annotate scripts/ode/ode23.m @ 23219:3ac9f9ecfae5 stable

maint: Update copyright dates.
author John W. Eaton <jwe@octave.org>
date Wed, 22 Feb 2017 12:39:29 -0500
parents e9a0469dedd9
children 092078913d54
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1 ## Copyright (C) 2016-2017 Carlo de Falco
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2 ## Copyright (C) 2016 Francesco Faccio <francesco.faccio@mail.polimi.it>
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3 ## Copyright (C) 2014-2016 Jacopo Corno <jacopo.corno@gmail.com>
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4 ## Copyright (C) 2013-2016 Roberto Porcu' <roberto.porcu@polimi.it>
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5 ## Copyright (C) 2006-2016 Thomas Treichl <treichl@users.sourceforge.net>
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6 ##
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7 ## This file is part of Octave.
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8 ##
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9 ## Octave is free software; you can redistribute it and/or modify it
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10 ## under the terms of the GNU General Public License as published by
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11 ## the Free Software Foundation; either version 3 of the License, or (at
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12 ## your option) any later version.
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13 ##
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14 ## Octave is distributed in the hope that it will be useful, but
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15 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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16 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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17 ## General Public License for more details.
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18 ##
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19 ## You should have received a copy of the GNU General Public License
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20 ## along with Octave; see the file COPYING. If not, see
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21 ## <http://www.gnu.org/licenses/>.
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22
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23 ## -*- texinfo -*-
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24 ## @deftypefn {} {[@var{t}, @var{y}] =} ode23 (@var{fun}, @var{trange}, @var{init})
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25 ## @deftypefnx {} {[@var{t}, @var{y}] =} ode23 (@var{fun}, @var{trange}, @var{init}, @var{ode_opt})
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26 ## @deftypefnx {} {[@var{t}, @var{y}, @var{te}, @var{ye}, @var{ie}] =} ode23 (@dots{})
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27 ## @deftypefnx {} {@var{solution} =} ode23 (@dots{})
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28 ## @deftypefnx {} {} ode23 (@dots{})
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29 ##
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30 ## Solve a set of non-stiff Ordinary Differential Equations (non-stiff ODEs)
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31 ## with the well known explicit @nospell{Bogacki-Shampine} method of order 3.
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32 ## For the definition of this method see
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33 ## @url{http://en.wikipedia.org/wiki/List_of_Runge%E2%80%93Kutta_methods}.
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34 ##
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35 ## @var{fun} is a function handle, inline function, or string containing the
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36 ## name of the function that defines the ODE: @code{y' = f(t,y)}. The function
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37 ## must accept two inputs where the first is time @var{t} and the second is a
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38 ## column vector of unknowns @var{y}.
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39 ##
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40 ## @var{trange} specifies the time interval over which the ODE will be
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41 ## evaluated. Typically, it is a two-element vector specifying the initial and
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42 ## final times (@code{[tinit, tfinal]}). If there are more than two elements
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43 ## then the solution will also be evaluated at these intermediate time
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44 ## instances.
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45 ##
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46 ## By default, @code{ode23} uses an adaptive timestep with the
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47 ## @code{integrate_adaptive} algorithm. The tolerance for the timestep
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48 ## computation may be changed by using the options @qcode{"RelTol"}
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49 ## and @qcode{"AbsTol"}.
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50 ##
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51 ## @var{init} contains the initial value for the unknowns. If it is a row
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52 ## vector then the solution @var{y} will be a matrix in which each column is
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53 ## the solution for the corresponding initial value in @var{init}.
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54 ##
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55 ## The optional fourth argument @var{ode_opt} specifies non-default options to
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56 ## the ODE solver. It is a structure generated by @code{odeset}.
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57 ##
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58 ## The function typically returns two outputs. Variable @var{t} is a
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59 ## column vector and contains the times where the solution was found. The
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60 ## output @var{y} is a matrix in which each column refers to a different
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61 ## unknown of the problem and each row corresponds to a time in @var{t}.
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62 ##
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63 ## The output can also be returned as a structure @var{solution} which
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64 ## has a field @var{x} containing a row vector of times where the solution
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65 ## was evaluated and a field @var{y} containing the solution matrix such
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66 ## that each column corresponds to a time in @var{x}.
