numericalderivative 0.1

Numerical differentiation

numericalderivative

What is it?

The goal of this project is to compute the first derivative of a function using finite difference formulas. The difficulty with these formulas is that it must use a finite difference step which must be neither too large (otherwise truncation error dominates the error) nor too small (otherwise condition error dominates). To solve this issue, the module provides algorithms to compute an approximate optimal finite difference step.

Furthermore, this package provides benchmark problems for numerical differentiation.

This module allows you to do this:

import math
import numericalderivative as nd

def scaled_exp(x):
    alpha = 1.0e6
    return math.exp(-x / alpha)


h0 = 1.0e5
x = 1.0e0
algorithm = nd.SteplemanWinarsky(scaled_exp, x)
h_optimal, iterations = algorithm.compute_step(h0)
number_of_function_evaluations = algorithm.get_number_of_function_evaluations()
f_prime_approx = algorithm.compute_first_derivative(h_optimal)

Authors

• Michaël Baudin, 2024

Installation

To install from Github:

git clone https://github.com/mbaudin47/numerical_derivative.git
cd numerical_derivative
python setup.py install

References

• Gill, P. E., Murray, W., Saunders, M. A., & Wright, M. H. (1983). Computing forward-difference intervals for numerical optimization. SIAM Journal on Scientific and Statistical Computing, 4(2), 310-321.
• Adaptive numerical differentiation R. S. Stepleman and N. D. Winarsky Journal: Math. Comp. 33 (1979), 1257-1264
• Dumontet, J., & Vignes, J. (1977). Détermination du pas optimal dans le calcul des dérivées sur ordinateur. RAIRO. Analyse numérique, 11 (1), 13-25.

Roadmap

• Use bracket_step as a list of two floats in GillMurraySaundersWright and DumontetVignes (this is done in SteplemanWinarsky)
• Create a benchmark feature to test a given method on several benchmark problems
• Use a relative precision in SteplemanWinarsky and GillMurraySaundersWright.
• Remove NumericalDerivative: move it to FiniteDifferenceFormula.