public void ComplexExpReflection()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Exp(-z), 1.0 / ComplexMath.Exp(z)));
}
}
public void ComplexLogExp()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Exp(ComplexMath.Log(z)), z));
}
}
public void ComplexDiLogConjugation () {
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-1, 1.0E1, 8)) {
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.DiLog(z.Conjugate), AdvancedComplexMath.DiLog(z).Conjugate
));
}
}
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 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 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 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 FourierLinearity()
{
foreach (int n in sizes)
{
Console.WriteLine(n);
FourierTransformer ft = new FourierTransformer(n);
Random rng = new Random(1);
Complex[] x = TestUtilities.GenerateComplexValues(0.1, 10.0, n, rng);
Complex[] y = TestUtilities.GenerateComplexValues(0.1, 10.0, n, rng);
Complex[] z = new Complex[n];
for (int i = 0; i < n; i++)
{
z[i] = x[i] + y[i];
}
Complex[] xt = ft.Transform(x);
Complex[] yt = ft.Transform(y);
Complex[] zt = ft.Transform(z);
for (int i = 0; i < n; i++)
{
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(xt[i], yt[i], zt[i]));
}
}
}
public void FourierParseval()
{
foreach (int n in sizes)
{
//int n = 15;
Console.WriteLine(n);
FourierTransformer ft = new FourierTransformer(n);
Random rng = new Random(1);
Complex[] x = TestUtilities.GenerateComplexValues(0.1, 10.0, n, rng);
Complex[] y = TestUtilities.GenerateComplexValues(0.1, 10.0, n, rng);
Complex s = 0.0;
for (int i = 0; i < n; i++)
{
s += x[i] * y[i].Conjugate;
}
Complex[] xt = ft.Transform(x);
Complex[] yt = ft.Transform(y);
Complex st = 0.0;
for (int i = 0; i < n; i++)
{
st += xt[i] * yt[i].Conjugate;
}
st /= n;
Console.WriteLine("{0} {1}", s, st);
Assert.IsTrue(TestUtilities.IsNearlyEqual(s, st));
}
}
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 ComplexTanTanh()
{
foreach (Complex x in TestUtilities.GenerateComplexValues(1.0E-3, 1.0E3, 16))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tanh(x), -ComplexMath.I * ComplexMath.Tan(ComplexMath.I * x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tanh(-ComplexMath.I * x), -ComplexMath.I * ComplexMath.Tan(x)));
}
}
public void ComplexTrigPeriodicity()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 8))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(z), ComplexMath.Sin(z + 2.0 * Math.PI)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(z), ComplexMath.Cos(z + 2.0 * Math.PI)));
}
}
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 ComplexCosCosh()
{
foreach (Complex x in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 10))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cosh(x), ComplexMath.Cos(ComplexMath.I * x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cosh(-ComplexMath.I * x), ComplexMath.Cos(x)));
}
}
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 ComplexAbsSquared()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 10))
{
double abs = ComplexMath.Abs(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(abs * abs, z * z.Conjugate));
}
}
public void ComplexPsiConjugation () {
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E3, 12)) {
Console.WriteLine(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.Psi(z.Conjugate),
AdvancedComplexMath.Psi(z).Conjugate
));
}
}
public void ComplexPsiDuplication () {
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E3, 12)) {
Console.WriteLine(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.Psi(2.0 * z),
AdvancedComplexMath.Psi(z) / 2.0 + AdvancedComplexMath.Psi(z + 0.5) / 2.0 + Math.Log(2.0)
));
}
}
public void ComplexSinhCoshRelation()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 10))
{
Complex sinh = ComplexMath.Sinh(z);
Complex cosh = ComplexMath.Cosh(z);
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(cosh * cosh, -sinh * sinh, 1));
}
}
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 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 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 ComplexLogGammaConjugation () {
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 24)) {
if (z.Re <= 0.0) continue;
Console.WriteLine("z={0} lnG(z*)={1} lnG*(z)={2}", z, AdvancedComplexMath.LogGamma(z.Conjugate), AdvancedComplexMath.LogGamma(z).Conjugate);
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.LogGamma(z.Conjugate),
AdvancedComplexMath.LogGamma(z).Conjugate
));
}
}
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 ComplexLogGammaConjugation()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 24))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.LogGamma(z.Conjugate),
AdvancedComplexMath.LogGamma(z).Conjugate
));
}
}
public void ComplexSqrt()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 32))
{
Complex sz = ComplexMath.Sqrt(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sqr(sz), z, TestUtilities.RelativeTarget));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Arg(z) / 2.0, ComplexMath.Arg(sz), TestUtilities.RelativeTarget));
Assert.IsTrue(TestUtilities.IsNearlyEqual(Math.Sqrt(ComplexMath.Abs(z)), ComplexMath.Abs(sz), TestUtilities.RelativeTarget));
}
}
public void ComplexFaddeevaConjugation()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 50))
{
if (z.Im * z.Im > Math.Log(Double.MaxValue / 10.0))
{
continue; // large imaginary values blow up
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(AdvancedComplexMath.Faddeeva(z.Conjugate), AdvancedComplexMath.Faddeeva(-z).Conjugate));
}
}
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 ComplexLogGammaRecurrance()
{
// Don't try for z << 1, because z + 1 won't retain enough digits to satisfy
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E4, 24))
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(
AdvancedComplexMath.LogGamma(z + 1.0),
AdvancedComplexMath.LogGamma(z) + ComplexMath.Log(z)
));
}
}
public void ComplexArcTrigInversion()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 32))
{
Complex asin = ComplexMath.Asin(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(asin), z));
Complex acos = ComplexMath.Acos(z);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(acos), z));
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(asin, acos, Math.PI / 2.0));
}
}
