Metadata-Version: 1.1
Name: aaa-approx
Version: 1.0.1
Summary: A Python implementation of the AAA algorithm for rational approximation
Home-page: https://github.com/c-f-h/aaa
Author: Clemens Hofreither
Author-email: chofreither@numa.uni-linz.ac.at
License: UNKNOWN
Description-Content-Type: text/markdown
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](http://www.chebfun.org/).
        The present Python version is a more or less direct port of the MATLAB version.
        
        ## Installation
        
        The implementation is in pure Python and requires only numpy and scipy as
        dependencies. Install it using pip:
        
            pip install aaa-approx
        
        ## Usage
        
        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:
        
            r.nodes
            r.values
            r.weights
        
        
Platform: UNKNOWN
Classifier: Programming Language :: Python :: 2.7
Classifier: Programming Language :: Python :: 3
Classifier: Intended Audience :: Science/Research
Classifier: Topic :: Scientific/Engineering :: Mathematics
Classifier: License :: OSI Approved :: BSD License
