def scatcoeffs(m, x, nstop): # see B/H eqn 4.88
# implement criterion used by BHMIE plus a couple more orders to
# be safe
nmx = int(array([nstop, np.round_(np.absolute(m*x))]).max()) + 20
Dnmx = mie_specfuncs.log_der_1(m*x, nmx, nstop)
n = np.arange(nstop+1)
psi, xi = mie_specfuncs.riccati_psi_xi(x, nstop)
psishift = np.concatenate((np.zeros(1), psi))[0:nstop+1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop+1]
an = ( (Dnmx/m + n/x)*psi - psishift ) / ( (Dnmx/m + n/x)*xi - xishift )
bn = ( (Dnmx*m + n/x)*psi - psishift ) / ( (Dnmx*m + n/x)*xi - xishift )
return array([an[1:nstop+1], bn[1:nstop+1]]) # output begins at n=1
def scatcoeffs(m, x, nstop): # see B/H eqn 4.88
# implement criterion used by BHMIE plus a couple more orders to
# be safe
nmx = int(array([nstop, np.round_(np.absolute(m * x))]).max()) + 20
Dnmx = mie_specfuncs.log_der_1(m * x, nmx, nstop)
n = np.arange(nstop + 1)
psi, xi = mie_specfuncs.riccati_psi_xi(x, nstop)
psishift = np.concatenate((np.zeros(1), psi))[0:nstop + 1]
xishift = np.concatenate((np.zeros(1), xi))[0:nstop + 1]
an = ((Dnmx / m + n / x) * psi - psishift) / (
(Dnmx / m + n / x) * xi - xishift)
bn = ((Dnmx * m + n / x) * psi - psishift) / (
(Dnmx * m + n / x) * xi - xishift)
return array([an[1:nstop + 1], bn[1:nstop + 1]]) # output begins at n=1
def internal_coeffs(m, x, n_max):
'''
Calculate internal Mie coefficients c_n and d_n given
relative index, size parameter, and maximum order of expansion.
Follow Bohren & Huffman's convention. Note that van de Hulst and Kerker
have different conventions (labeling of c_n and d_n and factors of m)
for their internal coefficients.
'''
ratio = mie_specfuncs.R_psi(x, m * x, n_max)
D1x, D3x = mie_specfuncs.log_der_13(x, n_max)
D1mx = mie_specfuncs.log_der_1(m * x, n_max + 15, n_max)
cl = m * ratio * (D3x - D1x) / (D3x - m * D1mx)
dl = m * ratio * (D3x - D1x) / (m * D3x - D1mx)
return array([cl[1:], dl[1:]]) # start from l = 1
def internal_coeffs(m, x, n_max):
'''
Calculate internal Mie coefficients c_n and d_n given
relative index, size parameter, and maximum order of expansion.
Follow Bohren & Huffman's convention. Note that van de Hulst and Kerker
have different conventions (labeling of c_n and d_n and factors of m)
for their internal coefficients.
'''
ratio = mie_specfuncs.R_psi(x, m * x, n_max)
D1x, D3x = mie_specfuncs.log_der_13(x, n_max)
D1mx = mie_specfuncs.log_der_1(m * x, n_max + 15, n_max)
cl = m * ratio * (D3x - D1x) / (D3x - m * D1mx)
dl = m * ratio * (D3x - D1x) / (m * D3x - D1mx)
return array([cl[1:], dl[1:]]) # start from l = 1