public void ComplexPowExponent()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 6))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(Math.E, z), ComplexMath.Exp(z)));
}
}
public void ComplexReimannZetaPrimesTest()
{
// pick high enough values so that p^-x == 1 within double precision before we reach the end of our list of primes
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0, 100.0, 8))
{
Complex zz = z;
if (zz.Re < 0.0)
{
zz = -zz;
}
zz += 10.0;
Console.WriteLine(zz);
Complex f = 1.0;
for (int p = 2; p < 100; p++)
{
if (!AdvancedIntegerMath.IsPrime(p))
{
continue;
}
Complex t = Complex.One - ComplexMath.Pow(p, -zz);
if (t == Complex.One)
{
break;
}
f = f * t;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(1.0 / AdvancedComplexMath.RiemannZeta(zz), f));
}
}
public void ComplexPowOneHalf()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, 0.5), ComplexMath.Sqrt(z)));
}
}
public void ComplexPowSpecialCases()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 10))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, -1), 1.0 / z));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, 0), 1.0));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, 1), z));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, 2), z * z));
}
}
public void ComplexPow()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 8))
{
Complex p = 1.0;
for (int k = 1; k < 16; k++)
{
p *= z;
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, k), p));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(z, -k), 1.0 / p));
}
}
}
public void ComplexPowSpecialValues()
{
Assert.IsTrue(ComplexMath.Pow(Complex.Zero, Complex.Zero) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(Complex.One, Complex.Zero) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(-Complex.One, Complex.Zero) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(Complex.I, Complex.Zero) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(a, Complex.Zero) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(Complex.Zero, Complex.One) == Complex.Zero);
Assert.IsTrue(ComplexMath.Pow(Complex.One, Complex.One) == Complex.One);
Assert.IsTrue(ComplexMath.Pow(-Complex.One, Complex.One) == -Complex.One);
Assert.IsTrue(ComplexMath.Pow(Complex.I, Complex.One) == Complex.I);
Assert.IsTrue(ComplexMath.Pow(a, Complex.One) == a);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(Complex.I, Complex.I), Math.Exp(-Math.PI / 2.0), TestUtilities.RelativeTarget));
}
public void ComplexPowMultiplication()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(a, 2.0) * ComplexMath.Pow(a, 3.0), ComplexMath.Pow(a, 5.0)));
}
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)));
}
}