Mercurial > octave
view scripts/ode/private/starting_stepsize.m @ 30893:e1788b1a315f
maint: Use "fcn" as preferred abbreviation for "function" in m-files.
* accumarray.m, accumdim.m, quadl.m, quadv.m, randi.m, structfun.m,
__is_function__.m, uigetfile.m, uimenu.m, uiputfile.m, doc_cache_create.m,
colorspace_conversion_input_check.m, imageIO.m, argnames.m, vectorize.m,
vectorize.m, normest1.m, inputname.m, nthargout.m, display_info_file.m,
decic.m, ode15i.m, ode15s.m, ode23.m, ode23s.m, ode45.m, odeset.m,
check_default_input.m, integrate_adaptive.m, ode_event_handler.m,
runge_kutta_23.m, runge_kutta_23s.m, runge_kutta_45_dorpri.m,
runge_kutta_interpolate.m, starting_stepsize.m, __all_opts__.m, fminbnd.m,
fminsearch.m, fminunc.m, fsolve.m, fzero.m, sqp.m, fplot.m, plotyy.m,
__bar__.m, __ezplot__.m, flat_entry.html, profexport.m, movfun.m, bicg.m,
bicgstab.m, cgs.m, eigs.m, gmres.m, pcg.m, __alltohandles__.m, __sprand__.m,
qmr.m, tfqmr.m, dump_demos.m:
Replace "func", "fun", "fn" in documentation and variable names with "fcn".
author | Rik <rik@octave.org> |
---|---|
date | Mon, 04 Apr 2022 18:14:56 -0700 |
parents | 796f54d4ddbf |
children | 597f3ee61a48 |
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######################################################################## ## ## Copyright (C) 2013-2022 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{h} =} starting_stepsize (@var{order}, @var{fcn}, @var{t0}, @var{x0}, @var{AbsTol}, @var{RelTol}, @var{normcontrol}, @var{args}) ## ## Determine a good initial timestep for an ODE solver of order @var{order} ## using the algorithm described in reference [1]. ## ## The input argument @var{fcn}, is the function describing the differential ## equations, @var{t0} is the initial time, and @var{x0} is the initial ## condition. @var{AbsTol} and @var{RelTol} are the absolute and relative ## tolerance on the ODE integration taken from an ode options structure. ## ## Reference: ## E. Hairer, S.P. Norsett and G. Wanner, ## @cite{Solving Ordinary Differential Equations I: Nonstiff Problems}, ## Springer. ## @end deftypefn ## ## @seealso{odepkg} function h = starting_stepsize (order, fcn, t0, x0, AbsTol, RelTol, normcontrol, args = {}) ## compute norm of initial conditions d0 = AbsRel_norm (x0, x0, AbsTol, RelTol, normcontrol); ## compute norm of the function evaluated at initial conditions y = fcn (t0, x0, args{:}); if (iscell (y)) y = y{1}; endif d1 = AbsRel_norm (y, y, AbsTol, RelTol, normcontrol); if (d0 < 1e-5 || d1 < 1e-5) h0 = 1e-6; else h0 = .01 * (d0 / d1); endif ## compute one step of Explicit-Euler x1 = x0 + h0 * y; ## approximate the derivative norm yh = fcn (t0+h0, x1, args{:}); if (iscell (yh)) yh = yh{1}; endif d2 = (1 / h0) * ... AbsRel_norm (yh - y, yh - y, AbsTol, RelTol, normcontrol); if (max (d1, d2) <= 1e-15) h1 = max (1e-6, h0 * 1e-3); else h1 = (1e-2 / max (d1, d2)) ^(1 / (order+1)); endif h = min (100 * h0, h1); endfunction