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dmalcom gcc jit import
author Stefan Mahr <dac922@gmx.de>
date Fri, 27 Feb 2015 16:59:36 +0100
parents 7503499a252b
children
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1 ## Copyright (C) 2008-2015 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} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb})
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21 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol})
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22 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf})
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23 ## @deftypefnx {Function File} {} triplequad (@var{f}, @var{xa}, @var{xb}, @var{ya}, @var{yb}, @var{za}, @var{zb}, @var{tol}, @var{quadf}, @dots{})
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24 ## Numerically evaluate the triple 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{w = f(x,y,z)} where either @var{x} or @var{y} is a vector and the
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29 ## remaining inputs are scalars. It should return a vector of the same length
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30 ## and orientation as @var{x} or @var{y}.
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31 ##
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32 ## @var{xa}, @var{ya}, @var{za} and @var{xb}, @var{yb}, @var{zb} are the lower
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33 ## and upper limits of integration for x, y, and z respectively. The
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34 ## underlying integrator determines whether infinite bounds are accepted.
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35 ##
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36 ## The optional argument @var{tol} defines the absolute tolerance used to
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37 ## integrate each sub-integral. The default value is 1e-6.
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38 ##
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39 ## The optional argument @var{quadf} specifies which underlying integrator
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40 ## function to use. Any choice but @code{quad} is available and the default
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41 ## is @code{quadcc}.
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42 ##
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43 ## Additional arguments, are passed directly to @var{f}. To use the default
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44 ## value for @var{tol} or @var{quadf} one may pass @qcode{':'} or an empty
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45 ## matrix ([]).
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46 ## @seealso{dblquad, quad, quadv, quadl, quadgk, quadcc, trapz}
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47 ## @end deftypefn
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48
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49 function q = triplequad (f, xa, xb, ya, yb, za, zb, tol = 1e-6, quadf = @quadcc, varargin)
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50
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51 if (nargin < 7)
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52 print_usage ();
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53 endif
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54
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55 ## Allow use of empty matrix ([]) to indicate default
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56 if (isempty (tol))
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57 tol = 1e-6;
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58 endif
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59 if (isempty (quadf))
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60 quadf = @quadcc;
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61 endif
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62
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63 inner = @__triplequad_inner__;
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64 if (ischar (f))
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65 f = @(x,y,z) feval (f, x, y, z, varargin{:});
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66 varargin = {};
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67 endif
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68
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69 q = dblquad (@(y, z) inner (y, z, f, xa, xb, tol, quadf, varargin{:}), ...
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70 ya, yb, za, zb, tol);
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71
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72 endfunction
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73
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74 function q = __triplequad_inner__ (y, z, f, xa, xb, tol, quadf, varargin)
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75 q = zeros (size (y));
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76 for i = 1 : length (y)
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77 q(i) = feval (quadf, @(x) f (x, y(i), z, varargin{:}), xa, xb, tol);
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78 endfor
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79 endfunction
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80
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81
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82 %!assert (triplequad (@(x,y,z) exp (-x.^2 - y.^2 - z.^2) , -1, 1, -1, 1, -1, 1, [], @quadcc), pi^(3/2) * erf (1).^3, 1e-6)
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83
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84 ## These tests are too expensive to run normally (~30 sec each). Disable them
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85 #%!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)
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86 #%!#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)
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87 #%!#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)
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88