Mercurial > octave-nkf
annotate scripts/ode/private/integrate_adaptive.m @ 20584:eb9e2d187ed2
maint: Use Octave coding conventions in scripts/ode/private dir.
* 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:
Wrap long lines to < 80 chars.
Use double quotes rather than single quotes where possible.
Use ';' at end of keywords "return;" and "break;"
Use '##" for stand-alone comments and '#' for end-of-line comments.
Use two spaces after period before starting new sentence.
Use '!' instead of '~' for logical negation.
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author | Rik <rik@octave.org> |
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date | Sun, 04 Oct 2015 22:18:54 -0700 |
parents | 25623ef2ff4f |
children | b7ac1e94266e |
rev | line source |
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1 ## Copyright (C) 2013, Roberto Porcu' <roberto.porcu@polimi.it> |
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2 ## |
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3 ## This file is part of Octave. |
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4 ## |
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5 ## Octave is free software; you can redistribute it and/or modify it |
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6 ## under the terms of the GNU General Public License as published by |
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7 ## the Free Software Foundation; either version 3 of the License, or (at |
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8 ## your option) any later version. |
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9 ## |
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10 ## Octave is distributed in the hope that it will be useful, but |
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11 ## WITHOUT ANY WARRANTY; without even the implied warranty of |
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12 ## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU |
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13 ## General Public License for more details. |
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14 ## |
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15 ## You should have received a copy of the GNU General Public License |
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16 ## along with Octave; see the file COPYING. If not, see |
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17 ## <http://www.gnu.org/licenses/>. |
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18 |
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19 ## -*- 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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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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102 "init", options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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103 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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104 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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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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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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111 solution.vcntloop = 2; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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112 solution.vcntcycles = 1; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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113 vcntiter = 0; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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114 solution.vunhandledtermination = true; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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115 solution.vcntsave = 2; |
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116 |
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117 z = t; |
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118 u = x; |
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119 |
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120 k_vals = []; |
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121 |
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122 while (counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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123 facmax = 1.5; |
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124 |
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125 ## Compute integration step from t to t+dt |
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126 if (isempty (k_vals)) |
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127 [s, y, y_est, new_k_vals] = stepper (func, z(end), u(:,end), |
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128 dt, options); |
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129 else |
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130 [s, y, y_est, new_k_vals] = stepper (func, z(end), u(:,end), |
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131 dt, options, k_vals); |
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132 endif |
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133 |
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134 if (options.vhavenonnegative) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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135 x(options.NonNegative,end) = abs (x(options.NonNegative,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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136 y(options.NonNegative,end) = abs (y(options.NonNegative,end)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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137 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.
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138 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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139 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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140 if (options.vhaveoutputfunction && options.vhaverefine) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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141 vSaveVUForRefine = u(:,end); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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142 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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143 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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144 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.
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145 options.vnormcontrol, y_est(:,end)); |
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146 |
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147 ## Solution accepted only if the error is less or equal to 1.0 |
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148 if (err <= 1) |
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149 |
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150 [tk, comp] = kahan (tk, comp, dt); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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151 options.comp = comp; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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152 s(end) = tk; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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153 |
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154 ## values on this interval for time and solution |
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155 z = [z(end); s]; |
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156 u = [u(:,end), y]; |
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157 k_vals = new_k_vals; |
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158 |
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159 ## if next tspan value is caught, update counter |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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160 if ((z(end) == tspan(counter)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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161 || (abs (z(end) - tspan(counter)) / |
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162 (max (abs (z(end)), abs (tspan(counter)))) < 8*eps) ) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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163 counter++; |
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164 |
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165 ## if there is an element in time vector at which the solution is |
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166 ## required the program must compute this solution before going on with |
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167 ## next steps |
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168 elseif (vdirection * z(end) > vdirection * tspan(counter)) |
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169 |
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170 ## initialize counter for the following cycle |
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171 i = 2; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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172 while (i <= length (z)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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173 |
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174 ## if next tspan value is caught, update counter |
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175 if ((counter <= k) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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176 && ((z(i) == tspan(counter)) |
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177 || (abs (z(i) - tspan(counter)) / |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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178 (max (abs (z(i)), abs (tspan(counter)))) < 8*eps)) ) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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179 counter++; |
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180 endif |
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181 ## else, loop until there are requested values inside this subinterval |
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182 while ((counter <= k) |
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183 && (vdirection * z(i) > vdirection * tspan(counter))) |
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184 ## choose interpolation scheme according to order of the solver |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
185 switch order |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
186 case 1 |
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187 u_interp = linear_interpolation ([z(i-1) z(i)], |
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188 [u(:,i-1) u(:,i)], |
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189 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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changeset
|
