Mercurial > octave
view scripts/general/cumtrapz.m @ 31248:8b75954a4670
delaunayn: adjust node ordering for positive outward normal vectors (bug #53397)
* delaunayn.m: Check sign of simplex volume, flip node order for negative
volumes to ensure positive (outward-pointing) normal vectors. Add BISTs to
check for positive volumes.
* etc/News.8.md: Append function improvement note to delaunayn change
paragraph under General Improvements.
author | Nicholas R. Jankowski <jankowski.nicholas@gmail.com> |
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date | Thu, 29 Sep 2022 23:09:05 -0400 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2000-2022 The Octave Project Developers ## ## See the file COPYRIGHT.md in the top-level directory of this ## distribution or <https://octave.org/copyright/>. ## ## This file is part of Octave. ## ## Octave is free software: you can redistribute it and/or modify it ## under the terms of the GNU General Public License as published by ## the Free Software Foundation, either version 3 of the License, or ## (at your option) any later version. ## ## Octave is distributed in the hope that it will be useful, but ## WITHOUT ANY WARRANTY; without even the implied warranty of ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the ## GNU General Public License for more details. ## ## You should have received a copy of the GNU General Public License ## along with Octave; see the file COPYING. If not, see ## <https://www.gnu.org/licenses/>. ## ######################################################################## ## -*- texinfo -*- ## @deftypefn {} {@var{q} =} cumtrapz (@var{y}) ## @deftypefnx {} {@var{q} =} cumtrapz (@var{x}, @var{y}) ## @deftypefnx {} {@var{q} =} cumtrapz (@dots{}, @var{dim}) ## Cumulative numerical integration of points @var{y} using the trapezoidal ## method. ## ## @w{@code{cumtrapz (@var{y})}} computes the cumulative integral of @var{y} ## along the first non-singleton dimension. Where @code{trapz} reports only ## the overall integral sum, @code{cumtrapz} reports the current partial sum ## value at each point of @var{y}. ## ## When the argument @var{x} is omitted an equally spaced @var{x} vector with ## unit spacing (1) is assumed. @code{cumtrapz (@var{x}, @var{y})} evaluates ## the integral with respect to the spacing in @var{x} and the values in ## @var{y}. This is useful if the points in @var{y} have been sampled ## unevenly. ## ## If the optional @var{dim} argument is given, operate along this dimension. ## ## Application Note: If @var{x} is not specified then unit spacing will be ## used. To scale the integral to the correct value you must multiply by the ## actual spacing value (deltaX). ## @seealso{trapz, cumsum} ## @end deftypefn function z = cumtrapz (x, y, dim) if (nargin < 1) print_usage (); endif have_xy = have_dim = false; if (nargin == 3) have_xy = true; have_dim = true; elseif (nargin == 2) if (isscalar (y) && ! isscalar (x)) have_dim = true; dim = y; else have_xy = true; endif endif if (have_xy) nd = ndims (y); sz = size (y); else nd = ndims (x); sz = size (x); endif if (! have_dim) ## Find the first non-singleton dimension. (dim = find (sz > 1, 1)) || (dim = 1); else if (!(isscalar (dim) && dim == fix (dim)) || !(1 <= dim && dim <= nd)) error ("trapz: DIM must be an integer and a valid dimension"); endif endif n = sz(dim); idx1 = idx2 = {':'}(ones (nd, 1)); # repmat ({':'}, [nd, 1]), but faster idx1{dim} = 2 : n; idx2{dim} = 1 : (n - 1); if (! have_xy) z = 0.5 * cumsum (x(idx1{:}) + x(idx2{:}), dim); elseif (isscalar (x)) z = x * 0.5 * cumsum (y(idx1{:}) + y(idx2{:}), dim); elseif (isvector (x)) if (length (x) != n) error ("cumtrapz: length of X and length of Y along DIM must match"); endif ## Reshape vector to point along dimension DIM shape = ones (nd, 1); shape(dim) = n; x = reshape (x, shape); z = 0.5 * cumsum (diff (x) .* (y(idx1{:}) + y(idx2{:})), dim); else if (! size_equal (x, y)) error ("cumtrapz: X and Y must have same shape"); endif z = 0.5 * cumsum (diff (x, 1, dim) .* (y(idx1{:}) + y(idx2{:})), dim); endif sz(dim) = 1; z = cat (dim, zeros (sz), z); endfunction %!shared x1, x2, y %! x1 = [1:5]; %! x2 = [2:2:10]; %! y = [1:5]; %! %!assert (cumtrapz (y), [0, 1.5, 4, 7.5, 12]) %!assert (cumtrapz (y'), [0, 1.5, 4, 7.5, 12]') %!assert (cumtrapz (1, y), [0, 1.5, 4, 7.5, 12]) %!assert (cumtrapz (2, y), [0, 3, 8, 15, 24]) %!assert (cumtrapz (x1, y),[0, 1.5, 4, 7.5, 12]) %!assert (cumtrapz (x2, y),[0, 3, 8, 15, 24]) %!assert (cumtrapz (2, y, 2), [0, 3, 8, 15, 24]) %!assert (cumtrapz (x2, y, 2), [0, 3, 8, 15, 24]) %!assert (cumtrapz (y, 1), [0, 0, 0, 0, 0]) %!assert (cumtrapz (2, y, 1), [0, 0, 0, 0, 0]) %!assert (cumtrapz (y', 2), [0, 0, 0, 0, 0]') %!shared x1, x2, y %! x1 = [0,0,0;2,2,2]; %! x2 = [0,2,4;0,2,4]; %! y = [1,2,3;4,5,6]; %! %!assert (cumtrapz (y), [0,0,0;2.5,3.5,4.5]) %!assert (cumtrapz (x1, y), [0,0,0;5,7,9]) %!assert (cumtrapz (y, 1), [0,0,0;2.5,3.5,4.5]) %!assert (cumtrapz (x1, y, 1), [0,0,0;5,7,9]) %!assert (cumtrapz (y, 2), [0,1.5,4;0,4.5,10]) %!assert (cumtrapz (x2, y, 2), [0,3,8;0,9,20]) ## Test ND-array implementation %!shared x1,x2,y %! x1 = 1:3; %! x2 = reshape ([0,2,4;0,2,4], [1 2 3]); %! y = reshape ([1,2,3;4,5,6], [1 2 3]); %! %!assert (cumtrapz (y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3])) %!assert (cumtrapz (x1,y,3), reshape ([0,1.5,4;0,4.5,10],[1 2 3])) %!assert (cumtrapz (x2,y,3), reshape ([0,3,8;0,9,20],[1 2 3])) ## Test input validation %!error <Invalid call> cumtrapz () %!error <DIM must be an integer> cumtrapz (1, 2, [1 2]) %!error <DIM must be an integer> cumtrapz (1, 2, 1.5) %!error <DIM must be .* a valid dimension> cumtrapz (1, 2, 0) %!error <length of X and length of Y.*must match> cumtrapz ([1 2], [1 2 3]) %!error <X and Y must have same shape> cumtrapz (ones (2,3), ones (2,4))