Welcome to fsph’s documentation!¶
fsph is a library to compute series of complex spherical harmonics.
The Condon-Shortley phase is not included, although it is often used by many other libraries; to incorporate it, multiply the positive-m spherical harmonics by \((-1)^m\).
Install from PyPI:
pip install fsph
Or from source:
git clone https://github.com/glotzerlab/fsph.git cd fsph python setup.py install
pointwise_sph(phi, theta, lmax, negative_m=True)¶
Evaluate a series of spherical harmonics on an array of spherical coordinates.
The array objects phi and theta should have the same length and can hold single- or double-precision floating point numbers. The resulting array will be of length (N_coordinates, N_sphs) where N_coordinates is the length of the given coordinate arrays.
To map the columns of the result array to particular (l, m) values, see
- phi – Array-like object of polar angles in [-pi, pi]
- theta – Array-like object of azimuthal angles in [0, 2*pi]
- lmax – Integer maximum spherical harmonic degree to compute (inclusive)
- negative_m – Set to False to disable the negative-m spherical harmonics
Returns the (l, m) indices in the order that they are exposed by fsph.
Creates a (N_sphs, 2) array where the first column corresponds to the l values and the second column corresponds to the m values for any index in the series.