public static Complex Sqrt(Complex value)
{
if (value.IsRealNonNegative())
{
return new Complex((double)Math.Sqrt(value.Real), 0.0);
}
Complex result;
var absReal = Abs(value.Real);
var absImag = Abs(value.Imaginary);
double w;
if (absReal >= absImag)
{
var ratio = value.Imaginary / value.Real;
w = Sqrt(absReal) * Sqrt(0.5 * (1.0 + Sqrt(1.0 + (ratio * ratio))));
}
else
{
var ratio = value.Real / value.Imaginary;
w = Sqrt(absImag) * Sqrt(0.5 * (Abs(ratio) + Sqrt(1.0 + (ratio * ratio))));
}
if (value.Real >= 0.0)
{
result = new Complex(w, value.Imaginary / (2.0 * w));
}
else if (value.Imaginary >= 0.0)
{
result = new Complex((absImag / (2.0 * w)).Real, w);
}
else
{
result = new Complex((absImag / (2.0 * w)).Real, -w);
}
return result;
}
public static Complex Ln(Complex c)
{
/*if (c.IsReal() && c < 0.0) return Ln(-c) + (Constants.I * Constants.Pi);
if (c.IsReal()) return Quad.Log(c.Real);
return Math.Log(c.Module, Constants.E) + (Constants.I * (Complex)c.Argument);*/
if(c.IsRealNonNegative()) return new Complex(Math.Log(c.Real, Constants.E), 0.0);
return new Complex(0.5 * Math.Log(c.MagnitudeSquared(), Constants.E), c.Argument);
}