MATLAB Program for Calculating Correlation Dimension (MEX Function, High-Speed)

In research and learning processes, we often require MATLAB programs for calculating correlation dimensions. This particular program serves as a powerful tool that achieves exceptional computational speed through MEX function implementation. The program originated from the Research Learning Forum, where it was developed and refined by experienced researchers. When utilizing this program, users need to thoroughly study and master its usage methodology to fully leverage its advantages and effectiveness. The implementation typically involves: - Time series data preprocessing and phase space reconstruction - Calculation of correlation integrals using efficient distance computation algorithms - MEX functions written in C/C++ for optimized performance in distance matrix calculations - Logarithmic scaling and linear regression for dimension estimation Furthermore, through in-depth analysis and study of the program's architecture, researchers can enhance their capabilities in correlation dimension computation. Key aspects to examine include: - The embedding dimension selection algorithm - Time delay parameter optimization methods - The efficient nearest-neighbor search implementation - Error handling and convergence criteria in dimension calculation This comprehensive understanding enables users to not only apply the program effectively but also potentially contribute to its further development and optimization.