public void LegendreOrthonormality()
{
foreach (int n in TestUtilities.GenerateIntegerValues(1, 100, 3))
{
foreach (int m in TestUtilities.GenerateIntegerValues(1, 100, 3))
{
Func <double, double> f = delegate(double x) {
return(OrthogonalPolynomials.LegendreP(n, x) * OrthogonalPolynomials.LegendreP(m, x));
};
Interval r = Interval.FromEndpoints(-1.0, 1.0);
double I = FunctionMath.Integrate(f, r);
Console.WriteLine("{0} {1} {2}", n, m, I);
if (n == m)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(I, 2.0 / (2 * n + 1)));
}
else
{
Assert.IsTrue(Math.Abs(I) < TestUtilities.TargetPrecision);
}
}
}
}
public void LegendreInvalidArgument()
{
OrthogonalPolynomials.LegendreP(2, -1.1);
}
public void LegendreRecurrence()
{
foreach (int n in orders)
{
foreach (double x in bArguments)
{
Assert.IsTrue(TestUtilities.IsNearlyEqual((n + 1) * OrthogonalPolynomials.LegendreP(n + 1, x), (2 * n + 1) * x * OrthogonalPolynomials.LegendreP(n, x) - n * OrthogonalPolynomials.LegendreP(n - 1, x)));
}
}
}