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annotate scripts/ode/private/integrate_adaptive.m @ 20575:3339c9bdfe6a

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Activate FSAL property in dorpri timestepper * scripts/ode/private/runge_kutta_45_dorpri.m: don't compute first stage if values from previous iteration are passed. * scripts/ode/private/integrate_adaptive.m: do not update cmputed stages if timestep is rejected.
author Carlo de Falco <carlo.defalco@polimi.it>
date Sat, 03 Oct 2015 07:32:50 +0200
parents 6256f6e366ac
children 25623ef2ff4f
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rev   line source
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1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it>
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2 ##
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3 ## This file is part of Octave.
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4 ##
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5 ## Octave is free software; you can redistribute it and/or modify it
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6 ## under the terms of the GNU General Public License as published by
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7 ## the Free Software Foundation; either version 3 of the License, or (at
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8 ## your option) any later version.
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9 ##
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10 ## Octave is distributed in the hope that it will be useful, but
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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13 ## General Public License for more details.
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14 ##
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15 ## You should have received a copy of the GNU General Public License
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16 ## along with Octave; see the file COPYING. If not, see
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17 ## <http://www.gnu.org/licenses/>.
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18
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19
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20 ## -*- texinfo -*-
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21 ## @deftypefn {Command} {[@var{t}, @var{y}] =}
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22 ## integrate_adaptive (@var{@@stepper}, @var{order}, @var{@@fun}, @var{tspan},
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23 ## @var{x0}, @var{options})
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24 ##
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25 ## This function file can be called by a ODE solver function in order to
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26 ## integrate the set of ODEs on the interval @var{[t0,t1]} with an
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27 ## adaptive timestep.
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28 ##
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29 ## This function must be called with two output arguments: @var{t} and @var{y}.
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30 ## Variable @var{t} is a column vector and contains the time stamps, instead
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31 ## @var{y} is a matrix in which each column refers to a different unknown
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32 ## of the problem and the rows number is the same of @var{t} rows number so
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33 ## that each row of @var{y} contains the values of all unknowns at the time
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34 ## value contained in the corresponding row in @var{t}.
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35 ##
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36 ## The first input argument must be a function_handle or an inline function
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37 ## representing the stepper, that is the function responsible for step-by-step
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38 ## integration. This function discriminates one method from the others.
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39 ##
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40 ## The second input argument is the order of the stepper. It is needed
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41 ## to compute the adaptive timesteps.
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42 ##
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43 ## The third input argument is a function_handle or an inline function that
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44 ## defines the set of ODE:
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45 ## @ifhtml
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46 ## @example
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47 ## @math{y' = f(t,y)}
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48 ## @end example
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49 ## @end ifhtml
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50 ## @ifnothtml
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51 ## @math{y' = f(t,y)}.
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52 ## @end ifnothtml
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53 ##
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54 ## The fourth input argument is the time vector which defines integration
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55 ## interval, that is @var{[tspan(1),tspan(end)]} and all the intermediate
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56 ## elements are taken as times at which the solution is required.
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57 ##
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58 ## The fifth argument represents the initial conditions for the ODEs and the
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59 ## last input argument contains some options that may be needed for the stepper.
