public static Tuple<List<BigFloat>, List<BigFloat>> Solve(int n, int n_iters, BigFloat tolerance, List<BigFloat> initialGuess, List<BigFloat> zi)
{
int m = initialGuess.Count, i, j, k;
BigFloat d = 0, pa, pb, a, b, qa, qb, k1, k2, k3, na, nb, s1, s2;
for (i = 0; i < n_iters; ++i)
{
d = 0.0;
for (j = 0; j < m; ++j)
{
//Read in zj
pa = initialGuess[j];
pb = zi[j];
//Compute denominator
//
// (zj - z0) * (zj - z1) * ... * (zj - z_{n-1})
//
a = 1.0;
b = 0.0;
for (k = 0; k < m; ++k)
{
if (k == j)
{
continue;
}
qa = pa - initialGuess[k];
qb = pb - zi[k];
if (qa * qa + qb * qb < tolerance)
{
continue;
}
k1 = qa * (a + b);
k2 = a * (qb - qa);
k3 = b * (qa + qb);
a = k1 - k3;
b = k1 + k2;
}
//Compute numerator
na = RealNumbers[n - 1];
nb = ImaginaryNumbers[n - 1];
s1 = pb - pa;
s2 = pa + pb;
for (k = n - 2; k >= 0; --k)
{
k1 = pa * (na + nb);
k2 = na * s1;
k3 = nb * s2;
na = k1 - k3 + RealNumbers[k];
nb = k1 + k2 + ImaginaryNumbers[k];
}
//Compute reciprocal
k1 = a * a + b * b;
if (BigFloat.Abs(k1) > Epsilon)
{
a /= k1;
b /= -k1;
}
else
{
a = 1.0;
b = 0.0;
}
//Multiply and accumulate
k1 = na * (a + b);
k2 = a * (nb - na);
k3 = b * (na + nb);
qa = k1 - k3;
qb = k1 + k2;
initialGuess[j] = pa - qa;
zi[j] = pb - qb;
d = BigFloat.Max(d, BigFloat.Max(BigFloat.Abs(qa), BigFloat.Abs(qb)));
}
//If converged, exit early
if (d < tolerance)
{
break;
}
}
// Post process: Combine any repeated roots
int count;
for (i = 0; i < m; ++i)
{
count = 1;
a = initialGuess[i];
b = zi[i];
for (j = 0; j < m; ++j)
{
if (i == j)
{
continue;
}
if (Near(initialGuess[i], zi[i], initialGuess[j], zi[j], tolerance))
{
++count;
a += initialGuess[j];
b += zi[j];
}
}
if (count > 1)
{
a /= count;
b /= count;
for (j = 0; j < m; ++j)
{
if (i == j)
{
continue;
}
if (Near(initialGuess[i], zi[i], initialGuess[j], zi[j], tolerance))
{
initialGuess[j] = a;
zi[j] = b;
}
}
initialGuess[i] = a;
zi[i] = b;
}
}
for(i=0;i<initialGuess.Count;i++)
{
if(BigFloat.Abs(zi[i]) < Epsilon)
{
zi[i] = 0;
}
if (BigFloat.Abs(initialGuess[i]) < Epsilon)
{
initialGuess[i] = 0;
}
}
// Order by size
List<Tuple<BigFloat, BigFloat>> Elements = initialGuess.Zip(zi, (x, y) => Tuple.Create(x, y)).OrderByDescending(x => x.Item2.IsZero()).ToList();
Elements = Elements.OrderBy(x => x.Item1).ToList();
// Clear
zi = new List<BigFloat>();
initialGuess = new List<BigFloat>();
for (i = 0; i < Elements.Count; i++)
{
bool found = false;
for (j = 0; j < zi.Count; j++)
{
if (zi[j] == Elements[i].Item2 && initialGuess[j] == Elements[i].Item1)
{
found = true;
}
}
if (!found)
{
zi.Add(Elements[i].Item2);
initialGuess.Add(Elements[i].Item1);
}
}
// Round the result
foreach(BigFloat s in initialGuess)
{
BigFloat c = new BigFloat(s);
c.FPart();
if (BigFloat.Abs(c) < tolerance)
{
s.Floor();
}
}
return new Tuple<List<BigFloat>, List<BigFloat>>(initialGuess, zi);
}