Data structures in Java for matrix computations

Abstract

SUMMARYIn this paper we show how to utilize Java's native arrays for matrix computations. The disadvantages of Java arrays used as a 2D array for dense matrix computation are discussed and ways to improve the performance are examined. We show how to create efficient dynamic data structures for sparse matrix computations using Java's native arrays. This data structure is unique for Java and shown to be more dynamic and efficient than the traditional storage schemes for large sparse matrices. Numerical testing indicates that this new data structure, called Java Sparse Array, is competitive with the traditional Compressed Row Storage scheme on matrix computation routines. Java gives increased flexibility without losing efficiency. Compared with other object-oriented data structures Java Sparse Array is shown to have the same flexibility.

Review of Storage Techniques for Sparse Matrices

“…The advantages that the format offers are low storage requirements, a flexible structure for element manipulations and allowing for efficient operations [7]. The Java Sparse Array (JSA) format is a new concept for storing sparse matrices that is unique for Java [10]. JSA has been created to exploit Java's flexible definition of multi-dimensional arrays.…”

“…Specific formats: Some formats are optimized for specific types of matrices that mostly arise from a particular field. An example is Block Compressed Row Storage (BCRS), which is efficient for block matrices [9,10]. The sparse storage formats can mainly be divided into following categories [11].…”

“…General formats: Some storage formats are for general types of matrices, like the Compressed Row Storage (CRS) format, which make no assumption of the structure of distribution of non-zeros [9,10]. Specific formats: Some formats are optimized for specific types of matrices that mostly arise from a particular field.…”

Storage Formats for Sparse Matrices in Java

“…The JSA-GS implementation is the code made available by Gundersen and Steihaug [6]. This code does not include a specialised case for symmetric matrices 1 .…”

“…Section 2 introduces the most commonly used storage formats for sparse matrices. The Java Sparse Array (JSA) storage format was recently proposed by Gundersen and Steihaug [6] to take advantage of Java arrays; Section 3 briefly describes JSA. The performance evaluation (see Section 5) consider a specific kernel from iterative methods, namely matrix-vector multiplication, and compares this operation on two different computational platforms with nine different storage formats.…”