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maint: merge stable to default.
author Rik <rik@octave.org>
date Sun, 07 Jan 2018 09:57:32 -0800
parents 194eb4bd202b ba8b828ee4f2
children 6652d3823428
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1 ## Copyright (C) 2008-2017 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
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8 ## (at 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
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13 ## GNU 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 ## <https://www.gnu.org/licenses/>.
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18
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19 ## -*- texinfo -*-
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20 ## @deftypefn {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb})
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21 ## @deftypefnx {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol})
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22 ## @deftypefnx {} {} dblquad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{tol}, @var{quadf})
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23 ## @deftypefnx {} {} 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 ##
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26 ## @var{f} is a function handle, inline function, or string containing the name
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27 ## of the function to evaluate. The function @var{f} must have the form
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28 ## @math{z = f(x,y)} where @var{x} is a vector and @var{y} is a scalar. It
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29 ## should return a vector of the same length and orientation as @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 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{quadcc}.
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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 @qcode{':'} or an empty
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44 ## matrix ([]).
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45 ## @seealso{integral2, integral3, triplequad, quad, quadv, quadl, quadgk,
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46 ## quadcc, trapz}
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47 ## @end deftypefn
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48
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49 function q = dblquad (f, xa, xb, ya, yb, tol = 1e-6, quadf = @quadcc, varargin)
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50
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51 if (nargin < 5)
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52 print_usage ();
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53 endif
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54 if (isempty (tol))
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55 tol = 1e-6;
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56 endif
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57 if (isempty (quadf))
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58 quadf = @quadcc;
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59 endif
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60
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61 inner = @__dblquad_inner__;
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62 if (ischar (f))
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63 f = @(x,y) feval (f, x, y, varargin{:});
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64 varargin = {};
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65 endif
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66
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67 q = feval (quadf, @(y) inner (y, f, xa, xb, tol, quadf,
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68 varargin{:}), ya, yb, tol);
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69
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70 endfunction
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71
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72 function q = __dblquad_inner__ (y, f, xa, xb, tol, quadf, varargin)
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73 q = zeros (size (y));
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74 for i = 1 : length (y)
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75 q(i) = feval (quadf, @(x) f(x, y(i), varargin{:}), xa, xb, tol);
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76 endfor
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77 endfunction
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78
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79
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80 ## Nasty integrand to show quadcc off
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81 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log (2), 1e-6)
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82
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83 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadgk), pi * erf (1).^2, 1e-6)
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84 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadl), pi * erf (1).^2, 1e-6)
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85 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadv), pi * erf (1).^2, 1e-6)