/
DormandPrince54.cs
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/
DormandPrince54.cs
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/*
* Copyright Lamont Granquist, Sebastien Gaggini and the MechJeb contributors
* SPDX-License-Identifier: MIT-0 OR LGPL-2.1+ OR CC0-1.0
*/
#nullable enable
using System;
using MechJebLib.Primitives;
// ReSharper disable CompareOfFloatsByEqualityOperator
namespace MechJebLib.Core.ODE
{
using IVPFunc = Action<Vn, double, Vn>;
using IVPEvent = Func<double, Vn, Vn, (double x, bool dir, bool stop)>;
/// <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 DormandPrince54 : 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 t, double habs, int direction, Vn y, Vn dy, Vn ynew, Vn dynew, Vn err)
{
double h = habs * direction;
dy.CopyTo(K[1]);
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]);
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;
K[7].CopyTo(dynew);
}
protected override void InitInterpolant(double habs, int direction, Vn y, Vn dy, Vn ynew, Vn dynew)
{
// intentionally left blank
}
// https://doi.org/10.1016/0898-1221(86)90025-8
protected override void Interpolate(double x, double t, double h, Vn y, Vn yout)
{
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]);
}
}
}
}