/**
* Computes the N<sup>th</sup> root of a complex number. There are
* N distinct N<sup>th</sup> roots.
*
* @param a Complex number
* @param N The root's magnitude
* @param k Specifies which root. 0 ≤ k < N
* @param result Computed root
*/
public static void root(Complex_F32 a, int N, int k, Complex_F32 result)
{
float r = a.getMagnitude();
float theta = (float)Math.Atan2(a.imaginary, a.real);
r = (float)Math.Pow(r, 1.0f / N);
theta = (theta + 2.0f * k * UtilEjml.F_PI) / N;
result.real = r * (float)Math.Cos(theta);
result.imaginary = r * (float)Math.Sin(theta);
}
/**
* Computes the square root of the complex number.
*
* @param input Input complex number.
* @param root Output. The square root of the input
*/
public static void sqrt(Complex_F32 input, Complex_F32 root)
{
float r = input.getMagnitude();
float a = input.real;
root.real = (float)Math.Sqrt((r + a) / 2.0f);
root.imaginary = (float)Math.Sqrt((r - a) / 2.0f);
if (input.imaginary < 0)
{
root.imaginary = -root.imaginary;
}
}
/**
* <p>
* Converts a complex number into polar notation.
* </p>
*
* @param input Standard notation
* @param output Polar notation
*/
public static void convert(Complex_F32 input, ComplexPolar_F32 output)
{
output.r = input.getMagnitude();
output.theta = (float)Math.Atan2(input.imaginary, input.real);
}
