public void IntegralCinReflection()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E4, 8))
{
Assert.IsTrue(AdvancedMath.IntegralCin(-x) == AdvancedMath.IntegralCin(x));
}
}
public void IntegralCinDefinition()
{
// To avoid cancellation error, near cos(x) ~ 1, use half-angle formula
// 1 - \cos(x) = 2 \sin^2(x/2)
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
FunctionMath.Integrate(t => 2.0 * MoreMath.Sqr(MoreMath.Sin(t / 2.0)) / t, 0.0, x),
AdvancedMath.IntegralCin(x)
));
}
}
public void ComplexEinCinSiAgreement()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-2, 1.0E2, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.Ein(Complex.I * x).Im,
AdvancedMath.IntegralSi(x)
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.Ein(Complex.I * x).Re,
AdvancedMath.IntegralCin(x)
));
}
}
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 IntegralCinSpecialCases()
{
Assert.IsTrue(AdvancedMath.IntegralCin(0.0) == 0.0);
}
