# compute_coeffs_discrete¶

gala.potential.scf.compute_coeffs_discrete(xyz, mass, nmax, lmax, r_s, skip_odd=False, skip_even=False, skip_m=False, compute_var=False)[source]

Compute the expansion coefficients for representing the density distribution of input points as a basis function expansion. The points, xyz, are assumed to be samples from the density distribution.

Computing the coefficients involves computing triple integrals which are computationally expensive. For an example of how to parallelize the computation of the coefficients, see examples/parallel_compute_Anlm.py.

Parameters
xyzarray_like

Samples from the density distribution. Should have shape (n_samples,3).

massarray_like

Mass of each sample. Should have shape (n_samples,).

nmaxint

Maximum value of n for the radial expansion.

lmaxint

Maximum value of l for the spherical harmonics.

r_snumeric

skip_oddbool (optional)

Skip the odd terms in the angular portion of the expansion. For example, only take $$l=0,2,4,...$$

skip_evenbool (optional)

Skip the even terms in the angular portion of the expansion. For example, only take $$l=1,3,5,...$$

skip_mbool (optional)

Ignore terms with $$m > 0$$.

compute_varbool (optional)

Also compute the variances of the coefficients. This does not compute the full covariance matrix of the coefficients, just the individual variances. TODO: separate function to compute full covariance matrix?

Returns
Snlmfloat

The value of the cosine expansion coefficient.

Tnlmfloat

The value of the sine expansion coefficient.