def compute_resonances(elt=None, K0=None, K1=None, K2=None, neigs=0):
"""
Compute resonances via a generalized linear eigenvalue problem.
Input:
elt
K0
K1
K2
neigs -- Number of poles desired (default: 0 --> compute all)
Output:
l
V
"""
if elt is not None:
(N, nnz) = problem_size(elt)
issparse = (neigs != 0) and (nnz < 0.2 * N ** 2) and (N > 100)
(K0, K1, K2) = form_operators(elt, issparse)
N = len(K0)
# TODO: Adding sparsity
Z = np.zeros((N, N))
I = np.eye(N)
A = np.vstack((np.hstack((K0, Z)), np.hstack((Z, I))))
B = np.vstack((np.hstack((-K1, -K2)), np.hstack((I, Z))))
ll = eig(a=A, b=B, left=False, right=False)
ll_sorted = (np.unique(ll.round(decimals=4)))[np.argsort(np.abs(np.unique(ll.round(decimals=4))))]
ll_sorted = ll_sorted[np.abs(ll_sorted) < 1e308]
return ll_sorted * 1.0j
def compute_scatter (elt, l):
"""
Compute the scattered wave in response to a plane wave of the form exp(i*l*x)
"""
(K0, K1, K2) = form_operators (elt, l)
F = plane_forcing (elt, l)
return np.linalg.solve((-l*l*K2 + 1.0j*l*K1 + K0), F)