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67 ## Use @code{fieldnames (@var{solution})} to see the other fields and
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68 ## additional information returned.
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69 ##
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70 ## If no output arguments are requested, and no @code{OutputFcn} is
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71 ## specified in @var{ode_opt}, then the @code{OutputFcn} is set to
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72 ## @code{odeplot} and the results of the solver are plotted immediately.
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73 ##
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74 ## If using the @qcode{"Events"} option then three additional outputs may
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75 ## be returned. @var{te} holds the time when an Event function returned a
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76 ## zero. @var{ye} holds the value of the solution at time @var{te}. @var{ie}
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77 ## contains an index indicating which Event function was triggered in the case
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78 ## of multiple Event functions.
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79 ##
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80 ## Example: Solve the @nospell{Van der Pol} equation
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81 ##
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82 ## @example
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83 ## @group
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84 ## fvdp = @@(@var{t},@var{y}) [@var{y}(2); (1 - @var{y}(1)^2) * @var{y}(2) - @var{y}(1)];
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85 ## [@var{t},@var{y}] = ode23 (fvdp, [0, 20], [2, 0]);
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86 ## @end group
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87 ## @end example
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88 ## @seealso{odeset, odeget, ode45}
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89 ## @end deftypefn
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90
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91 function varargout = ode23 (fun, trange, init, varargin)
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92
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93 if (nargin < 3)
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94 print_usage ();
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95 endif
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96
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97 order = 3;
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98 solver = "ode23";
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99
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100 if (nargin >= 4)
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101 if (! isstruct (varargin{1}))
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102 ## varargin{1:len} are parameters for fun
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103 odeopts = odeset ();
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104 funarguments = varargin;
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105 elseif (numel (varargin) > 1)
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106 ## varargin{1} is an ODE options structure opt
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107 odeopts = varargin{1};
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108 funarguments = {varargin{2:numel (varargin)}};
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109 else # if (isstruct (varargin{1}))
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parents: 22445
diff changeset
110 odeopts = varargin{1};
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parents: 22445
diff changeset
111 funarguments = {};
20901
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diff changeset
112 endif
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113 else # nargin == 3
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
114 odeopts = odeset ();
22593
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diff changeset
115 funarguments = {};
20901
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diff changeset
116 endif
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117
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diff changeset
118 if (! isnumeric (trange) || ! isvector (trange))
20901
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diff changeset
119 error ("Octave:invalid-input-arg",
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
120 "ode23: TRANGE must be a numeric vector");
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121 endif
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diff changeset
122
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diff changeset
123 if (numel (trange) < 2)
20901
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diff changeset
124 error ("Octave:invalid-input-arg",
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
125 "ode23: TRANGE must contain at least 2 elements");
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diff changeset
126 elseif (trange(2) == trange(1))
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diff changeset
127 error ("Octave:invalid-input-arg",
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diff changeset
128 "ode23: invalid time span, TRANGE(1) == TRANGE(2)");
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129 else
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130 direction = sign (trange(2) - trange(1));
20901
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131 endif
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132 trange = trange(:);
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133
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134 if (! isnumeric (init) || ! isvector (init))
20901
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135 error ("Octave:invalid-input-arg",
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diff changeset
136 "ode23: INIT must be a numeric vector");
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137 endif
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138 init = init(:);
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139
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diff changeset
140 if (ischar (fun))
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diff changeset
141 try
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142 fun = str2func (fun);
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143 catch
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144 warning (lasterr);
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diff changeset
145 end_try_catch
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146 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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147 if (! isa (fun, "function_handle"))
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diff changeset
148 error ("Octave:invalid-input-arg",
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diff changeset
149 "ode23: FUN must be a valid function handle");
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150 endif
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diff changeset
151
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152 ## Start preprocessing, have a look which options are set in odeopts,
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153 ## check if an invalid or unused option is set.
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154 [defaults, classes, attributes] = odedefaults (numel (init),
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155 trange(1), trange(end));
20901
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156
22660
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
157 persistent ode23_ignore_options = ...
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
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diff changeset
158 {"BDF", "InitialSlope", "Jacobian", "JPattern",
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
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diff changeset
159 "MassSingular", "MaxOrder", "MvPattern", "Vectorized"};
22707
413a19bca7f3 maint: Strip trailing whitespace from source files.
