public void IntegerBesselSpecialCase()
{
Assert.IsTrue(AdvancedMath.BesselJ(0, 0.0) == 1.0);
Assert.IsTrue(AdvancedMath.BesselJ(1, 0.0) == 0.0);
Assert.IsTrue(AdvancedMath.BesselY(0, 0.0) == Double.NegativeInfinity);
Assert.IsTrue(AdvancedMath.BesselY(1, 0.0) == Double.NegativeInfinity);
}
public void BesselAtZero()
{
// Normal Bessel \nu = 0
Assert.IsTrue(AdvancedMath.BesselJ(0, 0.0) == 1.0);
Assert.IsTrue(AdvancedMath.BesselJ(0.0, 0.0) == 1.0);
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(0, 0.0)));
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(0.0, 0.0)));
SolutionPair jy0 = AdvancedMath.Bessel(0.0, 0.0);
Assert.IsTrue(jy0.FirstSolutionValue == 1.0);
Assert.IsTrue(jy0.FirstSolutionDerivative == 0.0);
Assert.IsTrue(Double.IsNegativeInfinity(jy0.SecondSolutionValue));
Assert.IsTrue(Double.IsPositiveInfinity(jy0.SecondSolutionDerivative));
// Normal Bessel 0 < \nu < 1
Assert.IsTrue(AdvancedMath.BesselJ(0.1, 0.0) == 0.0);
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(0.1, 0.0)));
SolutionPair jyf = AdvancedMath.Bessel(0.9, 0.0);
Assert.IsTrue(jyf.FirstSolutionValue == 0.0);
Assert.IsTrue(jyf.FirstSolutionDerivative == Double.PositiveInfinity);
Assert.IsTrue(Double.IsNegativeInfinity(jyf.SecondSolutionValue));
Assert.IsTrue(Double.IsPositiveInfinity(jyf.SecondSolutionDerivative));
// Normal Bessel \nu = 1
Assert.IsTrue(AdvancedMath.BesselJ(1, 0.0) == 0.0);
Assert.IsTrue(AdvancedMath.BesselJ(1.0, 0.0) == 0.0);
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(1, 0.0)));
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(1.0, 0.0)));
SolutionPair jy1 = AdvancedMath.Bessel(1.0, 0.0);
Assert.IsTrue(jy1.FirstSolutionValue == 0.0);
Assert.IsTrue(jy1.FirstSolutionDerivative == 0.5);
Assert.IsTrue(Double.IsNegativeInfinity(jy1.SecondSolutionValue));
Assert.IsTrue(Double.IsPositiveInfinity(jy1.SecondSolutionDerivative));
// Normal Bessel \nu > 1
Assert.IsTrue(AdvancedMath.BesselJ(2, 0.0) == 0.0);
Assert.IsTrue(AdvancedMath.BesselJ(1.2, 0.0) == 0.0);
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(2, 0.0)));
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.BesselY(1.2, 0.0)));
SolutionPair jy2 = AdvancedMath.Bessel(1.7, 0.0);
Assert.IsTrue(jy2.FirstSolutionValue == 0.0);
Assert.IsTrue(jy2.FirstSolutionDerivative == 0.0);
Assert.IsTrue(Double.IsNegativeInfinity(jy2.SecondSolutionValue));
Assert.IsTrue(Double.IsPositiveInfinity(jy2.SecondSolutionDerivative));
}
public void IntegerBesselNegativeOrder()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 1000, 4))
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E6, 8))
{
int s = (n % 2 == 0) ? +1 : -1;
Assert.IsTrue(AdvancedMath.BesselJ(-n, x) == s * AdvancedMath.BesselJ(n, x));
Assert.IsTrue(AdvancedMath.BesselY(-n, x) == s * AdvancedMath.BesselY(n, x));
}
}
}
public void IntegerBesselRecurrence()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 1000, 4))
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E6, 16))
{
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(
AdvancedMath.BesselJ(n - 1, x), AdvancedMath.BesselJ(n + 1, x), 2 * n / x * AdvancedMath.BesselJ(n, x)
));
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(
AdvancedMath.BesselY(n - 1, x), AdvancedMath.BesselY(n + 1, x), 2 * n / x * AdvancedMath.BesselY(n, x)
));
}
}
}
public void BesselY0Integral()
{
// Abromowitz & Stegen 9.1.19
Interval r = Interval.FromEndpoints(0.0, Math.PI / 2.0);
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 8))
{
Func <double, double> f = delegate(double t) {
double s = Math.Sin(t);
return(Math.Cos(x * Math.Cos(t)) * (AdvancedMath.EulerGamma + Math.Log(2.0 * x * s * s)));
};
double Y0 = 4.0 / (Math.PI * Math.PI) * FunctionMath.Integrate(f, r).Estimate.Value;
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.BesselY(0, x), Y0));
}
}
public void SphericalBesselRealBesselAgreement()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 100, 8))
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E4, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.SphericalBesselJ(n, x),
Math.Sqrt(Math.PI / 2.0 / x) * AdvancedMath.BesselJ(n + 0.5, x)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.SphericalBesselY(n, x),
Math.Sqrt(Math.PI / 2.0 / x) * AdvancedMath.BesselY(n + 0.5, x)
));
}
}
}
public void IntegerBesselCrossProduct()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 1000, 4))
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E6, 8))
{
double Jn = AdvancedMath.BesselJ(n, x);
double Jp = AdvancedMath.BesselJ(n + 1, x);
double Yn = AdvancedMath.BesselY(n, x);
double Yp = AdvancedMath.BesselY(n + 1, x);
if (Double.IsInfinity(Yn))
{
continue;
}
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(
Jp * Yn, -Jn * Yp, 2.0 / Math.PI / x
));
}
}
}
