public static IList <double> GetCubicPolynomialRoots(IList <double> coefficients)
{
if (coefficients == null)
{
throw new ArgumentNullException(nameof(coefficients));
}
if (coefficients.Count < 4)
{
throw new ArgumentException("The coefficients should at least have length 4.");
}
double coefficient1 = coefficients[3];
if (coefficient1 == 0.0)
{
throw new ArgumentException("Coefficient a is zero.");
}
double coefficient2 = coefficients[2];
double coefficient3 = coefficients[1];
double coefficient4 = coefficients[0];
double num1 = coefficient2 * coefficient2;
double num2 = coefficient1 * coefficient3;
double num3 = coefficient1 * coefficient4;
double a = num1 - 3.0 * num2;
double num4 = coefficient2 * (2.0 * num1 - 9.0 * num2) + 27.0 * coefficient1 * num3;
double d = num4 * num4 - 4.0 * a * a * a;
double[] numArray;
if (d < -8.88178419700125E-16)
{
double num5 = System.Math.Sqrt(-d);
ComplexD complexD = new ComplexD(0.5 * num4, 0.5 * num5);
ComplexD v = ComplexD.FromModulusAndArgument(System.Math.Pow(complexD.GetModulusSquared(), 1.0 / 6.0), 1.0 / 3.0 * complexD.GetArgument());
ComplexD conjugate = v.GetConjugate();
double num6 = -1.0 / (3.0 * coefficient1);
numArray = new double[3]
{
num6 *(coefficient2 + v.Real + conjugate.Real),
num6 *(coefficient2 + ComplexD.MultiplyAndGetReal(MathUtil.complexD_2, v) + ComplexD.MultiplyAndGetReal(MathUtil.complexD_3, conjugate)),
num6 *(coefficient2 + ComplexD.MultiplyAndGetReal(MathUtil.complexD_4, v) + ComplexD.MultiplyAndGetReal(MathUtil.complexD_5, conjugate))
};
}
else if (d > 8.88178419700125E-16)
{
double num5 = System.Math.Sqrt(d);
double x1 = 0.5 * (num4 + num5);
double x2 = 0.5 * (num4 - num5);
double num6 = x1 >= 0.0 ? System.Math.Pow(x1, 1.0 / 3.0) : -System.Math.Pow(-x1, 1.0 / 3.0);
double num7 = x2 >= 0.0 ? System.Math.Pow(x2, 1.0 / 3.0) : -System.Math.Pow(-x2, 1.0 / 3.0);
numArray = new double[1]
{
-(coefficient2 + num6 + num7) / (3.0 * coefficient1)
};
}
else if (MathUtil.AreApproxEqual(a, 0.0, 8.88178419700125E-16))
{
numArray = new double[1]
{
-coefficient2 / (3.0 * coefficient1)
}
}
;
else
{
numArray = new double[2]
{
(9.0 * num3 - coefficient2 * coefficient3) / (2.0 * a),
(4.0 * coefficient2 * num2 - 9.0 * coefficient1 * num3 - coefficient2 * num1) / (coefficient1 * a)
}
};
return((IList <double>)numArray);
}
