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doc: Rewrite docstrings for ode* family of functions. * scripts/ode/module.mk: Remove extra newline. * ode45.m, odeget.m, odeset.m: Rewrite docstrings. * AbsRel_Norm.m, fuzzy_compare.m, hermite_quartic_interpolation.m, integrate_adaptive.m, integrate_const.m, integrate_n_steps.m, kahan.m, ode_struct_value_check.m, odepkg_event_handle.m, odepkg_structure_check.m, runge_kutta_45_dorpri.m, starting_stepsize.m: Don't break @deftypefn lines. Wrap lines at 80 columns rather than 72.
author Rik <rik@octave.org>
date Sat, 03 Oct 2015 21:03:16 -0700
parents 3339c9bdfe6a
children eb9e2d187ed2
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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 ## -*- texinfo -*-
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20 ## @deftypefn {Function File} {[@var{t}, @var{y}] =} integrate_adaptive (@var{@@stepper}, @var{order}, @var{@@fun}, @var{tspan}, @var{x0}, @var{options})
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21 ##
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22 ## This function file can be called by an ODE solver function in order to
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23 ## integrate the set of ODEs on the interval @var{[t0,t1]} with an
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24 ## adaptive timestep.
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25 ##
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26 ## This function must be called with two output arguments: @var{t} and @var{y}.
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27 ## Variable @var{t} is a column vector and contains the time stamps, instead
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28 ## @var{y} is a matrix in which each column refers to a different unknown
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29 ## of the problem and the rows number is the same of @var{t} rows number so
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30 ## that each row of @var{y} contains the values of all unknowns at the time
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31 ## value contained in the corresponding row in @var{t}.
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32 ##
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33 ## The first input argument must be a function_handle or an inline function
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34 ## representing the stepper, that is the function responsible for step-by-step
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35 ## integration. This function discriminates one method from the others.
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36 ##
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37 ## The second input argument is the order of the stepper. It is needed
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38 ## to compute the adaptive timesteps.
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39 ##
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40 ## The third input argument is a function_handle or an inline function that
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41 ## defines the set of ODE:
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42 ## @ifhtml
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43 ## @example
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44 ## @math{y' = f(t,y)}
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45 ## @end example
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46 ## @end ifhtml
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47 ## @ifnothtml
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48 ## @math{y' = f(t,y)}.
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49 ## @end ifnothtml
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50 ##
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51 ## The fourth input argument is the time vector which defines integration
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52 ## interval, that is @var{[tspan(1),tspan(end)]} and all the intermediate
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53 ## elements are taken as times at which the solution is required.
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54 ##
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55 ## The fifth argument represents the initial conditions for the ODEs and the
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56 ## last input argument contains some options that may be needed for the stepper.
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57 ##
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58 ## @end deftypefn
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59 ##
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60 ## @seealso{integrate_const, integrate_n_steps}
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61
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62 function solution = integrate_adaptive (stepper, order, func, tspan, x0, options)
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63
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64 solution = struct;
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65
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66 ## first values for time and solution
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67 t = tspan(1);
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68 x = x0(:);
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69
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70 ## get first initial timestep
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71 dt = odeget (options, "InitialStep",
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72 starting_stepsize (order, func, t, x, options.AbsTol,
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73 options.RelTol, options.vnormcontrol),
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74 "fast_not_empty");
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75 vdirection = odeget (options, "vdirection", [], "fast");
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76 if (sign (dt) != vdirection)
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77 dt = -dt;
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78 endif
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79 dt = vdirection * min (abs (dt), options.MaxStep);
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80
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81 ## set parameters
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82 k = length (tspan);
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83 counter = 2;
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84 comp = 0.0;
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85 tk = tspan(1);
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86 options.comp = comp;
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87
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88 ## factor multiplying the stepsize guess
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89 facmin = 0.8;
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90 fac = 0.38^(1/(order+1)); ## formula taken from Hairer
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91 t_caught = false;
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92
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93
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94 ## Initialize the OutputFcn
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95 if (options.vhaveoutputfunction)
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96 if (options.vhaveoutputselection)
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97 solution.vretout = x(options.OutputSel,end);
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98 else
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99 solution.vretout = x;
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100 endif
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101 feval (options.OutputFcn, tspan, solution.vretout,
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102 "init", options.vfunarguments{:});
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103 endif
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104
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105 ## Initialize the EventFcn
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106 if (options.vhaveeventfunction)
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107 odepkg_event_handle (options.Events, t(end), x,
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108 "init", options.vfunarguments{:});
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109 endif
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110
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111 solution.vcntloop = 2;
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112 solution.vcntcycles = 1;
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113 vcntiter = 0;
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jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
114 solution.vunhandledtermination = true;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
115 solution.vcntsave = 2;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
116
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
117 z = t;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
118 u = x;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
119
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
120 k_vals = [];
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
121
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
122 while (counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
123 facmax = 1.5;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
124
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
125 ## compute integration step from t to t+dt
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
126 if (isempty (k_vals))
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
127 [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
128 dt, options);
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
129 else
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, k_vals);
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
132 endif
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
133
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
134 if (options.vhavenonnegative)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
135 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
136 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
137 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
138 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
139
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
140 if (options.vhaveoutputfunction && options.vhaverefine)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
141 vSaveVUForRefine = u(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
142 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
143
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
144 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
145 options.vnormcontrol, y_est(:,end));
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
146
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
147 ## 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
148 if (err <= 1)
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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 [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
151 options.comp = comp;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
152 s(end) = tk;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
153
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
154 ## values on this interval for time and solution
20575
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
155 z = [z(end); s];
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
156 u = [u(:,end), y];
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
157 k_vals = new_k_vals;
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
158
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
159 ## 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
160 if ((z(end) == tspan(counter))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
161 || (abs (z(end) - tspan(counter)) /
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
162 (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
163 counter++;
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
164
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
165 ## 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
166 ## the program must compute this solution before going on with next steps
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
167 elseif (vdirection * z(end) > vdirection * tspan(counter))
20575
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
168
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fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
169 ## 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
170 i = 2;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
171 while (i <= length (z))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
172
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
173 ## 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
174 if ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
175 && ((z(i) == tspan(counter))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
176 || (abs (z(i) - tspan(counter)) /
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
177 (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
178 counter++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
179 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
180 ## 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
181 while ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
182 && (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
183 ## 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
184 switch order
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
185 case 1
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
186 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
187 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
188 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
189 case 2
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
190 if (! isempty (k_vals))
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
191 der = k_vals(:,1);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
192 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
193 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
194 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
195 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
196 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
197 [u(:,i-1) u(:,i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
198 der, tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
199 case 3
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
200 u_interp = ...
