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def trajectory_to_distances(x):
"""X: [N,N_t,N_d]
ret [N,N_t]"""
from numpy import zeros
from numpy.linalg import norm
from itertools import product, combinations
x = [x[idx, ...] for idx in range(x.shape[0])]
pairwise_trajectories = combinations(x, 2)
_N_COMB = len(list(pairwise_trajectories))
N_max = x[0].shape[0]
distances = zeros((_N_COMB, N_max))
pairwise_trajectories = combinations(x, 2)
for idx, (a_t, b_t) in enumerate(pairwise_trajectories):
distances[idx, :] = norm(a_t[:N_max, :] - b_t[:N_max, :], axis=-1)
return distances
def Lyapunov_d(X):
"""X: [N,N_t]
λ_n = ln(|dX_n|/|dX_0|)/n; n = [1,2,...]"""
from numpy import zeros, log, repeat
Y = zeros((X.shape[0], X.shape[1] - 1))
Y = log(X[:, 1:] / repeat([X[:, 0]], Y.shape[1], axis=0).T) / (
repeat([range(Y.shape[1])], Y.shape[0], axis=0) + 1
)
return Y
def Lyapunov_t(X):
"""X: [N,N_t,N_d]"""
return Lyapunov_d(trajectory_to_distances(X))
Lyapunov = Lyapunov_d
def RelativeDistance_d(X):
"""X: [N,N_t]
λ_n = ln(|dX_n|/|dX_0|)/n; n = [1,2,...]"""
from numpy import zeros, log, repeat
Y = zeros((X.shape[0], X.shape[1] - 1))
Y = log(X[:, 1:] / repeat([X[:, 0]], Y.shape[1], axis=0).T)
return Y
def RelativeDistance_t(X):
"""X: [N,N_t,N_d]"""
return RelativeDistance_d(trajectory_to_distances(X))
RelativeDistance = RelativeDistance_d
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