute tolerance used to
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36 ## integrate each sub-integral. The default value is @math{1e^{-6}}.
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37 ##
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38 ## The optional argument @var{quadf} specifies which underlying integrator
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39 ## function to use. Any choice but @code{quad} is available and the default
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40 ## is @code{quadgk}.
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41 ##
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42 ## Additional arguments, are passed directly to @var{f}. To use the default
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43 ## value for @var{tol} or @var{quadf} one may pass an empty matrix ([]).
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44 ## @seealso{triplequad, quad, quadv, quadl, quadgk, quadcc, trapz}
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45 ## @end deftypefn
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46
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47 function q = dblquad(f, xa, xb, ya, yb, tol, quadf, varargin)
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48 if (nargin < 5)
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49 print_usage ();
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50 endif
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51 if (nargin < 6 || isempty (tol))
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52 tol = 1e-6;
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53 endif
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54 if (nargin < 7 || isempty (quadf))
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55 quadf = @quadgk;
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56 endif
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57
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58 inner = @__dblquad_inner__;
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59 if (ischar (f))
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60 f = @(x,y) feval (f, x, y, varargin{:});
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61 varargin = {};
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62 endif
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63
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64 q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
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65 varargin{:}), ya, yb, tol);
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66 endfunction
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67
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68 function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
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69 q = zeros (size(y));
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70 for i = 1 : length (y)
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71 q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
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72 endfor
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73 endfunction
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74
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75 %% Nasty integrand to show quadgk off
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76 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log(2), 1e-6)
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77
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78 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadgk), pi * erf(1).^2, 1e-6)
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79 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadl), pi * erf(1).^2, 1e-6)
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80 %!assert (dblquad (@(x,y) exp(-x.^2 - y.^2) , -1, 1, -1, 1, [], @quadv), pi * erf(1).^2, 1e-6)
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