FIST-HOSVD: fused in-place sequentially truncated higher order singular value decomposition.

In this paper, several novel methods of improving the memory locality of the Sequentially Truncated Higher Order Singular Value Decomposition (ST-HOSVD) algorithm for computing the Tucker decomposition are presented. We show how the two primary computational kernels of the ST-HOSVD can be fused together into a single kernel to significantly improve memory locality. We then extend matrix tiling techniques to tensors to further improve cache utilization. This block-based approach is then coupled with a novel in-place transpose algorithm to drastically reduce the memory requirements of the algorithm by overwriting the original tensor with the result. Our approach's effectiveness is demonstrated by comparing the multi-threaded performance of our optimized ST-HOSVD algorithm to TuckerMPI, a state-of-the-art ST-HOSVD implementation, in compressing two combustion simulation datasets. We demonstrate up to ~ 135x reduction in auxiliary memory consumption thereby increasing the problem size that can be computed for a given memory allocation by up to ~ 3x, whilst maintaining comparable runtime performance.