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annotate scripts/general/trapz.m @ 11117:3cbc0d77db48 ss-3-3-53
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Tue, 19 Oct 2010 02:25:32 -0400 |
| parents | be55736a0783 |
| children | 1740012184f9 |
| rev | line source |
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| 8920 | 1 ## Copyright (C) 2000, 2006, 2007, 2008, 2009 Kai Habel |
| 5820 | 2 ## |
| 3 ## This file is part of Octave. | |
| 4 ## | |
| 5 ## Octave is free software; you can redistribute it and/or modify it | |
| 6 ## under the terms of the GNU General Public License as published by | |
| 7016 | 7 ## the Free Software Foundation; either version 3 of the License, or (at |
| 8 ## your option) any later version. | |
| 5820 | 9 ## |
| 10 ## Octave is distributed in the hope that it will be useful, but | |
| 11 ## WITHOUT ANY WARRANTY; without even the implied warranty of | |
| 12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU | |
| 13 ## General Public License for more details. | |
| 14 ## | |
| 15 ## You should have received a copy of the GNU General Public License | |
| 7016 | 16 ## along with Octave; see the file COPYING. If not, see |
| 17 ## <http://www.gnu.org/licenses/>. | |
| 5820 | 18 |
| 19 ## -*- texinfo -*- | |
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20 ## @deftypefn {Function File} {@var{z} =} trapz (@var{y}) |
| 5820 | 21 ## @deftypefnx {Function File} {@var{z} =} trapz (@var{x}, @var{y}) |
| 22 ## @deftypefnx {Function File} {@var{z} =} trapz (@dots{}, @var{dim}) | |
| 23 ## | |
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24 ## Numerical integration using trapezoidal method. @code{trapz |
| 5820 | 25 ## (@var{y})} computes the integral of the @var{y} along the first |
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26 ## non-singleton dimension. If the argument @var{x} is omitted a |
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27 ## equally spaced vector is assumed. @code{trapz (@var{x}, @var{y})} |
| 5820 | 28 ## evaluates the integral with respect to @var{x}. |
| 29 ## | |
| 30 ## @seealso{cumtrapz} | |
| 31 ## @end deftypefn | |
| 32 | |
| 10549 | 33 ## Author: Kai Habel <kai.habel@gmx.de> |
| 5820 | 34 ## |
| 35 ## also: June 2000 - Paul Kienzle (fixes,suggestions) | |
| 36 ## 2006-05-12 David Bateman - Modified for NDArrays | |
| 37 | |
| 38 function z = trapz (x, y, dim) | |
| 10549 | 39 |
| 5820 | 40 if (nargin < 1) || (nargin > 3) |
| 6046 | 41 print_usage (); |
| 5820 | 42 endif |
| 43 | |
| 44 nd = ndims (x); | |
| 45 sz = size (x); | |
| 46 | |
| 47 have_x = false; | |
| 48 have_dim = false; | |
| 49 if (nargin == 3) | |
| 50 have_x = true; | |
| 51 have_dim = true; | |
| 52 endif | |
| 53 if (nargin == 2) | |
| 6157 | 54 if (! size_equal (x, y) && isscalar (y)) |
| 5820 | 55 dim = y; |
| 56 have_dim = true; | |
| 57 else | |
| 58 have_x = true; | |
| 59 endif | |
| 60 endif | |
| 61 | |
| 62 if (! have_dim) | |
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63 ## Find the first non-singleton dimension. |
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64 dim = find (sz > 1, 1); |
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65 if (isempty (dim)) |
| 5820 | 66 dim = 1; |
| 67 endif | |
| 68 else | |
| 69 dim = floor (dim); | |
| 70 if (dim < 1 || dim > nd) | |
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71 error ("trapz: invalid dimension DIM along which to sort"); |
| 5820 | 72 endif |
| 73 endif | |
| 74 | |
| 75 n = sz(dim); | |
| 76 idx1 = cell (); | |
| 77 for i = 1:nd | |
| 78 idx1{i} = 1:sz(i); | |
| 79 endfor | |
| 80 idx2 = idx1; | |
| 10549 | 81 idx1{dim} = 2 : n; |
| 5820 | 82 idx2{dim} = 1 : (n - 1); |
| 83 | |
| 84 if (! have_x) | |
| 85 z = 0.5 * sum (x(idx1{:}) + x(idx2{:}), dim); | |
| 86 else | |
| 6157 | 87 if (! size_equal (x, y)) |
| 7992 | 88 error ("trapz: x and y must have same shape"); |
| 5820 | 89 endif |
| 90 z = 0.5 * sum ((x(idx1{:}) - x(idx2{:})) .* | |
| 10549 | 91 (y(idx1{:}) + y(idx2{:})), dim); |
| 5820 | 92 endif |
| 93 endfunction | |
| 94 | |
| 95 %!assert (trapz(1:5), 12) | |
| 96 %!assert (trapz(0:0.5:2,1:5), 6) | |
| 97 %!assert (trapz([1:5;1:5],2),[12;12]) | |
| 98 %!assert (trapz([1:5;1:5].',1),[12,12]) | |
| 99 %!assert (trapz([0:0.5:2;0:0.5:2],[1:5;1:5],2),[6;6]) | |
| 100 %!assert (trapz([0:0.5:2;0:0.5:2].',[1:5;1:5].',1),[6,6]) |