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annotate +time/ExplicitRungeKuttaDiscreteData.m @ 690:9c3c180c7ed3 feature/d1_staggered

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Implement RK4 for discrete data.
author Martin Almquist <malmquist@stanford.edu>
date Tue, 06 Mar 2018 11:59:43 -0800
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9c3c180c7ed3 Implement RK4 for discrete data.
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1 classdef ExplicitRungeKuttaDiscreteData < time.Timestepper
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2 properties
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3 D
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4 S % Function handle for time-dependent data
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5 data % Matrix of data vectors, one column per stage
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6 F
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7 k
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8 t
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9 v
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10 m
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11 n
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12 order
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13 a, b, c, s % Butcher tableau
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14 K % Stage rates
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15 U % Stage approximations
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16 T % Stage times
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17 end
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18
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19
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20 methods
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21 function obj = ExplicitRungeKuttaDiscreteData(D, S, data, k, t0, v0, order)
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22 default_arg('order', 4);
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23 default_arg('S', []);
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24 default_arg('data', []);
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25
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26 obj.D = D;
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27 obj.S = S;
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28 obj.k = k;
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29 obj.t = t0;
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30 obj.v = v0;
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31 obj.m = length(v0);
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32 obj.n = 0;
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33 obj.order = order;
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34 obj.data = data;
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35
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36 switch order
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37 case 4
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38 [obj.a, obj.b, obj.c, obj.s] = time.rkparameters.rk4();
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39 otherwise
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40 error('That RK method is not available');
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41 end
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42
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43 obj.K = sparse(obj.m, obj.s);
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44 obj.U = sparse(obj.m, obj.s);
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45
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46 end
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47
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48 function [v,t,U,T] = getV(obj)
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49 v = obj.v;
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50 t = obj.t;
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51 U = obj.U; % Stage approximations in previous time step.
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52 T = obj.T; % Stage times in previous time step.
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53 end
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54
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55 function [a,b,c,s] = getTableau(obj)
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56 a = obj.a;
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57 b = obj.b;
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58 c = obj.c;
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59 s = obj.s;
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60 end
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61
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62 function obj = step(obj)
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63 v = obj.v;
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64 a = obj.a;
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65 b = obj.b;
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66 c = obj.c;
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67 s = obj.s;
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68 S = obj.S;
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69 dt = obj.k;
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70 K = obj.K;
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71 U = obj.U;
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72 D = obj.D;
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73 data = obj.data;
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74
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75 for i = 1:s
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76 U(:,i) = v;
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77 for j = 1:i-1
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78 U(:,i) = U(:,i) + dt*a(i,j)*K(:,j);
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79 end
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80
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81 K(:,i) = D*U(:,i);
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82 obj.T(i) = obj.t + c(i)*dt;
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83
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84 % Data from continuos function and discrete time-points.
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85 if ~isempty(S)
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86 K(:,i) = K(:,i) + S(obj.T(i));
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87 end
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88 if ~isempty(data)
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89 K(:,i) = K(:,i) + data(:,obj.n*s + i);
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90 end
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91
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92 end
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93
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94 obj.v = v + dt*K*b;
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95 obj.t = obj.t + dt;
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96 obj.n = obj.n + 1;
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97 obj.U = U;
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98 end
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99 end
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100
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101
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102 methods (Static)
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103 function k = getTimeStep(lambda)
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104
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105 switch obj.order
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106 case 4
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107 k = rk4.get_rk4_time_step(lambda);
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108 otherwise
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109 error('Time-step function not available for this order');
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110 end
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111 end
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112 end
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113
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114 end