Mercurial > octave-nkf
view scripts/ode/private/runge_kutta_45_dorpri.m @ 20620:e5f36a7854a5
Remove fuzzy matching from odeset/odeget.
* levenshtein.cc: Deleted file.
* libinterp/corefcn/module.mk: Remove levenshtein.cc from build system.
* fuzzy_compare.m: Deleted file.
* scripts/ode/module.mk: Remove fuzzy_compare.m from build system
* odeget.m: Reword docstring. Use a persistent cellstr variable to keep track
of all options. Replace fuzzy_compare() calls with combination of strcmpi and
strncmpi. Report errors relative to function odeget rather than OdePkg.
Rewrite and extend BIST tests. Add input validation BIST tests.
* odeset.m: Reword docstring. Use a persistent cellstr variable to keep track
of all options. Replace fuzzy_compare() calls with combination of strcmpi and
strncmpi. Report errors relative to function odeset rather than OdePkg.
Use more meaningful variables names and create intermediate variables with
logical names to help make code readable. Remove interactive input when
multiple property names match and just issue an error. Rewrite BIST tests.
* ode_struct_value_check.m: Remove input checking for private function which
must always be invoked correctly by caller. Use intermediate variables opt and
val to make the code more understandable. Consolidate checks on values into
single if statements. Use 'val == fix (val)' to check for integer.
* __unimplemented__.m: Removed odeset, odeget, ode45 from list.
author | Rik <rik@octave.org> |
---|---|
date | Fri, 09 Oct 2015 12:03:23 -0700 |
parents | b7ac1e94266e |
children | a22d8a2eb0e5 |
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## Copyright (C) 2015, Carlo de Falco ## 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{t_next}, @var{x_next}] =} runge_kutta_45_dorpri (@var{@@fun}, @var{t}, @var{x}, @var{dt}, @var{options}, @var{k_vals_in}) ## @deftypefnx {Function File} {[@var{t_next}, @var{x_next}, @var{x_est}] =} runge_kutta_45_dorpri (@var{@@fun}, @var{t}, @var{x}, @var{dt}, @var{options}, @var{k_vals_in}) ## @deftypefnx {Function File} {[@var{t_next}, @var{x_next}, @var{x_est}, @var{k_vals_out}] =} runge_kutta_45_dorpri (@var{@@fun}, @var{t}, @var{x}, @var{dt}, @var{options}, @var{k_vals_in}) ## ## This function can be used to integrate a system of ODEs with a given initial ## condition @var{x} from @var{t} to @var{t+dt}, with the Dormand-Prince method. ## For the definition of this method see ## @url{http://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method}. ## ## First output argument is the final integration time value. ## ## Second output parameter is the higher order computed solution at time ## @var{t_next} (local extrapolation). ## ## Third output parameter is a lower order solution for the estimation of the ## error. ## ## Fourth output parameter is matrix containing the Runge-Kutta evaluations ## to use in a FSAL scheme or for dense output. ## ## First input argument is the function describing the system of ODEs to be ## integrated. ## ## Second input parameter is the first extreme of integration interval. ## ## Third input argument is the initial condition of the system. ## ## Fourth input argument is the timestep, that is the length of the ## integration interval. ## ## Fifth input parameter is optional and describes a set of options useful to ## adapt the computation to what is needed. ## ## Sixth input parameter is optional and describes the Runge-Kutta evaluations ## of the previous step to use in a FSAL scheme. ## @end deftypefn ## ## @seealso{odepkg} function [t_out, x_out, x_est, k] = ... runge_kutta_45_dorpri (f, t, x, dt, varargin) persistent a = [0 0 0 0 0 0; 1/5 0 0 0 0 0; 3/40 9/40 0 0 0 0; 44/45 -56/15 32/9 0 0 0; 19372/6561 -25360/2187 64448/6561 -212/729 0 0; 9017/3168 -355/33 46732/5247 49/176 -5103/18656 0; 35/384 0 500/1113 125/192 -2187/6784 11/84]; persistent b = [0 1/5 3/10 4/5 8/9 1 1]; persistent c = [(35/384) 0 (500/1113) (125/192) (-2187/6784) (11/84)]; ## x_est according to Shampine 1986: ## persistent c_prime = [(1951/21600) 0 (22642/50085) (451/720), ... ## (-12231/42400) (649/6300) (1/60)]; persistent c_prime = [(5179/57600) 0 (7571/16695) (393/640), ... (-92097/339200) (187/2100) (1/40)]; s = t + dt * b; cc = dt * c; aa = dt * a; k = zeros (rows (x), 7); if (nargin >= 5) # options are passed args = varargin{1}.vfunarguments; if (nargin >= 6) # both the options and the k values are passed k(:,1) = varargin{2}(:,end); # FSAL property else k(:,1) = feval (f, t, x, args{:}); endif else args = {}; endif k(:,2) = feval (f, s(2), x + k(:,1) * aa(2, 1).', args{:}); k(:,3) = feval (f, s(3), x + k(:,1:2) * aa(3, 1:2).', args{:}); k(:,4) = feval (f, s(4), x + k(:,1:3) * aa(4, 1:3).', args{:}); k(:,5) = feval (f, s(5), x + k(:,1:4) * aa(5, 1:4).', args{:}); k(:,6) = feval (f, s(6), x + k(:,1:5) * aa(6, 1:5).', args{:}); ## compute new time and new values for the unknowns t_out = t + dt; x_out = x + k(:,1:6) * cc(:); # 5th order approximation ## if the estimation of the error is required if (nargout >= 3) ## new solution to be compared with the previous one k(:,7) = feval (f, t + dt, x_out, args{:}); cc_prime = dt * c_prime; x_est = x + k * cc_prime(:); endif endfunction