public void IntegralCiCinRelation()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0, 4))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.EulerGamma + Math.Log(x) - AdvancedMath.IntegralCin(x),
AdvancedMath.IntegralCi(x)
));
}
foreach (double x in TestUtilities.GenerateRealValues(1.0, 1.0E4, 4))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.EulerGamma + Math.Log(x) - AdvancedMath.IntegralCi(x),
AdvancedMath.IntegralCin(x)
));
}
}
public void IntegralCiSiIntegrals()
{
// these integrals are from Oldham et al, An Atlas of Functions
// A & S 5.2.28
Assert.IsTrue(TestUtilities.IsNearlyEqual(
FunctionMath.Integrate(t => AdvancedMath.IntegralCi(t) * Math.Exp(-t), Interval.FromEndpoints(0.0, Double.PositiveInfinity)),
-Math.Log(2.0) / 2.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
FunctionMath.Integrate(t => AdvancedMath.IntegralSi(t) * Math.Exp(-t), Interval.FromEndpoints(0.0, Double.PositiveInfinity)),
Math.PI / 4.0
));
/*
* // the integral of [Ci(t)]^2 does not converge numerically
* Assert.IsTrue(TestUtilities.IsNearlyEqual(
* FunctionMath.Integrate(t => MoreMath.Sqr(AdvancedMath.IntegralCi(t)), Interval.FromEndpoints(0.0, Double.PositiveInfinity)),
* Math.PI / 2.0
* ));
*/
}
public void IntegralCiSpecialCases()
{
Assert.IsTrue(Double.IsNegativeInfinity(AdvancedMath.IntegralCi(0.0)));
Assert.IsTrue(Double.IsNaN(AdvancedMath.IntegralCi(Double.NaN)));
}
