def __init__(self, dist):
# This should be a normal class attribute so that that residual
# can compute the percent point function, but we don't not want
# to force a scipy dependency if the normal distribution is not
# needed.
if not hasattr(Distribution, "N"):
Distribution.N = normal_distribution(0,1)
self.dist = dist
def simulate_2D_radial(f_func,
n_particles,
n_steps,
D,
dt,
dt_sim,
initial_radius=6):
x, y = np.empty((2, n_steps, n_particles))
# random numbers in circle of radius 6
x0 = np.random.random(
n_particles * 2) * (initial_radius * 2) - initial_radius
y0 = np.random.random(
n_particles * 2) * (initial_radius * 2) - initial_radius
mask = x0**2 + y0**2 < initial_radius**2
x[0] = x0[mask][:n_particles]
y[0] = y0[mask][:n_particles]
# this simulation is valid when F and D are constant locally
dilution = int(dt // dt_sim)
n_steps_sim = n_steps * dilution
rv = normal_distribution(loc=0., scale=(2 * D * dt_sim)**0.5)
x_curr = x[0].copy()
y_curr = y[0].copy()
for i in range(1, n_steps_sim):
r_curr = np.sqrt(x_curr**2 + y_curr**2)
force = f_func(r_curr)
force_x = force * (x_curr / r_curr)
force_x[~np.isfinite(force_x)] = 0.
force_y = force * (y_curr / r_curr)
force_y[~np.isfinite(force_y)] = 0.
dx, dy = rv.rvs((2, n_particles))
# the mean of the distribution displaces by gamma * F * dt
# F is in units of kT/um, so gamma = D / kT = D
x_curr += dx + force_x * D * dt_sim
y_curr += dy + force_y * D * dt_sim
if i % dilution == 0:
x[i // dilution] = x_curr
y[i // dilution] = y_curr
return x, y
def simulate_1D(f_func, n_particles, n_steps, D, dt, dt_sim, force=0., kT=1.):
# this simulation is valid when F and D are constant locally
# that is (2*D*dt_sim)**0.5 << length at which force varies
x = np.empty((n_steps, n_particles))
x[0] = np.random.random(n_particles) * 10 - 5
dilution = int(dt // dt_sim)
n_steps_sim = n_steps * dilution
gamma = D / kT
rv = normal_distribution(loc=force * dt_sim * gamma,
scale=(2 * D * dt_sim)**0.5)
x_curr = x[0].copy()
for i in range(1, n_steps_sim):
force = f_func(x_curr)
dx = rv.rvs(n_particles)
# the mean of the distribution displaces by gamma * F * dt
# F is in units of kT/um, so gamma = D / kT = D
x_curr += dx + force * D * dt_sim
if i % dilution == 0:
x[i // dilution] = x_curr
return x
def __init__(self, mean=0, std=1):
self.dist = normal_distribution(mean, std)
self._nllf_scale = log(sqrt(2*pi*std**2))
def __init__(self, dist):
if not hasattr(Distribution, "N"):
Distribution.N = normal_distribution(0,1)
self.dist = dist
# for n in range(N_REALISATIONS):
# plt.plot(x, np.log(plot_realisations[n] / x0), color=r_colors[n])
plt.xlabel('t')
plt.ylabel(r'log(x(t)/$x_{0}$)')
plt.legend()
# Compute Distributions
n_bins = 50
# Analytical
xT_mean = np.exp(all_realisations_log_mean[-1])
xT_std = np.exp(all_realisations_log_std[-1])
print(
f"For the Analytical Solution, mean={xT_mean} (log:{np.log(xT_mean)}), std={xT_std} (log:{np.log(xT_std)})"
)
norm = normal_distribution(loc=np.log(xT_mean), scale=np.log(xT_std))
plt.figure()
count, bins, ignored = plt.hist(all_realisations_log[:, -1],
n_bins,
color='grey')
plt.plot(bins, norm.pdf(bins), color='black')
plt.axvline(x=all_realisations_log_mean[-1] +
(1.96 * all_realisations_log_std[-1]),
color='darkmagenta')
plt.axvline(x=all_realisations_log_mean[-1] -
(1.96 * all_realisations_log_std[-1]),
color='darkmagenta')
# Explicit-Explicit
xT_mean_ee = np.exp(all_realisations_ee_log_mean[-1])
xT_std_ee = np.exp(all_realisations_ee_log_std[-1])
def __init__(self, mean=0, std=1):
Distribution.__init__(self, normal_distribution(mean, std))
self._nllf_scale = log(sqrt(2 * pi * std ** 2))