190 case 2 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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191 if (! isempty (k_vals)) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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192 der = k_vals(:,1); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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193 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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194 der = feval (func, z(i-1) , u(:,i-1), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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195 options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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196 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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197 u_interp = quadratic_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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198 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
199 der, tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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changeset
|
200 case 3 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
201 u_interp = ... |
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202 hermite_cubic_interpolation ([z(i-1) z(i)], |
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203 [u(:,i-1) u(:,i)], |
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204 [k_vals(:,1) k_vals(:,end)], |
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205 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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changeset
|
206 case 4 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
207 ## if ode45 is used without local extrapolation this function |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
208 ## doesn't require a new function evaluation. |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
209 u_interp = dorpri_interpolation ([z(i-1) z(i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
210 [u(:,i-1) u(:,i)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
211 k_vals, 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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|
212 case 5 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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213 ## ode45 with Dormand-Prince scheme: |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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214 ## 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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215 ## Shampine in Lawrence, Shampine, "Some Practical |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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216 ## Runge-Kutta Formulas", 1986. |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
217 u_half = u(:,i-1) ... |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
218 + 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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219 + (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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220 - (2691868925/45128329728) * k_vals(:,4) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
221 + (187940372067/1594534317056) * k_vals(:,5) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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222 - (1776094331/19743644256) * k_vals(:,6) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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223 + (11237099/235043384) * k_vals(:,7)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
224 u_interp = ... |
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225 hermite_quartic_interpolation ([z(i-1) z(i)], |
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226 [u(:,i-1) u_half u(:,i)], |
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227 [k_vals(:,1) k_vals(:,end)], |
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228 tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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229 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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230 ## 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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231 ## the quintic hermite interpolator |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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232 ## 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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|
233 ## options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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234 ## u_interp = |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
235 ## 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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|
236 ## [u(:,i-1) u_half u(:,i)], |
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237 ## [k_vals(:,1) f_half ... |
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238 ## k_vals(:,end)], |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
239 ## 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
|
240 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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changeset
|
241 warning ("High order interpolation not yet implemented: ", |
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|
242 "using cubic interpolation instead"); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
243 der(:,1) = feval (func, z(i-1) , u(:,i-1), |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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changeset
|
244 options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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245 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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|
246 options.vfunarguments{:}); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
247 u_interp = ... |
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248 hermite_cubic_interpolation ([z(i-1) z(i)], |
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249 [u(:,i-1) u(:,i)], |
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250 der, tspan(counter)); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
251 endswitch |
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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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|
253 ## add the interpolated value of the solution |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
254 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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|
255 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
256 ## add the time requested |
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parents:
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|
257 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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|
258 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
259 ## 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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|
260 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 i++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
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|
262 endwhile |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
263 |
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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 ## 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>
parents:
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|
265 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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|
266 && (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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|
267 ## update the counter |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
268 i++; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
269 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
270 ## stop the cycle and go on with the next iteration |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
271 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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|
272 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
273 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
274 endwhile |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
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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|
276 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
277 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
|
278 x = [x,u(:,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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|
279 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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|
280 solution.vcntsave = solution.vcntsave + 1; |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
jcorno <jacopo.corno@gmail.com>
parents:
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|
281 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
|
282 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
|
283 vcntiter = 0; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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changeset
|
284 |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
285 ## Call plot only if a valid result has been found, therefore this |
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|
286 ## 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
|
287 ## returns 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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|
288 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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|
289 for vcnt = 0:options.Refine # Approximation between told and t |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
290 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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|
291 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
|
292 vapproxvals = (1 - vapproxtime) * vSaveVUForRefine ... |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
293 + (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
|
294 vapproxtime = s(end) + vapproxtime * dt; |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
295 else |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
296 vapproxvals = x(:,end); |
fcb792acab9b
Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
297 vapproxtime = t(end); |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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|
298 endif |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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|
299 if (options.vhaveoutputselection) |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
300 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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|
301 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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|
302 vpltret = feval (options.OutputFcn, vapproxtime, |
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Moving ode45, odeset, odeget, and levenshtein from odepkg to core.
