张量和n-d数组：数组数学（MoA），psi演算和张量和数组运算的合成
Tensors and n-d Arrays:A Mathematics of Arrays (MoA), psi-Calculus and the Composition of Tensor and Array Operations
摘要：
克罗内克积是一种关键算法，在物理学、生物学和计算社会科学中无处不在。因此，考虑最佳实施是重要的。对高性能和计算再现性的需求是至关重要的。此外，由于需要组合多个Kronecker产品，与数据结构、布局和索引代数相关的问题需要重新审视旧问题。本文讨论了外积/张量积和张量积的一种特殊情况：克罗内克积，以及组合时的最佳实现，并映射到复杂的处理器/存储层次结构。我们讨论如何使用“数组数学”（MoA）和PSI演算（一种形状索引演算），提供硬件和软件的最佳，可验证，可重复，可扩展和便携式实现。
英文摘要：
The Kronecker product is a key algorithm and is ubiquitous across the physical, biological, and computation social sciences. Thus considerations of optimal implementation are important. The need to have high performance and computational reproducibility is paramount. Moreover, due to the need to compose multiple Kronecker products, issues related to data structures, layout and indexing algebra require a new look at an old problem. This paper discusses the outer product/tensor product and a special case of the tensor product: the Kronecker product, along with optimal implementation when composed, and mapped to complex processor/memory hierarchies. We discuss how the use of ``A Mathematics of Arrays" (MoA), and the psi-Calculus, (a calculus of indexing with shapes), provides optimal, verifiable, reproducible, scalable, and portable implementations of both hardware and software.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
