The sparse cholesky factorization does not generally keep the user permutation given as parameter.
SuiteSparse performs post ordering which is not disabled (as far as I can tell) in the current Julia interface to SuiteSparse when a user permutation is given as parameter.
My impression is that the sparse cholesky should not permute the factorization of A when a user permutation is given as 1:size(A,1).
“fact_” method in SuiteSparse/cholmod.jl has a “postorder” keyword argument, but that is not set to false in “cholesky” method when cholesky is called with user permutation argument defined.
This can be easily tested by creating a random sparse positive definite matrix A and calling “cholesky” with user permutation set as 1:size(A,1). All cases I have tried for 10x10 matrices has permuted the factorization.
Juha