/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="Product">Incoming message from 'product'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'a' with 'product' integrated out.
/// The formula is <c>sum_product p(product) factor(product,a,b)</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="Product"/> is not a proper distribution</exception>
public static Gamma AAverageLogarithm([SkipIfUniform] Gamma Product, double B)
{
if (Product.IsPointMass)
{
return(AAverageLogarithm(Product.Point, B));
}
return(GammaProductOp.AAverageConditional(Product, B));
}
/// <summary>
/// VMP message to 'b'
/// </summary>
/// <param name="Product">Constant value for 'product'.</param>
/// <param name="A">Constant value for 'a'.</param>
/// <returns>The outgoing VMP message to the 'b' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'b' conditioned on the given values.
/// </para></remarks>
public static Gamma BAverageLogarithm(double Product, double A)
{
return(GammaProductOp.BAverageConditional(Product, A));
}
/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="ratio">Constant value for 'ratio'.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'a' conditioned on the given values.
/// </para></remarks>
public static Gamma AAverageLogarithm(double ratio, double B)
{
return(GammaProductOp.ProductAverageConditional(ratio, B));
}
/// <summary>
/// VMP message to 'a'
/// </summary>
/// <param name="ratio">Incoming message from 'ratio'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'a' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'a' with 'ratio' integrated out.
/// The formula is <c>sum_ratio p(ratio) factor(ratio,a,b)</c>.
/// </para></remarks>
public static Gamma AAverageLogarithm([SkipIfUniform] Gamma ratio, double B)
{
return(GammaProductOp.ProductAverageConditional(ratio, B));
}
/// <summary>
/// VMP message to 'ratio'
/// </summary>
/// <param name="A">Incoming message from 'a'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Constant value for 'b'.</param>
/// <returns>The outgoing VMP message to the 'ratio' argument</returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'ratio' as the random arguments are varied.
/// The formula is <c>proj[sum_(a) p(a) factor(ratio,a,b)]</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="A"/> is not a proper distribution</exception>
public static Gamma RatioAverageLogarithm([SkipIfUniform] Gamma A, double B)
{
return(GammaProductOp.AAverageConditional(A, B));
}
/// <summary>
/// Evidence message for EP
/// </summary>
/// <param name="ratio">Constant value for 'ratio'.</param>
/// <param name="a">Incoming message from 'a'.</param>
/// <param name="b">Constant value for 'b'.</param>
/// <returns>Logarithm of the factor's average value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>log(sum_(a) p(a) factor(ratio,a,b))</c>.
/// </para></remarks>
public static double LogAverageFactor(double ratio, Gamma a, double b)
{
Gamma to_ratio = GammaProductOp.AAverageConditional(a, b);
return(to_ratio.GetLogProb(ratio));
}
/// <summary>
/// Evidence message for EP
/// </summary>
/// <param name="product">Constant value for 'product'.</param>
/// <param name="a">Incoming message from 'a'.</param>
/// <param name="b">Constant value for 'b'.</param>
/// <returns>Logarithm of the factor's average value across the given argument distributions</returns>
/// <remarks><para>
/// The formula for the result is <c>log(sum_(a) p(a) factor(product,a,b))</c>.
/// </para></remarks>
public static double LogAverageFactor(double product, Gamma a, double b)
{
Gamma to_product = GammaProductOp.ProductAverageConditional(a, b);
return(to_product.GetLogProb(product));
}
