public void ComplexExpSpecialValues()
{
Assert.IsTrue(ComplexMath.Exp(0.0) == Complex.One);
Assert.IsTrue(ComplexMath.Exp(1.0) == Math.E);
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Exp(Complex.I * Math.PI), -Complex.One));
}
public void ComplexLogExtremeValues()
{
Assert.IsTrue(ComplexMath.Log(Double.MaxValue) == Math.Log(Double.MaxValue));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Log(Double.NaN)));
}
public void ComplexLogSum()
{
Complex[] z = TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 10);
for (int i = 0; i < z.Length; i++)
{
for (int j = 0; j < i; j++)
{
if (Math.Abs(ComplexMath.Arg(z[i]) + ComplexMath.Arg(z[j])) >= Math.PI)
{
continue;
}
Console.WriteLine("{0} {1}", z[i], z[j]);
Console.WriteLine("ln(z1) + ln(z2) = {0}", ComplexMath.Log(z[i]) + ComplexMath.Log(z[j]));
Console.WriteLine("ln(z1*z2) = {0}", ComplexMath.Log(z[i] * z[j]));
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(ComplexMath.Log(z[i]), ComplexMath.Log(z[j]), ComplexMath.Log(z[i] * z[j])));
}
}
}
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 ComplexPowMultiplication()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Pow(a, 2.0) * ComplexMath.Pow(a, 3.0), ComplexMath.Pow(a, 5.0)));
}
public void Bug5504()
{
// this eigenvalue non-convergence is solved by an ad hoc shift
// these "cyclic matrices" are good examples of situations that are difficult for the QR algorithm
for (int d = 2; d <= 8; d++)
{
Console.WriteLine(d);
SquareMatrix C = CyclicMatrix(d);
Complex[] lambdas = C.Eigenvalues();
foreach (Complex lambda in lambdas)
{
Console.WriteLine("{0} ({1} {2})", lambda, ComplexMath.Abs(lambda), ComplexMath.Arg(lambda));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Abs(lambda), 1.0));
}
}
}
public void ComplexExpSpecialCase()
{
Assert.IsTrue(ComplexMath.Exp(0.0) == 1.0);
Assert.IsTrue(ComplexMath.Exp(1.0) == Math.E);
}
public void ComplexAngleAdditionTest()
{
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(a + b), ComplexMath.Sin(a) * ComplexMath.Cos(b) + ComplexMath.Cos(a) * ComplexMath.Sin(b)), String.Format("{0} != {1}", ComplexMath.Sin(a + b), ComplexMath.Sin(a) * ComplexMath.Cos(b) + ComplexMath.Cos(a) * ComplexMath.Sin(b)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(a + b), ComplexMath.Cos(a) * ComplexMath.Cos(b) - ComplexMath.Sin(a) * ComplexMath.Sin(b)));
}
public void ComplexHyperbolicTrigExtremeValues()
{
Assert.IsTrue(Complex.IsNaN(ComplexMath.Sinh(Double.NaN)));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Cosh(Double.NaN)));
Assert.IsTrue(Complex.IsNaN(ComplexMath.Tanh(Double.NaN)));
}
public void ComplexNegativeAngles()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 16))
{
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue / 10.0))
{
continue; // sin and cos blow up in imaginary part of argument gets too big
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(-z), -ComplexMath.Sin(z)), String.Format("remainder {0}", ComplexMath.Sin(-a) + ComplexMath.Sin(a)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(-z), ComplexMath.Cos(z)), String.Format("{0} vs. {1}", ComplexMath.Cos(-a), ComplexMath.Cos(a)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Tan(-z), -ComplexMath.Tan(z)));
}
}
public void ComplexIDefinition()
{
Assert.IsTrue(ComplexMath.Sqrt(-1.0) == Complex.I);
}
public void ComplexDiLogSymmetry()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-2, 1.0E2, 12))
{
Assert.IsTrue(TestUtilities.IsSumNearlyEqual(
AdvancedComplexMath.DiLog(z), AdvancedComplexMath.DiLog(-z),
AdvancedComplexMath.DiLog(z * z) / 2.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
-AdvancedComplexMath.DiLog(1.0 / z),
AdvancedComplexMath.DiLog(z) + ComplexMath.Log(-z) * ComplexMath.Log(-z) / 2.0 + Math.PI * Math.PI / 6.0
));
Assert.IsTrue(TestUtilities.IsNearlyEqual(
-AdvancedComplexMath.DiLog(1.0 - z),
AdvancedComplexMath.DiLog(z) + ComplexMath.Log(z) * ComplexMath.Log(1.0 - z) - Math.PI * Math.PI / 6.0
));
}
}
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)));
}
}
public void ComplexDoubleAngle()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-4, 1.0E4, 16))
{
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue / 10.0))
{
continue;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Sin(2.0 * z), 2.0 * ComplexMath.Sin(z) * ComplexMath.Cos(z)));
//Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cos(2.0 * z), ComplexMath.Sqr(ComplexMath.Cos(z)) - ComplexMath.Sqr(ComplexMath.Sin(z))));
}
}
public void ComplexExpExtremeValues()
{
Assert.IsTrue(ComplexMath.Exp(Double.NegativeInfinity) == Complex.Zero);
Assert.IsTrue(Complex.IsNaN(ComplexMath.Exp(Double.NaN)));
}
public void ComplexCosCosh()
{
foreach (Complex z in TestUtilities.GenerateComplexValues(1.0E-3, 1.0E3, 16))
{
// Since sin(z) and cos(z) have factors that go like e^{\pm Im(z)}, they will blow up if the imaginary
// part of z gets too big. We just skip over those problematic values.
if (Math.Abs(z.Im) > Math.Log(Double.MaxValue) / 2.0)
{
continue;
}
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cosh(z), ComplexMath.Cos(ComplexMath.I * z)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(ComplexMath.Cosh(-ComplexMath.I * z), ComplexMath.Cos(z)));
}
}
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 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 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 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)));
}
}
