Deriving Efficient Parallel Implementations of Algorithms Operating on General Sparse Matrices using Automatic Program Transformation

. We show how efficient implementations can be derived from highlevel functional specifications of numerical algorithms using automatic program transformation. We emphasize the automatic tailoring of implementations for manipulation of sparse data sets. Execution times are reported for a conjugate gradient algorithm. Keywords: Program Transformation and Program Derivation, Automatic Parallelization and Mapping, Sparse Matrices, Functional Programming. 1 Introduction Developing an implementation of a numerical mathematical algorithm is a difficult task---from a simple textbook specification of an algorithm a programmer must create an implementation efficient in execution. The textbook specifier emphasizes clarity and ignores the detail of how an algorithm may be executed efficiently; the implementer will often sacrifice clarity in order to achieve efficient execution. For many numerical mathematical algorithms an efficient implementation is essential because of their computational requ..