Mercurial > octave-nkf
view scripts/ode/private/kahan.m @ 20596:87b557ee8e5d
clean up and vectorize code for dense output in ode45
* scripts/ode/private/ode_rk_interpolate.m: new file
* scripts/ode/private/ode_rk_interpolate.m(hermite_quartic_interpolation):
move to internal function, use vectorization and broadcasting.
* scripts/ode/private/hermite_quartic_interpolation.m: remove file
* scripts/ode/module.mk: list added and removed files
* scripts/ode/private/integrate_adaptive.m: use new interpolation code.
author | Carlo de Falco <carlo.defalco@polimi.it> |
---|---|
date | Tue, 06 Oct 2015 19:28:59 +0200 |
parents | eb9e2d187ed2 |
children |
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## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it> ## ## 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 ## <http://www.gnu.org/licenses/>. ## -*- texinfo -*- ## @deftypefn {Function File} {@var{sum} =} kahan (@var{sum}, @var{comp}, @var{temp}) ## @deftypefnx {Function File} {[@var{sum}, @var{comp}] =} kahan (@var{sum}, @var{comp}, @var{temp}) ## ## This function is the implementation of the Kahan summation algorithm, ## also known as compensated summation. ## ## It significantly reduces the numerical error in the total obtained by adding ## a sequence of finite precision floating point numbers, compared to the ## obvious approach. For more details ## see @url{http://en.wikipedia.org/wiki/Kahan_summation_algorithm}. ## This function is called in @command{integrate_adaptive} and in ## @command{integrate_const} to better catch equality comparisons. ## ## The first input argument is the variable that will contain the summation, ## so that is also returned as first output argument in order to reuse it in ## next calls to kahan function. ## ## The second input argument contains the compensation term and it is returned ## as second output argument so that it can be reused in the next calls of the ## same computation. ## ## The third input argument is the variable that contains the term to be added ## to @var{Sum}. ## @end deftypefn function [Sum, comp] = kahan (Sum, comp, term) y = term - comp; t = Sum + y; comp = (t - Sum) - y; Sum = t; endfunction