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 ComplexRealAgreement()
{
foreach (double x in TestUtilities.GenerateRealValues(0.01, 1000.0, 8))
{
Assert.IsTrue(ComplexMath.Exp(x) == Math.Exp(x));
Assert.IsTrue(ComplexMath.Log(x) == Math.Log(x));
Assert.IsTrue(ComplexMath.Sqrt(x) == Math.Sqrt(x));
Assert.IsTrue(ComplexMath.Abs(x) == Math.Abs(x));
Assert.IsTrue(ComplexMath.Arg(x) == 0.0);
}
}
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 DifficultEigenvalue()
{
// This is from a paper describing difficult eigenvalue problems.
// https://www.mathworks.com/company/newsletters/news_notes/pdf/sum95cleve.pdf
SquareMatrix A = new SquareMatrix(4);
A[0, 0] = 0.0; A[0, 1] = 2.0; A[0, 2] = 0.0; A[0, 3] = -1.0;
A[1, 0] = 1.0; A[1, 1] = 0.0; A[1, 2] = 0.0; A[1, 3] = 0.0;
A[2, 0] = 0.0; A[2, 1] = 1.0; A[2, 2] = 0.0; A[2, 3] = 0.0;
A[3, 0] = 0.0; A[3, 1] = 0.0; A[3, 2] = 1.0; A[3, 3] = 0.0;
Complex[] zs = A.Eigenvalues();
foreach (Complex z in zs)
{
Console.WriteLine("{0} ({1} {2})", z, ComplexMath.Abs(z), ComplexMath.Arg(z));
}
}
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));
}
}
}
