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annotate scripts/general/trapz.m @ 9051:1bf0ce0930be
Grammar check TexInfo in all .m files
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| author | Rik <rdrider0-list@yahoo.com> |
|---|---|
| date | Fri, 27 Mar 2009 22:31:03 -0700 |
| parents | eb63fbe60fab |
| children | 95c3e38098bf |
| rev | line source |
|---|---|
| 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 -*- | |
| 20 ## @deftypefn {Function File} {@var{z} =} trapz (@var{y}) | |
| 21 ## @deftypefnx {Function File} {@var{z} =} trapz (@var{x}, @var{y}) | |
| 22 ## @deftypefnx {Function File} {@var{z} =} trapz (@dots{}, @var{dim}) | |
| 23 ## | |
|
9051
1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
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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9051
1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
26 ## non-singleton dimension. If the argument @var{x} is omitted a |
|
1bf0ce0930be
Grammar check TexInfo in all .m files
Rik <rdrider0-list@yahoo.com>
parents:
8920
diff
changeset
|
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 | |
| 33 ## Author: Kai Habel <kai.habel@gmx.de> | |
| 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) | |
| 39 | |
| 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; | |
| 53 endif | |
| 54 if (nargin == 2) | |
| 6157 | 55 if (! size_equal (x, y) && isscalar (y)) |
| 5820 | 56 dim = y; |
| 57 have_dim = true; | |
| 58 else | |
| 59 have_x = true; | |
| 60 endif | |
| 61 endif | |
| 62 | |
| 63 if (! have_dim) | |
| 64 ## Find the first singleton dimension. | |
| 65 dim = 0; | |
| 66 while (dim < nd && sz(dim+1) == 1) | |
| 67 dim++; | |
| 68 endwhile | |
| 69 dim++; | |
| 70 if (dim > nd) | |
| 71 dim = 1; | |
| 72 endif | |
| 73 else | |
| 74 dim = floor (dim); | |
| 75 if (dim < 1 || dim > nd) | |
| 7992 | 76 error ("trapz: invalid dimension along which to sort"); |
| 5820 | 77 endif |
| 78 endif | |
| 79 | |
| 80 n = sz(dim); | |
| 81 idx1 = cell (); | |
| 82 for i = 1:nd | |
| 83 idx1{i} = 1:sz(i); | |
| 84 endfor | |
| 85 idx2 = idx1; | |
| 86 idx1{dim} = 2 : n; | |
| 87 idx2{dim} = 1 : (n - 1); | |
| 88 | |
| 89 if (! have_x) | |
| 90 z = 0.5 * sum (x(idx1{:}) + x(idx2{:}), dim); | |
| 91 else | |
| 6157 | 92 if (! size_equal (x, y)) |
| 7992 | 93 error ("trapz: x and y must have same shape"); |
| 5820 | 94 endif |
| 95 z = 0.5 * sum ((x(idx1{:}) - x(idx2{:})) .* | |
| 96 (y(idx1{:}) + y(idx2{:})), dim); | |
| 97 endif | |
| 98 endfunction | |
| 99 | |
| 100 %!assert (trapz(1:5), 12) | |
| 101 %!assert (trapz(0:0.5:2,1:5), 6) | |
| 102 %!assert (trapz([1:5;1:5],2),[12;12]) | |
| 103 %!assert (trapz([1:5;1:5].',1),[12,12]) | |
| 104 %!assert (trapz([0:0.5:2;0:0.5:2],[1:5;1:5],2),[6;6]) | |
| 105 %!assert (trapz([0:0.5:2;0:0.5:2].',[1:5;1:5].',1),[6,6]) |