Computational Experience with Diagonally Structured Linear Algebra in Java

It is a commonly held view that Java's lack of support for true rectangular arrays is one of the main impediments to its widespread applicability in numerical computing. In a recent work, we have proposed efficient implementation of linear algebra kernels such as matrix-vector and matrix-matrix multiplications by formulating arithmetic calculations in terms of diagonals, and thereby giving an orientation-neutral (column-/row-major layout) computational scheme. Diagonally-structured computation is especially suitable for banded matrices. In this paper we show that, using our diagonal framework, Java native arrays can yield superior computational performance. We present two alternative implementations for matrix-matrix multiplication operation in Java. The results from numerical testing demonstrate the advantage of our proposed methods.