/// <summary>
/// Returns the largest quantile such that ((quantile - lowerItem)/(upperItem - lowerItem) + lowerIndex)/(n-1) <= probability.
/// </summary>
/// <param name="probability">A number between 0 and 1.</param>
/// <param name="lowerIndex"></param>
/// <param name="lowerItem">Must be finite.</param>
/// <param name="upperItem">Must be finite and at least lowerItem.</param>
/// <param name="n">Must be greater than 1</param>
/// <returns></returns>
internal static double GetQuantile(double probability, double lowerIndex, double lowerItem, double upperItem, long n)
{
if (probability < 0)
{
throw new ArgumentOutOfRangeException(nameof(probability), probability, $"{nameof(probability)} < 0");
}
if (probability > 1)
{
throw new ArgumentOutOfRangeException(nameof(probability), probability, $"{nameof(probability)} > 1");
}
if (n <= 1)
{
throw new ArgumentOutOfRangeException(nameof(n), n, "n <= 1");
}
double pos = MMath.LargestDoubleProduct(probability, n - 1);
double frac = MMath.LargestDoubleSum(-lowerIndex, pos);
if (upperItem < lowerItem)
{
throw new ArgumentOutOfRangeException(nameof(upperItem), upperItem, $"{nameof(upperItem)} ({upperItem}) < {nameof(lowerItem)} ({lowerItem})");
}
if (upperItem == lowerItem)
{
return(lowerItem);
}
// The above check ensures diff > 0
double diff = upperItem - lowerItem;
double offset = MMath.LargestDoubleProduct(frac, diff);
return(MMath.LargestDoubleSum(lowerItem, offset));
}
/// <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");
}
// The zero-based index of item in the sorted List<T>, if item is found;
// otherwise, a negative number that is the bitwise complement of the index of the next element that is larger than item
// or, if there is no larger element, the bitwise complement of Count.
int index = Array.BinarySearch(probabilities, probability);
if (index >= 0)
{
return(quantiles[index]);
}
else
{
// Linear interpolation
int largerIndex = ~index;
if (largerIndex == 0)
{
return(quantiles[largerIndex]);
}
int smallerIndex = largerIndex - 1;
if (largerIndex == probabilities.Length)
{
return(quantiles[smallerIndex]);
}
double upperItem = quantiles[largerIndex];
double lowerItem = quantiles[smallerIndex];
double diff = upperItem - lowerItem;
if (diff > double.MaxValue)
{
double scale = System.Math.Max(System.Math.Abs(upperItem), System.Math.Abs(lowerItem));
double lowerItemOverScale = lowerItem / scale;
diff = upperItem / scale - lowerItemOverScale;
double slope = diff / (probabilities[largerIndex] - probabilities[smallerIndex]);
double frac = MMath.LargestDoubleSum(-probabilities[smallerIndex], probability);
double offset = MMath.LargestDoubleProduct(frac, slope);
return(MMath.LargestDoubleSum(lowerItemOverScale, offset) * scale);
}
else
{
double slope = diff / (probabilities[largerIndex] - probabilities[smallerIndex]);
// Solve for the largest x such that probabilities[smallerIndex] + (x - quantiles[smallerIndex]) / slope <= probability.
double frac = MMath.LargestDoubleSum(-probabilities[smallerIndex], probability);
double offset = MMath.LargestDoubleProduct(frac, slope);
return(MMath.LargestDoubleSum(lowerItem, offset));
}
}
}
/// <summary>
/// Returns the largest quantile such that ((quantile - lowerItem)/(upperItem - lowerItem) + lowerIndex)/(n-1) <= probability.
/// </summary>
/// <param name="probability"></param>
/// <param name="lowerIndex"></param>
/// <param name="lowerItem"></param>
/// <param name="upperItem"></param>
/// <param name="n"></param>
/// <returns></returns>
internal static double GetQuantile(double probability, long lowerIndex, double lowerItem, double upperItem, long n)
{
if (n == 1)
{
throw new ArgumentOutOfRangeException("n == 1");
}
double pos = MMath.LargestDoubleProduct(n - 1, probability);
double frac = MMath.LargestDoubleSum(-lowerIndex, pos);
double diff = upperItem - lowerItem;
if (diff == 0)
{
return(lowerItem);
}
double offset = MMath.LargestDoubleProduct(diff, frac);
return(MMath.LargestDoubleSum(lowerItem, offset));
}
/// <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");
}
// The zero-based index of item in the sorted List<T>, if item is found;
// otherwise, a negative number that is the bitwise complement of the index of the next element that is larger than item
// or, if there is no larger element, the bitwise complement of Count.
