xnn.gnn.featurizers.spherical_bessel.spherical_bessel_zeros#

xnn.gnn.featurizers.spherical_bessel.spherical_bessel_zeros(l_max, n)[source]#

The first n positive zeros z_ln of j_l for every order up to l_max.

Parameters:

l_max (int) – Highest order.
n (int) – Zeros per order.

Returns:

Float64 zeros of shape (l_max + 1, n), z_l1 < z_l2 < ....

Return type:

numpy.ndarray

Notes

j_0 vanishes at n pi; the zeros of consecutive orders interlace (z_{l-1,n} < z_ln < z_{l-1,n+1}), so each z_ln is bracketed by two zeros of the previous order and found by bisection to machine precision. l_max extra zeros of j_0 seed the recursion so that every order keeps n brackets.