Improving performance of hypermatrix cholesky factorization

Abstract

This paper shows how a sparse hypermatrix Cholesky factorization can be improved. This is accomplished by means of efficient codes which operate on very small dense matrices. Different matrix sizes or target platforms may require different codes to obtain good performance. We write a set of codes for each matrix operation using different loop orders and unroll factors. Then, for each matrix size, we automatically compile each code fixing matrix leading dimensions and loop sizes, run the resulting executable and keep its Mflops. The best combination is then used to produce the object introduced in a library. Thus, a routine for each desired matrix size is available from the library. The large overhead incurred by the hypermatrix Cholesky factorization of sparse matrices can therefore be lessened by reducing the block size when those routines are used. Using the routines, e.g. matrix multiplication, in our small matrix library produced important speed-ups in our sparse Cholesky code. © Springer-Verlag 2003.