Routines for Legendre to Chebyshev (and inverse) transforms.
This is first and foremost the implementation of a Fast Multipole Method similar to (but not exactly like) the one described in
- B. K. Alpert and V. Rokhlin, A fast algorithm for the evaluation of legendre expansions, 389 SIAM Journal on Scientific and Statistical Computing, 12 (1991), pp. 158–179, https://doi.390org/10.1137/0912009.391
The implemented method is described in the preprint A faster Legendre-to-Chebyshev transform.
There are several implementations in the src directory:
- python - A short, vectorized Python implementation
- C - An efficient C implementation
- cython - Wrapping of the fast C code using cython
- ctypes - Wrapping of the fast C code using ctypes
- Multiprec - Multiprecision implementations of a direct method using both Python and C++. The multiprecision methods are only used for verification.
In addition there is
- bin - An executable l2c that can run various tests
The code is set up to be compiled with the meson build system. It should work by cloning this repository and then
cd src
meson setup build
meson install -C build
If you want to install just locally, then use, e.g.,
meson setup build --prefix=$PWD/build-install
The installation can be tested with
meson test -C build
Another simple way to test this code is to create a codespace. The environment.yml file in the root folder will then make sure that the codespace creates a conda environment with all necessary dependencies already built. Just press the codespace button and wait awhile for the environment to build. Then enable the environment and run some tests or test the executable l2c
source activate ./venv
cd src
meson setup build --prefix=$PWD/build-install --includedir=$CONDA_PREFIX/include --libdir=$CONDA_PREFIX/lib
meson install -C build
export PATH=$PWD/build-install/bin:$PATH
l2c -N1000 -d2 # runs a forward and backward transform and computes the error for an array of length 1000
meson test -C build # runs all the tests