Towards a Lightweight Method to Predict the Performance of Sparse Triangular Solvers on Heterogeneous Hardware Platforms

The solution of sparse triangular linear systems (SpTrSV) is a fundamental building block for many numerical methods. The important presence in different fields and the considerable computational cost of this operation have motivated several efforts to accelerate it on different hardware platforms and, in particular, on those equipped with massively-parallel processors. Until recently, the dominant approach to parallelize this operation on this sort of hardware was the level-set method, which relies on a costly preprocessing phase. For this reason, much of the research on the subject is focused on the case where several triangular linear systems have to be solved for the same matrix. However, the latest efforts have proposed efficient one-phase routines that can be advantageous even when only one SpTrSV needs to be applied for each matrix. In these cases, the decision of which solver to employ strongly depends of the degree of parallelism offered by the linear system. In this work we provide an inexpensive algorithm to estimate the degree of parallelism of a triangular matrix, and explore some heuristics to select between the SpTrSV routine provided by the Intel MKL library and our one-phase GPU solver. The experimental evaluation performed shows that our proposal achieves generally accurate predictions with runtimes two orders lower than the state of the art method to compute the DAG levels.