John W. Eaton <jwe@octave.org>
parents: 22661
diff changeset
160
22660
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
161 defaults = rmfield (defaults, ode23_ignore_options);
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
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diff changeset
162 classes = rmfield (classes, ode23_ignore_options);
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
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parents: 22659
diff changeset
163 attributes = rmfield (attributes, ode23_ignore_options);
20901
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diff changeset
164
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diff changeset
165 odeopts = odemergeopts ("ode23", odeopts, defaults, classes, attributes);
20901
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diff changeset
166
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167 odeopts.funarguments = funarguments;
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diff changeset
168 odeopts.direction = direction;
20901
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169
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diff changeset
170 if (! isempty (odeopts.NonNegative))
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diff changeset
171 if (isempty (odeopts.Mass))
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diff changeset
172 odeopts.havenonnegative = true;
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173 else
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diff changeset
174 odeopts.havenonnegative = false;
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diff changeset
175 warning ("Octave:invalid-input-arg",
22626
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diff changeset
176 ['ode23: option "NonNegative" is ignored', ...
20901
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diff changeset
177 " when mass matrix is set\n"]);
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diff changeset
178 endif
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179 else
20901
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diff changeset
180 odeopts.havenonnegative = false;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
181 endif
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182
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parents:
diff changeset
183 if (isempty (odeopts.OutputFcn) && nargout == 0)
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parents:
diff changeset
184 odeopts.OutputFcn = @odeplot;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
185 odeopts.haveoutputfunction = true;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
186 else
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parents:
diff changeset
187 odeopts.haveoutputfunction = ! isempty (odeopts.OutputFcn);
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diff changeset
188 endif
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diff changeset
189
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diff changeset
190 if (isempty (odeopts.InitialStep))
20908
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parents: 20902
diff changeset
191 odeopts.InitialStep = odeopts.direction * ...
22626
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parents: 22625
diff changeset
192 starting_stepsize (order, fun, trange(1), init,
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parents: 22625
diff changeset
193 odeopts.AbsTol, odeopts.RelTol,
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Rik <rik@octave.org>
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diff changeset
194 strcmp (odeopts.NormControl, "on"),
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diff changeset
195 odeopts.funarguments);
20901
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diff changeset
196 endif
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diff changeset
197
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diff changeset
198 if (! isempty (odeopts.Mass) && isnumeric (odeopts.Mass))
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
199 havemasshandle = false;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
200 mass = odeopts.Mass; # constant mass
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
201 elseif (isa (odeopts.Mass, "function_handle"))
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
202 havemasshandle = true; # mass defined by a function handle
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
203 else # no mass matrix - creating a diag-matrix of ones for mass
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
204 havemasshandle = false; # mass = diag (ones (length (init), 1), 0);
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
205 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
206
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diff changeset
207 ## Starting the initialization of the core solver ode23
20928
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diff changeset
208
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
209 if (havemasshandle) # Handle only the dynamic mass matrix,
22626
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
210 if (! strcmp (odeopts.MStateDependence, "none"))
22661
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Rik <rik@octave.org>
parents: 22660
diff changeset
211 ## constant mass matrices have already been handled
20901
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parents:
diff changeset
212 mass = @(t,x) odeopts.Mass (t, x, odeopts.funarguments{:});
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
213 fun = @(t,x) mass (t, x, odeopts.funarguments{:}) ...
22626
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parents: 22625
diff changeset
214 \ fun (t, x, odeopts.funarguments{:});
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parents: 22625
diff changeset
215 else
20901
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parents:
diff changeset
216 mass = @(t) odeopts.Mass (t, odeopts.funarguments{:});
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
217 fun = @(t,x) mass (t, odeopts.funarguments{:}) ...
22626
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
218 \ fun (t, x, odeopts.funarguments{:});
20901
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parents:
diff changeset
219 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
220 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
221
22659
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
222 if (nargout == 1)
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
223 ## Single output requires auto-selected intermediate times,
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
224 ## which is obtained by NOT specifying specific solution times.
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
225 trange = [trange(1); trange(end)];
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
226 odeopts.Refine = []; # disable Refine when single output requested
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
227 elseif (numel (trange) > 2)
04fc7e9c5f96 Disable Refine option of ode solvers for certain input/output combinations (partial fix bug #49408).
