differint 0.3

Collection of algorithms for numerically calculating fractional derivatives.

## differint
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 'improved' 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.

## Motivation
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.

## Installation
This project requires Python 3+ and NumPy to run.

Installation from the Python Packaging index (https://pypi.python.org/pypi) is simple using pip.

```python
pip install differint
```

## Example Usage
Taking a fractional derivative is easy with the *differint* package. Let'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.

```python
import numpy as np
import 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.

```python
DF = df.RL(0.5, f, 0, 1, 128)
```

## Tests
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
python setup.py tests
```

Alternatively, you can run the test script directly.

```python
cd <file_path>/differint/tests/
python test.py
```

## API Reference
In this section we cover the usage of the various functions within the *differint* package.

Main Function | Usage
------------- | -----
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

Auxiliary Function | Usage
------------------ | -----
isInteger | Determine if a number is an integer
checkValues | Used to check for valid algorithm input types
GLIinterpolat | Define interpolating 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

## How to use?


## Contribute

To contribute to this project, see the [contributing guidelines](https://github.com/snimpids/differint/blob/master/CONTRIBUTING.md).

## Credits
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.

## License

MIT © [Matthew Adams](2018)