Mercurial > octave-nkf
annotate scripts/ode/private/integrate_adaptive.m @ 20570:6256f6e366ac
Fix copyright text in private ode functions
* script/ode/private/*.m: Fox the copyright text.
author | Carlo de Falco <carlo.defalco@polimi.it> |
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date | Fri, 02 Oct 2015 05:50:43 +0200 |
parents | fcb792acab9b |
children | 3339c9bdfe6a |
rev | line source |
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20568
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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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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
105 "init", options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
106 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
107 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
108 ## Initialize the EventFcn |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
109 if (options.vhaveeventfunction) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
110 odepkg_event_handle (options.Events, t(end), x, |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
111 "init", options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
112 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
113 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
114 solution.vcntloop = 2; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
115 solution.vcntcycles = 1; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
116 vcntiter = 0; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
117 solution.vunhandledtermination = true; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
118 solution.vcntsave = 2; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
119 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
120 z = t; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
121 u = x; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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122 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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123 k_vals = feval (func, t , x, options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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124 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
125 while (counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
126 facmax = 1.5; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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127 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
128 ## compute integration step from t to t+dt |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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129 [s, y, y_est, k_vals] = stepper (func, z(end), u(:,end), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
130 dt, options, k_vals); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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131 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
132 if (options.vhavenonnegative) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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133 x(options.NonNegative,end) = abs (x(options.NonNegative,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
134 y(options.NonNegative,end) = abs (y(options.NonNegative,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
135 y_est(options.NonNegative,end) = abs (y_est(options.NonNegative,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
136 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
137 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
138 if (options.vhaveoutputfunction && options.vhaverefine) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
139 vSaveVUForRefine = u(:,end); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
140 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
141 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
142 err = AbsRel_Norm (y(:,end), u(:,end), options.AbsTol, options.RelTol, |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
143 options.vnormcontrol, y_est(:,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
144 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
145 ## solution accepted only if the error is less or equal to 1.0 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
146 if (err <= 1) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
147 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
148 [tk, comp] = kahan (tk, comp, dt); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
149 options.comp = comp; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
150 s(end) = tk; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
151 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
152 ## values on this interval for time and solution |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
153 z = [z(end);s]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
154 u = [u(:,end),y]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
155 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
156 ## if next tspan value is caught, update counter |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
157 if ((z(end) == tspan(counter)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
158 || (abs (z(end) - tspan(counter)) / |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
159 (max (abs (z(end)), abs (tspan(counter)))) < 8*eps) ) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
160 counter++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
161 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
162 ## if there is an element in time vector at which the solution is required |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
163 ## the program must compute this solution before going on with next steps |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
164 elseif (vdirection * z(end) > vdirection * tspan(counter)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
165 ## initialize counter for the following cycle |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
166 i = 2; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
167 while (i <= length (z)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
168 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
169 ## if next tspan value is caught, update counter |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
170 if ((counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
171 && ((z(i) == tspan(counter)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
172 || (abs (z(i) - tspan(counter)) / |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
173 (max (abs (z(i)), abs (tspan(counter)))) < 8*eps)) ) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
174 counter++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
175 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
176 ## else, loop until there are requested values inside this subinterval |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
177 while ((counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
178 && (vdirection * z(i) > vdirection * tspan(counter))) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
179 ## choose interpolation scheme according to order of the solver |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
180 switch order |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
181 case 1 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
182 u_interp = linear_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
183 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
184 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
185 case 2 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
186 if (! isempty (k_vals)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
187 der = k_vals(:,1); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
188 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
189 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
|
190 options.vfunarguments{:}); |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
191 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
192 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
|
193 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
194 der, tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
195 case 3 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
196 u_interp = ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
197 hermite_cubic_interpolation ([z(i-1) z(i)], |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
198 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
199 [k_vals(:,1) k_vals(:,end)], |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
200 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
201 case 4 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
202 ## if ode45 is used without local extrapolation this function |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
203 ## 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
|
204 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
|
205 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
206 k_vals, tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
207 case 5 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
208 ## ode45 with Dormand-Prince scheme: |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
209 ## 4th order approximation of y in t+dt/2 as proposed by |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
210 ## Shampine in Lawrence, Shampine, "Some Practical |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
211 ## Runge-Kutta Formulas", 1986. |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
212 u_half = u(:,i-1) ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
213 + 1/2*dt*((6025192743/30085553152) * k_vals(:,1) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
214 + (51252292925/65400821598) * k_vals(:,3) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
215 - (2691868925/45128329728) * k_vals(:,4) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
216 + (187940372067/1594534317056) * k_vals(:,5) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
217 - (1776094331/19743644256) * k_vals(:,6) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
218 + (11237099/235043384) * k_vals(:,7)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
219 u_interp = ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
220 hermite_quartic_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
221 [u(:,i-1) u_half u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
222 [k_vals(:,1) k_vals(:,end)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
223 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
224 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
225 ## it is also possible to do a new function evaluation and use |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
226 ## the quintic hermite interpolator |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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227 ## f_half = feval (func, t+1/2*dt, u_half, |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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228 ## options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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229 ## u_interp = |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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230 ## hermite_quintic_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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231 ## [u(:,i-1) u_half u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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232 ## [k_vals(:,1) f_half k_vals(:,end)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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233 ## tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
234 otherwise |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
235 warning ("High order interpolation not yet implemented: ", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
236 "using cubic iterpolation instead"); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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237 der(:,1) = feval (func, z(i-1) , u(:,i-1), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
238 options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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239 der(:,2) = feval (func, z(i) , u(:,i), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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240 options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
241 u_interp = ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
242 hermite_cubic_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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243 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
244 der, tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
245 endswitch |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
246 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
247 ## add the interpolated value of the solution |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
248 u = [u(:,1:i-1), u_interp, u(:,i:end)]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
249 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
250 ## add the time requested |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
251 z = [z(1:i-1);tspan(counter);z(i:end)]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
252 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
253 ## update counters |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
254 counter++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
255 i++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
256 endwhile |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
