/// <summary>
/// Computes the sum of a geometric series <c>1 + w + w^2 + w^3 + ...</c>,
/// where <c>w</c> is a given weight.
/// If the sum diverges, replaces the infinite sum by a finite sum with a lot of terms.
/// </summary>
/// <param name="weight">The weight.</param>
/// <returns>The computed sum.</returns>
public static Weight ApproximateClosure(Weight weight)
{
const double Eps = 1e-20;
const double TermCount = 10000;
if (weight.LogValue < -Eps)
{
// The series converges
return(new Weight(-MMath.Log1MinusExp(weight.LogValue)));
}
if (weight.LogValue < Eps)
{
// The series diverges, geometric progression formula does not apply
return(new Weight(Math.Log(TermCount)));
}
// Compute geometric progression with a lot of terms
return(new Weight(MMath.LogExpMinus1(weight.LogValue * TermCount) - MMath.LogExpMinus1(weight.LogValue)));
}