public void CarlsonScaling()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-3, 1.0E1, 2))
{
foreach (double y in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 2))
{
foreach (double z in TestUtilities.GenerateRealValues(1.0E-1, 1.0E3, 2))
{
foreach (double lambda in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 4))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.CarlsonF(lambda * x, lambda * y, lambda * z),
AdvancedMath.CarlsonF(x, y, z) / Math.Sqrt(lambda)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.CarlsonG(lambda * x, lambda * y, lambda * z),
AdvancedMath.CarlsonG(x, y, z) * Math.Sqrt(lambda)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.CarlsonD(lambda * x, lambda * y, lambda * z),
AdvancedMath.CarlsonD(x, y, z) * Math.Pow(lambda, -1.5)
));
}
}
}
}
}
public void CarlsonNormalization()
{
// All Carlson integrals are normalized so that they are 1 when all arguments are 1.
Assert.IsTrue(AdvancedMath.CarlsonF(1.0, 1.0, 1.0) == 1.0);
Assert.IsTrue(AdvancedMath.CarlsonG(1.0, 1.0, 1.0) == 1.0);
Assert.IsTrue(AdvancedMath.CarlsonD(1.0, 1.0, 1.0) == 1.0);
}
public void CarslonDSpecialCases()
{
// DLMF 19.20.18
// R_D(x, x, x) = x^{-3/2}
// R_D(0, x, x) = 3/4 \pi x^{-3/2}
// R_D(0, 0, x) = \infty
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E4, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.CarlsonD(x, x, x), Math.Pow(x, -3.0 / 2.0)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedMath.CarlsonD(0, x, x), 3.0 * Math.PI / 4.0 * Math.Pow(x, -3.0 / 2.0)
));
}
}
