/// <summary>
/// Returns the largest value x such that GetProbLessThan(x) <= probability.
/// </summary>
/// <param name="probability">A real number in [0,1].</param>
/// <returns></returns>
public double GetQuantile(double probability)
{
if (probability < 0)
{
throw new ArgumentOutOfRangeException(nameof(probability), "probability < 0");
}
if (probability > 1.0)
{
throw new ArgumentOutOfRangeException(nameof(probability), "probability > 1.0");
}
int n = quantiles.Length;
if (probability < 1.0 / (n + 1.0))
{
return(Math.Min(quantiles[0], lowerGaussian.GetQuantile(probability)));
}
if (probability > n / (n + 1.0))
{
return(Math.Max(quantiles[n - 1], upperGaussian.GetQuantile(probability)));
}
if (n == 1)
{
return(quantiles[0]); // probability must be 0.5
}
double pos = MMath.LargestDoubleProduct(n + 1, probability) - 1;
int lower = (int)Math.Floor(pos);
if (lower == n - 1)
{
return(quantiles[lower]);
}
return(OuterQuantiles.GetQuantile(probability, lower + 1, quantiles[lower], quantiles[lower + 1], n + 2));
}
public InnerQuantiles(int quantileCount, CanGetQuantile canGetQuantile)
{
if (quantileCount == 0)
{
throw new ArgumentException("quantileCount == 0", nameof(quantiles));
}
this.quantiles = new double[quantileCount];
for (int i = 0; i < quantileCount; i++)
{
this.quantiles[i] = canGetQuantile.GetQuantile((i + 1.0) / (quantileCount + 1.0));
}
OuterQuantiles.AssertFinite(quantiles, nameof(canGetQuantile));
OuterQuantiles.AssertNondecreasing(quantiles, nameof(canGetQuantile));
lowerGaussian = GetLowerGaussian(quantiles);
upperGaussian = GetUpperGaussian(quantiles);
}
public InnerQuantiles(double[] quantiles)
{
if (quantiles == null)
{
throw new ArgumentNullException(nameof(quantiles));
}
if (quantiles.Length == 0)
{
throw new ArgumentException("quantiles array is empty", nameof(quantiles));
}
OuterQuantiles.AssertFinite(quantiles, nameof(quantiles));
OuterQuantiles.AssertNondecreasing(quantiles, nameof(quantiles));
this.quantiles = quantiles;
lowerGaussian = GetLowerGaussian(quantiles);
upperGaussian = GetUpperGaussian(quantiles);
}
/// <summary>
/// Returns the largest value x such that GetProbLessThan(x) <= probability.
/// </summary>
/// <param name="probability">A real number in [0,1].</param>
/// <returns></returns>
public double GetQuantile(double probability)
{
if (double.IsNaN(probability))
{
throw new ArgumentOutOfRangeException(nameof(probability), "probability is NaN");
}
if (probability < 0)
{
throw new ArgumentOutOfRangeException(nameof(probability), "probability < 0");
}
if (probability > 1.0)
{
throw new ArgumentOutOfRangeException(nameof(probability), "probability > 1.0");
}
// compute the min and max of the retained items
double lowerBound = double.PositiveInfinity, upperBound = double.NegativeInfinity;
bool countGreaterThanZero = false;
for (int bufferIndex = 0; bufferIndex < buffers.Length; bufferIndex++)
{
double[] buffer = buffers[bufferIndex];
int count = countInBuffer[bufferIndex];
if (count > 0)
{
countGreaterThanZero = true;
}
for (int i = 0; i < count; i++)
{
double item = buffer[i];
if (item < lowerBound)
{
lowerBound = item;
}
if (item > upperBound)
{
upperBound = item;
}
}
}
if (probability == 1.0)
{
return(MMath.NextDouble(upperBound));
}
if (probability == 0.0)
{
return(lowerBound);
}
if (!countGreaterThanZero)
{
throw new Exception("QuantileEstimator has no data");
