/// <summary>
/// Computes the unnormalized cumulative distribution function and other attributes for the
/// distribution (like mean, variance, and so on).
/// </summary>
/// <remarks>
/// Also remember to change <see cref="SetUp(int, IEnumerable{double}, out double[])"/>
/// when changing this method.
/// </remarks>
private void UpdateHelpers()
{
var weightsSum = _weights.Sum(); // It will store the sum of all UNNORMALIZED weights.
var cdf = new double[_weights.Count]; // It will store NORMALIZED cdf.
var tmpMean = 0.0;
var maxW = 0.0; // It will store max weight (all weights are positive).
var maxI = 0; // It will store max weight index.
// Let's normalize all weights, if necessary.
if (!TMath.AreEqual(weightsSum, 1.0))
{
for (var i = 0; i < _weights.Count; ++i)
{
_weights[i] /= weightsSum;
}
Debug.Assert(TMath.AreEqual(_weights.Sum(), 1.0));
}
weightsSum = 0.0; // Reset weight sum to use it for cdf.
// One big loop to compute all helpers needed by this distribution.
for (var i = 0; i < _weights.Count; ++i)
{
var w = _weights[i];
weightsSum += w;
cdf[i] = weightsSum;
tmpMean += w * (i + 1.0); // Plus one because it is zero-based.
if (w > maxW)
{
maxW = w;
maxI = i;
}
}
// Finalize some results...
_cdf = cdf;
Mean = tmpMean - 1.0; // Minus one to make it zero-based.
Mode = new double[] { maxI };
var halfWeightsSum = weightsSum / 2.0;
var tmpMedian = double.NaN;
var tmpVar = 0.0;
// We still need another loop to compute variance; as for the mean, the plus/minus one is needed.
for (var i = 0; i < _weights.Count; ++i)
{
if (double.IsNaN(tmpMedian) && _cdf[i] >= halfWeightsSum)
{
tmpMedian = i;
}
tmpVar += _weights[i] * TMath.Square(i + 1 - Mean);
}
// Finalize last results...
Median = tmpMedian;
Variance = tmpVar - 1.0;
}
