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def get_levy_flight(T=50, D=2, t0=0.1, alpha=3, periodic=False):
from numpy import vstack
from mistree import get_levy_flight as get_flight
if D == 2:
x, y = get_flight(T, mode="2D", periodic=periodic, t_0=t0, alpha=alpha)
xy = vstack([x, y]).T
elif D == 3:
x, y, z = get_flight(T, mode="3D", periodic=periodic, t_0=t0, alpha=alpha)
xy = vstack([x, y, z]).T
else:
raise ValueError(f"Dimension {D} not supported!")
return xy
def get_levy_flights(N=10, T=50, D=2, t0=0.1, alpha=3, periodic=False):
from numpy import moveaxis, array
trajectories = []
for _ in range(N):
xy = get_levy_flight(T=T, D=D, t0=t0, alpha=alpha, periodic=periodic)
trajectories.append(xy)
return moveaxis(array(trajectories), 0, 1)
def get_jitter_levy_flights(
N=10, T=50, D=2, t0=0.1, alpha=3, periodic=False, noise=5e-2
):
from numpy.random import randn
trajectories = get_levy_flights(
N=N, T=T, D=D, t0=t0, alpha=alpha, periodic=periodic
)
return trajectories + randn(*trajectories.shape) * noise
def get_gaussian_random_walk(T=50, D=2, R=5, step_size=0.5, soft=None):
from numpy import array, sin, cos, exp, zeros, pi
from numpy.random import randn, uniform, rand
from numpy.linalg import norm
def is_in(x, R=1):
from numpy.linalg import norm
return norm(x) < R
X = zeros((T, D))
for t in range(1, T):
while True:
if D == 2:
angle = uniform(0, pi * 2)
step = randn(1) * step_size
X[t, :] = X[t - 1, :] + array([cos(angle), sin(angle)]) * step
else:
X[t, :] = X[t - 1, :] + randn(D) / D * step_size
if soft is None:
if is_in(X[t, :], R):
break
elif rand() < exp(-(norm(X[t, :]) - R) * soft):
break
return X
def get_gaussian_random_walks(N=10, T=50, D=2, R=5, step_size=0.5, soft=None):
from numpy import moveaxis, array
trajectories = []
for _ in range(N):
xy = get_gaussian_random_walk(T=T, D=D, R=R, step_size=step_size, soft=soft)
trajectories.append(xy)
return moveaxis(array(trajectories), 0, 1)
def get_gaussian_sample(T=50, D=2):
from numpy.random import randn
return randn(T, D)
def get_gaussian_samples(N=10, T=50, D=2, R=5, step_size=0.5):
from numpy.random import randn
return randn(T, N, D)
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