I have a series of research-grade numerical routines that need to be implemented, tested, and benchmarked in both Python and MATLAB. The core work involves translating existing mathematical formulations into efficient, well-documented code, validating the results against reference datasets, and profiling performance so the same algorithm behaves consistently across the two languages. Much of the heavy lifting will rely on standard scientific stacks—NumPy, SciPy, pandas, and matplotlib on the Python side, with equivalent functions and toolboxes in MATLAB—so fluency with these libraries is essential. I will provide the underlying equations, sample input files, and baseline outputs; the task is to turn those pieces into clean, reusable functions or class modules, then verify accuracy to at least six significant figures and demonstrate runtime improvements where possible. Deliverables • Fully commented Python scripts (.py) and MATLAB files (.m) implementing each algorithm • A concise validation report comparing outputs between languages and against supplied reference data • A short performance summary highlighting any optimizations applied, plus recommendations for further speed-ups Please keep the code modular and include unit tests so I can drop your work straight into an existing pipeline.