A Computational study of sparse or structured matrix operations

Matrix computation is an important area in high-performance scientific computing. Major computer manufacturers and vendors typically provide architecture- aware implementation libraries such as Basic Linear Algebra Subroutines (BLAS). In this thesis, we perform an experimental study of a subset of matrix operations, where the matrices are dense, sparse, or structured in Java. We implement a subset of BLAS operations in Java and compare their performance with standard data structures Compressed Row Storage (CRS) and Java Sparse Array (JSA) for dense and sparse structured matrices. The diagonal storage format is shown to be a viable alternative for dense and structured matrices

On the block wavelet transform applied to the boundary element method

This paper follows an earlier work by Bucher et al. [1] on the application of wavelet transforms to the boundary element method, which shows how to reuse models stored in compressed form to solve new models with the same geometry but arbitrary load cases - the so-called virtual assembly technique. The extension presented in this paper involves a new computational procedure created to perform the required two-dimensional wavelet transforms by blocks, theoretically allowing the compression of matrices of arbitrary size. Details of the computer implementation that allows the use of this methodology for very large models or at high compression ratios are given. A numerical application shows a standard PC being used to solve a 131,072 DOF model, previously compressed, for 100 distinct load cases in less than 1 hour – or 33 seconds for each load case

SPARSKIT: A basic tool kit for sparse matrix computations

Presented here are the main features of a tool package for manipulating and working with sparse matrices. One of the goals of the package is to provide basic tools to facilitate the exchange of software and data between researchers in sparse matrix computations. The starting point is the Harwell/Boeing collection of matrices for which the authors provide a number of tools. Among other things, the package provides programs for converting data structures, printing simple statistics on a matrix, plotting a matrix profile, and performing linear algebra operations with sparse matrices

Format Abstraction for Sparse Tensor Algebra Compilers

This paper shows how to build a sparse tensor algebra compiler that is agnostic to tensor formats (data layouts). We develop an interface that describes formats in terms of their capabilities and properties, and show how to build a modular code generator where new formats can be added as plugins. We then describe six implementations of the interface that compose to form the dense, CSR/CSF, COO, DIA, ELL, and HASH tensor formats and countless variants thereof. With these implementations at hand, our code generator can generate code to compute any tensor algebra expression on any combination of the aforementioned formats. To demonstrate our technique, we have implemented it in the taco tensor algebra compiler. Our modular code generator design makes it simple to add support for new tensor formats, and the performance of the generated code is competitive with hand-optimized implementations. Furthermore, by extending taco to support a wider range of formats specialized for different application and data characteristics, we can improve end-user application performance. For example, if input data is provided in the COO format, our technique allows computing a single matrix-vector multiplication directly with the data in COO, which is up to 3.6$\times$ faster than by first converting the data to CSR.Comment: Presented at OOPSLA 201