Mercurial > octave
annotate scripts/general/dblquad.m @ 24545:ba8b828ee4f2 stable
doc: Replace @math{1e^{XXX}} sequences with raw 1eXXX (bug #52827).
Expansion in TeX leads to incorrect interpretation of 1 * e^{XXX}
rather than 1 * 10^{XXX}.
* quad.txi, quad.cc (Fquad), quadcc.cc (Fquad.cc), dblquad.m, quadl.m:
Replace @math{1e^{XXX}} sequences with raw 1eXXX (bug #52827).
author | Rik <rik@octave.org> |
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date | Sun, 07 Jan 2018 08:26:41 -0800 |
parents | 3ac9f9ecfae5 |
children | d3a507ca2d5d |
rev | line source |
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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 (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 {} {} 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{triplequad, quad, quadv, quadl, quadgk, quadcc, trapz} |
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46 ## @end deftypefn |
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47 |
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48 function q = dblquad (f, xa, xb, ya, yb, tol = 1e-6, quadf = @quadcc, varargin) |
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49 |
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50 if (nargin < 5) |
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51 print_usage (); |
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52 endif |
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53 if (isempty (tol)) |
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54 tol = 1e-6; |
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55 endif |
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56 if (isempty (quadf)) |
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57 quadf = @quadcc; |
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58 endif |
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59 |
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60 inner = @__dblquad_inner__; |
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61 if (ischar (f)) |
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62 f = @(x,y) feval (f, x, y, varargin{:}); |
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63 varargin = {}; |
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64 endif |
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65 |
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10549 | 67 varargin{:}), ya, yb, tol); |
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68 |
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69 endfunction |
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70 |
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72 q = zeros (size (y)); |
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73 for i = 1 : length (y) |
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75 endfor |
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76 endfunction |
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77 |
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78 |
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79 ## Nasty integrand to show quadcc off |
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80 %!assert (dblquad (@(x,y) 1 ./ (x+y), 0, 1, 0, 1), 2*log (2), 1e-6) |
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81 |
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82 %!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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83 %!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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84 %!assert (dblquad (@(x,y) exp (-x.^2 - y.^2) , -1, 1, -1, 1, 1e-6, @quadv), pi * erf (1).^2, 1e-6) |