code = """
dx0 = i1 - sinf(x0) + alpha * (i2 - sinf(x1)) + (a1 + alpha * a2) * cosf(omega * t + phi0);
dx1 = i2 - sinf(x1) + alpha * (i1 - sinf(x0)) + (alpha * a1 + a2) * cosf(omega * t + phi0);
"""
ns_map = {0: ['ns0', 0], 1: [0, 'ns0']}
period_map = {
0: sde.PeriodInfo(period=2.0 * math.pi, freq=1),
1: sde.PeriodInfo(period=2.0 * math.pi, freq=1)
}
sdei = sde.SDE(code,
sim_params,
num_vars=2,
num_noises=2,
const_pars=const_pars,
noise_map=ns_map,
period_map=period_map,
local_vars=local_vars)
output = {
'path': {
'main': [sde.OutputDecl(func=sde.avg_moments, vars=[0, 1])],
},
'summary': {
'main': [sde.OutputDecl(func=sde.drift_velocity, vars=[0, 1])],
# 'abs': [sde.OutputDecl(func=sde.abs_drift_velocity, vars=[0, 1])],
}
}
sdei.prepare(sde.SRK2, init_vector, freq_var='omega')
# Solves the lorenz SDE and draws one generated path
import sde
import numpy as np
# define the lorenz SDE
sigma, rho, beta, lam = 10.0, 28.0, 8 / 3.0, 0.1
def a(X_t):
x, y, z = X_t
return np.array([sigma * (y - x), x * (rho - z) - y, x * y - beta * z])
def b(X_t):
x, y, z = X_t
return lam * (x + y + z) * np.ones((3, 3))
x_0 = [0.1, 0.2, 0.0]
lorenz = sde.SDE(a, b, x_0)
lorenz.solve(method='euler_maruyama', T=50, N=100000)
lorenz.draw_path_3(max_pts=1000)
(alpha * (a1 + a3) + a2) * cosf(omega * t);
dx2 = r3 * (i3 - ic3 * sinf(x2) + alpha * (i2 - ic2 * sinf(x1)) +
(a3 + alpha * a2) * cosf(omega * t);
"""
ns_map = {0: ['ns0'], 1: ['ns0']}
period_map = {
0: sde.PeriodInfo(period=2.0 * math.pi, freq=1),
1: sde.PeriodInfo(period=2.0 * math.pi, freq=1),
2: sde.PeriodInfo(period=2.0 * math.pi, freq=1)
}
sdei = sde.SDE(code,
sim_params,
num_vars=3,
num_noises=1,
noise_map=ns_map,
period_map=period_map,
local_vars=local_vars)
output = {
'path': {
'main': [sde.OutputDecl(func=sde.avg_moments, vars=[0, 1, 2])],
},
'summary': {
'main': [sde.OutputDecl(func=sde.drift_velocity, vars=[0, 1, 2])],
}
}
sdei.prepare(sde.SRK2, init_vector, freq_var='omega')
sdei.simulate(output)
local_vars = {
'ns': lambda sdei: sympy.sqrt(sdei.S.d0 * sdei.S.dt * 2.0 * sdei.S.gamma_)
}
code = """
dx0 = x1;
dx1 = -psd * sinf(x0) - gamma_ * x1 + force;
"""
noise_map = {1: ['ns']}
period_map = {0: sde.PeriodInfo(period=2.0 * numpy.pi, freq=1)}
sde_ = sde.SDE(code,
params,
num_vars=2,
num_noises=1,
noise_map=noise_map,
period_map=period_map,
local_vars=local_vars)
output = {
'summary': {
'main': [sde.OutputDecl(func=sde.diffusion_coefficient, vars=[0])],
},
'path': {
'main': [
sde.OutputDecl(func=diffusion_coefficient, vars=[0]),
sde.OutputDecl(func=max_min, vars=[0])
],
'vhist': [sde.OutputDecl(func=myhist, vars=[1])],
}