Exploring the Offload Execution Model in the Intel Xeon Phi via Matrix Inversion

The explicit inversion of dense matrices appears in a numerous key scientific and engineering applications such as model reduction or optimal control, asking for the exploitation of high performance computing techniques and architectures when the problem dimension is large. Gauss-Jordan elimination (GJE) is an efficient in-place method for matrix inversion that exposes large amounts of dataparallelism, making it very convenient for hardware accelerators such as graphics processors (GPUs) or the Intel Xeon Phi. In this paper, we present and evaluate several practical implementations of GJE, with partial row pivoting, that especially exploit the off-load execution model available on the Intel Xeon Phi to carry out a significant fraction of the computations on the accelerator. Numerical experiments on a system with two Intel Xeon E5-2640v3 processors and an Intel Xeon Phi 7120P compare the efficiency of these implementations, with the most efficient case delivering about 700 billions double-precision floating-point operations per second.