I want to solve a system of sparse matrix equations where my left hand matrix is lower triangular matrix. Now this process is not as expensive as decomposition of the matrix. Here, only a back-substitution step is enough. Now my questions is that if I want to do this in parallel, how can I use PARADISO (specifically cluster interface) to solve this system of equations? Can I use just one of the steps of the solver to perform back-substitution? If yes, how?
This is my first time using PARADISO so kindly hep me with this and apologies if I said anything worng.
Thanks in advance,
Thanks for your quick response. I looked at the developer reference you mentioned. As far as I understand, iparm (Parallel forward/backward solve control) is used to instruct the solver to perform the forward/backward substitution in parallel. But my query is to perform only one susbtitution step without performing any decomposition. Also, I am trying to figure out a way to use cluster_sparse_solver API as my matrix will be distributed.
Thanks in advance.
Answering your questions, you definitely can use the cluster version of Intel MKL PARDISO to solve a system with a distributed triangular matrix in the same way as you can use the solver for a general non-symmetric matrix. Unfortunately, currently you cannot avoid calling first and second phases (reordering and factorization). So, you need first to do phases 11 and 22, and then call the solving phase (33) (multiple times for different rhs if you want). Since it will all be done in parallel, with optimized algorithms and load balancing, I'd expect you will get reasonable performance.
I suggest you try this setup.
Hope this would be helpful!
Thanks for your response. I am assuming that performing the decomposition will be much more expensive than only performing substitution. Is that correct?
Is there a way (maybe another library) to perform only forward/backward substitution (in parallel and with sparse matrix support)?
Thanks in advance.
Yes, it will be more expensive than a pure solving step. But I'd give it a try (it might be not as slow as you think). Unfortunately, I cannot suggest any other simple solution if you want to use MPI.
Notice that if you are fine with OpenMP parallelization, you can use mkl_sparse_?_trsv (https://software.intel.com/en-us/mkl-developer-reference-c-mkl-sparse-trsv) functionality.