Rik <rik@octave.org>
parents: 22658
diff changeset
228 odeopts.Refine = []; # disable Refine when specific times requested
22658
56d7d423aff9 Return intermediate integration times when single output argument used in ode solver (bug #49417).
Rik <rik@octave.org>
parents: 22655
diff changeset
229 endif
56d7d423aff9 Return intermediate integration times when single output argument used in ode solver (bug #49417).
Rik <rik@octave.org>
parents: 22655
diff changeset
230
22626
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
231 solution = integrate_adaptive (@runge_kutta_23,
22593
dba5074bdc79 simplify options management in ode solvers
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22445
diff changeset
232 order, fun, trange, init, odeopts);
22625
081a201b77c7 Clean up ode options implementation to follow Octave coding standards.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22605
diff changeset
233
20901
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parents:
diff changeset
234 ## Postprocessing, do whatever when terminating integration algorithm
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
235 if (odeopts.haveoutputfunction) # Cleanup plotter
22639
7efa2d0e22c9 More Matlab-compatible implementation of OutputFcn. Clean up odeplot.m.
Rik <rik@octave.org>
parents: 22626
diff changeset
236 feval (odeopts.OutputFcn, [], [], "done", odeopts.funarguments{:});
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
237 endif
22593
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 22445
diff changeset
238 if (! isempty (odeopts.Events)) # Cleanup event function handling
22626
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
239 ode_event_handler (odeopts.Events, solution.t(end),
22655
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
240 solution.x(end,:).', "done", odeopts.funarguments{:});
20901
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parents:
diff changeset
241 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
242
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
243 ## Print additional information if option Stats is set
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parents:
diff changeset
244 if (strcmp (odeopts.Stats, "on"))
21955
0f3e875d9078 Fix statistics on solution solving for ode45, ode23 (bug #48243).
jcorno <jacopo.corno@gmail.com>
parents: 21751
diff changeset
245 nsteps = solution.cntloop; # cntloop from 2..end
0f3e875d9078 Fix statistics on solution solving for ode45, ode23 (bug #48243).
jcorno <jacopo.corno@gmail.com>
parents: 21751
diff changeset
246 nfailed = solution.cntcycles - nsteps; # cntcycl from 1..end
0f3e875d9078 Fix statistics on solution solving for ode45, ode23 (bug #48243).
jcorno <jacopo.corno@gmail.com>
parents: 21751
diff changeset
247 nfevals = 3 * solution.cntcycles + 1; # number of ode evaluations
21443
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
248 ndecomps = 0; # number of LU decompositions
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
249 npds = 0; # number of partial derivatives
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
250 nlinsols = 0; # no. of solutions of linear systems
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
251 ## Print cost statistics if no output argument is given
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
252 if (nargout == 0)
21634
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
253 printf ("Number of successful steps: %d\n", nsteps);
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
254 printf ("Number of failed attempts: %d\n", nfailed);
96518f623c91 Backed out changeset dcf8922b724b
Mike Miller <mtmiller@octave.org>
parents: 21633
diff changeset
255 printf ("Number of function calls: %d\n", nfevals);
20901
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parents:
diff changeset
256 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
257 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
258
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
259 if (nargout == 2)
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
260 varargout{1} = solution.t; # Time stamps are first output argument
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parents:
diff changeset
261 varargout{2} = solution.x; # Results are second output argument
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parents:
diff changeset
262 elseif (nargout == 1)
22655
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
263 varargout{1}.x = solution.t.'; # Time stamps are saved in field x (row vector)
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
264 varargout{1}.y = solution.x.'; # Results are saved in field y (row vector)
20901
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parents:
diff changeset
265 varargout{1}.solver = solver; # Solver name is saved in field solver
22593
dba5074bdc79 simplify options management in ode solvers
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22445
diff changeset
266 if (! isempty (odeopts.Events))
20901
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parents:
diff changeset
267 varargout{1}.ie = solution.event{2}; # Index info which event occurred
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
268 varargout{1}.xe = solution.event{3}; # Time info when an event occurred
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parents:
diff changeset
269 varargout{1}.ye = solution.event{4}; # Results when an event occurred
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parents:
diff changeset
270 endif
22593
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 22445
diff changeset
271 if (strcmp (odeopts.Stats, "on"))
20901
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parents:
diff changeset
272 varargout{1}.stats = struct ();
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
273 varargout{1}.stats.nsteps = nsteps;
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parents:
diff changeset
274 varargout{1}.stats.nfailed = nfailed;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
275 varargout{1}.stats.nfevals = nfevals;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
276 varargout{1}.stats.npds = npds;
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diff changeset
277 varargout{1}.stats.ndecomps = ndecomps;
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diff changeset
278 varargout{1}.stats.nlinsols = nlinsols;
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parents:
diff changeset
279 endif
22937
2b2ac017c901 Fix undefined return argument for more than 2 outputs from ode solver (bug #49890).
