public static Complex FindRootLaguerre(this Polynomial <Complex, ComplexField> polynomial, Complex start)
{
Polynomial <Complex, ComplexField> p;
Polynomial <Complex, ComplexField> pd1;
Polynomial <Complex, ComplexField> pd2;
Complex x;
p = polynomial.RemoveMultipleRoots().MakeMonic();
if (p.Degree == 0)
{
return(Complex.Zero);
}
pd1 = p.Differentiate();
pd2 = pd1.Differentiate();
x = start;
while (true)
{
Complex y;
y = p.Evaluate(x);
if (y == 0)
{
break;
}
Complex g = pd1.Evaluate(x) / y;
Complex gSquared = g * g;
Complex h = gSquared - (pd2.Evaluate(x) / y);
Complex denomPart = Complex.Sqrt((p.Degree - 1) * (p.Degree * h - gSquared));
Complex denom = g + denomPart;
Complex denom2 = g - denomPart;
if (denom2.Abs > denom.Abs)
{
denom = denom2;
}
Complex newX = x - ((double)p.Degree / denom);
if (x.ApproxEquals(newX))
{
break;
}
x = newX;
}
return(x);
}
public static Complex[] FindRootsDk(this Polynomial <Complex, ComplexField> polynomial, Complex start)
{
Polynomial <Complex, ComplexField> p;
Complex[] roots;
bool[] done;
int doneCount = 0;
p = polynomial.RemoveMultipleRoots().MakeMonic();
if (p.Degree == 0)
{
return(new Complex[0]);
}
roots = new Complex[p.Degree];
done = new bool[p.Degree];
for (int i = 0; i < roots.Length; i++)
{
roots[i] = Complex.Pow(start, i);
}
while (true)
{
for (int i = 0; i < roots.Length; i++)
{
Complex oldRoot;
Complex nom;
Complex denom;
if (done[i])
{
continue;
}
oldRoot = roots[i];
nom = p.Evaluate(oldRoot);
denom = 1;
for (int j = 0; j < roots.Length; j++)
{
if (j == i)
{
continue;
}
denom *= oldRoot - roots[j];
}
roots[i] = oldRoot - nom / denom;
if (roots[i].ApproxEquals(oldRoot))
{
done[i] = true;
doneCount++;
}
}
if (doneCount == roots.Length)
{
break;
}
}
return(roots);
}
