/// <summary>
/// Computes the complex digamma (ψ) function.
/// </summary>
/// <param name="z">The complex argument.</param>
/// <returns>The value of ψ(z).</returns>
/// <remarks>
/// <para>The image below shows the complex ψ function near the origin using domain coloring.</para>
/// <img src="../images/ComplexPsiPlot.png" />
/// </remarks>
/// <seealso cref="AdvancedMath.Psi(double)" />
public static Complex Psi(Complex z)
{
if (z.Re < 0.5)
{
// reduce z.Re in order to handle large real values!
return(Psi(1.0 - z) - Math.PI / ComplexMath.Tan(Math.PI * z));
}
else
{
// add Stirling for large z
return(Lanczos.Psi(z));
}
}
public void Tan()
{
Complex cd1 = new Complex(1.1, -2.2);
Complex cd2 = new Complex(0, -2.2);
Complex cd3 = new Complex(1.1, 0);
Complex cd4 = new Complex(-1.1, 2.2);
ComplexFloat cf1 = new ComplexFloat(1.1f, -2.2f);
ComplexFloat cf2 = new ComplexFloat(0, -2.2f);
ComplexFloat cf3 = new ComplexFloat(1.1f, 0);
ComplexFloat cf4 = new ComplexFloat(-1.1f, 2.2f);
Complex cdt = ComplexMath.Tan(cd1);
Assert.AreEqual(cdt.Real, 0.020, TOLERENCE);
Assert.AreEqual(cdt.Imag, -1.014, TOLERENCE);
cdt = ComplexMath.Tan(cd2);
Assert.AreEqual(cdt.Real, 0, TOLERENCE);
Assert.AreEqual(cdt.Imag, -0.976, TOLERENCE);
cdt = ComplexMath.Tan(cd3);
Assert.AreEqual(cdt.Real, 1.965, TOLERENCE);
Assert.AreEqual(cdt.Imag, 0, TOLERENCE);
cdt = ComplexMath.Tan(cd4);
Assert.AreEqual(cdt.Real, -0.020, TOLERENCE);
Assert.AreEqual(cdt.Imag, 1.014, TOLERENCE);
ComplexFloat cft = ComplexMath.Tan(cf1);
Assert.AreEqual(cft.Real, 0.020, TOLERENCE);
Assert.AreEqual(cft.Imag, -1.014, TOLERENCE);
cft = ComplexMath.Tan(cf2);
Assert.AreEqual(cft.Real, 0, TOLERENCE);
Assert.AreEqual(cft.Imag, -0.976, TOLERENCE);
cft = ComplexMath.Tan(cf3);
Assert.AreEqual(cft.Real, 1.965, TOLERENCE);
Assert.AreEqual(cft.Imag, 0, TOLERENCE);
cft = ComplexMath.Tan(cf4);
Assert.AreEqual(cft.Real, -0.020, TOLERENCE);
Assert.AreEqual(cft.Imag, 1.014, TOLERENCE);
}