Rik <rik@octave.org>
parents: 22707
diff changeset
280 elseif (nargout > 2)
20901
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parents:
diff changeset
281 varargout = cell (1,5);
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
282 varargout{1} = solution.t;
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
283 varargout{2} = solution.x;
22593
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parents: 22445
diff changeset
284 if (! isempty (odeopts.Events))
20901
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parents:
diff changeset
285 varargout{3} = solution.event{3}; # Time info when an event occurred
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parents:
diff changeset
286 varargout{4} = solution.event{4}; # Results when an event occurred
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parents:
diff changeset
287 varargout{5} = solution.event{2}; # Index info which event occurred
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parents:
diff changeset
288 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
289 endif
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
290
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
291 endfunction
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
292
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
293
21599
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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parents: 21596
diff changeset
294 %!demo
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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parents: 21596
diff changeset
295 %! ## Demonstrate convergence order for ode23
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diff changeset
296 %! tol = 1e-5 ./ 10.^[0:8];
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diff changeset
297 %! for i = 1 : numel (tol)
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diff changeset
298 %! opt = odeset ("RelTol", tol(i), "AbsTol", realmin);
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
299 %! [t, y] = ode23 (@(t, y) -y, [0, 1], 1, opt);
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
300 %! h(i) = 1 / (numel (t) - 1);
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
301 %! err(i) = norm (y .* exp (t) - 1, Inf);
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
Rik <rik@octave.org>
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diff changeset
302 %! endfor
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
303 %!
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
304 %! ## Estimate order visually
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diff changeset
305 %! loglog (h, tol, "-ob",
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
306 %! h, err, "-b",
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
307 %! h, (h/h(end)) .^ 2 .* tol(end), "k--",
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
Rik <rik@octave.org>
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diff changeset
308 %! h, (h/h(end)) .^ 3 .* tol(end), "k-");
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diff changeset
309 %! axis tight
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diff changeset
310 %! xlabel ("h");
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diff changeset
311 %! ylabel ("err(h)");
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
312 %! title ("Convergence plot for ode23");
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diff changeset
313 %! legend ("imposed tolerance", "ode23 (relative) error",
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
314 %! "order 2", "order 3", "location", "northwest");
22647
cf8ec7abb4ae Clean up demo and test blocks for ode functions.
Rik <rik@octave.org>
parents: 22644
diff changeset
315 %!
cf8ec7abb4ae Clean up demo and test blocks for ode functions.
Rik <rik@octave.org>
parents: 22644
diff changeset
316 %! ## Estimate order numerically
cf8ec7abb4ae Clean up demo and test blocks for ode functions.
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diff changeset
317 %! p = diff (log (err)) ./ diff (log (h))
21599
f29d68e24c5a ode23.m, ode45.m: More reformatting of demos to Octave coding standards.
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diff changeset
318
20901
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parents:
diff changeset
319 ## We are using the "Van der Pol" implementation for all tests that are done
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
320 ## for this function.
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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diff changeset
321 ## For further tests we also define a reference solution (computed at high
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
322 ## accuracy)
22626
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
323 %!function ydot = fpol (t, y) # The Van der Pol ODE
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
324 %! ydot = [y(2); (1 - y(1)^2) * y(2) - y(1)];
20901
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parents:
diff changeset
325 %!endfunction
21443
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diff changeset
326 %!function ref = fref () # The computed reference sol
22626
869c02fde46c Further clean-up of ode functions.