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parents:
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changeset
|
303 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
|
304 if (vpltret) # Leave refinement loop |
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|
305 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
|
306 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
|
307 endfor |
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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 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
|
309 solution.vunhandledtermination = false; |
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310 break; |
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311 endif |
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312 endif |
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313 |
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314 ## Call event only if a valid result has been found, therefore this |
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315 ## code fragment has moved here. Stop integration if veventbreak is |
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316 ## true |
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317 if (options.vhaveeventfunction) |
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318 solution.vevent = odepkg_event_handle (options.Events, t(end), |
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319 x(:,end), [], |
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320 options.vfunarguments{:}); |
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321 if (! isempty (solution.vevent{1}) |
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322 && solution.vevent{1} == 1) |
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323 t(solution.vcntloop-1,:) = solution.vevent{3}(end,:); |
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324 x(:,solution.vcntloop-1) = solution.vevent{4}(end,:)'; |
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325 solution.vunhandledtermination = false; |
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326 break; |
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327 endif |
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328 endif |
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329 |
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330 else |
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331 |
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332 facmax = 1.0; |
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333 |
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334 endif |
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335 |
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336 ## Compute next timestep, formula taken from Hairer |
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337 err += eps; # adding an eps to avoid divisions by zero |
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338 dt = dt * min (facmax, |
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339 max (facmin, fac * (1 / err)^(1 / (order + 1)))); |
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340 dt = vdirection * min (abs (dt), options.MaxStep); |
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341 |
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342 ## Update counters that count the number of iteration cycles |
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343 solution.vcntcycles += 1; # Needed for cost statistics |
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344 vcntiter += 1; # Needed to find iteration problems |
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345 |
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346 ## Stop solving because in the last 1000 steps no successful valid |
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347 ## value has been found |
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348 if (vcntiter >= 5000) |
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349 error (["Solving has not been successful. The iterative", |
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350 " integration loop exited at time t = %f before endpoint at", |
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351 " tend = %f was reached. This happened because the iterative", |
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352 " integration loop does not find a valid solution at this time", |
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353 " stamp. Try to reduce the value of 'InitialStep' and/or", |
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354 " 'MaxStep' with the command 'odeset'.\n"], |
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355 s(end), tspan(end)); |
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356 endif |
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357 |
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358 ## if this is the last iteration, save the length of last interval |
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359 if (counter > k) |
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360 j = length (z); |
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361 endif |
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362 endwhile |
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363 |
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364 ## Check if integration of the ode has been successful |
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365 if (vdirection * z(end) < vdirection * tspan(end)) |
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366 if (solution.vunhandledtermination == true) |
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367 error ("OdePkg:InvalidArgument", |
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368 ["Solving has not been successful. The iterative", |
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369 " integration loop exited at time t = %f", |
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370 " before endpoint at tend = %f was reached. This may", |
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371 " happen if the stepsize grows smaller than defined in", |
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372 " vminstepsize. Try to reduce the value of 'InitialStep'", |
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373 " and/or 'MaxStep' with the command 'odeset'.\n"], |
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374 z(end), tspan(end)); |
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375 else |
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376 warning ("OdePkg:InvalidArgument", |
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377 ["Solver has been stopped by a call of 'break' in the main", |
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378 " iteration loop at time t = %f before endpoint at tend = %f ", |
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379 " was reached. This may happen because the @odeplot function", |
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380 " returned 'true' or the @event function returned", |
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381 " 'true'.\n"], |
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382 z(end), tspan(end)); |
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383 endif |
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384 endif |
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385 |
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386 ## Compute how many values are out of time inerval |
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387 d = vdirection * t((end-(j-1)):end) > vdirection * tspan(end)*ones (j, 1); |
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388 f = sum (d); |
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389 |
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390 ## Remove not-requested values of time and solution |
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391 solution.t = t(1:end-f); |
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392 solution.x = x(:,1:end-f)'; |
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|
393 |
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394 endfunction |
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395 |