SHF: Small: From Matrix Computations to Tensor Computations

矩阵计算库对计算科学产生了巨大的影响，因为许多计算都可以用线性代数来表示。因此，广泛使用的库已经存在并被广泛使用了几十年。最近，多线性计算，也称为张量计算，已经变得重要起来。应用领域包括计算化学、物理和大数据分析。到目前为止，很少有研究致力于为这种计算开发高质量、高性能的库。这个项目将朝着补救这个方向迈进一大步。这个项目将十多年来作为NSF赞助的FLAMP项目的一部分的密集线性代数库的研究和开发的见解转移到张量计算领域。其目标是为表示算法及其实现创建新的抽象，导出能够利用张量的对称性的新算法，并发现如何利用现代处理器的存储器层次结构。将建立一个原型库，并向科学计算界提供。总而言之，这将推动这一领域的最先进水平。

Libraries for matrix computations have had a huge impact on computational science since many computations can be cast in terms of linear algebra. As a result, widely used libraries have been available and in broad use for decades. More recently, multi-linear computations, also known as tensor computations, have become important. Application areas include computational chemistry, physics, and large data analysis. Until now, little research has been dedicated towards the development of high quality, high performing libraries for such computations. This project will make strides towards remedying this.This project transfers insights from more than a decade of research and development of dense linear algebra libraries as part of the NSF-sponsored FLAME project to the field of tensor computations. The goal is to create new abstractions for expressing algorithms and their implementations, to derive new algorithms that can take advantage of symmetry in tensors, and discover how to take advantage of the memory hierarchies of modern processors. A prototype library will be implemented and made available to the scientific computing community. Together, this will advance the state-of-the-art in this domain.