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diff changeset
327 %! ref = [0.32331666704577, -1.83297456798624];
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
328 %!endfunction
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
329 %!function [val, trm, dir] = feve (t, y, varargin)
22626
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
330 %! val = fpol (t, y, varargin); # We use the derivatives
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parents: 22625
diff changeset
331 %! trm = zeros (2,1); # that's why component 2
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
332 %! dir = ones (2,1); # does not seem to be exact
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
333 %!endfunction
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
334 %!function [val, trm, dir] = fevn (t, y, varargin)
22626
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
335 %! val = fpol (t, y, varargin); # We use the derivatives
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
336 %! trm = ones (2,1); # that's why component 2
869c02fde46c Further clean-up of ode functions.
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parents: 22625
diff changeset
337 %! dir = ones (2,1); # does not seem to be exact
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
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parents:
diff changeset
338 %!endfunction
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339 %!function mas = fmas (t, y, varargin)
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340 %! mas = [1, 0; 0, 1]; # Dummy mass matrix for tests
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341 %!endfunction
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342 %!function mas = fmsa (t, y, varargin)
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343 %! mas = sparse ([1, 0; 0, 1]); # A sparse dummy matrix
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344 %!endfunction
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345 %!function out = fout (t, y, flag, varargin)
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346 %! out = false;
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347 %! if (strcmp (flag, "init"))
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348 %! if (! isequal (size (t), [2, 1]))
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349 %! error ('fout: step "init"');
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350 %! endif
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351 %! elseif (isempty (flag))
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352 %! if (! isequal (size (t), [1, 1]))
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353 %! error ('fout: step "calc"');
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354 %! endif
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355 %! elseif (strcmp (flag, "done"))
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356 %! if (! isempty (t))
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357 %! warning ('fout: step "done"');
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358 %! endif
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359 %! else
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360 %! error ("fout: invalid flag <%s>", flag);
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361 %! endif
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362 %!endfunction
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363 %!
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364 %!test # two output arguments
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365 %! [t, y] = ode23 (@fpol, [0 2], [2 0]);
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366 %! assert ([t(end), y(end,:)], [2, fref], 1e-3);
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367 %!test # anonymous function instead of real function
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368 %! fvdp = @(t,y) [y(2); (1 - y(1)^2) * y(2) - y(1)];
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369 %! [t, y] = ode23 (fvdp, [0 2], [2 0]);
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370 %! assert ([t(end), y(end,:)], [2, fref], 1e-3);
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371 %!test # extra input arguments passed through
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372 %! [t, y] = ode23 (@fpol, [0 2], [2 0], 12, 13, "KL");
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373 %! assert ([t(end), y(end,:)], [2, fref], 1e-3);
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374 %!test # empty OdePkg structure *but* extra input arguments
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375 %! opt = odeset;
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376 %! [t, y] = ode23 (@fpol, [0 2], [2 0], opt, 12, 13, "KL");
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377 %! assert ([t(end), y(end,:)], [2, fref], 1e-2);
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378 %!test # Solve another anonymous function below zero
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379 %! ref = [0, 14.77810590694212];
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380 %! [t, y] = ode23 (@(t,y) y, [-2 0], 2);
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381 %! assert ([t(end), y(end,:)], ref, 1e-2);
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382 %!test # InitialStep option
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383 %! opt = odeset ("InitialStep", 1e-8);
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384 %! [t, y] = ode23 (@fpol, [0 0.2], [2 0], opt);
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385 %! assert ([t(2)-t(1)], [1e-8], 1e-9);
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386 %!test # MaxStep option
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387 %! opt = odeset ("MaxStep", 1e-3);
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388 %! sol = ode23 (@fpol, [0 0.2], [2 0], opt);
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389 %! assert ([sol.x(5)-sol.x(4)], [1e-3], 1e-4);
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390 %!test # Solve in backward direction starting at t=0
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391 %! ref = [-1.205364552835178, 0.951542399860817];
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392 %! sol = ode23 (@fpol, [0 -2], [2 0]);
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393 %! assert ([sol.x(end); sol.y(:,end)], [-2; ref'], 5e-3);
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394 %!test # Solve in backward direction starting at t=2
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395 %! ref = [-1.205364552835178, 0.951542399860817];
