/// <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)); }
/// <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)); } } } }