/// <summary>
/// VMP message to 'innerProduct'
/// </summary>
/// <param name="AMean">Buffer 'AMean'.</param>
/// <param name="AVariance">Buffer 'AVariance'.</param>
/// <param name="BMean">Buffer 'BMean'.</param>
/// <param name="BVariance">Buffer 'BVariance'.</param>
/// <returns>The outgoing VMP message to the 'innerProduct' argument</returns>
/// <remarks><para>
/// The outgoing message is the factor viewed as a function of 'innerProduct' conditioned on the given values.
/// </para></remarks>
public static Gaussian InnerProductAverageLogarithm(Vector AMean, PositiveDefiniteMatrix AVariance, Vector BMean, PositiveDefiniteMatrix BVariance)
{
Gaussian result = new Gaussian();
// p(x|a,b) = N(E[a]'*E[b], E[b]'*var(a)*E[b] + E[a]'*var(b)*E[a] + trace(var(a)*var(b)))
// Uses John Winn's rule for deterministic factors.
// Strict variational inference would set the variance to 0.
result.SetMeanAndVariance(AMean.Inner(BMean), AVariance.QuadraticForm(BMean) + BVariance.QuadraticForm(AMean) + AVariance.Inner(BVariance));
return result;
}
/// <summary>VMP message to <c>innerProduct</c>.</summary>
/// <param name="AMean">Buffer <c>AMean</c>.</param>
/// <param name="AVariance">Buffer <c>AVariance</c>.</param>
/// <param name="BMean">Buffer <c>BMean</c>.</param>
/// <param name="BVariance">Buffer <c>BVariance</c>.</param>
/// <returns>The outgoing VMP message to the <c>innerProduct</c> argument.</returns>
/// <remarks>
/// <para>The outgoing message is the factor viewed as a function of <c>innerProduct</c> conditioned on the given values.</para>
/// </remarks>
public static Gaussian InnerProductAverageLogarithm(Vector AMean, PositiveDefiniteMatrix AVariance, Vector BMean, PositiveDefiniteMatrix BVariance)
{
Gaussian result = new Gaussian();
// p(x|a,b) = N(E[a]'*E[b], E[b]'*var(a)*E[b] + E[a]'*var(b)*E[a] + trace(var(a)*var(b)))
// Uses John Winn's rule for deterministic factors.
// Strict variational inference would set the variance to 0.
result.SetMeanAndVariance(AMean.Inner(BMean), AVariance.QuadraticForm(BMean) + BVariance.QuadraticForm(AMean) + AVariance.Inner(BVariance));
return(result);
}
