public static ComplexD EvaluatePolynomialAndFirstDerivative(
IList <double> coefficients,
ComplexD x,
out ComplexD firstDerivative)
{
int index1 = coefficients.Count - 1;
double coefficient1 = coefficients[index1];
firstDerivative = (ComplexD)(coefficient1 * (double)index1);
ComplexD complexD = (ComplexD)coefficient1;
int index2;
for (index2 = index1 - 1; index2 > 0; --index2)
{
double coefficient2 = coefficients[index2];
firstDerivative = x * firstDerivative + (ComplexD)(coefficient2 * (double)index2);
complexD = x * complexD + (ComplexD)coefficient2;
}
if (index2 == 0)
{
double coefficient2 = coefficients[index2];
complexD = x * complexD + (ComplexD)coefficient2;
}
return(complexD);
}
public static bool AreApproxEqual(ComplexD u, ComplexD v, double tolerance)
{
if (System.Math.Abs(v.Real - u.Real) <= tolerance)
{
return(System.Math.Abs(v.Imaginary - u.Imaginary) <= tolerance);
}
return(false);
}
public bool Equals(ComplexD other)
{
if (this.Real == other.Real)
{
return(this.Imaginary == other.Imaginary);
}
return(false);
}
public ComplexD GetSqrt()
{
if (this.Imaginary == 0.0)
{
return(ComplexD.Sqrt(this.Real));
}
double modulus = this.GetModulus();
return(new ComplexD((double)System.Math.Sign(this.Imaginary) * System.Math.Sqrt(0.5 * (modulus + this.Real)), System.Math.Sqrt(0.5 * (modulus - this.Real))));
}
public static ComplexD EvaluatePolynomial(IList <double> coefficients, ComplexD x)
{
int num = coefficients.Count - 1;
IList <double> doubleList = coefficients;
int index1 = num;
int index2 = index1 - 1;
ComplexD complexD = (ComplexD)doubleList[index1];
for (; index2 >= 0; --index2)
{
complexD = x * complexD + (ComplexD)coefficients[index2];
}
return(complexD);
}
public static bool AreApproxEqual(ComplexD u, ComplexD v)
{
return(ComplexD.AreApproxEqual(u, v, 8.88178419700125E-16));
}
public static double MultiplyAndGetReal(ComplexD u, ComplexD v)
{
return(u.Real * v.Real - u.Imaginary * v.Imaginary);
}
public static void GetPolynomialRoots(
IList <double> coefficients,
IList <double> roots,
double epsilon)
{
if (roots == null)
{
throw new ArgumentNullException(nameof(roots));
}
if (coefficients.Count < 2)
{
throw new ArgumentException("Number of coefficients must be 2 or greater.");
}
if (coefficients[coefficients.Count - 1] == 0.0)
{
throw new ArgumentException("The highest coefficient is expected to be non-zero.");
}
if (epsilon == 0.0)
{
epsilon = -1E-08;
}
if (coefficients.Count == 2)
{
roots.Add(-coefficients[0] / coefficients[1]);
}
else if (coefficients.Count == 3)
{
MathUtil.GetQuadraticPolynomialRoots(coefficients, roots);
}
else if (coefficients.Count == 4)
{
IList <double> cubicPolynomialRoots = MathUtil.GetCubicPolynomialRoots(coefficients);
for (int index = 0; index < cubicPolynomialRoots.Count; ++index)
{
roots.Add(cubicPolynomialRoots[index]);
}
}
else
{
double rootBoundsRadius = MathUtil.GetPolynomialSingleRootBoundsRadius(coefficients);
Pair <ComplexD> pair1 = new Pair <ComplexD>((ComplexD)(-rootBoundsRadius), (ComplexD)MathUtil.EvaluatePolynomial(coefficients, -rootBoundsRadius));