257 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
258 ## if new time requested is not out of this interval |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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|
259 if ((counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
260 && (vdirection * z(end) > vdirection * tspan(counter))) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
261 ## update the counter |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
262 i++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
263 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
264 ## stop the cycle and go on with the next iteration |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
265 i = length (z) + 1; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
266 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
267 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
268 endwhile |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
269 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
270 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
271 if (mod (solution.vcntloop-1, options.OutputSave) == 0) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
272 x = [x,u(:,2:end)]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
273 t = [t;z(2:end)]; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
274 solution.vcntsave = solution.vcntsave + 1; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
275 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
276 solution.vcntloop = solution.vcntloop + 1; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
277 vcntiter = 0; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
278 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
279 ## Call plot only if a valid result has been found, therefore this |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
280 ## code fragment has moved here. Stop integration if plot function |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
281 ## returns false |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
282 if (options.vhaveoutputfunction) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
283 for vcnt = 0:options.Refine # Approximation between told and t |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
284 if (options.vhaverefine) # Do interpolation |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
285 vapproxtime = (vcnt + 1) / (options.Refine + 2); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
286 vapproxvals = (1 - vapproxtime) * vSaveVUForRefine ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
287 + (vapproxtime) * y(:,end); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
288 vapproxtime = s(end) + vapproxtime * dt; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
289 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
290 vapproxvals = x(:,end); |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
291 vapproxtime = t(end); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
292 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
293 if (options.vhaveoutputselection) |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
294 vapproxvals = vapproxvals(options.OutputSel); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
295 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
296 vpltret = feval (options.OutputFcn, vapproxtime, |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
297 vapproxvals, [], options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
298 if (vpltret) # Leave refinement loop |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
299 break |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
300 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
301 endfor |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
302 if (vpltret) # Leave main loop |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
303 solution.vunhandledtermination = false; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
304 break |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
305 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
306 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
diff
changeset
|
307 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
308 ## 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:
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changeset
|
309 ## code fragment has moved here. Stop integration if veventbreak is |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
310 ## true |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
311 if (options.vhaveeventfunction) |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
diff
changeset
|
312 solution.vevent = odepkg_event_handle (options.Events, t(end), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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313 x(:,end), [], options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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314 if (! isempty (solution.vevent{1}) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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315 && solution.vevent{1} == 1) |
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316 t(solution.vcntloop-1,:) = solution.vevent{3}(end,:); |
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317 x(:,solution.vcntloop-1) = solution.vevent{4}(end,:)'; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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318 solution.vunhandledtermination = false; |
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319 break |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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320 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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321 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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322 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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323 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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324 facmax = 1.0; |
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325 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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326 |
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327 ## Compute next timestep, formula taken from Hairer |
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328 err += eps; # adding an eps to avoid divisions by zero |
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329 dt = dt * min (facmax, max (facmin, |
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330 fac * (1 / err)^(1 / (order + 1)))); |
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331 dt = vdirection * min (abs (dt), options.MaxStep); |
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332 |
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333 ## Update counters that count the number of iteration cycles |
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334 solution.vcntcycles = solution.vcntcycles + 1; # Needed for cost statistics |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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335 vcntiter = vcntiter + 1; # Needed to find iteration problems |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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336 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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337 ## Stop solving because in the last 1000 steps no successful valid |
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338 ## value has been found |
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339 if (vcntiter >= 5000) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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340 error (["Solving has not been successful. The iterative", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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341 " integration loop exited at time t = %f before endpoint at", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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342 " tend = %f was reached. This happened because the iterative", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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343 " integration loop does not find a valid solution at this time", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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344 " stamp. Try to reduce the value of ''InitialStep'' and/or", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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345 " ''MaxStep'' with the command ''odeset''.\n"], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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346 s(end), tspan(end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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347 endif |
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348 |
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349 ## if this is the last iteration, save the length of last interval |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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350 if (counter > k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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351 j = length (z); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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352 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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353 endwhile |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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354 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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355 ## Check if integration of the ode has been successful |
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parents:
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356 if (vdirection * z(end) < vdirection * tspan(end)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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357 if (solution.vunhandledtermination == true) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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358 error ("OdePkg:InvalidArgument", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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359 ["Solving has not been successful. The iterative", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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360 " integration loop exited at time t = %f", |
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361 " before endpoint at tend = %f was reached. This may", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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362 " happen if the stepsize grows smaller than defined in", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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363 " vminstepsize. Try to reduce the value of ''InitialStep''", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
364 " and/or ''MaxStep'' with the command ''odeset''.\n"], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
365 z(end), tspan(end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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|
366 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
367 warning ("OdePkg:InvalidArgument", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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368 ["Solver has been stopped by a call of ''break'' in the main", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
369 " iteration loop at time t = %f before endpoint at tend = %f ", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
370 " was reached. This may happen because the @odeplot function", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
371 " returned ''true'' or the @event function returned", |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
372 " ''true''.\n"], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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373 z(end), tspan(end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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374 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
375 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
376 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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|
377 ## Compute how many values are out of time inerval |
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378 d = vdirection * t((end-(j-1)):end) > vdirection * tspan(end)*ones (j, 1); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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379 f = sum (d); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
380 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
381 ## Remove not-requested values of time and solution |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
382 solution.t = t(1:end-f); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
383 solution.x = x(:,1:end-f)'; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
384 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
385 endfunction |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
386 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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changeset
|
387 ## Local Variables: *** |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
388 ## mode: octave *** |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
389 ## End: *** |