add kron

[johnczito]

The kronecker product of positive definite matrices is positive definite, and the cholesky factor of a kronecker product is the kronecker product of the cholesky factors. So this PR adds

Base.kron(A::PDMat, B::PDMat) = PDMat(kron(A.mat, B.mat), Cholesky(kron(A.chol.U, B.chol.U), 'U', A.chol.info))

This functionality would be used to improve two spots in Distributions.jl where a covariance matrix is computed as the kronecker product of two PDMat instances, but we currently ignore the PDMat nature of the factors: here and here.

Turns out that directly supplying both mat and chol is faster than just supplying chol and letting mat be computed from it. MWE:

using LinearAlgebra, PDMats

X = randn(7, 7)
Y = randn(11, 11)
PDA = PDMat(X * X')
PDB = PDMat(Y * Y')

kron1(A::PDMat, B::PDMat) = PDMat(Cholesky(kron(A.chol.U, B.chol.U), 'U', A.chol.info))
kron2(A::PDMat, B::PDMat) = PDMat(kron(A.mat, B.mat), Cholesky(kron(A.chol.U, B.chol.U), 'U', A.chol.info))

julia> @time PDMat(kron(PDA.mat, PDB.mat))
  0.000183 seconds (13 allocations: 93.203 KiB)

julia> @time kron1(PDA, PDB)
  0.000176 seconds (15 allocations: 139.625 KiB)

julia> @time kron2(PDA, PDB)
  0.000108 seconds (12 allocations: 93.156 KiB)