/
DP5.cs
177 lines (143 loc) · 7.15 KB
/
DP5.cs
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
/*
* Copyright Lamont Granquist, Sebastien Gaggini and the MechJeb contributors
* SPDX-License-Identifier: LicenseRef-PD-hp OR Unlicense OR CC0-1.0 OR 0BSD OR MIT-0 OR MIT OR LGPL-2.1+
*/
using System;
using System.Collections.Generic;
using MechJebLib.Primitives;
using static MechJebLib.Utils.Statics;
using static System.Math;
// ReSharper disable CompareOfFloatsByEqualityOperator
namespace MechJebLib.ODE
{
using IVPFunc = Action<IList<double>, double, IList<double>>;
/// <summary>
/// https://doi.org/10.1016/0771-050X(80)90013-3
/// https://github.com/PyNumAl/Python-Numerical-Analysis/blob/main/Initial-Value%20Problems/RK%20tableaus/DP54.txt
/// https://github.com/blackstonep/Numerical-Recipes/blob/master/stepperdopr5.h
/// https://github.com/SciML/OrdinaryDiffEq.jl/blob/master/src/tableaus/low_order_rk_tableaus.jl
/// https://github.com/scipy/scipy/blob/main/scipy/integrate/_ivp/rk.py
/// https://github.com/zachjweiner/scipy/blob/8ba609c313f09bf2a333849ca3ac2bd24d7655e7/scipy/integrate/_ivp/rk.py
/// </summary>
public class DP5 : AbstractRungeKutta
{
protected override int Order => 5;
protected override int Stages => 6;
protected override int ErrorEstimatorOrder => 4;
#region IntegrationConstants
// constants for DP5(4)7FM
private const double A21 = 1.0 / 5.0;
private const double A31 = 3.0 / 40.0;
private const double A32 = 9.0 / 40.0;
private const double A41 = 44.0 / 45.0;
private const double A42 = -56.0 / 15.0;
private const double A43 = 32.0 / 9.0;
private const double A51 = 19372.0 / 6561.0;
private const double A52 = -25360.0 / 2187.0;
private const double A53 = 64448.0 / 6561.0;
private const double A54 = -212.0 / 729.0;
private const double A61 = 9017.0 / 3168.0;
private const double A62 = -355.0 / 33.0;
private const double A63 = 46732.0 / 5247.0;
private const double A64 = 49.0 / 176.0;
private const double A65 = -5103.0 / 18656.0;
private const double A71 = 35.0 / 384.0;
private const double A73 = 500.0 / 1113.0;
private const double A74 = 125.0 / 192.0;
private const double A75 = -2187.0 / 6784.0;
private const double A76 = 11.0 / 84.0;
private const double C2 = 1.0 / 5.0;
private const double C3 = 3.0 / 10.0;
private const double C4 = 4.0 / 5.0;
private const double C5 = 8.0 / 9.0;
private const double E1 = 71.0 / 57600.0;
private const double E3 = -71.0 / 16695.0;
private const double E4 = 71.0 / 1920.0;
private const double E5 = -17253.0 / 339200.0;
private const double E6 = 22.0 / 525.0;
private const double E7 = -1.0 / 40.0;
private const double B10 = 11282082432.0 / 11282082432.0;
private const double B11 = -32272833064.0 / 11282082432.0;
private const double B12 = 34969693132.0 / 11282082432.0;
private const double B13 = -13107642775.0 / 11282082432.0;
private const double B14 = 157015080.0 / 11282082432.0;
private const double B31 = -100 * -1323431896.0 / 32700410799.0;
private const double B32 = -100 * 2074956840.0 / 32700410799.0;
private const double B33 = -100 * -914128567.0 / 32700410799.0;
private const double B34 = -100 * 15701508.0 / 32700410799.0;
private const double B41 = 25.0 * -889289856.0 / 5641041216.0;
private const double B42 = 25.0 * 2460397220.0 / 5641041216.0;
private const double B43 = 25.0 * -1518414297.0 / 5641041216.0;
private const double B44 = 25.0 * 94209048.0 / 5641041216.0;
private const double B51 = -2187.0 * -259006536.0 / 199316789632.0;
private const double B52 = -2187.0 * 687873124.0 / 199316789632.0;
private const double B53 = -2187.0 * -451824525.0 / 199316789632.0;
private const double B54 = -2187.0 * 52338360.0 / 199316789632.0;
private const double B61 = 11.0 * -361440756.0 / 2467955532.0;
private const double B62 = 11.0 * 946554244.0 / 2467955532.0;
private const double B63 = 11.0 * -661884105.0 / 2467955532.0;
private const double B64 = 11.0 * 106151040.0 / 2467955532.0;
private const double B71 = 44764047.0 / 29380423.0;
private const double B72 = -82437520.0 / 29380423.0;
private const double B73 = 8293050.0 / 29380423.0;
#endregion
protected override void RKStep(IVPFunc f)
{
double h = Habs * Direction;
K[1].CopyFrom(Dy);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A21 * Dy[i]);
f(Ynew, T + C2 * h, K[2]);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A31 * K[1][i] + A32 * K[2][i]);
f(Ynew, T + C3 * h, K[3]);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A41 * K[1][i] + A42 * K[2][i] + A43 * K[3][i]);
f(Ynew, T + C4 * h, K[4]);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A51 * K[1][i] + A52 * K[2][i] + A53 * K[3][i] + A54 * K[4][i]);
f(Ynew, T + C5 * h, K[5]);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A61 * K[1][i] + A62 * K[2][i] + A63 * K[3][i] + A64 * K[4][i] + A65 * K[5][i]);
f(Ynew, T + h, K[6]);
for (int i = 0; i < N; i++)
Ynew[i] = Y[i] + h * (A71 * K[1][i] + A73 * K[3][i] + A74 * K[4][i] + A75 * K[5][i] + A76 * K[6][i]);
f(Ynew, T + h, K[7]);
K[7].CopyTo(Dynew);
}
protected override double ScaledErrorNorm()
{
using var err = Vn.Rent(N);
for (int i = 0; i < N; i++)
err[i] = K[1][i] * E1 + K[3][i] * E3 + K[4][i] * E4 + K[5][i] * E5 + K[6][i] * E6 + K[7][i] * E7;
double error = 0.0;
for (int i = 0; i < N; i++)
{
double scale = Atol + Rtol * Max(Abs(Y[i]), Abs(Ynew[i]));
error += Powi(err[i] / scale, 2);
}
return Sqrt(error / N);
}
protected override void InitInterpolant()
{
// intentionally left blank
}
// https://doi.org/10.1016/0898-1221(86)90025-8
protected override void Interpolate(double x, Vn yout)
{
double h = Habs * Direction;
double s = (x - T) / h;
double s2 = s * s;
double s3 = s * s2;
double s4 = s2 * s2;
double bs1 = B10 + B11 * s + B12 * s2 + B13 * s3 + B14 * s4;
double bs3 = s * (B31 + B32 * s + B33 * s2 + B34 * s3);
double bs4 = s * (B41 + B42 * s + B43 * s2 + B44 * s3);
double bs5 = s * (B51 + B52 * s + B53 * s2 + B54 * s3);
double bs6 = s * (B61 + B62 * s + B63 * s2 + B64 * s3);
double bs7 = (1.0 - s) * s * (B71 + B72 * s + B73 * s2);
for (int i = 0; i < N; i++)
yout[i] = Y[i] + h * s * (bs1 * K[1][i] + bs3 * K[3][i] + bs4 * K[4][i] + bs5 * K[5][i] + bs6 * K[6][i] + bs7 * K[7][i]);
}
}
}