Pair <ComplexD> pair2 = new Pair <ComplexD>((ComplexD)0.0, (ComplexD)MathUtil.EvaluatePolynomial(coefficients, 0.0));
Pair <ComplexD> pair3 = new Pair <ComplexD>((ComplexD)rootBoundsRadius, (ComplexD)double.NaN);
double num1 = epsilon > 0.0 ? epsilon : -epsilon * rootBoundsRadius;
double num2 = num1 * num1;
int num3;
ComplexD first1;
for (num3 = 50; (pair3.First - pair2.First).GetModulusSquared() > num2 && num3 > 0; pair3 = new Pair <ComplexD>(first1, new ComplexD(double.NaN)))
{
--num3;
Pair <ComplexD> pair4 = new Pair <ComplexD>(pair3.First, MathUtil.EvaluatePolynomial(coefficients, pair3.First));
ComplexD dividedDifference = MathUtil.GetDividedDifference((IList <Pair <ComplexD> >) new Pair <ComplexD>[3] {
pair1, pair2, pair4
}, 0, 3);
ComplexD complexD1 = MathUtil.GetDividedDifference((IList <Pair <ComplexD> >) new Pair <ComplexD>[2] {
pair2, pair4
}, 0, 2) + dividedDifference * (pair4.First - pair2.First);
ComplexD second = pair4.Second;
ComplexD complexD2 = complexD1 * complexD1 - 4.0 * dividedDifference * second;
first1 = new ComplexD(double.NaN);
if (complexD2.Imaginary == 0.0)
{
if (complexD2.Real >= 0.0)
{
first1 = second.Imaginary != 0.0 || complexD1.Imaginary != 0.0 ? pair4.First - 2.0 * second / (complexD1 + (ComplexD)((double)System.Math.Sign(complexD1.Real) * System.Math.Sqrt(complexD2.Real))) : pair4.First - (ComplexD)(2.0 * second.Real / (complexD1.Real + (double)System.Math.Sign(complexD1.Real) * System.Math.Sqrt(complexD2.Real)));
}
else
{
ComplexD complexD3 = ComplexD.Sqrt(complexD2.Real);
ComplexD complexD4 = complexD1 + complexD3;
ComplexD complexD5 = complexD1 - complexD3;
ComplexD complexD6 = complexD4.GetModulusSquared() >= complexD5.GetModulusSquared() ? complexD4 : complexD5;
first1 = pair4.First - 2.0 * second / complexD6;
}
}
else
{
ComplexD sqrt = complexD2.GetSqrt();
ComplexD complexD3 = complexD1 + sqrt;
ComplexD complexD4 = complexD1 - sqrt;
ComplexD complexD5 = complexD3.GetModulusSquared() >= complexD4.GetModulusSquared() ? complexD3 : complexD4;
first1 = pair4.First - 2.0 * second / complexD5;
}
pair1 = pair2;
pair2 = pair4;
}
if (num3 <= 0)
{
return;
}
if (MathUtil.AreApproxEqual(pair3.First.Imaginary, 0.0, num1))
{
double real = pair3.First.Real;
roots.Add(real);
IList <double> coefficients1 = MathUtil.DeflatePolynomial(coefficients, real);
if (epsilon > 0.0)
{
while (coefficients1.Count > 1 && MathUtil.AreApproxEqual(MathUtil.EvaluatePolynomial(coefficients1, real), 0.0, epsilon))
{
coefficients1 = MathUtil.DeflatePolynomial(coefficients1, real);
}
}
else
{
double largestTerm;
while (coefficients1.Count > 1 && MathUtil.AreApproxEqual(MathUtil.EvaluatePolynomial(coefficients1, real, out largestTerm), 0.0, -epsilon * largestTerm))
{
coefficients1 = MathUtil.DeflatePolynomial(coefficients1, real);
}
}
MathUtil.GetPolynomialRoots(coefficients1, roots, num1);
}
else
{
ComplexD first2 = pair3.First;
double real = first2.Real;
double imaginary = first2.Imaginary;
double a1 = -2.0 * real;
double a0 = real * real + imaginary * imaginary;
MathUtil.GetPolynomialRoots(MathUtil.DeflatePolynomial(coefficients, a0, a1), roots, num1);
}
}
}
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);
}
