cheby 0.3.1

Functions represented as Chebyshev series

# cheby

This package provides: * Basis of Chebyshev polynomials of the first kind * Functions represented as Chebyshev series

It is intended to be used for the resolution of differential equations using spectral methods. It is primarily a C++ library with a Python wrapper using [pybind11](https://pybind11.readthedocs.io/en/stable/). It also relies on [Eigen](http://eigen.tuxfamily.org/index.php?title=Main_Page) for linear algebra.

## Installation

The simplest way is to use pip:

`bash pip install cheby `

The package can be installed directly from source:

`bash git clone https://github.com/GwenaelGabard/cheby cd cheby git submodule update --init --recursive pip install . ` This will require a C++ compiler and cmake.

## Usage

The Python class Basis1D provides the following features: * Evaluation of Chebyshev polynomials of the first kind and their derivatives * Chebyshev points of the first and second kinds * Differentiation matrix * Matrix for Dirichlet recombination

The Python classes RealFunction and ComplexFunction provide representations of univariate functions as Chebyshev series. THey provide the following features: * Construction of the Chebyshev representation based on a Python function * Evaluation of the function and its derivatives * Addition, subtraction and multiplication * Primitive and integrals (over the whole domain or over a subsegment) * Roots and extrema * Integer powers

See the Jupyter notebooks in the examples folder for examples of usage.

## Unit tests

Unit tests are written using [pytest](https://docs.pytest.org/en/latest/). They can be run using

`bash pytest tests `

## License

This project is licensed under the MIT License - see the [LICENSE](LICENSE) file for details