public void Multiply(PolynomialFactor factor)
{
var len = Coefficients.Count;
Coefficients.AddRange(factor.Coefficients);
PolynomialMultiplication(0, len, len, factor.Coefficients.Count, 0, 1, 1);
for (var i = 0; i < Coefficients.Count; ++i)
{
Coefficients[i] = Destination[i];
}
SetKey();
}
/// <summary>
/// Computes the coefficients of a real monic polynomial given its real and complex roots.
/// The final monic polynomial is represented as:
/// coefficients[0] + coefficients[1] * X + coefficients[2] * X^2 + ... + coefficients[n-1] * X^(n-1) + X^n
///
/// Note: the constant 1 coefficient of the highest degree term is implicit and not included in the output of the method.
/// </summary>
/// <param name="roots">The input (complex) roots</param>
/// <param name="coefficients">The output real coefficients</param>
/// <returns>A boolean flag indicating whether the algorithm was successful.</returns>
public static bool FindPolynomialCoefficients(Complex[] roots, ref Double[] coefficients)
{
Contracts.CheckParam(Utils.Size(roots) > 0, nameof(roots), "There must be at least 1 input root.");
int i;
int n = roots.Length;
var hash = new Dictionary <Complex, FactorMultiplicity>();
int destinationOffset = 0;
var factors = new List <PolynomialFactor>();
for (i = 0; i < n; ++i)
{
if (Double.IsNaN(roots[i].Real) || Double.IsNaN(roots[i].Imaginary))
{
return(false);
}
if (roots[i].Equals(Complex.Zero)) // Zero roots
{
destinationOffset++;
}
else if (roots[i].Imaginary == 0) // Real roots
{
var f = new PolynomialFactor(new[] { (decimal) - roots[i].Real });
factors.Add(f);
}
else // Complex roots
{
var conj = Complex.Conjugate(roots[i]);
FactorMultiplicity temp;
if (hash.TryGetValue(conj, out temp))
{
temp.Multiplicity--;
var f = new PolynomialFactor(new[]
{
(decimal)(roots[i].Real * roots[i].Real + roots[i].Imaginary * roots[i].Imaginary),
(decimal)(-2 * roots[i].Real)
});
factors.Add(f);
if (temp.Multiplicity <= 0)
{
hash.Remove(conj);
}
}
else
{
if (hash.TryGetValue(roots[i], out temp))
{
temp.Multiplicity++;
}
else
{
hash.Add(roots[i], new FactorMultiplicity());
}
}
}
}
if (hash.Count > 0)
{
return(false);
}
var comparer = new ByMaximumCoefficient();
factors.Sort(comparer);
if (destinationOffset < n - 1)
{
if (Utils.Size(PolynomialFactor.Destination) < n)
{
PolynomialFactor.Destination = new decimal[n];
}
while (factors.Count > 1)
{
var k1 = Math.Abs(factors.ElementAt(0).Key);
var k2 = Math.Abs(factors.ElementAt(factors.Count - 1).Key);
PolynomialFactor f1;
if (k1 < k2)
{
f1 = factors.ElementAt(0);
factors.RemoveAt(0);
}
else
{
f1 = factors.ElementAt(factors.Count - 1);
factors.RemoveAt(factors.Count - 1);
}
var ind = factors.BinarySearch(new PolynomialFactor(-f1.Key), comparer);
if (ind < 0)
{
ind = ~ind;
}
ind = Math.Min(factors.Count - 1, ind);
var f2 = factors.ElementAt(ind);
factors.RemoveAt(ind);
f1.Multiply(f2);
ind = factors.BinarySearch(f1, comparer);
if (ind >= 0)
{
factors.Insert(ind, f1);
}
else
{
factors.Insert(~ind, f1);
}
}
}
if (Utils.Size(coefficients) < n)
{
coefficients = new Double[n];
}
for (i = 0; i < destinationOffset; ++i)
{
coefficients[i] = 0;
}
if (destinationOffset < n)
{
var coeff = factors.ElementAt(0).Coefficients;
for (i = destinationOffset; i < n; ++i)
{
coefficients[i] = Decimal.ToDouble(coeff[i - destinationOffset]);
}
}
return(true);
}