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
201 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
202 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
203 [k_vals(:,1) k_vals(:,end)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
204 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
205 case 4
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
206 ## 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
207 ## 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
208 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
209 [u(:,i-1) u(:,i)],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
210 k_vals, tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
211 case 5
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
212 ## ode45 with Dormand-Prince scheme:
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
213 ## 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
214 ## 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
215 ## Runge-Kutta Formulas", 1986.
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
216 u_half = u(:,i-1) ...
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
217 + 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
218 + (51252292925/65400821598) * k_vals(:,3)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
219 - (2691868925/45128329728) * k_vals(:,4)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
220 + (187940372067/1594534317056) * k_vals(:,5)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
221 - (1776094331/19743644256) * k_vals(:,6)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
222 + (11237099/235043384) * k_vals(:,7));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
223 u_interp = ...
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Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
224 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
225 [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
226 [k_vals(:,1) k_vals(:,end)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
227 tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
228
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
229 ## 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
230 ## the quintic hermite interpolator
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
231 ## 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
232 ## options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
233 ## u_interp =
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
234 ## 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
235 ## [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
236 ## [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
237 ## tspan(counter));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
238 otherwise
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
239 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
240 "using cubic iterpolation instead");
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
241 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
242 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
243 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
244 options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
245 u_interp = ...
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
246 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
247 [u(:,i-1) u(:,i)],
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
248 der, tspan(counter));
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
249 endswitch
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
250
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
251 ## 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
252 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
253
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
254 ## add the time requested
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
255 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
256
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
257 ## update counters
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
258 counter++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
259 i++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
260 endwhile
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
261
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
262 ## 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
263 if ((counter <= k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
264 && (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
265 ## update the counter
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
266 i++;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
267 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
268 ## 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
269 i = length (z) + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
270 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
271
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
272 endwhile
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 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
276 x = [x,u(:,2:end)];
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
277 t = [t;z(2:end)];
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
278 solution.vcntsave = solution.vcntsave + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
279 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
280 solution.vcntloop = solution.vcntloop + 1;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
281 vcntiter = 0;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
282
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
283 ## 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
284 ## 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
285 ## returns false
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
286 if (options.vhaveoutputfunction)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
287 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
288 if (options.vhaverefine) # Do interpolation
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
289 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
290 vapproxvals = (1 - vapproxtime) * vSaveVUForRefine ...
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
291 + (vapproxtime) * y(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
292 vapproxtime = s(end) + vapproxtime * dt;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
293 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
294 vapproxvals = x(:,end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
295 vapproxtime = t(end);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
296 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
297 if (options.vhaveoutputselection)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
298 vapproxvals = vapproxvals(options.OutputSel);
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 vpltret = feval (options.OutputFcn, vapproxtime,
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
301 vapproxvals, [], options.vfunarguments{:});
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
302 if (vpltret) # Leave refinement loop
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
303 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
304 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
305 endfor
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
306 if (vpltret) # Leave main loop
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
307 solution.vunhandledtermination = false;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
308 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
309 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
310 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
311
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
312 ## 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
313 ## 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
314 ## true
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
315 if (options.vhaveeventfunction)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
316 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
317 x(:,end), [], options.vfunarguments{:});
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
318 if (! isempty (solution.vevent{1})
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
319 && solution.vevent{1} == 1)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
320 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
321 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
322 solution.vunhandledtermination = false;
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
323 break
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
324 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
325 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
326
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
327 else
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
328
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
329 facmax = 1.0;
20575
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
330
20568
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
331 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
332
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
333 ## 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
334 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
335 dt = dt * min (facmax,
3339c9bdfe6a Activate FSAL property in dorpri timestepper
Carlo de Falco <carlo.defalco@polimi.it>
parents: 20570
diff changeset
336 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
337 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
338
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
339 ## 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
340 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
341 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
342
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
343 ## 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
344 ## value has been found
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
345 if (vcntiter >= 5000)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
346 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
347 " 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
348 " 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
349 " 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
350 " 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
351 " ''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
352 s(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
353 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
354
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
355 ## 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
356 if (counter > k)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
357 j = length (z);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
358 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
359 endwhile
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
360
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
361 ## 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
362 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
363 if (solution.vunhandledtermination == true)
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
364 error ("OdePkg:InvalidArgument",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
365 ["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
366 " 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
367 " 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
368 " 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
369 " 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
370 " 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
371 z(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
372 else
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
373 warning ("OdePkg:InvalidArgument",
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
374 ["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
375 " 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
376 " 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
377 " 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
378 " ''true''.\n"],
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
379 z(end), tspan(end));
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
380 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
381 endif
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
382
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
383 ## 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
384 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
385 f = sum (d);
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
386
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
387 ## 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
388 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
389 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
390
fcb792acab9b Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff changeset
391 endfunction