G-P Algorithm for Correlation Dimension Calculation

In this enhanced MATLAB implementation of the G-P algorithm, we introduce a novel temporary separation threshold parameter. This parameter effectively removes correlations between consecutive points on the same trajectory when its value exceeds the sequence's average period. The implementation uses advanced mex functions for optimized performance, significantly accelerating the correlation dimension calculation process. The key algorithmic improvement ensures that at small r values, the ln r versus ln C(r) curve maintains better linearity, thereby enhancing computational accuracy. The mex function implementation leverages compiled C code for core computational routines, providing substantial speed advantages over standard MATLAB scripts while maintaining full compatibility with the MATLAB environment. This enhanced version offers researchers and engineers a robust tool for accurate and efficient correlation dimension analysis, particularly beneficial for studying chaotic systems and fractal dimensions in time series data. The code structure follows modular design principles, allowing easy integration with existing MATLAB workflows and custom modifications for specific research requirements.