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