Custom Data Analysis Algorithm Coding

I have designed an algorithm that tackles a very specific data-analysis challenge and now need it translated into clean, efficient code. The underlying logic is settled; what I need from you is a production-ready implementation, thorough inline documentation, and a compact demo script that proves it works on a small sample dataset.

Language is flexible—Python, R, or MATLAB all fit the brief—so pick the one you are most comfortable using while ensuring the final deliverable is easy for me to maintain and extend. I will share the mathematical formulation and sample data once we start; you will convert that into well-structured functions or classes, add comments that make each step clear, and provide a short README explaining inputs, outputs, dependencies, and how to run the demo.

Accuracy and runtime efficiency matter more than fancy packaging. If external libraries give a genuine performance or clarity boost, feel free to use them so long as you note every dependency. Upon delivery I should be able to drop your code into my environment, call a single entry point, and reproduce the expected results without tweaks.