def test_GaussianPrior():
mean = 20
sigma = 4
P1 = GaussianPrior(mean=mean, sigma=sigma, variable_indices=[0])
# Check some basic properties
assert P1.mean == mean
assert P1.sigma == sigma
assert P1.bounds == [(None, None)]
# Check that log probability is symmetric about mean
log_probability = [P1(array([i])) for i in range(1, mean * 2)]
assert log_probability[:mean] == log_probability[mean - 1 :][::-1]
def analytic_probability(x, mu, sigma):
return (1.0 / sqrt(2 * pi * sigma**2)) * exp(
-((x - mu) ** 2) / (2 * sigma**2)
)
test_point = mean - 2 * sigma
assert isclose(
exp(P1(array([test_point]))), analytic_probability(test_point, mean, sigma)
)
assert isclose(exp(P1(array([-1]))), analytic_probability(-1, mean, sigma))
# Check sampling produces expected distribution
sample = array([P1.sample() for _ in range(1000)])
assert isclose(sample.mean(), mean, rtol=0.2)
assert isclose(sample.std(), sigma, rtol=0.2)
def test_GaussianPrior_combined():
# test combining multiple Gaussians
P1 = GaussianPrior(mean=10, sigma=1, variable_indices=[0])
P2 = GaussianPrior(mean=20, sigma=2, variable_indices=[1])
P3 = GaussianPrior(mean=[30, 40], sigma=[3, 4], variable_indices=[2, 3])
combo = GaussianPrior.combine([P1, P2, P3])
# check the combined distribution has the right values
assert (combo.mean == array([10.0, 20.0, 30.0, 40.0])).all()
assert (combo.sigma == array([1.0, 2.0, 3.0, 4.0])).all()
assert all(a == b for a, b in zip(combo.variables, [0, 1, 2, 3]))
assert combo.bounds == [(None, None), (None, None), (None, None), (None, None)]
def test_GaussianPrior_gradient():
# test combining multiple Gaussians
P1 = GaussianPrior(mean=10, sigma=1, variable_indices=[0])
P2 = GaussianPrior(mean=20, sigma=2, variable_indices=[1])
P3 = GaussianPrior(mean=[30, 40], sigma=[3, 4], variable_indices=[2, 3])
combo = GaussianPrior.combine([P1, P2, P3])
# evaluate the prior at a test point
test_point = array([9.0, 21.0, 34.0, 35.0])
# check the analytic gradient calculation against finite difference
analytic_gradient = combo.gradient(test_point)
numeric_gradient = finite_difference(
func=combo, x0=test_point, vectorised_arguments=True
)
assert allclose(analytic_gradient, numeric_gradient)
def test_JointPrior_gradient():
P1 = ExponentialPrior(beta=10, variable_indices=[1])
P2 = GaussianPrior(mean=20, sigma=2, variable_indices=[0])
P3 = UniformPrior(lower=8, upper=16, variable_indices=[2])
JP = JointPrior(components=[P1, P2, P3], n_variables=3)
test_point = array([4.0, 23.0, 12.0])
analytic_gradient = JP.gradient(test_point)
numeric_gradient = finite_difference(
func=JP, x0=test_point, vectorised_arguments=True
)
assert allclose(analytic_gradient, numeric_gradient)
def test_JointPrior():
P1 = ExponentialPrior(beta=10, variable_indices=[1])
P2 = GaussianPrior(mean=20, sigma=2, variable_indices=[0])
P3 = UniformPrior(lower=8, upper=16, variable_indices=[2])
components = [P1, P2, P3]
JP = JointPrior(components=components, n_variables=3)
sample = array([JP.sample() for _ in range(1000)])
assert sample.shape[1] == len(components)
assert isclose(sample[:, 0].mean(), P2.mean, rtol=0.2)
assert isclose(sample[:, 0].std(), P2.sigma, rtol=0.2)
for index, (lower, upper) in enumerate(JP.bounds):
if lower is not None:
assert all(sample[:, index] >= lower)
if upper is not None:
assert all(sample[:, index] <= upper)
def test_JointPrior_repeat_variable():
P1 = ExponentialPrior(beta=10, variable_indices=[0])
P2 = GaussianPrior(mean=20, sigma=2, variable_indices=[0])
P3 = UniformPrior(lower=8, upper=16, variable_indices=[2])
with pytest.raises(ValueError):
JointPrior(components=[P1, P2, P3], n_variables=3)
def test_GaussianPrior_bad_sigma():
with pytest.raises(ValueError):
GaussianPrior(mean=zeros(2), sigma=[1.0, 0.0], variable_indices=[0])
def test_GaussianPrior_inconsistent_dimensions():
with pytest.raises(ValueError):
GaussianPrior(mean=zeros((2, 2)), sigma=ones(4), variable_indices=[0])
with pytest.raises(ValueError):
GaussianPrior(mean=zeros(4), sigma=ones((2, 2)), variable_indices=[0])
def test_GaussianPrior_inconsistent_size_squeezed_dim():
with pytest.raises(ValueError):
GaussianPrior(mean=zeros((2, 1, 2)), sigma=ones(2), variable_indices=[0, 1])
def test_GaussianPrior_inconsistent_size():
with pytest.raises(ValueError):
GaussianPrior(mean=zeros(1), sigma=ones(2), variable_indices=[0])