sphericart

This is sphericart, a multi-language library for the efficient calculation of real spherical harmonics and their derivatives in Cartesian coordinates.

For instructions and examples on the usage of the library, please refer to our documentation.

If you are using sphericart for your academic work, you can cite it as

@article{sphericart,
    title={Fast evaluation of spherical harmonics with sphericart},
    author={Bigi, Filippo and Fraux, Guillaume and Browning, Nicholas J. and Ceriotti, Michele},
    journal={J. Chem. Phys.},
    year={2023},
    number={159},
    pages={064802},
}

This library is dual-licensed under the Apache License 2.0 and the MIT license. You can use to use it under either of the two licenses.

Installation

Python

Pre-built (https://pypi.org/project/sphericart/).

pip install sphericart             # numpy interface, CPU only
pip install sphericart[torch]      # Torch (and TorchScript) interface, CPU and GPU
pip install sphericart[jax]        # JAX interface, CPU and GPU

Note that the pre-built packages are compiled for a generic CPU, and might be less performant than they could be on a specific processor. To generate libraries that are optimized for the target system, you can build from source:

git clone https://github.com/lab-cosmo/sphericart
pip install .

# if you also want the torch bindings (CPU and GPU)
pip install .[torch]

# torch bindings, CPU-only version
pip install --extra-index-url https://download.pytorch.org/whl/cpu .[torch]

If you want to enable the CUDA version of the code when builing from source, you'll need to set the CUDA_HOME environement variable. You can build a CUDA enabled sphericart, but the calculations though numpy will only run on CPU.

Julia

A native Julia implementation of sphericart is provided, called SpheriCart. Install the package by opening a REPL, switch to the package manager by typing ] and then add SpheriCart. See julia/README.md for usage. SpheriCart.jl is compatible with ChainRules.jl and Lux.jl and provides GPU kernels via KernelAbstractions.jl.

C and C++

From source

git clone https://github.com/lab-cosmo/sphericart
cd sphericart

mkdir build && cd build

cmake .. <cmake configuration options>
cmake --build . --target install

The following cmake configuration options are available:

• -DSPHERICART_BUILD_TORCH=ON/OFF: build the torch bindings in addition to the main library
• -DSPHERICART_BUILD_TESTS=ON/OFF: build C++ unit tests
• -DSPHERICART_BUILD_EXAMPLES=ON/OFF: build C++ examples and benchmarks
• -DSPHERICART_OPENMP=ON/OFF: enable OpenMP parallelism
• -DCMAKE_INSTALL_PREFIX=<where/you/want/to/install> set the root path for installation

GPU Support

The support for GPU offload could be controled with the following CMake variables at configuration:

• -DSPHERICART_ENABLE_CUDA=ON/OFF: build with CUDA support also set CUDA_HOME environement variable.
• -DSPHERICART_ENABLE_SYCL=ON/OFF: build with SYCL support, configure tool will search for sycl/sycl.h header.
• -DSPHERICART_SYCL_DEVICE=all/cpu/gpu: target architecute for SYCL support, check which devices are available with sycl-ls, for all (default) is possible to control at execution with export ONEAPI_DEVICE_SELECTOR=opencl:gpu or export ONEAPI_DEVICE_SELECTOR=opencl:cpu.

The following flags have been tested with Intel OneAPI 2025.3 for enabling SYCL support:

• -DCMAKE_CXX_COMPILER=icpx
• -DCMAKE_C_COMPILER=icx
• -DCMAKE_CXX_FLAGS=" -qopenmp --intel -fsycl -fsycl-targets=spir64 -Wno-deprecated-declarations -Wno-macro-redefined -Wno-unused-parameter -w"

Note: Only tested in C++, python/JAX/Torch support is in progress.

Running tests and documentation

Tests and the local build of the documentation can be run with tox. The default tests, which are also run on the CI, can be executed by simply running

tox

in the main folder of the repository.

To run tests in a CPU-only environment you can set the environment variable PIP_EXTRA_INDEX_URL before calling tox, e.g.

PIP_EXTRA_INDEX_URL=https://download.pytorch.org/whl/cpu tox -e docs

will build the documentation in a CPU-only environment.

Other flavors of spherical harmonics

Although sphericart natively calculates real solid and spherical harmonics from Cartesian positions, it is easy to manipulate its output it to calculate complex spherical harmonics and/or to accept spherical coordinates as inputs. You can see examples here.

Maintainers

This project is maintained by @frostedoyster and @Luthaf. The maintainers will reply to issues and pull requests opened on this repository as soon as possible. You can mention them directly if you have not received an answer after a couple of days.