Gray System GM(1, n) Model Source Code

This article presents the source code implementation of the Gray System GM(1, n) model. The model is designed for predicting complex systems under the influence of multiple factors, applicable to various domains including economics, environmental studies, population analysis, sales forecasting, and more. The core algorithm implementation features a differential equation-based approach that handles limited data scenarios effectively. The code typically includes key functions for data preprocessing (accumulated generating operation), parameter estimation using least squares method, and prediction computation through inverse accumulated generating operation. A significant advantage of this model lies in its ability to perform accurate predictions with minimal data requirements, substantially reducing forecasting errors caused by data scarcity. The implementation also incorporates sensitivity analysis modules that quantify the influence degree of different factors on system predictions, enabling more precise forecasting and decision-making. The source code structure generally comprises: - Data input and validation functions - Gray accumulation and inverse accumulation operations - Model parameter estimation algorithms - Prediction calculation and error analysis modules - Factor influence evaluation components This model serves as a valuable tool for better understanding and managing complex systems through its robust mathematical foundation and practical implementation approach.