int index = Array.BinarySearch(probabilities, probability);
if (index >= 0)
{
return(quantiles[index]);
}
else
{
// Linear interpolation
int largerIndex = ~index;
if (largerIndex == 0)
{
return(quantiles[largerIndex]);
}
int smallerIndex = largerIndex - 1;
if (largerIndex == probabilities.Length)
{
return(quantiles[smallerIndex]);
}
double slope = (quantiles[largerIndex] - quantiles[smallerIndex]) / (probabilities[largerIndex] - probabilities[smallerIndex]);
// Solve for the largest x such that probabilities[smallerIndex] + (x - quantiles[smallerIndex]) / slope <= probability.
double frac = MMath.LargestDoubleSum(-probabilities[smallerIndex], probability);
double offset = MMath.LargestDoubleProduct(slope, frac);
return(MMath.LargestDoubleSum(quantiles[smallerIndex], offset));
}
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="PlusGammaOp"]/message_doc[@name="SumAverageConditional(GammaPower, double)"]/*'/>
public static GammaPower SumAverageConditional([SkipIfUniform] GammaPower a, double b)
{
if (double.IsInfinity(b) || double.IsNaN(b))
{
throw new ArgumentOutOfRangeException(nameof(b), b, $"Argument is outside the range of supported values.");
}
if (a.IsUniform() || b == 0)
{
return(a);
}
else if (a.Power == 0)
{
throw new ArgumentException($"Cannot add {b} to {a}");
}
else if (a.IsPointMass)
{
return(GammaPower.PointMass(a.Point + b, a.Power));
}
else if (a.Power < 0)
{
if (a.Shape <= a.Power)
{
return(a); // mode is at zero
}
// The mode is ((Shape - Power)/Rate)^Power
// We want to shift the mode by b, preserving the Shape and Power.
// This implies ((Shape - Power)/newRate)^Power = newMode
// newRate = (Shape - Power)/newMode^(1/Power)
// = (a.Shape - a.Power) * Math.Pow(a.GetMode() + b, -1 / a.Power);
//double logMode = a.Power * (Math.Log(Math.Max(0, a.Shape - a.Power)) - Math.Log(a.Rate));
//if (logMode > double.MaxValue) return a; // mode is at infinity
double logShapeMinusPower = Math.Log(a.Shape - a.Power);
double mode = a.GetMode();
if (mode > double.MaxValue)
{
return(a); // mode is at infinity
}
double newMode = Math.Max(0, mode + b);
double newLogMode = Math.Log(newMode);
// Find newLogRate to satisfy a.Power*(logShapeMinusPower - newLogRate) <= newLogMode
// logShapeMinusPower - newLogRate >= newLogMode/a.Power
// newLogRate - logShapeMinusPower <= -newLogMode/a.Power
double newLogModeOverPower = MMath.LargestDoubleRatio(newLogMode, -a.Power);
double newLogRate = MMath.LargestDoubleSum(logShapeMinusPower, newLogModeOverPower);
if ((double)((logShapeMinusPower - newLogRate) * a.Power) > newLogMode)
{
throw new Exception();
}
// Ideally this would find largest newRate such that log(newRate) <= newLogRate
double newRate = Math.Exp(newLogRate);
if (logShapeMinusPower == newLogRate)
{
newRate = a.Shape - a.Power;
}
if (a.Rate > 0)
{
newRate = Math.Max(double.Epsilon, newRate);
}
if (!double.IsPositiveInfinity(a.Rate))
{
newRate = Math.Min(double.MaxValue, newRate);
}
return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power));
}
else if (!a.IsProper())
{
return(a);
}
else
{
// The mean is Math.Exp(Power * (MMath.RisingFactorialLnOverN(Shape, Power) - Math.Log(Rate)))
// We want to shift the mean by b, preserving the Shape and Power.
// This implies log(newRate) = MMath.RisingFactorialLnOverN(Shape, Power) - log(newMean)/Power
double logShape = MMath.RisingFactorialLnOverN(a.Shape, a.Power);
//double logMean = a.GetLogMeanPower(1);
//double newLogMean = (b > 0) ?
// MMath.LogSumExp(logMean, Math.Log(b)) :
// MMath.LogDifferenceOfExp(logMean, Math.Log(-b));
double newMean = Math.Max(0, a.GetMean() + b);
double newLogMean = Math.Log(newMean);
// If logShape is big, this difference can lose accuracy
// Find newLogRate to satisfy logShape - newLogRate <= newLogMean/a.Power
double newLogMeanOverPower = MMath.LargestDoubleRatio(newLogMean, a.Power);
double newLogRate = -MMath.LargestDoubleSum(-logShape, newLogMeanOverPower);
// check: (logShape - newLogRate)*a.Power <= newLogMean
if ((double)((logShape - newLogRate) * a.Power) > newLogMean)
{
throw new Exception();
}
double newRate = Math.Exp(newLogRate);
newRate = Math.Max(double.Epsilon, newRate);
if (!double.IsPositiveInfinity(a.Rate))
{
newRate = Math.Min(double.MaxValue, newRate);
}
return(GammaPower.FromShapeAndRate(a.Shape, newRate, a.Power));
}
}