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. Particularly, in order to approximate numerical functions with well-behaved interpolation functions.

Automatic tests on github actions:

Paper about ChebTools in JOSS:

Example:

Try it in your browser:

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:

For which the Python code would read ``` python import scipy.special import ChebTools

Only keep the roots that are in [-1,1] in scaled coordinates

onlyindomain = 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.generateChebyshevexpansion(200, J0, 0, 30)

Roots of the function

rts = f.realroots(onlyin_domain)

Extrema of the function (roots of the derivative, where dy/dx =0)

extrema = f.deriv(1).realroots(onlyin_domain) ```

Changelog

• 1.1: Added integrate function for indefinite integral
• 1.2: Added some more operators, including division and unary negation
• 1.3: Added is_monotonic function to ascertain whether the nodes are monotonically increasing or decreasing
• 1.4: Added dyadic splitting into intervals (C++ only for now)
• 1.5: Added FFT-based function for getting expansion coefficient values from nodal values
• 1.7: Added ChebyshevCollection container class for fast evaluation of collection of expansions (generated from dyadic splitting maybe?)
• 1.8: Added __version__ attribute
• 1.9: Added the ability to construct inverse functions
• 1.10: Added 2D evaluation functions in double and complex<double> options (useful for model optimization with complex step derivatives)
• 1.10.1: Repaired universal2 binary wheels on Mac
• 1.11: Exposed get_coef function for Taylor series extrapolator
• 1.12.0: Switched interface for python to nanobind. Dropped pypy wheels.

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 --shallow-submodules 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 --shallow-submodules 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 --shallow-submodules 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.