aspcol.sphericalharmonics.translated_inner_product

aspcol.sphericalharmonics.translated_inner_product(pos1, pos2, dir_coeffs1, dir_coeffs2, wave_num)

Computes the inner product of translated sequences of coefficients

$langle T(r_1 - r_2, omega_m) gamma_2(omega_m), gamma_1(omega_m) rangle$

Parameters:

• pos1 (ndarray of shape (num_pos1, 3)) – positions of the first set of measurement points

• pos2 (ndarray of shape (num_pos2, 3)) – positions of the second set of measurement points

• dir_coeffs1 (ndarray of shape (num_freqs, num_coeffs1) or (num_freqs, num_pos1, num_coeffs1)) – coefficients of the directivity function for the first set of measurement points

• dir_coeffs2 (ndarray of shape (num_freqs, num_coeffs2) or (num_freqs, num_pos1, num_coeffs1)) – coefficients of the directivity function for the second set of mea surement points

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

Returns:

psi – inner product of the translated directivity functions

Return type:

ndarray of shape (num_freqs, num_pos1, num_pos2)