Code – A new computational approach to Henderson’s method for computing the inverse of a numerator relationship matrix

A new algorithm for computing the inverse of the numerator relationship matrix (A^-1) is presented in several (R, Julia, Python, and Awk) programming languages, and the code is shared.
The algorithm is based on the method of Henderson (1976) (doi: 10.2307/2529339) on each animal's contribution to the A^-1 matrix.

In the Jupyter notebook Example.ipynb (also Example.html), the procedure is presented using example data (example_ped.txt and example_inb.txt) and the 4 programming languages.

The algorithm was benchmarked on a pedigree of 20000 animals (PED2) and a pedigree of 180000 animals (PED4) with the corresponding files (ped.csv and PED4.csv) retrieved from doi:10.6084/m9.figshare.13497939.v1.
In BENCHMARKING.md (also BENCHMARKING.html), the benchmarking procedure for different programming languages, and the description of the files in this repository are given.