Implementation of the Bin Hierarchy Method for restoring a smooth function from a sampled histogram

TL;DR

The paper introduces BHM, a tool that reconstructs smooth functions from sampled histograms using the bin hierarchy method, producing minimal-knot polynomial splines suitable for various data qualities.

Contribution

It provides a practical implementation of the bin hierarchy method for smooth function restoration from histograms, with minimal user parameter input.

Findings

Automatically generates smooth polynomial splines

Works universally for regular distributions

Suitable for large-scale data analysis

Abstract

We present $\texttt{BHM}$, a tool for restoring a smooth function from a sampled histogram using the bin hierarchy method. The theoretical background of the method is presented in [arXiv:1707.07625]. The code automatically generates a smooth polynomial spline with the minimal acceptable number of knots from the input data. It works universally for any sufficiently regular shaped distribution and any level of data quality, requiring almost no external parameter specification. It is particularly useful for large-scale numerical data analysis. This paper explains the details of the implementation and the use of the program.