mittagleffler

This library implements the two-parameter Mittag-Leffler function.

Currently only the algorithm described in the paper by Roberto Garrapa (2015) <https://doi.org/10.1137/140971191>__ is implemented. This seems to be the most accurate and computationally efficient method to date for evaluating the Mittag-Leffler function.

Documentation <https://mittagleffler.readthedocs.io>__.
Code <https://github.com/alexfikl/mittagleffler>__.

Rust Crate

The library is available as a Rust crate that implements the main algorithms. Evaluating the Mittag Leffler function can be performed directly by

.. code:: rust

use mittagleffler::MittagLeffler;

let alpha = 0.75;
let beta = 1.25;
let z = Complex64::new(1.0, 2.0);
println!("E_{}_{}({}) = {}", alpha, beta, z, z.mittag_leffler(alpha, beta));

let z: f64 = 3.1415;
println!("E_{}_{}({}) = {}", alpha, beta, z, z.mittag_leffler(alpha, beta));

This method will call the best underlying algorithm and take care of any special cases that are known in the literature, e.g. for $(\alpha, \beta) = (1, 1)$ we know that the Mittag-Leffler function is equivalent to the standard exponential. To call a specific algorithm, we can do

.. code:: rust

use mittagleffler::GarrappaMittagLeffler

let eps = 1.0e-8;
let ml = GarrappaMittagLeffler::new(eps);

let z = Complex64::new(1.0, 2.0);
println!("E_{}_{}({}) = {}", alpha, beta, z, ml.evaluate(z, alpha, beta));

The algorithm from Garrappa2015 has several parameters that can be tweaked for better performance or accuracy. They can be found in the documentation of the structure, but should not be changed unless there is good reason!

Installation

The crate can be built from the root directory using

.. code:: bash

cargo build --all-features --release

To run the tests, you can do

.. code:: bash

cargo test --tests

Python Bindings

The library also has Python bindings (using pyo3 <https://github.com/PyO3/pyo3>__) that can be found in the python directory. The bindings are written to work with scalars and with numpy arrays equally. For example

.. code:: python

import numpy as np
from pymittagleffler import mittag_leffler

alpha, beta = 2.0, 2.0
z = np.linspace(0.0, 1.0, 128)
result = mittag_leffler(z, alpha, beta)

Installation

The bindings use the maturin <https://github.com/PyO3/maturin>__ build system to package the library. To create wheels for your system, directly run

.. code:: bash

python -m build --wheel .

To run the tests, you can do

.. code:: bash

python -m pytest -v -s test

mittagleffler 0.1.0

mittagleffler

Rust Crate

Installation

Python Bindings

Installation