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396 %! sol = ode23 (@fpol, [2 0 -2], fref);
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397 %! assert ([sol.x(end); sol.y(:,end)], [-2; ref'], 2e-2);
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398 %!test # Solve another anonymous function in backward direction
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399 %! ref = [-1, 0.367879437558975];
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400 %! sol = ode23 (@(t,y) y, [0 -1], 1);
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401 %! assert ([sol.x(end); sol.y(:,end)], ref', 1e-2);
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402 %!test # Solve another anonymous function below zero
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403 %! ref = [0, 14.77810590694212];
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404 %! sol = ode23 (@(t,y) y, [-2 0], 2);
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405 %! assert ([sol.x(end); sol.y(:,end)], ref', 1e-2);
21443
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406 %!test # Solve in backward direction starting at t=0 with MaxStep option
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407 %! ref = [-1.205364552835178, 0.951542399860817];
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408 %! opt = odeset ("MaxStep", 1e-3);
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409 %! sol = ode23 (@fpol, [0 -2], [2 0], opt);
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410 %! assert ([abs(sol.x(8)-sol.x(7))], [1e-3], 1e-3);
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411 %! assert ([sol.x(end); sol.y(:,end)], [-2; ref'], 1e-3);
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412 %!test # AbsTol option
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413 %! opt = odeset ("AbsTol", 1e-5);
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414 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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415 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
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416 %!test # AbsTol and RelTol option
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417 %! opt = odeset ("AbsTol", 1e-8, "RelTol", 1e-8);
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418 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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419 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
21443
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420 %!test # RelTol and NormControl option -- higher accuracy
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421 %! opt = odeset ("RelTol", 1e-8, "NormControl", "on");
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422 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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423 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-4);
21443
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424 %!test # Keeps initial values while integrating
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425 %! opt = odeset ("NonNegative", 2);
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426 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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427 %! assert ([sol.x(end); sol.y(:,end)], [2; 2; 0], 1e-1);
21443
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428 %!test # Details of OutputSel and Refine can't be tested
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429 %! opt = odeset ("OutputFcn", @fout, "OutputSel", 1, "Refine", 5);
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430 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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431 %!test # Stats must add further elements in sol
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432 %! opt = odeset ("Stats", "on");
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433 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
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434 %! assert (isfield (sol, "stats"));
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435 %! assert (isfield (sol.stats, "nsteps"));
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436 %!test # Events option add further elements in sol
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437 %! opt = odeset ("Events", @feve);
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438 %! sol = ode23 (@fpol, [0 10], [2 0], opt);
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439 %! assert (isfield (sol, "ie"));
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440 %! assert (sol.ie(1), 2);
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441 %! assert (isfield (sol, "xe"));
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diff changeset
442 %! assert (isfield (sol, "ye"));
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443 %!test # Events option, now stop integration
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444 %! warning ("off", "integrate_adaptive:unexpected_termination", "local");
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445 %! opt = odeset ("Events", @fevn, "NormControl", "on");
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diff changeset
446 %! sol = ode23 (@fpol, [0 10], [2 0], opt);
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ecce63c99c3f maint: Add semicolons to terminate code in %! blocks.
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diff changeset
447 %! assert ([sol.ie, sol.xe, sol.ye],
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448 %! [2.0, 2.496110, -0.830550, -2.677589], .5e-1);
21443
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449 %!test # Events option, five output arguments
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450 %! warning ("off", "integrate_adaptive:unexpected_termination", "local");
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451 %! opt = odeset ("Events", @fevn, "NormControl", "on");
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452 %! [t, y, vxe, ye, vie] = ode23 (@fpol, [0 10], [2 0], opt);
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diff changeset
453 %! assert ([vie, vxe, ye], [2.0, 2.496110, -0.830550, -2.677589], 1e-1);
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diff changeset
454 %!test # Mass option as function
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Rik <rik@octave.org>
parents: 21319
diff changeset
455 %! opt = odeset ("Mass", @fmas);
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
456 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
22654
bc61ed076549 Change orientation of output fields in struct returned from ode solvers (bug #49402).