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60 ##
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61 ## @end deftypefn
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62 ##
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63 ## @seealso{integrate_const, integrate_n_steps}
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64
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65 function solution = integrate_adaptive (stepper, order, func, tspan, x0, options)
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66
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67 solution = struct;
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68
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69 ## first values for time and solution
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70 t = tspan(1);
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71 x = x0(:);
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72
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73 ## get first initial timestep
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74 dt = odeget (options, "InitialStep",
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75 starting_stepsize (order, func, t, x, options.AbsTol,
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76 options.RelTol, options.vnormcontrol),
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77 "fast_not_empty");
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78 vdirection = odeget (options, "vdirection", [], "fast");
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79 if (sign (dt) != vdirection)
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80 dt = -dt;
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81 endif
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82 dt = vdirection * min (abs (dt), options.MaxStep);
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83
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84 ## set parameters
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85 k = length (tspan);
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86 counter = 2;
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87 comp = 0.0;
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88 tk = tspan(1);
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89 options.comp = comp;
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90
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91 ## factor multiplying the stepsize guess
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92 facmin = 0.8;
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93 fac = 0.38^(1/(order+1)); ## formula taken from Hairer
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94 t_caught = false;
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95
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96
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97 ## Initialize the OutputFcn
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98 if (options.vhaveoutputfunction)
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99 if (options.vhaveoutputselection)
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100 solution.vretout = x(options.OutputSel,end);
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101 else
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102 solution.vretout = x;
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103 endif
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104 feval (options.OutputFcn, tspan, solution.vretout,
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105 "init", options.vfunarguments{:});
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106 endif
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107
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108 ## Initialize the EventFcn
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109 if (options.vhaveeventfunction)
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110 odepkg_event_handle (options.Events, t(end), x,
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111 "init", options.vfunarguments{:});
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112 endif
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113
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114 solution.vcntloop = 2;
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115 solution.vcntcycles = 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
116 vcntiter = 0;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
117 solution.vunhandledtermination = true;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
118 solution.vcntsave = 2;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
119
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
120 z = t;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
121 u = x;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
122
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
123 k_vals = [];
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
124
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
125 while (counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
126 facmax = 1.5;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
127
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
128 ## compute integration step from t to t+dt
20575
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
129 if (isempty (k_vals))
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
130 [s, y, y_est, new_k_vals] = stepper (func, z(end), u(:,end),
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
131 dt, options);
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
132 else
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
133 [s, y, y_est, new_k_vals] = stepper (func, z(end), u(:,end),
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
134 dt, options, k_vals);
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
135 endif
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
136
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
137 if (options.vhavenonnegative)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
138 x(options.NonNegative,end) = abs (x(options.NonNegative,end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
139 y(options.NonNegative,end) = abs (y(options.NonNegative,end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
140 y_est(options.NonNegative,end) = abs (y_est(options.NonNegative,end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
141 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
142
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
143 if (options.vhaveoutputfunction && options.vhaverefine)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
144 vSaveVUForRefine = u(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
145 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
146
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
147 err = AbsRel_Norm (y(:,end), u(:,end), options.AbsTol, options.RelTol,
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
148 options.vnormcontrol, y_est(:,end));
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
149
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
150 ## solution accepted only if the error is less or equal to 1.0
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
151 if (err <= 1)
20575
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
152
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
153 [tk, comp] = kahan (tk, comp, dt);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
154 options.comp = comp;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
155 s(end) = tk;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
156
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
157 ## values on this interval for time and solution
20575
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
158 z = [z(end); s];
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
159 u = [u(:,end), y];
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
160 k_vals = new_k_vals;
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
161
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
162 ## if next tspan value is caught, update counter
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
163 if ((z(end) == tspan(counter))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
164 || (abs (z(end) - tspan(counter)) /
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
165 (max (abs (z(end)), abs (tspan(counter)))) < 8*eps) )
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
166 counter++;
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
167
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
168 ## if there is an element in time vector at which the solution is required
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
169 ## the program must compute this solution before going on with next steps
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
170 elseif (vdirection * z(end) > vdirection * tspan(counter))
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
171
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
172 ## initialize counter for the following cycle
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
173 i = 2;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
174 while (i <= length (z))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
175
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
176 ## if next tspan value is caught, update counter
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
177 if ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
178 && ((z(i) == tspan(counter))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
179 || (abs (z(i) - tspan(counter)) /
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
180 (max (abs (z(i)), abs (tspan(counter)))) < 8*eps)) )
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
181 counter++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
182 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
183 ## else, loop until there are requested values inside this subinterval
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
184 while ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
185 && (vdirection * z(i) > vdirection * tspan(counter)))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
186 ## choose interpolation scheme according to order of the solver
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
187 switch order
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
188 case 1
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
189 u_interp = linear_interpolation ([z(i-1) z(i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
190 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
191 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
192 case 2
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
193 if (! isempty (k_vals))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
194 der = k_vals(:,1);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
195 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
196 der = feval (func, z(i-1) , u(:,i-1),
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
197 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
198 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
199 u_interp = quadratic_interpolation ([z(i-1) z(i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
200 [u(:,i-1) u(:,i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
201 der, tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
202 case 3
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
203 u_interp = ...
