public void AiryBiExtremeValues()
{
Assert.IsTrue(Double.IsNaN(AdvancedMath.AiryBi(Double.NegativeInfinity)));
Assert.IsTrue(AdvancedMath.AiryBi(Double.MaxValue) == Double.PositiveInfinity);
Assert.IsTrue(AdvancedMath.AiryBi(Double.PositiveInfinity) == Double.PositiveInfinity);
Assert.IsTrue(Double.IsNaN(AdvancedMath.AiryBi(Double.NaN)));
}
public void AiryAgreement()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 4))
{
SolutionPair s = AdvancedMath.Airy(-x);
Assert.IsTrue(TestUtilities.IsNearlyEqual(s.FirstSolutionValue, AdvancedMath.AiryAi(-x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(s.SecondSolutionValue, AdvancedMath.AiryBi(-x)));
}
}
public void AiryZeroArgument()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.AiryAi(0.0), 1.0 / Math.Pow(3.0, 2.0 / 3.0) / AdvancedMath.Gamma(2.0 / 3.0)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.AiryBi(0.0), 1.0 / Math.Pow(3.0, 1.0 / 6.0) / AdvancedMath.Gamma(2.0 / 3.0)
));
}
public void AiryZeros()
{
foreach (int k in new int[] { 1, 10, 100, 1000 })
{
double a = AdvancedMath.AiryAiZero(k);
double ya = AdvancedMath.AiryAi(a);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ya, 0.0, 2.0E-16 * k));
double b = AdvancedMath.AiryBiZero(k);
double yb = AdvancedMath.AiryBi(b);
Assert.IsTrue(TestUtilities.IsNearlyEqual(yb, 0.0, 2.0E-16 * k));
}
}
public void AiryBairyIntegral()
{
// for small x: the integral will not converse for x <~ 5 because of the 1/sqrt(t) divergence near 0
// for large x: Bi explodes exponentially
// but in between, it is a decent test of Ai and Bi together
foreach (double x in TestUtilities.GenerateRealValues(5.0, 50.0, 8))
{
double I = FunctionMath.Integrate(
t => { return(Math.Exp(x * t - t * t * t / 12.0) / Math.Sqrt(t)); },
Interval.FromEndpoints(0.0, Double.PositiveInfinity)
);
Assert.IsTrue(TestUtilities.IsNearlyEqual(
MoreMath.Pow(AdvancedMath.AiryAi(x), 2) + MoreMath.Pow(AdvancedMath.AiryBi(x), 2), I / Math.Pow(Math.PI, 3.0 / 2.0)
));
}
}
