Question: Calling UMFPACK sparsedirect linearsolver using only sparse entries

In the past, you had shown how to use take a given sparse A matrix and store the LU components and use the same factorization for multiple backsolves at

When PDEs are solved, we are calling the A matrix at every time step (with some discretizations in x) and the factorization is done and stored at every time step (this is time-consuming and memory-consuming). Is it possible to call UMFPACK using only the sparse storage and entries? The main routine seems to provide the option

This would mean that the pattern is found only once for the Jacobian at t= 0, then only the non-zero sparse entries (vector/row, not a matrix) are updated at every time step.

To be clear, what I am asking for is create a random sparse matrix (say 4x4 or 10x10)
create a b Vector.

Solve AZ =b with method = SparseDirect. (This should internally create and store R, CC, X as at

Store R, CC, X and update only X for a different A matrix with the same sparsity pattern and solve for Z using stored (R, CC), and updated X.

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