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annotate scripts/ode/private/runge_kutta_45_dorpri.m @ 20634:80e630b37ba1

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maint: Remove unnecessary 'v' prefix before variables in ODE m-files. * ode_rk_interpolate.m: Deleted file. * odepkg_event_handle.m: Deleted file. * runge_kutta_interpolate.m: Renamed from ode_rk_interpolate.m. Remove 'v' prefix on variables. Delete blank space at end of lines. * ode_event_handler.m: Renamed from odepkg_event_handle.m. Remove 'v' prefix on variables. Delete blank space at end of lines. Use 'evt' for event rather than 'eve' in variable names. Use 'idx' rather than 'index' in variable names. * scripts/ode/module.mk: Add ode_event_handler.m and runge_kutta_interpolate.m to build system. * AbsRel_Norm.m, starting_stepsize.m, ode_struct_value_check.m, odeget.m, odeset.m: Delete blank space at end of lines. * integrate_adaptive, integrate_const.m, integrate_n_steps.m, runge_kutta_45_dorpri.m: Remove 'v' prefix on variable. Delete blank space at end of lines. * ode45.m: Expand docstring to cover more of the inputs/outputs. Remove 'v' prefix on variable. Use name of variable in input validation warnings. Use name of function as prefix in warnings and error messages. Delete long, unnecessary comments. Use faster 'isempty' rather than slow 'isequal' to check whether option has been set. Remove SubOpts variable. Shorten lines < 80 chars.
author Rik <rik@octave.org>
date Sun, 18 Oct 2015 09:55:41 -0700
parents b92f8e148936
children 516bb87ea72e
Ignore whitespace changes - Everywhere: Within whitespace: At end of lines:
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1 ## Copyright (C) 2015 Carlo de Falco
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2 ## Copyright (C) 2013 Roberto Porcu' <roberto.porcu@polimi.it>
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3 ##
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4 ## This file is part of Octave.
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5 ##
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6 ## Octave is free software; you can redistribute it and/or modify it
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7 ## under the terms of the GNU General Public License as published by
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8 ## the Free Software Foundation; either version 3 of the License, or (at
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9 ## your option) any later version.
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10 ##
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11 ## Octave is distributed in the hope that it will be useful, but
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12 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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13 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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14 ## General Public License for more details.
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15 ##
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16 ## You should have received a copy of the GNU General Public License
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17 ## along with Octave; see the file COPYING. If not, see
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18 ## <http://www.gnu.org/licenses/>.
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19
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20 ## -*- texinfo -*-
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21 ## @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})
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22 ## @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})
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23 ## @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})
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24 ##
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25 ## This function can be used to integrate a system of ODEs with a given initial
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26 ## condition @var{x} from @var{t} to @var{t+dt} with the Dormand-Prince method.
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27 ## For the definition of this method see
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28 ## @url{http://en.wikipedia.org/wiki/Dormand%E2%80%93Prince_method}.
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29 ##
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30 ## First output argument is the final integration time value.
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31 ##
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32 ## Second output parameter is the higher order computed solution at time
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33 ## @var{t_next} (local extrapolation).
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34 ##
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35 ## Third output parameter is a lower order solution for the estimation of the
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36 ## error.
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37 ##
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38 ## Fourth output parameter is matrix containing the Runge-Kutta evaluations
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39 ## to use in an FSAL scheme or for dense output.
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40 ##
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41 ## First input argument is the function describing the system of ODEs to be
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42 ## integrated.
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43 ##
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44 ## Second input parameter is the first extreme of integration interval.
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45 ##
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46 ## Third input argument is the initial condition of the system.
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47 ##
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48 ## Fourth input argument is the timestep, that is the length of the
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49 ## integration interval.
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50 ##
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51 ## Fifth input parameter is optional and describes a set of options useful to
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52 ## adapt the computation to what is needed.
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53 ##
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54 ## Sixth input parameter is optional and describes the Runge-Kutta evaluations
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55 ## of the previous step to use in an FSAL scheme.
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56 ## @end deftypefn
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57 ##
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58 ## @seealso{odepkg}
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59
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60 function [t_next, x_next, x_est, k] = runge_kutta_45_dorpri (f, t, x, dt,
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61 options = [],
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62 k_vals = [],
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63 t_next = t + dt)
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64
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65 persistent a = [0 0 0 0 0 0;
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66 1/5 0 0 0 0 0;
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67 3/40 9/40 0 0 0 0;
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68 44/45 -56/15 32/9 0 0 0;
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69 19372/6561 -25360/2187 64448/6561 -212/729 0 0;
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70 9017/3168 -355/33 46732/5247 49/176 -5103/18656 0;
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71 35/384 0 500/1113 125/192 -2187/6784 11/84];
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72 persistent b = [0 1/5 3/10 4/5 8/9 1 1];
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73 persistent c = [(35/384) 0 (500/1113) (125/192) (-2187/6784) (11/84)];
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74 persistent c_prime = [(5179/57600) 0 (7571/16695) (393/640), ...
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75 (-92097/339200) (187/2100) (1/40)];
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76 ## According to Shampine 1986:
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77 ## persistent c_prime = [(1951/21600) 0 (22642/50085) (451/720), ...
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78 ## (-12231/42400) (649/6300) (1/60)];
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79
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80 s = t + dt * b;
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81 cc = dt * c;
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82 aa = dt * a;
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83 k = zeros (rows (x), 7);
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84
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85 if (! isempty (options)) # extra arguments for function evaluator
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86 args = options.funarguments;
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87 else
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88 args = {};
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89 endif
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90
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91 if (! isempty (k_vals)) # k values from previous step are passed
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92 k(:,1) = k_vals(:,end); # FSAL property
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93 else
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94 k(:,1) = feval (f, t, x, args{:});
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95 endif
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96
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97 k(:,2) = feval (f, s(2), x + k(:,1) * aa(2, 1).' , args{:});
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98 k(:,3) = feval (f, s(3), x + k(:,1:2) * aa(3, 1:2).', args{:});
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99 k(:,4) = feval (f, s(4), x + k(:,1:3) * aa(4, 1:3).', args{:});
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100 k(:,5) = feval (f, s(5), x + k(:,1:4) * aa(5, 1:4).', args{:});
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101 k(:,6) = feval (f, s(6), x + k(:,1:5) * aa(6, 1:5).', args{:});
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102
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103 ## compute new time and new values for the unknowns
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104 ## t_next = t + dt;
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105 x_next = x + k(:,1:6) * cc(:); # 5th order approximation
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106
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107 ## if the estimation of the error is required
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jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
108 if (nargout >= 3)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
109 ## new solution to be compared with the previous one
20621
b92f8e148936 maint: Continued clean-up of functions in ode/private dir.
Rik <rik@octave.org>
parents: 20600
diff changeset
110 k(:,7) = feval (f, t_next, x_next, args{:});
20540
72cd24aa5f7a Clean up and vetorize Dormant&Prince RK timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20536
diff changeset
111 cc_prime = dt * c_prime;
20552
eb9e2d187ed2 maint: Use Octave coding conventions in scripts/ode/private dir.
Rik <rik@octave.org>
parents: 20548
diff changeset
112 x_est = x + k * cc_prime(:);
20533
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
113 endif
20634
80e630b37ba1 maint: Remove unnecessary 'v' prefix before variables in ODE m-files.
Rik <rik@octave.org>
parents: 20621
diff changeset
114
20533
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
115 endfunction
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
116