Sebastian Schöps <sebastian@schoeps.org>
parents: 22647
diff changeset
457 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
21443
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
458 %!test # Mass option as matrix
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
459 %! opt = odeset ("Mass", eye (2,2));
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
460 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
22654
bc61ed076549 Change orientation of output fields in struct returned from ode solvers (bug #49402).
Sebastian Schöps <sebastian@schoeps.org>
parents: 22647
diff changeset
461 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
21443
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
462 %!test # Mass option as sparse matrix
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
463 %! opt = odeset ("Mass", sparse (eye (2,2)));
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
464 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
22654
bc61ed076549 Change orientation of output fields in struct returned from ode solvers (bug #49402).
Sebastian Schöps <sebastian@schoeps.org>
parents: 22647
diff changeset
465 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
21443
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Rik <rik@octave.org>
parents: 21319
diff changeset
466 %!test # Mass option as function and sparse matrix
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
467 %! opt = odeset ("Mass", @fmsa);
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
468 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
22654
bc61ed076549 Change orientation of output fields in struct returned from ode solvers (bug #49402).
Sebastian Schöps <sebastian@schoeps.org>
parents: 22647
diff changeset
469 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
21443
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Rik <rik@octave.org>
parents: 21319
diff changeset
470 %!test # Mass option as function and MStateDependence
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
471 %! opt = odeset ("Mass", @fmas, "MStateDependence", "strong");
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
472 %! sol = ode23 (@fpol, [0 2], [2 0], opt);
22654
bc61ed076549 Change orientation of output fields in struct returned from ode solvers (bug #49402).
Sebastian Schöps <sebastian@schoeps.org>
parents: 22647
diff changeset
473 %! assert ([sol.x(end); sol.y(:,end)], [2; fref'], 1e-3);
22626
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
474
22660
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
475 ## Note: The following options have no effect on this solver
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
476 ## therefore it makes no sense to test them here:
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
477 ##
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
478 ## "BDF"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
479 ## "InitialSlope"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
480 ## "JPattern"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
481 ## "Jacobian"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
482 ## "MassSingular"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
483 ## "MaxOrder"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
484 ## "MvPattern"
7eb3f8ec1aed Remove FIXME comment about missing tests for ignored ODE options.
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22659
diff changeset
485 ## "Vectorized"
20901
afe9c529760d 2015 Code Sprint: move ode23 and runge_kutta_23 from odepkg to core
Stefan Miereis <stefan.miereis@gmx.de>
parents:
diff changeset
486
22655
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
487 %!test # Check that imaginary part of solution does not get inverted
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
488 %! sol = ode23 (@(x,y) 1, [0 1], 1i);
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
489 %! assert (imag (sol.y), ones (size (sol.y)))
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
490 %! [x, y] = ode23 (@(x,y) 1, [0 1], 1i);
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
491 %! assert (imag (y), ones (size (y)))
6b134d294d61 ode solvers: use ordinary transpose instead of Hermitian conjugate (bug #49410).
Carlo de Falco <carlo.defalco@polimi.it>
parents: 22654
diff changeset
492
21443
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Rik <rik@octave.org>
parents: 21319
diff changeset
493 ## Test input validation
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Rik <rik@octave.org>
parents: 21319
diff changeset
494 %!error ode23 ()
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
495 %!error ode23 (1)
acd6e203031d Alter BIST tests stop emitting warnings during runtests invocation.
Rik <rik@octave.org>
parents: 21319
diff changeset
496 %!error ode23 (1,2)
22626
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
497 %!error <TRANGE must be a numeric> ode23 (@fpol, {[0 25]}, [3 15 1])
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
498 %!error <TRANGE must be a .* vector> ode23 (@fpol, [0 25; 25 0], [3 15 1])
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
499 %!error <TRANGE must contain at least 2 elements> ode23 (@fpol, [1], [3 15 1])
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
500 %!error <invalid time span> ode23 (@fpol, [1 1], [3 15 1])
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
501 %!error <INIT must be a numeric> ode23 (@fpol, [0 25], {[3 15 1]})
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
502 %!error <INIT must be a .* vector> ode23 (@fpol, [0 25], [3 15 1; 3 15 1])
869c02fde46c Further clean-up of ode functions.
Rik <rik@octave.org>
parents: 22625
diff changeset
503 %!error <FUN must be a valid function handle> ode23 (1, [0 25], [3 15 1])