}
if (lowerBound == upperBound)
{
return(upperBound);
}
// use bisection
while (true)
{
double x = MMath.Average(lowerBound, upperBound);
double lowerItem;
double upperItem;
long lowerRank;
long lowerWeight, minLowerWeight, upperWeight, minUpperWeight;
long itemCount;
GetAdjacentItems(x, out lowerItem, out upperItem, out lowerRank, out lowerWeight, out upperWeight, out minLowerWeight, out minUpperWeight, out itemCount);
if (InterpolationType == 0)
{
double probabilityLessThanLowerItem = (double)(lowerRank - lowerWeight) / itemCount;
if (probability < probabilityLessThanLowerItem)
{
upperBound = MMath.PreviousDouble(lowerItem);
}
else
{
double probabilityLessThanUpperItem = (double)lowerRank / itemCount;
if (probability < probabilityLessThanUpperItem)
{
return(lowerItem);
}
double probabilityLessThanOrEqualUpperItem = (double)(lowerRank + upperWeight) / itemCount;
if (probability < probabilityLessThanOrEqualUpperItem)
{
return(upperItem);
}
lowerBound = MMath.NextDouble(upperItem);
}
if (lowerBound > upperBound)
{
throw new Exception("lowerBound > upperBound");
}
}
else if (InterpolationType == 1)
{
// Find frac such that (lowerRank - 0.5 + frac) / itemCount == probability
double scaledProbability = MMath.LargestDoubleProduct(itemCount, probability);
if (scaledProbability < 0.5)
{
return(lowerBound);
}
if (scaledProbability >= itemCount - 0.5)
{
return(upperBound);
}
// probability of lowerItem ranges from (lowerRank-lowerWeight+0.5) / itemCount
// to (lowerRank - 0.5) / itemCount
//if (scaledProbability == lowerRank - lowerWeight + 0.5) return lowerItem;
if ((scaledProbability > lowerRank - lowerWeight + 0.5) && (scaledProbability < lowerRank - 0.5))
{
return(lowerItem);
}
// probability of upperItem ranges from (lowerRank + 0.5) / itemCount
// to (lowerRank + upperWeight - 0.5) / itemCount
if (scaledProbability == lowerRank + 0.5)
{
return(upperItem);
}
if ((scaledProbability > lowerRank + 0.5) && (scaledProbability < lowerRank + upperWeight - 0.5))
{
return(upperItem);
}
double frac = scaledProbability - (lowerRank - 0.5);
if (frac < 0)
{
upperBound = MMath.PreviousDouble(x);
}
else if (frac > 1)
{
lowerBound = MMath.NextDouble(x);
}
else
{
return(OuterQuantiles.GetQuantile(probability, lowerRank - 0.5, lowerItem, upperItem, itemCount + 1));
}
}
else
{
double scaledProbability = MMath.LargestDoubleProduct(itemCount - 1, probability);
// probability of lowerItem ranges from (lowerRank-lowerWeight) / (itemCount - 1)
// to (lowerRank - 1) / (itemCount - 1).
if (scaledProbability == lowerRank - lowerWeight)
{
return(lowerItem);
}
if ((scaledProbability > lowerRank - lowerWeight) && (scaledProbability < lowerRank - 1))
{
return(lowerItem);
}
// probability of upperItem ranges from lowerRank / (itemCount - 1)
// to (lowerRank + upperWeight-1) / (itemCount - 1)
if (scaledProbability == lowerRank)
{
return(upperItem);
}
if ((scaledProbability > lowerRank) && (scaledProbability < lowerRank + upperWeight - 1))
{
return(upperItem);
}
// solve for frac in (lowerRank-1 + frac) / (itemCount - 1) == probability
double frac = scaledProbability - (lowerRank - 1);
if (frac < 0)
{
upperBound = MMath.PreviousDouble(x);
}
else if (frac > 1)
{
lowerBound = MMath.NextDouble(x);
}
else
{
return(OuterQuantiles.GetQuantile(probability, lowerRank - 1, lowerItem, upperItem, itemCount));
}
}
}
}
