public void EllipticPiZeroModulus()
{
// DLMF 19.6.3
foreach (double n in TestUtilities.GenerateUniformRealValues(-4.0, 1.0, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.EllipticPi(n, 0.0), Math.PI / 2.0 / Math.Sqrt(1.0 - n)));
}
}
public void EllipticPiSpecialCharacteristic()
{
foreach (double k in TestUtilities.GenerateRealValues(1.0E-4, 1.0, 4))
{
// DLMF 19.6.1
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.EllipticPi(k * k, k), AdvancedMath.EllipticE(k) / (1.0 - k * k)));
// DLMF 19.6.2
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.EllipticPi(-k, k), Math.PI / 4.0 / (1.0 + k) + AdvancedMath.EllipticK(k) / 2.0));
// DLMF 19.6.3
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.EllipticPi(0.0, k), AdvancedMath.EllipticK(k)));
Assert.IsTrue(Double.IsPositiveInfinity(AdvancedMath.EllipticPi(1.0, k)));
}
}
public void EllipticPiIntegration()
{
Interval i = Interval.FromEndpoints(0.0, Math.PI / 2.0);
foreach (double k in TestUtilities.GenerateRealValues(1.0E-2, 1.0, 4))
{
double m = k * k;
foreach (double n in TestUtilities.GenerateUniformRealValues(-2.0, 1.0, 4))
{
Func <double, double> f = delegate(double t) {
double s2 = MoreMath.Sqr(Math.Sin(t));
return(1.0 / (1.0 - n * s2) / Math.Sqrt(1.0 - m * s2));
};
Assert.IsTrue(TestUtilities.IsNearlyEqual(
FunctionMath.Integrate(f, i), AdvancedMath.EllipticPi(n, k)
));
}
}
}
public void EllipticPiSpecialCases()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedMath.EllipticPi(0.0, 0.0), Math.PI / 2.0));
}
