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)
assert np.allclose(inv.dot(cov), np.eye(5))
x_ = np.random.randn(5)
x = tt.vector()
x.tag.test_value = x_
pots = [
quadpotential.quad_potential(cov, False, False),
quadpotential.quad_potential(inv, True, False),
]
if quadpotential.chol_available:
pots.append(quadpotential.quad_potential(cov, False, False))
v = np.linalg.solve(cov, x_)
e = 0.5 * x_.dot(v)
for pot in pots:
v_function = theano.function([x], pot.velocity(x))
e_function = theano.function([x], pot.energy(x))
assert np.allclose(v_function(x_), v)
assert np.allclose(e_function(x_), e)
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)
assert np.allclose(inv.dot(cov), np.eye(5))
x_ = np.random.randn(5)
x = tt.vector()
x.tag.test_value = x_
pots = [
quadpotential.quad_potential(cov, False, False),
quadpotential.quad_potential(inv, True, False),
]
if quadpotential.chol_available:
pots.append(quadpotential.quad_potential(cov, False, False))
v = np.linalg.solve(cov, x_)
e = 0.5 * x_.dot(v)
for pot in pots:
v_function = theano.function([x], pot.velocity(x))
e_function = theano.function([x], pot.energy(x))
assert np.allclose(v_function(x_), v)
assert np.allclose(e_function(x_), e)
def test_elemwise_velocity():
scaling = np.array([1, 2, 3])
x_ = np.ones_like(scaling)
x = tt.vector()
x.tag.test_value = x_
pot = quadpotential.quad_potential(scaling, True, False)
v = theano.function([x], pot.velocity(x))
assert np.allclose(v(x_), scaling)
pot = quadpotential.quad_potential(scaling, True, True)
v = theano.function([x], pot.velocity(x))
assert np.allclose(v(x_), 1. / scaling)
def test_elemwise_energy():
scaling = np.array([1, 2, 3])
x_ = np.ones_like(scaling)
x = tt.vector()
x.tag.test_value = x_
pot = quadpotential.quad_potential(scaling, True, False)
energy = theano.function([x], pot.energy(x))
assert np.allclose(energy(x_), 0.5 * scaling.sum())
pot = quadpotential.quad_potential(scaling, True, True)
energy = theano.function([x], pot.energy(x))
assert np.allclose(energy(x_), 0.5 * (1. / scaling).sum())
def test_elemwise_energy():
scaling = np.array([1, 2, 3])
x_ = np.ones_like(scaling)
x = tt.vector()
x.tag.test_value = x_
pot = quadpotential.quad_potential(scaling, True, False)
energy = theano.function([x], pot.energy(x))
assert np.allclose(energy(x_), 0.5 * scaling.sum())
pot = quadpotential.quad_potential(scaling, True, True)
energy = theano.function([x], pot.energy(x))
assert np.allclose(energy(x_), 0.5 * (1. / scaling).sum())
def test_elemwise_velocity():
scaling = np.array([1, 2, 3])
x_ = np.ones_like(scaling)
x = tt.vector()
x.tag.test_value = x_
pot = quadpotential.quad_potential(scaling, True, False)
v = theano.function([x], pot.velocity(x))
assert np.allclose(v(x_), scaling)
pot = quadpotential.quad_potential(scaling, True, True)
v = theano.function([x], pot.velocity(x))
assert np.allclose(v(x_), 1. / scaling)
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_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./d, False),
quadpotential.quad_potential(np.diag(d), True),
quadpotential.quad_potential(np.diag(1./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./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_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. / diag, True),
quadpotential.quad_potential(np.diag(diag), False),
quadpotential.quad_potential(np.diag(1. / diag), True),
]
if quadpotential.chol_available:
diag_ = scipy.sparse.csc_matrix(np.diag(1. / diag))
pots.append(quadpotential.quad_potential(diag_, True))
v = np.diag(1. / diag).dot(x)
e = x.dot(np.diag(1. / diag).dot(x)) / 2
for pot in pots:
v_ = pot.velocity(x)
e_ = pot.energy(x)
npt.assert_allclose(v_, v)
npt.assert_allclose(e_, e)
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_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_equal_diag():
np.random.seed(42)
for _ in range(3):
diag = np.random.rand(5)
x_ = np.random.randn(5)
x = tt.vector()
x.tag.test_value = x_
pots = [
quadpotential.quad_potential(diag, False, False),
quadpotential.quad_potential(1. / diag, True, False),
quadpotential.quad_potential(np.diag(diag), False, False),
quadpotential.quad_potential(np.diag(1. / diag), True, False),
]
if quadpotential.chol_available:
diag_ = scipy.sparse.csc_matrix(np.diag(1. / diag))
pots.append(quadpotential.quad_potential(diag_, True, False))
v = np.diag(1. / diag).dot(x_)
e = x_.dot(np.diag(1. / diag).dot(x_)) / 2
for pot in pots:
v_function = theano.function([x], pot.velocity(x))
e_function = theano.function([x], pot.energy(x))
assert np.allclose(v_function(x_), v)
assert np.allclose(e_function(x_), e)
def test_equal_diag():
np.random.seed(42)
for _ in range(3):
diag = np.random.rand(5)
x_ = np.random.randn(5)
x = tt.vector()
x.tag.test_value = x_
pots = [
quadpotential.quad_potential(diag, False, False),
quadpotential.quad_potential(1. / diag, True, False),
quadpotential.quad_potential(np.diag(diag), False, False),
quadpotential.quad_potential(np.diag(1. / diag), True, False),
]
if quadpotential.chol_available:
diag_ = scipy.sparse.csc_matrix(np.diag(1. / diag))
pots.append(quadpotential.quad_potential(diag_, True, False))
v = np.diag(1. / diag).dot(x_)
e = x_.dot(np.diag(1. / diag).dot(x_)) / 2
for pot in pots:
v_function = theano.function([x], pot.velocity(x))
e_function = theano.function([x], pot.energy(x))
assert np.allclose(v_function(x_), v)
assert np.allclose(e_function(x_), e)
def test_elemwise_posdef2():
scaling = np.array([0, 2, 3])
quadpotential.quad_potential(scaling, True, False)
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 of aesara variables
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)
is_cov: bool, default=False
Treat scaling as a covariance matrix/vector if True, else treat
it as a precision matrix/vector
model: pymc3 Model instance
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
vars = inputvars(vars)
super().__init__(vars,
blocked=blocked,
model=model,
dtype=dtype,
**aesara_kwargs)
self.adapt_step_size = adapt_step_size
self.Emax = Emax
self.iter_count = 0
size = self._logp_dlogp_func.size
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=model)
scaling = guess_scaling(point, model=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
def test_elemwise_posdef():
scaling = np.array([0, 2, 3])
with pytest.raises(quadpotential.PositiveDefiniteError):
quadpotential.quad_potential(scaling, True)
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())