public void ComplexGammaConjugation () {
// limited to 10^-2 to 10^2 to avoid overflow
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 10)) {
Console.WriteLine("z={0} G(z*)={1} G*(z)={2}", z, AdvancedComplexMath.Gamma(z.Conjugate), AdvancedComplexMath.Gamma(z).Conjugate);
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(z.Conjugate), AdvancedComplexMath.Gamma(z).Conjugate));
}
}
public void ComplexGammaDuplicationTest()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(2.0 * z), ComplexMath.Pow(2.0, 2.0 * z - 0.5) * AdvancedComplexMath.Gamma(z) * AdvancedComplexMath.Gamma(z + 0.5) / Math.Sqrt(2.0 * Math.PI)));
}
}
public void ComplexGammaInequality()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 10))
{
Console.WriteLine(z);
Assert.IsTrue(ComplexMath.Abs(AdvancedComplexMath.Gamma(z)) <= Math.Abs(AdvancedMath.Gamma(z.Re)));
}
}
public void ComplexGammaConjugation()
{
// limited to 10^-2 to 10^2 to avoid overflow
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(z.Conjugate), AdvancedComplexMath.Gamma(z).Conjugate));
}
}
public void ComplexGammaRecurrance () {
// fails when extended to more numbers due to a loss of last 4 digits of accuracy in an extreme case; look into it
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 10)) {
Complex G = AdvancedComplexMath.Gamma(z);
Complex Gz = G * z;
Complex GP = AdvancedComplexMath.Gamma(z + 1.0);
Console.WriteLine("z={0:g16} G(z)={1:g16} G(z)*z={2:g16} G(z+1)={3:g16}", z, G, Gz, GP);
Assert.IsTrue(TestUtilities.IsNearlyEqual(Gz,GP));
}
}
public void ComplexGammaKnownLines () {
// to avoid problems with trig functions of large arguments, don't let x get too big
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E2, 16)) {
Console.WriteLine(x);
double px = Math.PI * x;
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(0.0, x)) * AdvancedComplexMath.Gamma(new Complex(0.0, -x)), Math.PI / x / Math.Sinh(px)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(0.5, x)) * AdvancedComplexMath.Gamma(new Complex(0.5, -x)), Math.PI / Math.Cosh(px)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(1.0, x)) * AdvancedComplexMath.Gamma(new Complex(1.0, -x)), px / Math.Sinh(px)));
}
}
public void ComplexLogGammaComplexGammaAgreement()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
ComplexMath.Exp(AdvancedComplexMath.LogGamma(z)),
AdvancedComplexMath.Gamma(z)
));
}
}
public void ComplexGammaRecurrance()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 16))
{
Complex G = AdvancedComplexMath.Gamma(z);
Complex Gz = G * z;
Complex GP = AdvancedComplexMath.Gamma(z + 1.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(Gz, GP));
}
}
public void ComplexGammaInequalities()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 16))
{
Assert.IsTrue(ComplexMath.Abs(AdvancedComplexMath.Gamma(z)) <= Math.Abs(AdvancedMath.Gamma(z.Re)));
if (z.Re >= 0.5)
{
Assert.IsTrue(ComplexMath.Abs(AdvancedComplexMath.Gamma(z)) >= Math.Abs(AdvancedMath.Gamma(z.Re)) / Math.Sqrt(Math.Cosh(Math.PI * z.Im)));
}
}
}
public void ComplexGammaRecurrance()
{
// G * z can loose digits from the cancelation of the two terms that contribute to its real and imaginary parts.
// This appears to be what happens when this fails. For now, just limit ourselves to few values that don't have this problem.
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-1, 1.0E1, 8))
{
Complex G = AdvancedComplexMath.Gamma(z);
Complex Gz = G * z;
Complex GP = AdvancedComplexMath.Gamma(z + 1.0);
Assert.IsTrue(TestUtilities.IsNearlyEqual(Gz, GP));
}
}
public void ComplexGammaKnownLines()
{
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4, 1.0E2, 16))
{
Console.WriteLine(x);
double px = Math.PI * x;
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(0.0, x)) * AdvancedComplexMath.Gamma(new Complex(0.0, -x)), Math.PI / x / Math.Sinh(px)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(0.5, x)) * AdvancedComplexMath.Gamma(new Complex(0.5, -x)), Math.PI / Math.Cosh(px)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(1.0, x)) * AdvancedComplexMath.Gamma(new Complex(1.0, -x)), px / Math.Sinh(px)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Gamma(new Complex(0.25, x)) * AdvancedComplexMath.Gamma(new Complex(0.75, -x)), Math.Sqrt(2.0) * Math.PI / new Complex(Math.Cosh(px), Math.Sinh(px))));
}
}