charged-shells/interactions.py

import expansion
import parameters
import functions as fn
from py3nj import wigner3j
import numpy as np
import time
from typing import Literal
import units_and_constants as uc


Array = np.ndarray
Expansion = expansion.Expansion
ModelParams = parameters.ModelParams
EnergyUnit = Literal['kT', 'eV', 'J']


def energy_units(units: EnergyUnit, params: ModelParams) -> float:
    match units:
        case 'eV':
            return 1 / (uc.CONSTANTS.e0 * uc.UNITS.voltage)
        case 'kT':
            return 1 / (params.temperature * uc.CONSTANTS.Boltzmann)
        case 'J':
            return uc.UNITS.energy


def charged_shell_energy(ex1: Expansion, ex2: Expansion, dist: float, params: ModelParams, units: EnergyUnit = 'kT'):

    ex1, ex2 = expansion.expansions_to_common_l(ex1, ex2)
    dist = dist * params.R

    full_l_array, full_m_array = ex1.lm_arrays

    # determine indices of relevant elements in the sum
    indices_l, indices_p = np.nonzero(full_m_array[:, None] == full_m_array[None, :])
    flat_l = full_l_array[indices_l]
    flat_p = full_l_array[indices_p]
    flat_m = full_m_array[indices_l]  # the same as full_m_array[indices_p]

    charge_factor = np.real(ex1.coefs[..., indices_l] * np.conj(ex2.coefs[..., indices_p]) +
                            (-1) ** (flat_l + flat_p) * ex1.coefs[..., indices_p] * np.conj(ex2.coefs[..., indices_l]))

    all_s_array = np.arange(2 * ex1.max_l + 1)
    bessels = fn.sph_bessel_k(all_s_array, params.kappa * dist)

    # additional selection that excludes terms where Wigner 3j symbols are 0 by definition
    s_bool1 = np.abs(flat_l[:, None] - all_s_array[None, :]) <= flat_p[:, None]
    s_bool2 = flat_p[:, None] <= (flat_l[:, None] + all_s_array[None, :])
    indices_lpm, indices_s = np.nonzero(s_bool1 * s_bool2)

    l_vals = flat_l[indices_lpm]
    p_vals = flat_p[indices_lpm]
    m_vals = flat_m[indices_lpm]
    s_vals = all_s_array[indices_s]
    bessel_vals = bessels[indices_s]

    # While all other arrays are 1D, this one can have extra leading axes corresponding to leading dimensions
    # of expansion coefficients. The last dimension is the same as other arrays.
    charge_vals = charge_factor[..., indices_lpm]

    lps_terms = (2 * s_vals + 1) * np.sqrt((2 * l_vals + 1) * (2 * p_vals + 1))

    # the same combination of l, s, and p is repeated many times
    _, unique_indices1, inverse1 = np.unique(np.stack((l_vals, s_vals, p_vals)),
                                             axis=1, return_inverse=True, return_index=True)
    wigner1 = wigner3j(2 * l_vals[unique_indices1], 2 * s_vals[unique_indices1], 2 * p_vals[unique_indices1],
                       0, 0, 0)[inverse1]

    # all the combinations (l, s, p, m) are unique
    wigner2 = wigner3j(2 * l_vals, 2 * s_vals, 2 * p_vals,
                       -2 * m_vals, 0, 2 * m_vals)

    constants = params.R ** 2 / (params.kappa * params.epsilon * uc.CONSTANTS.epsilon0) * energy_units(units, params)

    C_vals = fn.interaction_coeff_C(l_vals, p_vals, params.kappaR)
    lspm_vals = C_vals * (-1) ** (l_vals + m_vals) * lps_terms * bessel_vals * wigner1 * wigner2
    broadcasted_lspm_vals = np.broadcast_to(lspm_vals, charge_vals.shape)

    return 0.5 * constants * np.sum(broadcasted_lspm_vals * charge_vals, axis=-1)


if __name__ == '__main__':

    params = ModelParams(R=150, kappaR=3)
    ex1 = expansion.MappedExpansionQuad(0.44, params.kappaR, 0.001, max_l=20)
    ex2 = ex1.clone()

    dist = 2.

    # ex1, ex2 = expansions_to_common_l(ex1, ex2)
    # print(ex1.coeffs)
    # print(ex2.coeffs)

    t0 = time.perf_counter()
    energy = charged_shell_energy(ex1, ex2, dist, params)
    t1 = time.perf_counter()

    print('energy: ', energy)
    print('time: ', t1 - t0)

    # plt.plot(energy)
    # plt.show()