By the looks of it, the routines you'd be using would be coming from umfpack. cvxopt has chosen to package the details of LU factorization in opaque objects and instead offer routines to use these decompositions (via taking the opaque object as input). In scipy, umfpack is also used: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.spsolve.html#scipy.sparse.linalg.spsolve . Scipy also offers LU decomposition routines: https://docs.scipy.org/doc/scipy/reference/generated/scipy.sparse.linalg.splu.html#scipy.sparse.linalg.splu but that uses a different library. It looks suspicious that two packages offer umfpack for solving sparse problems, but don't give explicit access to LU factorizations produced in the process, when using UMFPACK. Perhaps UMFPACK isn't suited to provide the explicit factorization (but it may be very good at using its internally computed data).
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