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
204 hermite_cubic_interpolation ([z(i-1) z(i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
205 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
206 [k_vals(:,1) k_vals(:,end)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
207 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
208 case 4
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
209 ## if ode45 is used without local extrapolation this function
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
210 ## doesn't require a new function evaluation.
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
211 u_interp = dorpri_interpolation ([z(i-1) z(i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
212 [u(:,i-1) u(:,i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
213 k_vals, tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
214 case 5
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
215 ## ode45 with Dormand-Prince scheme:
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
216 ## 4th order approximation of y in t+dt/2 as proposed by
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
217 ## Shampine in Lawrence, Shampine, "Some Practical
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
218 ## Runge-Kutta Formulas", 1986.
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
219 u_half = u(:,i-1) ...
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
220 + 1/2*dt*((6025192743/30085553152) * k_vals(:,1)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
221 + (51252292925/65400821598) * k_vals(:,3)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
222 - (2691868925/45128329728) * k_vals(:,4)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
223 + (187940372067/1594534317056) * k_vals(:,5)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
224 - (1776094331/19743644256) * k_vals(:,6)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
225 + (11237099/235043384) * k_vals(:,7));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
226 u_interp = ...
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
227 hermite_quartic_interpolation ([z(i-1) z(i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
228 [u(:,i-1) u_half u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
229 [k_vals(:,1) k_vals(:,end)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
230 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
231
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
232 ## it is also possible to do a new function evaluation and use
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
233 ## the quintic hermite interpolator
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
234 ## f_half = feval (func, t+1/2*dt, u_half,
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
235 ## options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
236 ## u_interp =
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
237 ## hermite_quintic_interpolation ([z(i-1) z(i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
238 ## [u(:,i-1) u_half u(:,i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
239 ## [k_vals(:,1) f_half k_vals(:,end)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
240 ## tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
241 otherwise
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
242 warning ("High order interpolation not yet implemented: ",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
243 "using cubic iterpolation instead");
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
244 der(:,1) = feval (func, z(i-1) , u(:,i-1),
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
245 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
246 der(:,2) = feval (func, z(i) , u(:,i),
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
247 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
248 u_interp = ...
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
249 hermite_cubic_interpolation ([z(i-1) z(i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
250 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
251 der, tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
252 endswitch
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
253
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
254 ## add the interpolated value of the solution
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
255 u = [u(:,1:i-1), u_interp, u(:,i:end)];
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
256
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
257 ## add the time requested
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
258 z = [z(1:i-1); tspan(counter); z(i:end)];
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
259
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
260 ## update counters
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
261 counter++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
262 i++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
263 endwhile
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
264
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
265 ## if new time requested is not out of this interval
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
266 if ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
267 && (vdirection * z(end) > vdirection * tspan(counter)))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
268 ## update the counter
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
269 i++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
270 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
271 ## stop the cycle and go on with the next iteration
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
272 i = length (z) + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
273 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
274
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
275 endwhile
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
276 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
277
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
278 if (mod (solution.vcntloop-1, options.OutputSave) == 0)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
279 x = [x,u(:,2:end)];
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
280 t = [t;z(2:end)];
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
281 solution.vcntsave = solution.vcntsave + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
282 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
283 solution.vcntloop = solution.vcntloop + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
284 vcntiter = 0;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
285
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
286 ## Call plot only if a valid result has been found, therefore this
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
287 ## code fragment has moved here. Stop integration if plot function
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
288 ## returns false
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
289 if (options.vhaveoutputfunction)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
290 for vcnt = 0:options.Refine # Approximation between told and t
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
291 if (options.vhaverefine) # Do interpolation
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
292 vapproxtime = (vcnt + 1) / (options.Refine + 2);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
293 vapproxvals = (1 - vapproxtime) * vSaveVUForRefine ...
