/// <include file='FactorDocs.xml' path='factor_docs/message_op_class[@name="InnerProductOpBase"]/message_doc[@name="AAverageConditional(Gaussian, Vector, DenseVector, PositiveDefiniteMatrix, VectorGaussian)"]/*'/>
public static VectorGaussian AAverageConditional([SkipIfUniform] Gaussian innerProduct, Vector A, DenseVector BMean, PositiveDefiniteMatrix BVariance, VectorGaussian result)
{
if (innerProduct.IsUniform())
{
return(VectorGaussian.Uniform(A.Count));
}
// logZ = log N(mProduct; A'*BMean, vProduct + A'*BVariance*A)
// = -0.5 (mProduct - A'*BMean)^2 / (vProduct + A'*BVariance*A) -0.5 log(vProduct + A'*BVariance*A)
// v*innerProduct.Precision
double v = 1 + BVariance.QuadraticForm(A, A) * innerProduct.Precision;
double diff = innerProduct.MeanTimesPrecision - A.Inner(BMean) * innerProduct.Precision;
// dlogZ/dA = BMean * (mProduct - A'*BMean)/v + (BVariance*A) (diff)^2 / v^2 - (BVariance*A)/v
double diff2 = diff * diff;
double v2 = v * v;
var avb = BVariance * A;
var avbPrec = avb * innerProduct.Precision;
var dlogZ = (BMean * diff - avbPrec) / v + avb * diff2 / v2;
// -ddlogZ/dA^2 = (BMean.Outer(BMean) + BVariance) / v + avb.Outer(avb) * (4 * diff2 / (v2 * v))
// -(avb.Outer(avb - BMean * (2 * diff)) * 2 + BVariance * diff2) / v2;
PositiveDefiniteMatrix negativeHessian = BVariance * (innerProduct.Precision / v - diff2 / v2);
negativeHessian.SetToSumWithOuter(negativeHessian, innerProduct.Precision / v, BMean, BMean);
negativeHessian.SetToSumWithOuter(negativeHessian, 4 * diff2 / (v2 * v) - 2 * innerProduct.Precision / v2, avb, avbPrec);
negativeHessian.SetToSumWithOuter(negativeHessian, 2 * diff / v2, avbPrec, BMean);
negativeHessian.SetToSumWithOuter(negativeHessian, 2 * diff / v2, BMean, avbPrec);
negativeHessian.Symmetrize();
return(VectorGaussian.FromDerivatives(A, dlogZ, negativeHessian, GaussianProductOp.ForceProper));
}
private static void GetProductMoments(Matrix A, Vector BMean, PositiveDefiniteMatrix BVariance, Vector mean, PositiveDefiniteMatrix variance)
{
// P.mean = A*B.mean
// P.var = A*B.var*A'
mean.SetToProduct(A, BMean);
if (UseAccurateMethod)
{
int dim = BVariance.Rows;
LowerTriangularMatrix cholesky = new LowerTriangularMatrix(dim, dim);
cholesky.SetToCholesky(BVariance);
Matrix AL = A * cholesky;
variance.SetToOuter(AL);
}
else
{
variance.SetToProduct(A, (A * BVariance).Transpose());
variance.Symmetrize();
}
}
