def test_elemwise_velocity():
scaling = np.array([1, 2, 3])
x = floatX(np.ones_like(scaling))
pot = quadpotential.quad_potential(scaling, True)
v = pot.velocity(x)
npt.assert_allclose(v, scaling)
assert v.dtype == pot.dtype
def test_random_diag():
d = np.arange(10) + 1
np.random.seed(42)
pots = [
quadpotential.quad_potential(d, True),
quadpotential.quad_potential(1.0 / d, False),
quadpotential.quad_potential(np.diag(d), True),
quadpotential.quad_potential(np.diag(1.0 / d), False),
]
if quadpotential.chol_available:
d_ = scipy.sparse.csc_matrix(np.diag(d))
pot = quadpotential.quad_potential(d_, True)
pots.append(pot)
for pot in pots:
vals = np.array([pot.random() for _ in range(1000)])
npt.assert_allclose(vals.std(0), np.sqrt(1.0 / d), atol=0.1)
def test_equal_diag():
np.random.seed(42)
for _ in range(3):
diag = np.random.rand(5)
x = floatX(np.random.randn(5))
pots = [
quadpotential.quad_potential(diag, False),
quadpotential.quad_potential(1.0 / diag, True),
quadpotential.quad_potential(np.diag(diag), False),
quadpotential.quad_potential(np.diag(1.0 / diag), True),
]
if quadpotential.chol_available:
diag_ = scipy.sparse.csc_matrix(np.diag(1.0 / diag))
pots.append(quadpotential.quad_potential(diag_, True))
v = np.diag(1.0 / diag).dot(x)
e = x.dot(np.diag(1.0 / diag).dot(x)) / 2
for pot in pots:
v_ = pot.velocity(x)
e_ = pot.energy(x)
npt.assert_allclose(v_, v, rtol=1e-6)
npt.assert_allclose(e_, e, rtol=1e-6)
def test_equal_dense():
np.random.seed(42)
for _ in range(3):
cov = np.random.rand(5, 5)
cov += cov.T
cov += 10 * np.eye(5)
inv = np.linalg.inv(cov)
npt.assert_allclose(inv.dot(cov), np.eye(5), atol=1e-10)
x = floatX(np.random.randn(5))
pots = [
quadpotential.quad_potential(cov, False),
quadpotential.quad_potential(inv, True),
]
if quadpotential.chol_available:
pots.append(quadpotential.quad_potential(cov, False))
v = np.linalg.solve(cov, x)
e = 0.5 * x.dot(v)
for pot in pots:
v_ = pot.velocity(x)
e_ = pot.energy(x)
npt.assert_allclose(v_, v, rtol=1e-4)
npt.assert_allclose(e_, e, rtol=1e-4)
def test_elemwise_energy():
scaling = np.array([1, 2, 3])
x = floatX(np.ones_like(scaling))
pot = quadpotential.quad_potential(scaling, True)
energy = pot.energy(x)
npt.assert_allclose(energy, 0.5 * scaling.sum())
def test_elemwise_posdef():
scaling = np.array([0, 2, 3])
with pytest.raises(quadpotential.PositiveDefiniteError):
quadpotential.quad_potential(scaling, True)
def __init__(
self,
vars=None,
scaling=None,
step_scale=0.25,
is_cov=False,
model=None,
blocked=True,
potential=None,
dtype=None,
Emax=1000,
target_accept=0.8,
gamma=0.05,
k=0.75,
t0=10,
adapt_step_size=True,
step_rand=None,
**aesara_kwargs
):
"""Set up Hamiltonian samplers with common structures.
Parameters
----------
vars: list, default=None
List of Aesara variables. If None, all continuous RVs from the
model are included.
scaling: array_like, ndim={1,2}
Scaling for momentum distribution. 1d arrays interpreted matrix
diagonal.
step_scale: float, default=0.25
Size of steps to take, automatically scaled down by 1/n**(1/4),
where n is the dimensionality of the parameter space
is_cov: bool, default=False
Treat scaling as a covariance matrix/vector if True, else treat
it as a precision matrix/vector
model: pymc.Model
blocked: bool, default=True
potential: Potential, optional
An object that represents the Hamiltonian with methods `velocity`,
`energy`, and `random` methods.
**aesara_kwargs: passed to Aesara functions
"""
self._model = modelcontext(model)
if vars is None:
vars = self._model.cont_vars
else:
vars = [self._model.rvs_to_values.get(var, var) for var in vars]
super().__init__(vars, blocked=blocked, model=self._model, dtype=dtype, **aesara_kwargs)
self.adapt_step_size = adapt_step_size
self.Emax = Emax
self.iter_count = 0
# We're using the initial/test point to determine the (initial) step
# size.
# XXX: If the dimensions of these terms change, the step size
# dimension-scaling should change as well, no?
test_point = self._model.initial_point
nuts_vars = [test_point[v.name] for v in vars]
size = sum(v.size for v in nuts_vars)
self.step_size = step_scale / (size ** 0.25)
self.step_adapt = step_sizes.DualAverageAdaptation(
self.step_size, target_accept, gamma, k, t0
)
self.target_accept = target_accept
self.tune = True
if scaling is None and potential is None:
mean = floatX(np.zeros(size))
var = floatX(np.ones(size))
potential = QuadPotentialDiagAdapt(size, mean, var, 10)
if isinstance(scaling, dict):
point = Point(scaling, model=self._model)
scaling = guess_scaling(point, model=self._model, vars=vars)
if scaling is not None and potential is not None:
raise ValueError("Can not specify both potential and scaling.")
if potential is not None:
self.potential = potential
else:
self.potential = quad_potential(scaling, is_cov)
self.integrator = integration.CpuLeapfrogIntegrator(self.potential, self._logp_dlogp_func)
self._step_rand = step_rand
self._warnings = []
self._samples_after_tune = 0
self._num_divs_sample = 0
