aspcol.sphericalharmonics.basis_translation_3_92

aspcol.sphericalharmonics.basis_translation_3_92(pos, wave_num, max_order_input, max_order_output)

Translation operator for harmonic basis functions, such that shd_basis(pos_orig + pos) = T(pos) @ shd_basis(pos_orig)

Taken directly from 3.92 in P. Martin, Multiple scattering: Interaction of time-harmonic waves with N obstacles

Parameters:

  • pos (ndarray of shape (num_pos, 3)) – position argument to the translation operator

  • wave_num (ndarray of shape (num_freq,)) – wavenumber, defined as w / c where w is the angular frequency and c is the speed of sound.

  • max_order_input (int) – maximum order of the coefficients that should be translated

  • max_order_output (int) – maximum order of the translated coefficients

Returns:

T – translation operator, such that shd_coeffs(pos_orig + pos) = T(pos) @ shd_coeffs(pos_orig)

Return type:

ndarray of shape (num_freqs, num_pos, num_coeffs_output, num_coeffs_input)