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
294 + (vapproxtime) * y(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
295 vapproxtime = s(end) + vapproxtime * dt;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
296 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
297 vapproxvals = x(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
298 vapproxtime = t(end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
299 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
300 if (options.vhaveoutputselection)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
301 vapproxvals = vapproxvals(options.OutputSel);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
302 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
303 vpltret = feval (options.OutputFcn, vapproxtime,
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
304 vapproxvals, [], options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
305 if (vpltret) # Leave refinement loop
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
306 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
307 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
308 endfor
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
309 if (vpltret) # Leave main loop
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
310 solution.vunhandledtermination = false;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
311 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
312 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
313 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
314
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
315 ## Call event only if a valid result has been found, therefore this
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
316 ## code fragment has moved here. Stop integration if veventbreak is
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
317 ## true
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
318 if (options.vhaveeventfunction)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
319 solution.vevent = odepkg_event_handle (options.Events, t(end),
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
320 x(:,end), [], options.vfunarguments{:});
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
321 if (! isempty (solution.vevent{1})
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
322 && solution.vevent{1} == 1)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
323 t(solution.vcntloop-1,:) = solution.vevent{3}(end,:);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
324 x(:,solution.vcntloop-1) = solution.vevent{4}(end,:)';
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
325 solution.vunhandledtermination = false;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
326 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
327 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
328 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
329
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
330 else
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
331
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
332 facmax = 1.0;
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
333
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
334 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
335
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
336 ## Compute next timestep, formula taken from Hairer
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
337 err += eps; # adding an eps to avoid divisions by zero
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
338 dt = dt * min (facmax,
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
339 max (facmin, fac * (1 / err)^(1 / (order + 1))));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
340 dt = vdirection * min (abs (dt), options.MaxStep);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
341
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
342 ## Update counters that count the number of iteration cycles
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
343 solution.vcntcycles = solution.vcntcycles + 1; # Needed for cost statistics
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
344 vcntiter = vcntiter + 1; # Needed to find iteration problems
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
345
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
346 ## Stop solving because in the last 1000 steps no successful valid
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
347 ## value has been found
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
348 if (vcntiter >= 5000)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
349 error (["Solving has not been successful. The iterative",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
350 " integration loop exited at time t = %f before endpoint at",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
351 " tend = %f was reached. This happened because the iterative",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
352 " integration loop does not find a valid solution at this time",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
353 " stamp. Try to reduce the value of ''InitialStep'' and/or",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
354 " ''MaxStep'' with the command ''odeset''.\n"],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
355 s(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
356 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
357
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
358 ## if this is the last iteration, save the length of last interval
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
359 if (counter > k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
360 j = length (z);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
361 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
362 endwhile
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
363
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
364 ## Check if integration of the ode has been successful
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
365 if (vdirection * z(end) < vdirection * tspan(end))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
366 if (solution.vunhandledtermination == true)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
367 error ("OdePkg:InvalidArgument",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
368 ["Solving has not been successful. The iterative",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
369 " integration loop exited at time t = %f",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
370 " before endpoint at tend = %f was reached. This may",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
371 " happen if the stepsize grows smaller than defined in",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
372 " vminstepsize. Try to reduce the value of ''InitialStep''",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
373 " and/or ''MaxStep'' with the command ''odeset''.\n"],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
374 z(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
375 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
376 warning ("OdePkg:InvalidArgument",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
377 ["Solver has been stopped by a call of ''break'' in the main",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
378 " iteration loop at time t = %f before endpoint at tend = %f ",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
379 " was reached. This may happen because the @odeplot function",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
380 " returned ''true'' or the @event function returned",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
381 " ''true''.\n"],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
382 z(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
383 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
384 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
385
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
386 ## Compute how many values are out of time inerval
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
387 d = vdirection * t((end-(j-1)):end) > vdirection * tspan(end)*ones (j, 1);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
388 f = sum (d);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
389
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
390 ## Remove not-requested values of time and solution
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
391 solution.t = t(1:end-f);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
392 solution.x = x(:,1:end-f)';
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
393
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
394 endfunction