A fast general purpose algorithm for the computation of auto- and cross-correlation integrals from single channel data

We developed an optimized algorithm that allows computation of auto- and 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 subsets entering the distance function in the time-delay reconstruction of the phase space repeatedly for increasing embedding dimensions; this is most effective when using the maximum norm. Compared to more naive implementations an improvement of 2-3 was achieved, depending on the type of workstation, the operating system, and the compiler. An additional optimization for 80×86 assembly language allows torun the algorithm on a standard personal computer as fast as on a workstation. In contrast to other implementations, the execution speed of this algorithm is nearly unaffected by the type of underlying data. Thus, it is optimal for real-time analyses.