Leymosun: High-Entropy Randomness Research Toolkit

A package for randomness based research.  This is the version 0.2.38 release. 

The package provides tools and utilities for randomness based research with `High-Entropy Random Number Generation (HE-RNG)`. It means generation is performed with non-deterministic seeds every time a random
library function is called. 

High-entropy random number utilities 

The core package is providing strong randomness improving the simulation quality. We use NumPy grammar and as a backend.

• HE-RNG random states.
  •  Distributions:
    • Bionomial
    • Uniform integer on the given range
    • Uniform float on the given range
    • Normal distribution (Gaussian)
    • Random sampling from a set, choice.

Random Matrices

• Generation of Gaussian ensembles (Orthogonal).
• Generation of Mixed Gaussian ensembles (Orthogonal) via `Mixed Matrix Ensemble Sampling (MMES) algoritm`
• Extract offdiagonal elements.
• Spectra generation given ensemble.
• Robust Spectral unfolding.
• Nearest-Neigbour Spacing Densities (NNSD).
• Adjacent gap ratio.
• Analytic distributions: Wigner semi-circle law, nearest-neigbour spacing.

Statistics

• Centered PDF computation.
• Bootstrapped uncertainty quantification given observation matrix. 

Lectures

Lectures notes that introduce randomization concepts with the usage of `Leymosun`.

• Lecture on the Wigner's semicircle law
• Lecture on the Wigner-Dyson nearest-neighbour distribution 
• Lecture on the Wigner's cats
• Understanding High-Entropy RNGs with NIST  benchmark

Publications

Papers, datasets and other material that used `leymosun`. 

* Empirical deviations of semicircle law in mixed-matrix ensembles, M. Suzen, HAL-Science,
  hal-03464130 (2021).    
 2025 improvements with the `leymosun` package.

 License 

(c) 2025   
M. Süzen

All codes are released under GPLv3.  
Documentations are released under CC BY 4.0.