public static __ct__ operator !(__ct__ a)
{
__ct__ c = a;
c.Conjugate();
return(c);
}
public static __ct__ operator *(__ft__ b, __ct__ a)
{
__ct__ c = a;
c.Multiply(b);
return(c);
}
public static __ct__ operator /(__ft__ a, __ct__ b)
{
__ct__ c = a;
c.Divide(b);
return(c);
}
public static __ct__ operator -(__ct__ a, __ft__ b)
{
__ct__ c = a;
c.Subtract(b);
return(c);
}
public static __ct__ operator -(__ft__ b, __ct__ a)
{
__ct__ c = -1.0f * a;
c.Add(b);
return(c);
}
/// <summary>
/// Multiplies a complex number with this
/// </summary>
/// <param name="number"></param>
public void Multiply(__ct__ number)
{
__ft__ real = Real;
__ft__ imag = Imag;
Real = real * number.Real - imag * number.Imag;
Imag = real * number.Imag + imag * number.Real;
}
public static __ct__ operator +(__ct__ a, __ft__ b)
{
__ct__ c = a;
c.Add(b);
return(c);
}
/// <summary>
/// Calculates both Square-Roots of a complex number
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public __ct__[] Sqrt(__ct__ number)
{
__ct__ res0 = __ct__.CreateRadial((__ft__)System.Math.Sqrt(number.Norm), number.Argument / 2.0f);
__ct__ res1 = __ct__.CreateRadial((__ft__)System.Math.Sqrt(number.Norm), number.Argument / 2.0f + (__ft__)Constant.Pi);
return(new __ct__[2] {
res0, res1
});
}
/// <summary>
/// Exponentiates a complex by another
/// </summary>
/// <returns></returns>
public static __ct__ Pow(__ct__ number, __ct__ exponent)
{
__ft__ r = number.Norm;
__ft__ phi = number.Argument;
__ft__ a = exponent.Real;
__ft__ b = exponent.Imag;
return(__ct__.CreateRadial((__ft__)System.Math.Exp(System.Math.Log(r) * a - b * phi), a * phi + b * (__ft__)System.Math.Log(r)));
}
/// <summary>
/// Divides this by a complex number
/// </summary>
/// <param name="number"></param>
public void Divide(__ct__ number)
{
__ft__ t = 1 / number.NormSquared;
__ft__ real = Real;
__ft__ imag = Imag;
Real = t * (real * number.Real + imag * number.Imag);
Imag = t * (imag * number.Real - real * number.Imag);
}
/// <summary>
/// Calculates e^Complex
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public static __ct__ Exp(__ct__ number)
{
__ct__ c = __ct__.Zero;
__ft__ factor = (__ft__)System.Math.Pow(Constant.E, number.Real);
c.Real = factor * (__ft__)System.Math.Cos(number.Imag);
c.Imag = factor * (__ft__)System.Math.Sin(number.Imag);
return(c);
}
/// <summary>
/// Calculates the n-th Root of a Complex number and returns n Solutions
/// </summary>
/// <param name="number"></param>
/// <param name="order">n</param>
/// <returns></returns>
public __ct__[] Root(__ct__ number, int order)
{
__ct__[] values = new __ct__[order];
__ft__ phi = number.Argument / 2.0f;
__ft__ dphi = (__ft__)Constant.PiTimesTwo / (__ft__)order;
__ft__ r = (__ft__)System.Math.Pow(number.Norm, 1.0f / order);
for (int i = 1; i < order; i++)
{
values[i] = __ct__.CreateRadial(r, phi + dphi * i);
}
return(values);
}
/// <summary>
/// Natural Logartihm for complex numbers
/// </summary>
/// <param name="number"></param>
/// <returns></returns>
public static __ct__ Log(__ct__ number)
{
return(__ct__.CreateOrthogonal((__ft__)System.Math.Log(number.Norm), number.Argument));
}
/// <summary>
/// Exponentiates a complex by a real number
/// </summary>
/// <returns></returns>
public static __ct__ Pow(__ct__ number, __ft__ scalar)
{
number.Pow(scalar);
return(number);
}
/// <summary>
/// Subtracts a complex number from this
/// </summary>
/// <param name="number"></param>
public void Subtract(__ct__ number)
{
Real -= number.Real;
Imag -= number.Imag;
}
/// <summary>
/// Adds a complex number to this
/// </summary>
/// <param name="number"></param>
public void Add(__ct__ number)
{
Real += number.Real;
Imag += number.Imag;
}