Collection of algorithms for numerically calculating fractional derivatives.
This package is used for numerically calculating fractional derivatives and integrals (differintegrals). Options for varying definitions of the differintegral are available, including the Grunwald-Letnikov (GL), the â€˜improvedâ€™ Grunwald-Letnikov (GLI), the Riemann-Liouville (RL), and the Caputo (coming soon!). Through the API, you can compute differintegrals at a point or over an array of function values.
There is little in the way of readily available, easy-to-use code for numerical fractional calculus. What is currently available are functions that are generally either smart parts of a much larger package, or only offer one numerical algorithm. The differint package offers a variety of algorithms for computing differintegrals and several auxiliary functions relating to generalized binomial coefficients.
This project requires Python 3+ and NumPy to run.
Installation from the Python Packaging index (https://pypi.python.org/pypi) is simple using pip.
pip install differint
Taking a fractional derivative is easy with the differint package. Letâ€™s take the 1/2 derivative of the square root function on the interval [0,1], using the Riemann-Liouville definition of the fractional derivative.
import numpy as np import differint.differint as df def f(x): return x**0.5 DF = df.RL(0.5, f) print(DF)
You can also specify the endpoints of the domain and the number of points used as follows.
DF = df.RL(0.5, f, 0, 1, 128)
All tests can be run with nose from the command line. Setup will automatically install nose if it is not present on your machine.
python setup.py tests
Alternatively, you can run the test script directly.
cd <file_path>/differint/tests/ python test.py
In this section we cover the usage of the various functions within the differint package.
|GLpoint||Computes the GL differintegral at a point|
|GL||Computes the GL differintegral over an entire array of function values using the Fast Fourier Transform|
|GLI||Computes the improved GL differintegral over an entire array of function values|
|RLpoint||Computes the RL differintegral at a point|
|RL||Computes the RL differintegral over an entire array of function values using matrix methods|
|isInteger||Determine if a number is an integer|
|checkValues||Used to check for valid algorithm input types|
|GLIinterpolat||Define interpolatin g coefficients for the improved GL algorithm|
|functionCheck||Determines if algorithm function input is callable or an array of numbers|
|test_func||Testing function for docstring examples|
|poch||Computes the Pochhammer symbol|
|GLcoeffs||Determines the convolution filter composed of generalized binomial coefficients used in the GL algorithm|
|RLcoeffs||Calculates the coefficients used in the RLpoint and RL algorithms|
|RLmatrix||Determines the matrix used in the RL algorithm|
To contribute to this project, see the contributing guidelines.
Baleanu, D., Diethelm, K., Scalas, E., & Trujillo, J.J. (2012). Fractional Calculus: Models and Numerical Methods. World Scientific.
Oldham, K.B. & Spanier, J. (1974). The Fractional Calculus: Theory and Applications of Differentiation and Integration to Arbitrary Order. Academic Press Inc.
MIT Â© Matthew Adams
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