Mercurial > octave
annotate scripts/general/cumtrapz.m @ 12642:f96b9b9f141b stable
doc: Periodic grammarcheck and spellcheck of documentation.
* func.txi: Correct two misspellings
* cumtrapz.m, dblquad.m, quadgk.m, quadl.m, quadv.m, trapz.m, triplequad.m,
cond.m, gmres.m, bzip2.m, compare_versions.m, getappdata.m, unpack.m, ver.m,
glpk.m, pkg.m, axis.m, uigetdir.m, uigetfile.m, view.m, prctile.m, quantile.m,
unidcdf.m, unidinv.m, isstrprop.m, balance.cc, besselj.cc, cellfun.cc,
colamd.cc, dot.cc, eigs.cc, fftw.cc, matrix_type.cc, pinv.cc, qr.cc, quad.cc,
quadcc.cc, qz.cc, regexp.cc, schur.cc, time.cc (gmtime), typecast.cc
urlwrite.cc bitfcns.cc (bitshift), data.cc (rem, norm, merge) debug.cc
(dbstatus), dirfns.cc (glob), file-io.cc (freport), load-path.cc (genpath),
load-save.cc (save), mappers.cc (islower, isupper, tolower, toupper)
oct-hist.cc (edit_history), ov-fcn-inline.cc (vectorize), ov.cc (subsref),
syscalls.cc (stat), variables.cc (whos, clear): Improve docstrings.
Removed trailing whitespace characters on line.
| author | Rik <octave@nomad.inbox5.com> |
|---|---|
| date | Sun, 01 May 2011 11:39:50 -0700 |
| parents | 16cca721117b |
| children | d8aff843a9e9 |
| rev | line source |
|---|---|
| 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{q} =} cumtrapz (@var{y}) |
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21 ## @deftypefnx {Function File} {@var{q} =} cumtrapz (@var{x}, @var{y}) |
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22 ## @deftypefnx {Function File} {@var{q} =} cumtrapz (@dots{}, @var{dim}) |
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23 ## |
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24 ## Cumulative numerical integration of points @var{y} using the trapezoidal |
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25 ## method. |
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26 ## @w{@code{cumtrapz (@var{y})}} computes the cumulative integral of @var{y} |
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27 ## along the first non-singleton dimension. Where @code{trapz} reports |
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28 ## only the overall integral sum, @code{cumtrapz} reports the current partial |
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29 ## sum value at each point of @var{y}. When the argument @var{x} is omitted |
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30 ## an equally spaced @var{x} vector with unit spacing (1) is assumed. |
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31 ## @code{cumtrapz (@var{x}, @var{y})} evaluates the integral with respect to |
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32 ## the spacing in @var{x} and the values in @var{y}. This is useful if the |
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33 ## points in @var{y} have been sampled unevenly. If the optional @var{dim} |
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34 ## argument is given, operate along this dimension. |
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35 ## |
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36 ## If @var{x} is not specified then unit spacing will be used. To scale |
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37 ## the integral to the correct value you must multiply by the actual spacing |
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38 ## value (deltaX). |
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39 ## @seealso{trapz, cumsum} |
| 5820 | 40 ## @end deftypefn |
| 41 | |
| 10549 | 42 ## Author: Kai Habel <kai.habel@gmx.de> |
| 5820 | 43 ## |
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44 ## also: June 2000 Paul Kienzle (fixes,suggestions) |
| 5820 | 45 ## 2006-05-12 David Bateman - Modified for NDArrays |
| 46 | |
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47 function z = cumtrapz (x, y, dim) |
| 5820 | 48 |
| 49 if (nargin < 1) || (nargin > 3) | |
| 6046 | 50 print_usage (); |
| 5820 | 51 endif |
| 52 | |
| 53 nd = ndims (x); | |
| 54 sz = size (x); | |
| 55 | |
| 56 have_x = false; | |
| 57 have_dim = false; | |
| 58 if (nargin == 3) | |
| 59 have_x = true; | |
| 60 have_dim = true; | |
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61 elseif (nargin == 2) |
| 6157 | 62 if (! size_equal (x, y) && isscalar (y)) |
| 5820 | 63 dim = y; |
| 64 have_dim = true; | |
| 65 else | |
| 66 have_x = true; | |
| 67 endif | |
| 68 endif | |
| 69 | |
| 70 if (! have_dim) | |
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71 ## Find the first non-singleton dimension. |
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72 dim = find (sz > 1, 1); |
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73 if (isempty (dim)) |
| 5820 | 74 dim = 1; |
| 75 endif | |
| 76 else | |
| 77 dim = floor (dim); | |
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78 if (! (isscalar (dim) && 1 <= dim && dim <= nd)) |
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79 error ("cumtrapz: invalid dimension DIM"); |
| 5820 | 80 endif |
| 81 endif | |
| 82 | |
| 83 n = sz(dim); | |
| 84 idx1 = cell (); | |
| 85 for i = 1:nd | |
| 86 idx1{i} = 1:sz(i); | |
| 87 endfor | |
| 88 idx2 = idx1; | |
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89 idx1{dim} = 2 : n; |
| 5820 | 90 idx2{dim} = 1 : (n - 1); |
| 91 | |
| 92 if (! have_x) | |
| 93 z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim); | |
| 94 else | |
| 6157 | 95 if (! size_equal (x, y)) |
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96 error ("cumtrapz: X and Y must have the same shape"); |
| 5820 | 97 endif |
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98 z = 0.5 * cumsum ((x(idx1{:}) - x(idx2{:})) .* |
| 10549 | 99 (y(idx1{:}) + y(idx2{:})), dim); |
| 5820 | 100 endif |
| 101 | |
| 102 sz(dim) = 1; | |
| 103 z = cat (dim, zeros (sz), z); | |
| 104 | |
| 105 endfunction | |
| 106 | |
| 107 %!shared x1,x2,y | |
| 108 %! x1 = [0,0,0;2,2,2]; | |
| 109 %! x2 = [0,2,4;0,2,4]; | |
| 110 %! y = [1,2,3;4,5,6]; | |
| 111 %!assert (cumtrapz(y),[0,0,0;2.5,3.5,4.5]) | |
| 112 %!assert (cumtrapz(x1,y),[0,0,0;5,7,9]) | |
| 113 %!assert (cumtrapz(y,1),[0,0,0;2.5,3.5,4.5]) | |
| 114 %!assert (cumtrapz(x1,y,1),[0,0,0;5,7,9]) | |
| 115 %!assert (cumtrapz(y,2),[0,1.5,4;0,4.5,10]) | |
| 116 %!assert (cumtrapz(x2,y,2),[0,3,8;0,9,20]) |