/// <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));
}
}
