/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="GammaPowerProductOp_Laplace"]/message_doc[@name="LogAverageFactor(GammaPower, GammaPower, GammaPower, Gamma)"]/*'/>
public static double LogAverageFactor(GammaPower product, GammaPower A, GammaPower B, Gamma q)
{
if (B.Shape < A.Shape)
{
return(LogAverageFactor(product, B, A, q));
}
if (B.IsPointMass)
{
return(GammaProductOp.LogAverageFactor(product, A, B.Point));
}
if (A.IsPointMass)
{
return(GammaProductOp.LogAverageFactor(product, A.Point, B));
}
double qPoint = q.GetMean();
double logf;
if (product.IsPointMass)
{
// Ga(y/q; s, r)/q
if (qPoint == 0)
{
if (product.Point == 0)
{
logf = A.GetLogProb(0);
}
else
{
logf = double.NegativeInfinity;
}
}
else
{
logf = A.GetLogProb(product.Point / qPoint) - Math.Log(qPoint);
}
}
else
{
// int Ga^y_p(a^pa b^pb; y_s, y_r) Ga(a; s, r) da = q^(y_s-y_p) / (r + q y_r)^(y_s + s-pa) Gamma(y_s+s-pa)
double shape = product.Shape - product.Power;
double shape2 = GammaFromShapeAndRateOp_Slow.AddShapesMinus1(product.Shape, A.Shape) + (1 - A.Power);
if (IsProper(product) && product.Shape > A.Shape)
{
// same as below but product.GetLogNormalizer() is inlined and combined with other terms
double AShapeMinusPower = A.Shape - A.Power;
logf = shape * Math.Log(qPoint)
- Gamma.FromShapeAndRate(A.Shape, A.Rate).GetLogNormalizer()
- product.Shape * Math.Log(A.Rate / product.Rate + qPoint)
- Math.Log(Math.Abs(product.Power));
if (AShapeMinusPower != 0)
{
logf += AShapeMinusPower * (MMath.RisingFactorialLnOverN(product.Shape, AShapeMinusPower) - Math.Log(A.Rate + qPoint * product.Rate));
}
}
else
{
logf = shape * Math.Log(qPoint)
- shape2 * Math.Log(A.Rate + qPoint * product.Rate)
+ MMath.GammaLn(shape2)
- Gamma.FromShapeAndRate(A.Shape, A.Rate).GetLogNormalizer()
- product.GetLogNormalizer();
// normalizer is -MMath.GammaLn(Shape) + Shape * Math.Log(Rate) - Math.Log(Math.Abs(Power))
}
}
double logz = logf + Gamma.FromShapeAndRate(B.Shape, B.Rate).GetLogProb(qPoint) - q.GetLogProb(qPoint);
return(logz);
}
