def test_logp_scalar_ode():
"""Test the computation of the log probability for these models"""
# Differential equation
def system_1(y, t, p):
return np.exp(-t) - p[0] * y[0]
# Parameters and inital condition
alpha = 0.4
y0 = 0.0
times = np.arange(0.5, 8, 0.5)
yobs = np.array(
[0.30, 0.56, 0.51, 0.55, 0.47, 0.42, 0.38, 0.30, 0.26, 0.21, 0.22, 0.13, 0.13, 0.09, 0.09]
)[:, np.newaxis]
ode_model = DifferentialEquation(func=system_1, t0=0, times=times, n_theta=1, n_states=1)
integrated_solution, *_ = ode_model._simulate([y0], [alpha])
assert integrated_solution.shape == yobs.shape
# compare automatic and manual logp values
manual_logp = norm.logpdf(x=np.ravel(yobs), loc=np.ravel(integrated_solution), scale=1).sum()
with pm.Model() as model_1:
forward = ode_model(theta=[alpha], y0=[y0])
y = pm.Normal("y", mu=forward, sd=1, observed=yobs)
pymc_logp = model_1.logp()
np.testing.assert_allclose(manual_logp, pymc_logp)
def test_simulate():
"""Tests the integration in DifferentialEquation"""
# Create an ODe to integrate
def ode_func(y, t, p):
return np.exp(-t) - p[0] * y[0]
# Evaluate exact solution
y0 = 0
t = np.arange(0, 12, 0.25).reshape(-1, 1)
a = 0.472
y = 1.0 / (a - 1) * (np.exp(-t) - np.exp(-a * t))
# Instantiate ODE model
ode_model = DifferentialEquation(func=ode_func,
t0=0,
times=t,
n_states=1,
n_theta=1)
simulated_y, sens = ode_model._simulate([y0], [a])
assert simulated_y.shape == (len(t), 1)
assert sens.shape == (len(t), 1, 1 + 1)
np.testing.assert_allclose(y, simulated_y, rtol=1e-5)