/// <summary>EP message to <c>indexOfMaximumDouble</c>.</summary>
/// <param name="list">Incoming message from <c>list</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</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 <c>indexOfMaximumDouble</c> as the random arguments are varied. The formula is <c>proj[p(indexOfMaximumDouble) sum_(list) p(list) factor(indexOfMaximumDouble,list)]/p(indexOfMaximumDouble)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="list" /> is not a proper distribution.</exception>
public static Discrete IndexOfMaximumDoubleAverageConditional2(IList <Gaussian> list, Discrete result)
{
// Fast approximate calculation of downward message
// TODO: sort list first
// best accuracy is achieved by processing in decreasing order of means
Gaussian max = list[0];
Vector probs = result.GetWorkspace();
probs[0] = 1.0;
for (int i = 1; i < list.Count; i++)
{
Gaussian A = max;
Gaussian B = list[i];
double pMax = ProbGreater(A, B).GetProbTrue();
for (int j = 0; j < i; j++)
{
probs[j] *= pMax;
}
probs[i] = 1 - pMax;
max = MaxGaussianOp.MaxAverageConditional(Gaussian.Uniform(), A, B);
}
result.SetProbs(probs);
return(result);
}
/// <summary>EP message to <c>indexOfMaximumDouble</c>.</summary>
/// <param name="list">Incoming message from <c>list</c>. Must be a proper distribution. If any element is uniform, the result will be uniform.</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 <c>indexOfMaximumDouble</c> as the random arguments are varied. The formula is <c>proj[p(indexOfMaximumDouble) sum_(list) p(list) factor(indexOfMaximumDouble,list)]/p(indexOfMaximumDouble)</c>.</para>
/// </remarks>
/// <exception cref="ImproperMessageException">
/// <paramref name="list" /> is not a proper distribution.</exception>
public static Discrete IndexOfMaximumDoubleAverageConditional([SkipIfAnyUniform, Proper] IList <Gaussian> list, Discrete result)
{
// Fast approximate calculation of downward message
if (list.Count <= 1)
{
return(result);
}
Gaussian[] maxBefore = new Gaussian[list.Count];
maxBefore[1] = list[0];
for (int i = 2; i < list.Count; i++)
{
maxBefore[i] = MaxGaussianOp.MaxAverageConditional(Gaussian.Uniform(), maxBefore[i - 1], list[i - 1]);
}
Gaussian[] maxAfter = new Gaussian[list.Count];
maxAfter[list.Count - 2] = list[list.Count - 1];
for (int i = list.Count - 3; i >= 0; i--)
{
maxAfter[i] = MaxGaussianOp.MaxAverageConditional(Gaussian.Uniform(), maxAfter[i + 1], list[i + 1]);
}
Vector probs = result.GetWorkspace();
probs[0] = ProbGreater(list[0], maxAfter[0]).GetProbTrue();
int last = list.Count - 1;
probs[last] = ProbGreater(list[last], maxBefore[last]).GetProbTrue();
for (int i = 1; i < last; i++)
{
Gaussian maxOther = MaxGaussianOp.MaxAverageConditional(Gaussian.Uniform(), maxBefore[i], maxAfter[i]);
probs[i] = ProbGreater(list[i], maxOther).GetProbTrue();
}
result.SetProbs(probs);
return(result);
}