C++ tools for working with Chebyshev expansion interpolants
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Ian Bell
Latest commit 67e5a46 Jul 12, 2018

README.md

ChebTools

Chebyshev-basis expansions, and more broadly, orthogonal polynomial expansions, are commonly used as numerical approximations of continuous functions on closed domains. One of the most successful projects that makes use of the Chebyshev expansions is the chebfun library for MATLAB. Other similar libraries are pychebfun, chebpy, and Approxfun. Our library ChebTools fills a similar niche as that of chebfun -- working with Chebyshev expansions.

The primary motivation for the development of ChebTools is the need for a highly optimized and fast C++11 library for working with Chebyshev expansions.

Automatic tests status on TravisCI: Build Status

Paper about ChebTools in JOSS: DOI

Example:

Try it in your browser: Binder

Suppose we wanted to calculate the roots and extrema of the 0-th Bessel function in [0, 30]. That results in a picture like this:

Roots and extrema of the 0-th Bessel function

For which the Python code would read

import scipy.special
import ChebTools
# Only keep the roots that are in [-1,1] in scaled coordinates
only_in_domain = True
# The 0-th Bessel function (for code concision)
def J0(x): return scipy.special.jn(0,x)
# Make a 200-th order expansion of the 0-th Bessel function in [0,30]
f = ChebTools.generate_Chebyshev_expansion(200, J0, 0, 30)
# Roots of the function
rts = f.real_roots(only_in_domain)
# Extrema of the function (roots of the derivative, where dy/dx =0)
extrema = f.deriv(1).real_roots(only_in_domain)

License

*MIT licensed (see LICENSE for specifics), not subject to copyright in the USA.

Uses unmodified Eigen for matrix operations

Contributing/Getting Help

If you would like to contribute to ChebTools or report a problem, please open a pull request or submit an issue. Especially welcome would be additional tests.

Installation

Prerequisites

You will need:

  • cmake (on windows, install from cmake, on linux sudo apt install cmake should do it, on OSX, brew install cmake)
  • Python (the anaconda distribution is used by the authors)
  • a compiler (on windows, Visual Studio 2015+ (express version is fine), g++ on linux/OSX)

If on linux you use Anaconda and end up with an error like

ImportError: /home/theuser/anaconda3/bin/../lib/libstdc++.so.6: version `GLIBCXX_3.4.20' not found (required by /home/theuser/anaconda3/lib/python3.5/site-packages/ChebTools.cpython-35m-x86_64-linux-gnu.so)

it can be sometimes fixed by installing libgcc with conda: conda install libgcc. This is due to an issue in Anaconda

To install in one line from github (easiest)

This will download the sources into a temporary directory and build and install the python extension so long as you have the necessary prerequisites:

pip install git+git://github.com/usnistgov/ChebTools.git

From a cloned repository

Alternatively, you can clone (recursively!) and run the setup.py script

git clone --recursive https://github.com/usnistgov/ChebTools
cd ChebTools
python setup.py install

to install, or

python setup.py develop

to use a locally-compiled version for testing. If you want to build a debug version, you can do so with

python setup.py build -g develop

With a debug build, you can step into the debugger to debug the C++ code, for instance.

Cmake build

Starting in the root of the repo (a debug build with the default compiler, here on linux):

git clone --recursive https://github.com/usnistgov/ChebTools
cd ChebTools
mkdir build
cd build
cmake ..
cmake --build .

For those using Anaconda on Linux, please use the following for cmake:

mkdir build
cd build
cmake .. -DPYTHON_EXECUTABLE=`which python`
cmake --build .

For Visual Studio 2015 (64-bit) in release mode, you would do:

git clone --recursive https://github.com/usnistgov/ChebTools
cd ChebTools
mkdir build
cd build
cmake .. -G "Visual Studio 14 2015 Win64"
cmake --build . --config Release

If you need to update your submodules (pybind11 and friends)

git submodule update --init

For other options, see the cmake docs