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annotate scripts/general/cumtrapz.m @ 11523:fd0a3ac60b0e
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| author | John W. Eaton <jwe@octave.org> |
|---|---|
| date | Fri, 14 Jan 2011 05:47:45 -0500 |
| parents | 35adf2a71f3f |
| children | c792872f8942 |
| rev | line source |
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| 11523 | 1 ## Copyright (C) 2000-2011 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} =} cumtrapz (@var{y}) |
| 5820 | 21 ## @deftypefnx {Function File} {@var{z} =} cumtrapz (@var{x}, @var{y}) |
| 22 ## @deftypefnx {Function File} {@var{z} =} cumtrapz (@dots{}, @var{dim}) | |
| 23 ## | |
| 7001 | 24 ## Cumulative numerical integration using trapezoidal method. |
| 25 ## @code{cumtrapz (@var{y})} computes the cumulative integral of the | |
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26 ## @var{y} along the first non-singleton dimension. If the argument |
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27 ## @var{x} is omitted an equally spaced vector is assumed. @code{cumtrapz |
| 7001 | 28 ## (@var{x}, @var{y})} evaluates the cumulative integral with respect |
| 5820 | 29 ## to @var{x}. |
| 30 ## | |
| 31 ## @seealso{trapz,cumsum} | |
| 32 ## @end deftypefn | |
| 33 | |
| 10549 | 34 ## Author: Kai Habel <kai.habel@gmx.de> |
| 5820 | 35 ## |
| 36 ## also: June 2000 Paul Kienzle (fixes,suggestions) | |
| 37 ## 2006-05-12 David Bateman - Modified for NDArrays | |
| 38 | |
| 10549 | 39 function z = cumtrapz (x, y, dim) |
| 5820 | 40 |
| 41 if (nargin < 1) || (nargin > 3) | |
| 6046 | 42 print_usage (); |
| 5820 | 43 endif |
| 44 | |
| 45 nd = ndims (x); | |
| 46 sz = size (x); | |
| 47 | |
| 48 have_x = false; | |
| 49 have_dim = false; | |
| 50 if (nargin == 3) | |
| 51 have_x = true; | |
| 52 have_dim = true; | |
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53 elseif (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); | |
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70 if (! (isscalar (dim) && 1 <= dim && dim <= nd)) |
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71 error ("cumtrapz: invalid dimension DIM"); |
| 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 * cumsum (x(idx1{:}) + x(idx2{:}), dim); | |
| 86 else | |
| 6157 | 87 if (! size_equal (x, y)) |
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88 error ("cumtrapz: X and Y must have the same shape"); |
| 5820 | 89 endif |
| 90 z = 0.5 * cumsum ((x(idx1{:}) - x(idx2{:})) .* | |
| 10549 | 91 (y(idx1{:}) + y(idx2{:})), dim); |
| 5820 | 92 endif |
| 93 | |
| 94 sz(dim) = 1; | |
| 95 z = cat (dim, zeros (sz), z); | |
| 96 | |
| 97 endfunction | |
| 98 | |
| 99 %!shared x1,x2,y | |
| 100 %! x1 = [0,0,0;2,2,2]; | |
| 101 %! x2 = [0,2,4;0,2,4]; | |
| 102 %! y = [1,2,3;4,5,6]; | |
| 103 %!assert (cumtrapz(y),[0,0,0;2.5,3.5,4.5]) | |
| 104 %!assert (cumtrapz(x1,y),[0,0,0;5,7,9]) | |
| 105 %!assert (cumtrapz(y,1),[0,0,0;2.5,3.5,4.5]) | |
| 106 %!assert (cumtrapz(x1,y,1),[0,0,0;5,7,9]) | |
| 107 %!assert (cumtrapz(y,2),[0,1.5,4;0,4.5,10]) | |
| 108 %!assert (cumtrapz(x2,y,2),[0,3,8;0,9,20]) |