def test_stratHeun_ND_additive():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = np.zeros(3)
def f(y, t):
return np.array([ -1.0*y[0],
y[2],
-1.0*y[1] - 0.4*y[2] ])
def G(y, t):
return np.diag([0.2, 0.0, 0.5])
y = sdeint.stratHeun(f, G, y0, tspan)
w = np.fft.rfft(y[:, 2])
def test_stratHeun_ND_additive():
tspan = np.arange(0.0, 2000.0, 0.002)
y0 = np.zeros(3)
def f(y, t):
return np.array([-1.0 * y[0], y[2], -1.0 * y[1] - 0.4 * y[2]])
def G(y, t):
return np.diag([0.2, 0.0, 0.5])
y = sdeint.stratHeun(f, G, y0, tspan)
w = np.fft.rfft(y[:, 2])
def test_stratHeun_R74(self, exact_solution_R74):
(dW, I, J, f, f_strat, G, G_separate, y0, tspan,
y) = exact_solution_R74
yHeun = sdeint.stratHeun(f_strat, G, y0, tspan, dW=dW)
_assert_close(yHeun, y, 1e-2, 1e-2)
return yHeun
def test_stratHeun_KPS445(self, exact_solution_KPS445):
(dW, I, J, f, f_strat, G, y0, tspan, y) = exact_solution_KPS445
yHeun = sdeint.stratHeun(f_strat, G, y0, tspan, dW=dW)[:, 0]
_assert_close(yHeun, y, 1e-2, 1e-2)
return yHeun
def test_stratHeun_R74(self, exact_solution_R74):
(dW, I, J, f, f_strat, G, G_separate, y0, tspan,y) = exact_solution_R74
yHeun = sdeint.stratHeun(f_strat, G, y0, tspan, dW=dW)
_assert_close(yHeun, y, 1e-2, 1e-2)
return yHeun
def test_stratHeun_KPS445(self, exact_solution_KPS445):
(dW, I, J, f, f_strat, G, y0, tspan, y) = exact_solution_KPS445
yHeun = sdeint.stratHeun(f_strat, G, y0, tspan, dW=dW)[:,0]
_assert_close(yHeun, y, 1e-2, 1e-2)
return yHeun
return w
def g(x, t):
""" This simulates the right part of equation (5.1).
"""
z = x * sigma[alpha[time_to_index[t]]]
return z
def f(x, t):
""" Simulates left part of equation (5.1).
"""
return x * (b[alpha[time_to_index[t]]] -
x * a[alpha[time_to_index[t]]])
result = sdeint.stratHeun(f, g, x0, tspan)
import matplotlib.pylab as plt
plt.style.use('ggplot')
fig = plt.figure()
ax = plt.subplot()
ax.clear()
ax.plot(tspan, result)
ax.legend()
fig.tight_layout()