A FAST GENERAL-PURPOSE ALGORITHM FOR THE COMPUTATION OF AUTO-CORRELATION AND CROSS-CORRELATION INTEGRALS FROM SINGLE-CHANNEL DATA

We developed an optimized algorithm that allows computation of auto- a nd cross-correlation integrals from single channel time series without restricting the range of hypersphere radii and embedding dimensions. Optimization was achieved by eliminating any multiple computation of s ubsets entering the distance function in the time-delay reconstruction of the phase space repeatedly for increasing embedding dimensions; th is is most effective when using the maximum norm. Compared to more nai ve implementations an improvement of 2-3 was achieved, depending on th e type of workstation, the operating system, and the compiler. An addi tional optimization for 80 x 86 assembly language allows to run the al gorithm on a standard personal computer as fast as on a workstation. I n contrast to other implementations, the execution speed of this algor ithm is nearly unaffected by the type of underlying data. Thus, it is optimal for real-time analyses. (C) 1998 Elsevier Science B.V.