README.md

• finite_difference contains basic first and second order finite differencing methods. The first order method supports iterative application.
• kalman_smooth contains Kalman filtering and smoothing methods, currently constant-derivative methods up to 3rd order (jerk) and a classic linear Kalman Filter based on known dynamics.
• linear_model is a bit of a miscellaneous module, containing methods which work linearly: lineardiff, polydiff, savgoldiff, and spectraldiff.
• optimize contains code to find best parameter settings for methods, tuned using Nelder-Mead according to the paper "Numerical differentiation of noisy data: A unifying multi-objective optimization framework"
• smooth_finite_difference contains methods which do a smoothing step followed by simple finite difference.
• tests contains pytest unit tests of
  1. all the differentiation methods, checking their results against a suite of known analytic functions (including an ability to plot if the --plot command is passed to pytest, see conftest.py)
  2. the optimizer
  3. utilities, auxiliary functions used throughout the code
• total_variation_regularization contains code to take the derivative based on a finite differencing scheme which is regularized by shrinking changes of value in some derivative (1st, 2nd, or 3rd order)
• utils contains utility functions used throughout differentation methods, evaluate functions used by the parameter optimizer, and simulate examples for demonstrating and testing the methods.