/// <summary>
/// Natural Logarithm of this <c>Complex</c> (Base E).
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <returns>
/// The natural logarithm of this complex number.
/// </returns>
public static Complex NaturalLogarithm(this Complex complex)
{
if (complex.IsRealNonNegative())
{
return(new Complex(Math.Log(complex.Real), 0.0));
}
return(new Complex(0.5 * Math.Log(complex.MagnitudeSquared()), complex.Phase));
}
/// <summary>
/// The Square Root (power 1/2) of this <c>Complex</c>
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <returns>
/// The square root of this complex number.
/// </returns>
public static Complex SquareRoot(this Complex complex)
{
// Note: the following code should be equivalent to Complex.Sqrt(complex),
// but it turns out that is implemented poorly in System.Numerics,
// hence we provide our own implementation here. Do not replace.
if (complex.IsRealNonNegative())
{
return(new Complex(Math.Sqrt(complex.Real), 0.0));
}
Complex result;
var absReal = Math.Abs(complex.Real);
var absImag = Math.Abs(complex.Imaginary);
double w;
if (absReal >= absImag)
{
var ratio = complex.Imaginary / complex.Real;
w = Math.Sqrt(absReal) * Math.Sqrt(0.5 * (1.0 + Math.Sqrt(1.0 + (ratio * ratio))));
}
else
{
var ratio = complex.Real / complex.Imaginary;
w = Math.Sqrt(absImag) * Math.Sqrt(0.5 * (Math.Abs(ratio) + Math.Sqrt(1.0 + (ratio * ratio))));
}
if (complex.Real >= 0.0)
{
result = new Complex(w, complex.Imaginary / (2.0 * w));
}
else if (complex.Imaginary >= 0.0)
{
result = new Complex(absImag / (2.0 * w), w);
}
else
{
result = new Complex(absImag / (2.0 * w), -w);
}
return(result);
}
/// <summary>
/// The Square Root (power 1/2) of this <c>Complex</c>
/// </summary>
/// <param name="complex">The <see cref="Complex"/> number to perfom this operation on.</param>
/// <returns>
/// The square root of this complex number.
/// </returns>
public static Complex SquareRoot(this Complex complex)
{
if (complex.IsRealNonNegative())
{
return(new Complex(Math.Sqrt(complex.Real), 0.0));
}
Complex result;
var absReal = Math.Abs(complex.Real);
var absImag = Math.Abs(complex.Imaginary);
double w;
if (absReal >= absImag)
{
var ratio = complex.Imaginary / complex.Real;
w = Math.Sqrt(absReal) * Math.Sqrt(0.5 * (1.0 + Math.Sqrt(1.0 + (ratio * ratio))));
}
else
{
var ratio = complex.Real / complex.Imaginary;
w = Math.Sqrt(absImag) * Math.Sqrt(0.5 * (Math.Abs(ratio) + Math.Sqrt(1.0 + (ratio * ratio))));
}
if (complex.Real >= 0.0)
{
result = new Complex(w, complex.Imaginary / (2.0 * w));
}
else if (complex.Imaginary >= 0.0)
{
result = new Complex(absImag / (2.0 * w), w);
}
else
{
result = new Complex(absImag / (2.0 * w), -w);
}
return(result);
}
