Computing Renyi Entropy for One-Dimensional Vectors

This article presents a method for computing Renyi entropy for one-dimensional vectors. The implementation has been structured as a header file, allowing direct integration into computational projects. Renyi entropy serves as a crucial generalization of Shannon entropy, widely applied in mathematics, physics, statistics, and information theory. The core algorithm involves estimating probability distributions from input vectors using histogram-based methods or kernel density estimation, followed by entropy calculation through the formula H_α = (1/(1-α)) * log(∑p_i^α) where α represents the entropy order. By computing Renyi entropy for one-dimensional data vectors, researchers can extract vital information about dataset characteristics, including uncertainty measurements and complexity assessments. The implementation includes error handling for invalid inputs and normalization procedures for probability distributions. This methodology proves particularly valuable for data analysis tasks, pattern recognition systems, and information-theoretic modeling. Subsequent sections will detail the computational approach, parameter configuration options, and practical applications across scientific domains.