Mercurial > octave-nkf
view scripts/ode/private/hermite_quartic_interpolation.m @ 20584:eb9e2d187ed2
maint: Use Octave coding conventions in scripts/ode/private dir.
* AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m,
integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m,
ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m,
runge_kutta_45_dorpri.m, starting_stepsize.m:
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author | Rik <rik@octave.org> |
---|---|
date | Sun, 04 Oct 2015 22:18:54 -0700 |
parents | 25623ef2ff4f |
children |
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## Copyright (C) 2015 Jacopo Corno <jacopo.corno@gmail.com> ## ## 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{x_out} =} hermite_quartic_interpolation (@var{t}, @var{x}, @var{der}, @var{t_out}) ## ## This function file can be called by an ODE solver function in order to ## interpolate the solution at the time @var{t_out} using a 4th order ## Hermite interpolation. ## ## The first input @var{t} is a vector with two given times. ## ## The second input argument is the vector with the values of the function ## to interpolate at the times specified in @var{t} and at the middle point. ## ## The third input argument is the value of the derivatives of the function ## evaluated at the two extreme points. ## ## The output @var{x_out} is the evaluation of the Hermite interpolant at ## @var{t_out}. ## ## @end deftypefn ## ## @seealso{linear_interpolation, quadratic_interpolation, ## hermite_cubic_interpolation, hermite_quintic_interpolation, ## dorpri_interpolation} function x_out = hermite_quartic_interpolation (t, x, der, t_out) ## Rescale time on [0,1] s = (t_out - t(1)) / (t(2) - t(1)); ## Hermite basis functions ## H0 = 1 - 11*s.^2 + 18*s.^3 - 8*s.^4; ## H1 = s - 4*s.^2 + 5*s.^3 - 2*s.^4; ## H2 = 16*s.^2 - 32*s.^3 + 16*s.^4; ## H3 = - 5*s.^2 + 14*s.^3 - 8*s.^4; ## H4 = s.^2 - 3*s.^3 + 2*s.^4; x_out = zeros (rows (x), length (t_out)); for ii = 1:rows (x) x_out(ii,:) = (1 - 11*s.^2 + 18*s.^3 - 8*s.^4)*x(ii,1) ... + ( s - 4*s.^2 + 5*s.^3 - 2*s.^4)*(t(2)-t(1))*der(ii,1) ... + ( 16*s.^2 - 32*s.^3 + 16*s.^4)*x(ii,2) ... + ( - 5*s.^2 + 14*s.^3 - 8*s.^4)*x(ii,3) ... + ( s.^2 - 3*s.^3 + 2*s.^4)*(t(2)-t(1))*der(ii,2); endfor endfunction