def test_against_elementwise_transformation(self):
# Test general case gives the same result as the elementwise case
t1 = pints.IdentityTransformation(1) # This is element-wise
t_elem = pints.ComposedTransformation(t1, self.t2, self.t3)
self.assertTrue(t_elem.elementwise()) # This is element-wise
# Test log-Jacobian determinant
self.assertAlmostEqual(self.t.log_jacobian_det(self.x),
t_elem.log_jacobian_det(self.x))
# Test log-Jacobian determinant derivatives
_, t_deriv = self.t.log_jacobian_det_S1(self.x)
_, t_elem_deriv = t_elem.log_jacobian_det_S1(self.x)
self.assertTrue(np.allclose(t_deriv, t_elem_deriv))
def setUpClass(cls):
# Create Transformation class
cls.t1 = TestNonElementWiseIdentityTransformation(1)
lower2 = np.array([1, 2])
upper2 = np.array([10, 20])
cls.t2 = pints.RectangularBoundariesTransformation(lower2, upper2)
cls.t3 = pints.LogTransformation(1)
cls.t = pints.ComposedTransformation(cls.t1, cls.t2, cls.t3)
cls.p = [0.1, 1.5, 15., 999.]
cls.x = [0.1, -2.8332133440562162, 0.9555114450274365,
6.9067547786485539]
cls.j = np.diag([1., 0.4722222222222225, 3.6111111111111098, 999.])
cls.j_s1_diag = [0., 0.4197530864197533, -1.6049382716049378, 999.]
cls.j_s1 = np.zeros((4, 4, 4))
for i in range(4):
cls.j_s1[i, i, i] = cls.j_s1_diag[i]
cls.log_j_det = 7.4404646962481324
cls.log_j_det_s1 = [0., 0.8888888888888888, -0.4444444444444445, 1.]
def inference(model, values, times):
# Create an object with links to the model and time series
problem = pints.SingleOutputProblem(model, times, values)
# Create a log-likelihood function (adds an extra parameter!)
log_likelihood = pints.GaussianLogLikelihood(problem)
# Create a uniform prior over both the parameters and the new noise variable
lower_bounds = np.array([1e-3, 0.0, 0.4, 0.1, 1e-6, 8.0, 1e-4])
upper_bounds = np.array([10.0, 0.4, 0.6, 100.0, 100e-6, 10.0, 0.2])
log_prior = pints.UniformLogPrior(lower_bounds, upper_bounds)
# Create a posterior log-likelihood (log(likelihood * prior))
log_posterior = pints.LogPosterior(log_likelihood, log_prior)
# Choose starting points for 3 mcmc chains
# params = ['k0', 'E0', 'a', 'Ru', 'Cdl', 'freq', 'sigma']
start_parameters = np.array(
[0.0101, 0.214, 0.53, 8.0, 20.0e-6, 9.0152, 0.01])
transform = pints.ComposedTransformation(
pints.LogTransformation(1),
pints.RectangularBoundariesTransformation(lower_bounds[1:],
upper_bounds[1:]),
)
sigma0 = [0.1 * (h - l) for l, h in zip(lower_bounds, upper_bounds)]
boundaries = pints.RectangularBoundaries(lower_bounds, upper_bounds)
found_parameters, found_value = pints.optimise(log_posterior,
start_parameters,
sigma0,
boundaries,
transform=transform,
method=pints.CMAES)
xs = [
found_parameters * 1.001,
found_parameters * 1.002,
found_parameters * 1.003,
]
for x in xs:
x[5] = found_parameters[5]
print('start_parameters', start_parameters)
print('found_parameters', found_parameters)
print('lower_bounds', lower_bounds)
print('upper_bounds', upper_bounds)
# Create mcmc routine with four chains
mcmc = pints.MCMCController(log_posterior,
3,
xs,
method=pints.HaarioBardenetACMC,
transform=transform)
# Add stopping criterion
mcmc.set_max_iterations(10000)
# Run!
chains = mcmc.run()
# Save chains for plotting and analysis
pickle.dump((xs, pints.GaussianLogLikelihood, log_prior, chains,
'HaarioBardenetACMC'), open('results.pickle', 'wb'))
