GP Algorithm Source Code for Calculating Correlation Dimension (GP-method)

In nonlinear dynamics research, the GP algorithm (Grassberger-Procaccia algorithm) serves as a classical method for computing the correlation dimension from time series data. As a type of fractal dimension, the correlation dimension effectively quantifies the complexity of chaotic systems.

This package provides a complete GP algorithm implementation workflow: initially reading standardized chaotic data generated by the Lorenz system (replaceable with user data), followed by phase space reconstruction using delay coordinates. The core computation phase employs log-linear fitting methodology to determine the scaling region slope of correlation integral curves in double logarithmic coordinates. The program specifically addresses boundary effects and noise interference to ensure accurate dimension estimation.

For practical applications, users need to focus on three critical parameter configurations: embedding dimension selection, time delay determination, and scaling region identification. The output correlation dimension values help characterize system chaotic properties, with significant applications in fault diagnosis, biological signal analysis, and related fields. This implementation overcomes efficiency issues in traditional neighborhood search methods by optimizing distance matrix calculations, significantly enhancing processing capability for large-scale datasets through vectorized operations and efficient memory management.