/// <summary>
/// EP message to 'array'.
/// </summary>
/// <param name="allTrue">Incoming message from 'allTrue'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="array">Incoming message from 'array'.</param>
/// <param name="result">Modified to contain the outgoing message.</param>
/// <returns><paramref name="result"/></returns>
/// <remarks><para>
/// The outgoing message is a distribution matching the moments of 'array' as the random arguments are varied.
/// The formula is <c>proj[p(array) sum_(allTrue) p(allTrue) factor(allTrue,array)]/p(array)</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="allTrue"/> is not a proper distribution</exception>
public static BernoulliList ArrayAverageConditional <BernoulliList>([SkipIfUniform] Bernoulli allTrue, IList <Bernoulli> array, BernoulliList result)
where BernoulliList : IList <Bernoulli>
{
if (result.Count == 0)
{
}
else if (result.Count == 1)
{
result[0] = allTrue;
}
else if (result.Count == 2)
{
result[0] = BooleanAndOp.AAverageConditional(allTrue, array[1]);
result[1] = BooleanAndOp.BAverageConditional(allTrue, array[0]);
}
else // result.Count >= 3
{
double notallTruePrevious = Double.NegativeInfinity;
double[] notallTrueNext = new double[result.Count];
notallTrueNext[notallTrueNext.Length - 1] = Double.NegativeInfinity;
for (int i = notallTrueNext.Length - 2; i >= 0; i--)
{
notallTrueNext[i] = Bernoulli.Or(-array[i + 1].LogOdds, notallTrueNext[i + 1]);
}
for (int i = 0; i < result.Count; i++)
{
double notallTrueExcept = Bernoulli.Or(notallTruePrevious, notallTrueNext[i]);
result[i] = Bernoulli.FromLogOdds(-Bernoulli.Gate(-allTrue.LogOdds, notallTrueExcept));
notallTruePrevious = Bernoulli.Or(notallTruePrevious, -array[i].LogOdds);
}
}
return(result);
}
/// <summary>
/// EP message to 'a'.
/// </summary>
/// <param name="and">Incoming message from 'and'. Must be a proper distribution. If uniform, the result will be uniform.</param>
/// <param name="B">Incoming message from 'b'.</param>
/// <returns>The outgoing EP message to the 'a' argument.</returns>
/// <remarks><para>
/// The outgoing message is the integral of the factor times incoming messages, over all arguments except 'a'.
/// The formula is <c>int f(a,x) q(x) dx</c> where <c>x = (and,b)</c>.
/// </para></remarks>
/// <exception cref="ImproperMessageException"><paramref name="and"/> is not a proper distribution</exception>
public static Bernoulli AAverageConditional([SkipIfUniform] Bernoulli and, Bernoulli B)
{
if (B.IsPointMass)
{
return(AAverageConditional(and, B.Point));
}
return(Bernoulli.FromLogOdds(-Bernoulli.Gate(-and.LogOdds, -B.LogOdds)));
}