public void OdeSine2()
{
Func <double, IList <double>, IList <double> > f2 = (double x, IList <double> y) => new double[] { -y[0] };
double[] y0 = new double[] { 0.0 };
double[] yp0 = new double[] { 1.0 };
ColumnVector z = MultiFunctionMath.SolveConservativeOde(f2, 0.0, y0, yp0, 5.0);
}
public void OdeOrbit()
{
// This is a simple Keplerian orbit.
// Hull (1972) constructed initial conditions that guarantee a given orbital eccentricity
// and a period of 2 \pi with unit masses and unit gravitational constant.
Func <double, IList <double>, IList <double> > rhs = (double t, IList <double> r) => {
double d = MoreMath.Hypot(r[0], r[1]);
double d3 = MoreMath.Pow(d, 3);
return(new double[] { -r[0] / d3, -r[1] / d3 });
};
EvaluationSettings settings = new EvaluationSettings()
{
RelativePrecision = 1.0E-12, AbsolutePrecision = 1.0E-24, EvaluationBudget = 10000
};
settings.UpdateHandler = (EvaluationResult a) => {
OdeResult <IList <double> > b = (OdeResult <IList <double> >)a;
Console.WriteLine("{0} {1}", b.EvaluationCount, b.X);
};
//double e = 0.5;
foreach (double e in TestUtilities.GenerateUniformRealValues(0.0, 1.0, 8))
{
Console.WriteLine("e = {0}", e);
ColumnVector r0 = new ColumnVector(1.0 - e, 0.0);
ColumnVector rp0 = new ColumnVector(0.0, Math.Sqrt((1.0 + e) / (1.0 - e)));
settings.UpdateHandler = (EvaluationResult a) => {
OdeResult <IList <double> > b = (OdeResult <IList <double> >)a;
Console.WriteLine(" {0} {1}", b.EvaluationCount, b.X);
Console.WriteLine(" {0} ?= {1}", OrbitEnergy(b.Y, b.YPrime), OrbitEnergy(r0, rp0));
Assert.IsTrue(TestUtilities.IsNearlyEqual(OrbitAngularMomentum(b.Y, b.YPrime), OrbitAngularMomentum(r0, rp0), settings));
Assert.IsTrue(TestUtilities.IsNearlyEqual(OrbitEnergy(b.Y, b.YPrime), OrbitEnergy(r0, rp0), new EvaluationSettings()
{
RelativePrecision = 2.0E-12
}));
};
ColumnVector r1 = MultiFunctionMath.SolveConservativeOde(rhs, 0.0, r0, rp0, 2.0 * Math.PI, settings);
// The
Assert.IsTrue(TestUtilities.IsNearlyEqual(r0, r1, new EvaluationSettings()
{
RelativePrecision = 1.0E-9
}));
}
}
