A Native Tensor–Vector Multiplication Algorithm for High Performance Computing

Tensor computations are important mathematical operations for applications that rely on multidimensional data. The tensor–vector multiplication (TVM) is the most memory-bound tensor contraction in this class of operations. This article proposes an open-source TVM algorithm which much simpler and efficient than previous approaches, making it suitable integration popular BLAS libraries available today. Our has been written from scratch features unit-stride memory accesses, cache awareness, mode obliviousness, full vectorization multi-threading as well NUMA awareness non-hierarchically stored dense tensors. Numerical experiments carried out tensors up to order 10 various compilers hardware architectures equipped with traditional DDR high bandwidth (HBM). For large average performance ranges between 62% 76% theoretical systems remains independent mode. On HBM exhibits some dependency but manages reach figures close peak values. Finally, higher-order power method benchmarked proposed kernel delivers 58% 69%