Skip to main content
Donate to the Python Software Foundation or Purchase a PyCharm License to Benefit the PSF! Donate Now

A Python implementation of the AAA algorithm for rational approximation

Project description

The AAA algorithm for rational approximation

This is a Python implementation of the AAA algorithm for rational approximation described in the paper "The AAA Algorithm for Rational Approximation" by Yuji Nakatsukasa, Olivier Sète, and Lloyd N. Trefethen, SIAM Journal on Scientific Computing 2018 40:3, A1494-A1522.

A MATLAB implementation of this algorithm is contained in Chebfun. The present Python version is a more or less direct port of the MATLAB version.


The implementation is in pure Python and requires only numpy and scipy as dependencies. Install it using pip:

pip install aaa-approx


Here's an example of how to approximate a function in the interval [0,1]:

import numpy as np
from aaa import aaa

Z = np.linspace(0.0, 1.0, 1000)
F = np.exp(Z) * np.sin(2*np.pi*Z)

r = aaa(F, Z, mmax=10)

Instead of the maximum number of terms mmax, it's also possible to specify the error tolerance tol. Both arguments work exactly as in the MATLAB version.

The returned object r is an instance of the class aaa.BarycentricRational and can be called like a function. For instance, you can compute the error on Z like this:

err = F - r(Z)
print(np.linalg.norm(err, np.inf))

If you are interested in the poles and residues of the computed rational function, you can query them like

pol,res = r.polres()

and the zeroes using

zer = r.zeros()

Finally, the nodes, values and weights used for interpolation (called zj, fj and wj in the original implementation) can be accessed as properties:


Project details

Download files

Download the file for your platform. If you're not sure which to choose, learn more about installing packages.

Filename, size & hash SHA256 hash help File type Python version Upload date
aaa_approx-1.0.1-py3-none-any.whl (4.0 kB) Copy SHA256 hash SHA256 Wheel py3
aaa-approx-1.0.1.tar.gz (3.8 kB) Copy SHA256 hash SHA256 Source None

Supported by

Elastic Elastic Search Pingdom Pingdom Monitoring Google Google BigQuery Sentry Sentry Error logging AWS AWS Cloud computing DataDog DataDog Monitoring Fastly Fastly CDN SignalFx SignalFx Supporter DigiCert DigiCert EV certificate StatusPage StatusPage Status page