MvNormalCanon Extension

[BA1437]

Would it be impossible to extend this package to work with Distributions.MvNormalCanon? I realize one could take the precision matrix of an MvNormalCanon distribution, invert it and create a MvNormal distribution, but it feels like that may be missing out on some computational efficiencies that could be taken advantage of given we already know the precision matrix.

[PharmCat]

If you know how easy to get cholesky factor of correlation matrix that correspond to covariance matrix from precision matrix - it can be possible from the firs view. I'll try to think about it.

[BA1437]

Given the cholesky decomposition of the precision matrix, how about something like the following to get the cholesky decomposition of the corresponding covariance matrix:

P= [4. 12. -16.; 12. 37. -43.; -16. -43. 98.] # Precision matrix
C = cholesky(P)

R = zeros(size(P)) #Allocate for the cholesky decomposition of the covariance matrix
n = size(P,1)

for l=n:-1:1
    R[l,l] = sqrt(sum(C.U[1:l,l].^2)-sum(R[l,l+1:n].^2))

    for j=l:-1:1
        R[j,l] = (sum(C.U[1:j,l].*C.U[1:j,j]) - sum(R[l,l+1:n].*R[j,l+1:n]))/R[l,l]
    end

end

r = inv(R)

# check
b = cholesky(Hermitian(inv(P)))
isapprox(r,Matrix(b.U); rtol = 0.001)