Solving linear systems with vectorz

I am trying to solve a sparse linear system with Vectorz, but it seems to lack some basic algorithms to do it efficiently.

I want to solve Ku=F, where K is a sparse matrix and F a dense vector.
The classic way to solve this system is to get a decomposition of K, let's say K=LU, and then solve the easy triangular problems Ly=F and Uu=y.

I am not sure the implemented factorizations in Vectorz are optimized for sparse matrix (it seems the implementations are coming from a dense matrix manipulation library), but most importantly Vectorz seems to lack forward and backward substitution algorithms to solve triangular problems.

Start by reviewing Vectorz's implemented matrix factorizations and the sparse-matrix handling described in the issue. Then determine the scope of forward and backward substitution for Ku=F, including whether existing factorizations are suitable for sparse matrices. Done means the required triangular solves are available and the sparse linear-system workflow is covered.