https://github.com/olivierverdier/padexp

Padé approximations of exponential (phi) functions
https://github.com/olivierverdier/padexp

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Padé approximations of exponential (phi) functions

• Host: GitHub
• URL: https://github.com/olivierverdier/padexp
• Owner: olivierverdier
• License: mit
• Created: 2015-01-20T16:49:51.000Z (almost 10 years ago)
• Default Branch: main
• Last Pushed: 2024-09-04T12:49:28.000Z (3 months ago)
• Last Synced: 2024-09-05T15:03:59.174Z (2 months ago)
• Language: Python
• Size: 33.2 KB
• Stars: 0
• Watchers: 3
• Forks: 1
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

        
# Padé approximations of exponential (phi) functions

[![Build Status](https://github.com/olivierverdier/padexp/actions/workflows/python_package.yml/badge.svg?branch=main)](https://github.com/olivierverdier/padexp/actions/workflows/python_package.yml?query=branch%3Amain)

![Python version](https://img.shields.io/badge/python-3.9,_3.10,_3.11,_3.12-blue.svg?style=flat-square)

[![codecov](https://codecov.io/github/olivierverdier/padexp/graph/badge.svg?token=Ea4XsTXw6A)](https://codecov.io/github/olivierverdier/padexp)

Exponential functions, in a general sense, are defined as

```math

E_j(x) = \sum_{k=0}^{∞} \frac{x^k}{(k+j)!}

```

So for $j=0$, this is the regular exponential.

The main application is to apply that exponential function to a *matrix*.

Here is a minimal example:

```python

from padexp import Exponential

import numpy as np

e = Exponential(4) # to compute the functions E_j for 0 ≤ j ≤ 4

M = np.array([[1.,2.],[3.,4]])

e(M) # returns a list containing [E_0(M), E_1(M),...,E_4(M)]

```

This code is useful for exponential integrators, and is a port of the [expint Matlab package](https://dl.acm.org/doi/10.1145/1206040.1206044).