public static Wishart SampleAverageConditional2(double shape, [Proper] Wishart rate, Wishart to_rate, Wishart result)
{
Wishart ratePost = rate * to_rate;
PositiveDefiniteMatrix r = ratePost.GetMean();
return(WishartFromShapeAndRateOp.SampleAverageConditional(shape, r, result));
}
/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="WishartFromShapeAndRateOp_Laplace2"]/message_doc[@name="RateAverageConditional(Wishart, double, Wishart, Wishart, Wishart)"]/*'/>
public static Wishart RateAverageConditional([SkipIfUniform] Wishart sample, double shape, Wishart rate, Wishart to_rate, Wishart result)
{
if (sample.IsPointMass)
{
return(WishartFromShapeAndRateOp.RateAverageConditional(sample.Point, shape, result));
}
// f(Y,R) = |Y|^(a-c) |R|^a exp(-tr(YR))
// p(Y) = |Y|^(a_y-c) exp(-tr(YB_y)
// p(R) = |R|^(a_r-c) exp(-tr(RB_r)
// int_Y f(Y,R) p(Y) dY = |R|^a |R+B_y|^-(a+a_y-c)
int dim = sample.Dimension;
double c = 0.5 * (dim + 1);
double shape2 = shape - c + sample.Shape;
Wishart ratePost = rate * to_rate;
PositiveDefiniteMatrix r = ratePost.GetMean();
PositiveDefiniteMatrix rby = r + sample.Rate;
PositiveDefiniteMatrix invrby = rby.Inverse();
PositiveDefiniteMatrix rInvrby = rby;
rInvrby.SetToProduct(r, invrby);
double xxddlogp = Matrix.TraceOfProduct(rInvrby, rInvrby) * shape2;
double delta = -xxddlogp / dim;
PositiveDefiniteMatrix invR = r.Inverse();
PositiveDefiniteMatrix dlogp = invrby;
dlogp.Scale(-shape2);
LowerTriangularMatrix rChol = new LowerTriangularMatrix(dim, dim);
rChol.SetToCholesky(r);
result.SetDerivatives(rChol, invR, dlogp, xxddlogp, GammaFromShapeAndRateOp.ForceProper, shape);
return(result);
}
