How to use the cusolverSP with multiple right hand side

I need to solve a sparse complex symmetric matrix with multiple right hand side (a matrix, not vector). Obviously, cusolverSpcsrlsvlu() and cusolverSpcsrlsvqr() are not useful, because they just support single right hand side (a vector). cusolverSpXcsrqrBatched() is also not a good choice, because all the A matrix are the same, it takes time to factorize the same matrix A for a lot of time. Is it possible to extract the q and r matrix after numeric factorization?

Not really an answer to your question, but you can get a GPU-accelerated sparse solver in SuiteSparse:

the cholmod routines would basically be:

cholmod_l_analyze (...) ;   /* analyze A */
cholmod_l_factorize (...) ; /* factorize A to L */
cholmod_l_solve (...) ;     /* solve Ax=b using factorized L */

The last step would be repeated for each RHS vector.