CONCURRENCY AND COMPUTATION: PRACTICE AND EXPERIENCE Concurrency Computat.: Pract. Exper. 2004; 16:1 Prepared using cpeauth.cls [Version: 2002/09/19 v2.02] On the Conditions Necessary for Removing Abstraction Penalties in OOLALA Mikel Luj´ an 1, ∗ T. L. Freeman 1 and John R. Gurd 1 1 Centre for Novel Computing, University of Manchester Oxford Road, Manchester M13 9PL, United Kingdom. {mlujan, jgurd, lfreeman}@cs.man.ac.uk SUMMARY OoLaLa is an object oriented linear algebra library designed to reduce the effort of software development and maintenance. In contrast with traditional (Fortran-based) libraries, it provides two high abstraction levels that significantly reduce the number of implementations necessary for particular linear algebra operations. Initial performance evaluations of a Java implementation of OoLaLa show that the two high abstraction levels are not competitive with the low abstraction level of traditional libraries. These initial performance results motivate the present contribution – the characterisation of a set of storage formats (data structures) and matrix properties (special features) for which implementations at the two high abstraction levels can be transformed into implementations at the low (more efficient) abstraction level. Note: This is a preprint of an article accepted for publication in Concurrency and Computation: Practice & Experience Copyright c 2003 John Wiley & Sons, Ltd. The volume, issue and pages are not known at the moment. key words: Object Oriented Programming, Numerical Linear Algebra, Java, Abstraction Penalty 1. Introduction Object oriented software construction can be used to simplify the interface of numerical linear algebra libraries and thus make them easier to use. It can also be used to arrive at several fundamentally different implementations of linear algebra operations. The objective is to reduce the effort of developing and maintaining these libraries; thus a suitable design ∗ Correspondence to: M. Luj´ an, Centre for Novel Computing, University of Manchester, Oxford Road, Manchester M13 9PL, United Kingdom. Contract/grant sponsor: ML acknowledges the support of a Postdoctoral Fellowship from the Department of Education, Universities and Research of the Basque Government. Copyright c  2004 John Wiley & Sons, Ltd.