{ "info": { "author": "Matthew Adams", "author_email": "Matthew.Adams@ucalgary.ca", "bugtrack_url": null, "classifiers": [ "Development Status :: 4 - Beta", "Intended Audience :: Science/Research", "License :: OSI Approved :: MIT License", "Programming Language :: Python :: 3.3", "Programming Language :: Python :: 3.4", "Programming Language :: Python :: 3.5", "Topic :: Scientific/Engineering :: Mathematics" ], "description": "differint\n---------\n\nThis package is used for numerically calculating fractional derivatives\nand integrals (differintegrals). Options for varying definitions of the\ndifferintegral are available, including the Grunwald-Letnikov (GL), the\n\u00e2\u20ac\u02dcimproved\u00e2\u20ac\u2122 Grunwald-Letnikov (GLI), the Riemann-Liouville (RL), and the\nCaputo (coming soon!). Through the API, you can compute differintegrals\nat a point or over an array of function values.\n\nMotivation\n----------\n\nThere is little in the way of readily available, easy-to-use code for\nnumerical fractional calculus. What is currently available are functions\nthat are generally either smart parts of a much larger package, or only\noffer one numerical algorithm. The *differint* package offers a variety\nof algorithms for computing differintegrals and several auxiliary\nfunctions relating to generalized binomial coefficients.\n\nInstallation\n------------\n\nThis project requires Python 3+ and NumPy to run.\n\nInstallation from the Python Packaging index\n(https://pypi.python.org/pypi) is simple using pip.\n\n.. code:: python\n\n pip install differint\n\nExample Usage\n-------------\n\nTaking a fractional derivative is easy with the *differint* package.\nLet\u00e2\u20ac\u2122s take the 1/2 derivative of the square root function on the\ninterval [0,1], using the Riemann-Liouville definition of the fractional\nderivative.\n\n.. code:: python\n\n import numpy as np\n import differint.differint as df\n\n def f(x):\n return x**0.5\n\n DF = df.RL(0.5, f)\n print(DF)\n\nYou can also specify the endpoints of the domain and the number of\npoints used as follows.\n\n.. code:: python\n\n DF = df.RL(0.5, f, 0, 1, 128)\n\nTests\n-----\n\nAll tests can be run with nose from the command line. Setup will\nautomatically install nose if it is not present on your machine.\n\n.. code:: python\n\n python setup.py tests\n\nAlternatively, you can run the test script directly.\n\n.. code:: python\n\n cd /differint/tests/\n python test.py\n\nAPI Reference\n-------------\n\nIn this section we cover the usage of the various functions within the\n*differint* package.\n\n+---------------------------------------------------+-------------------+\n| Main Function | Usage |\n+===================================================+===================+\n| GLpoint | Computes the GL |\n| | differintegral at |\n| | a point |\n+---------------------------------------------------+-------------------+\n| GL | Computes the GL |\n| | differintegral |\n| | over an entire |\n| | array of function |\n| | values using the |\n| | Fast Fourier |\n| | Transform |\n+---------------------------------------------------+-------------------+\n| GLI | Computes the |\n| | improved GL |\n| | differintegral |\n| | over an entire |\n| | array of function |\n| | values |\n+---------------------------------------------------+-------------------+\n| RLpoint | Computes the RL |\n| | differintegral at |\n| | a point |\n+---------------------------------------------------+-------------------+\n| RL | Computes the RL |\n| | differintegral |\n| | over an entire |\n| | array of function |\n| | values using |\n| | matrix methods |\n+---------------------------------------------------+-------------------+\n\n+-------------------------------------------------------+--------------+\n| Auxiliary Function | Usage |\n+=======================================================+==============+\n| isInteger | Determine if |\n| | a number is |\n| | an integer |\n+-------------------------------------------------------+--------------+\n| checkValues | Used to |\n| | check for |\n| | valid |\n| | algorithm |\n| | input types |\n+-------------------------------------------------------+--------------+\n| GLIinterpolat | Define |\n| | interpolatin |\n| | g |\n| | coefficients |\n| | for the |\n| | improved GL |\n| | algorithm |\n+-------------------------------------------------------+--------------+\n| functionCheck | Determines |\n| | if algorithm |\n| | function |\n| | input is |\n| | callable or |\n| | an array of |\n| | numbers |\n+-------------------------------------------------------+--------------+\n| test_func | Testing |\n| | function for |\n| | docstring |\n| | examples |\n+-------------------------------------------------------+--------------+\n| poch | Computes the |\n| | Pochhammer |\n| | symbol |\n+-------------------------------------------------------+--------------+\n| GLcoeffs | Determines |\n| | the |\n| | convolution |\n| | filter |\n| | composed of |\n| | generalized |\n| | binomial |\n| | coefficients |\n| | used in the |\n| | GL algorithm |\n+-------------------------------------------------------+--------------+\n| RLcoeffs | Calculates |\n| | the |\n| | coefficients |\n| | used in the |\n| | RLpoint and |\n| | RL |\n| | algorithms |\n+-------------------------------------------------------+--------------+\n| RLmatrix | Determines |\n| | the matrix |\n| | used in the |\n| | RL algorithm |\n+-------------------------------------------------------+--------------+\n\nContribute\n----------\n\nTo contribute to this project, see the `contributing guidelines`_.\n\nCredits\n-------\n\nBaleanu, D., Diethelm, K., Scalas, E., & Trujillo, J.J. (2012).\nFractional Calculus: Models and Numerical Methods. World Scientific.\n\nOldham, K.B. & Spanier, J. (1974). The Fractional Calculus: Theory and\nApplications of Differentiation and Integration to Arbitrary Order.\nAcademic Press Inc.\n\nLicense\n-------\n\nMIT \u00c2\u00a9 `Matthew Adams`_\n\n.. _contributing guidelines: https://github.com/snimpids/differint/blob/master/CONTRIBUTING.md\n.. _Matthew Adams: 2018\n\n\n", "description_content_type": null, "docs_url": null, "download_url": "", "downloads": { "last_day": -1, "last_month": -1, "last_week": -1 }, "home_page": "http://github.com/differint/differint", "keywords": "", "license": "MIT", "maintainer": "", "maintainer_email": "", "name": "differint", "package_url": "https://pypi.org/project/differint/", "platform": "", "project_url": "https://pypi.org/project/differint/", "project_urls": { "Homepage": "http://github.com/differint/differint" }, "release_url": "https://pypi.org/project/differint/0.3.2/", "requires_dist": [ "numpy" ], "requires_python": "", "summary": "Collection of algorithms for numerically calculating fractional 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