public void ComplexFaddeevaDawson () {
foreach (double x in TestUtilities.GenerateRealValues(1.0E-4,1.0E4,10)) {
Complex w = AdvancedComplexMath.Faddeeva(x);
double F = AdvancedMath.Dawson(x);
Console.WriteLine("x={0} F={1} w={2}", x, F, w);
Assert.IsTrue(TestUtilities.IsNearlyEqual(w.Re, Math.Exp(-x * x)));
Assert.IsTrue(TestUtilities.IsNearlyEqual(w.Im, (2.0/Math.Sqrt(Math.PI)) * AdvancedMath.Dawson(x)));
}
}
public void OdeDawson()
{
// The Dawson function fulfills a simple ODE.
// \frac{dF}{dx} + 2 x F = 1 \qquad F(0) = 0
// See e.g. https://en.wikipedia.org/wiki/Dawson_function
// Verify that we get correct values via ODE integration.
Func <double, double, double> rhs = (double x, double F) => 1.0 - 2.0 * x * F;
foreach (double x1 in TestUtilities.GenerateRealValues(0.1, 10.0, 8))
{
EvaluationSettings s = new EvaluationSettings()
{
RelativePrecision = 1.0E-13,
AbsolutePrecision = 0.0
};
OdeResult r = FunctionMath.IntegrateOde(rhs, 0.0, 0.0, x1);
Debug.WriteLine("{0}: {1} {2}: {3}", x1, r.Y, AdvancedMath.Dawson(x1), r.EvaluationCount);
Assert.IsTrue(TestUtilities.IsNearlyEqual(r.Y, AdvancedMath.Dawson(x1), s));
}
}
