def _space_product(eA_eigen_vals,eB_eigen_vals):
""" Returns a list containing the eigen-values and their multiplicities
of the Laplacien in the E_A X E_B manifold.
eA_eigen_vals : [list of dict] eigen-values and their multiplicities of a manifold eA
eB_eigen_vals : [list of dict] eigen-values and their multiplicities of a manifold eB
"""
eA_ev_factor = [ v['value'] for v in eA_eigen_vals]
eB_ev_factor = [ v['value'] for v in eB_eigen_vals]
eA_m_factor = [ v['multiplicity'] for v in eA_eigen_vals]
eB_m_factor = [ v['multiplicity'] for v in eB_eigen_vals]
ev_cartesian_prod = cartesian([eA_ev_factor,eB_ev_factor])
m_cartesian_prod = cartesian([eA_m_factor,eA_m_factor])
values = [np.sum(ev_cartesian_prod[k]) for k in range(len(ev_cartesian_prod))]
multiplicities = [np.prod(m_cartesian_prod[k]) for k in range(len(m_cartesian_prod))]
eigen_vals = [ {'value' : values[k],
'multiplicity' : multiplicities[k] }
for k in range(len(values))
]
return eigen_vals
def n_torus(F=[0.1], c=3.4e2, j_max=1, **unusedkwargs):
""" Returns a list containing eigen-values of the Laplacien in the n-torus manifold.
c : [float] sound velocity
F : [list] list of length = containing c/l1, c/l2, ...; where l1, l2, ... are the n-torus lengths
j_max : [int] set index of eigen-values to compute as {-j_max, ..., j_max} in each direction
"""
n = len(F)
k_list = [ [np.square(2*np.pi*j*F[index]/c) for j in range(1, j_max+1)] for index in range(n) ]
cartesian_prod = cartesian(k_list)
values = [np.sum(cartesian_prod[k]) for k in range(len(cartesian_prod))]
eigen_vals = [ {'value' : values[k], 'multiplicity' : 2**(n-1) }
for k in range(len(values))
]
return eigen_vals
