def incomplete_beta_ps(a, b, value):
"""Power series for incomplete beta
Use when b*x is small and value not too close to 1.
Based on Cephes library by Steve Moshier (incbet.c)
"""
one = aet.constant(1, dtype="float64")
ai = one / a
u = (one - b) * value
t1 = u / (a + one)
t = u
threshold = np.MachAr().eps * ai
s = aet.constant(0, dtype="float64")
def _step(i, t, s):
t *= (i - b) * value / i
step = t / (a + i)
s += step
return ((t, s), until(aet.abs_(step) < threshold))
(t, s), _ = scan(_step,
sequences=[aet.arange(2, 302)],
outputs_info=[e for e in aet.cast((t, s), "float64")])
s = s[-1] + t1 + ai
t = gammaln(a +
b) - gammaln(a) - gammaln(b) + a * aet.log(value) + aet.log(s)
return aet.exp(t)
def test_constant_output(self):
# Test that if the output is a constant, we respect the aesara memory interface
f = function([], aet.constant([4]))
# print f.maker.fgraph.toposort()
out = f()
assert (out == 4).all()
out[0] = 3
out2 = f()
# If the following 2 asserts fail it mean Aesara broke it's memory contract.
assert out2 is not out
assert (out2 == 4).all()
# Test that if the output is a constant and borrow, we respect the aesara memory interface
f = function([], Out(aet.constant([4]), borrow=True))
# print f.maker.fgraph.toposort()
out = f()
assert (out == 4).all()
out[0] = 3
out2 = f()
if isinstance(get_default_mode(), DebugMode):
# In DebugMode, we don't implement optimization based on borrow on the output.
assert (out2 == 4).all()
else:
assert out2 is out
assert (out2 == 3).all()
def test_draw_value():
npt.assert_equal(_draw_value(np.array([5, 6])), [5, 6])
npt.assert_equal(_draw_value(np.array(5.0)), 5)
npt.assert_equal(_draw_value(aet.constant([5.0, 6.0])), [5, 6])
assert _draw_value(aet.constant(5)) == 5
npt.assert_equal(_draw_value(2 * aet.constant([5.0, 6.0])), [10, 12])
val = aesara.shared(np.array([5.0, 6.0]))
npt.assert_equal(_draw_value(val), [5, 6])
npt.assert_equal(_draw_value(2 * val), [10, 12])
a = aet.scalar("a")
a.tag.test_value = 6
npt.assert_equal(_draw_value(2 * a, givens=[(a, 1)]), 2)
assert _draw_value(5) == 5
assert _draw_value(5.0) == 5
assert isinstance(_draw_value(5.0), type(5.0))
assert isinstance(_draw_value(5), type(5))
with pm.Model():
mu = 2 * aet.constant(np.array([5.0, 6.0])) + aesara.shared(
np.array(5))
a = pm.Normal("a", mu=mu, sigma=5, shape=2)
val1 = _draw_value(a)
val2 = _draw_value(a)
assert np.all(val1 != val2)
with pytest.raises(ValueError) as err:
_draw_value([])
err.match("Unexpected type")
def test_observed_with_column_vector(self):
"""This test is related to https://github.com/pymc-devs/aesara/issues/390 which breaks
broadcastability of column-vector RVs. This unexpected change in type can lead to
incompatibilities during graph rewriting for model.logp evaluation.
"""
with pm.Model() as model:
# The `observed` is a broadcastable column vector
obs = at.as_tensor_variable(
np.ones((3, 1), dtype=aesara.config.floatX))
assert obs.broadcastable == (False, True)
# Both shapes describe broadcastable volumn vectors
size64 = at.constant([3, 1], dtype="int64")
# But the second shape is upcasted from an int32 vector
cast64 = at.cast(at.constant([3, 1], dtype="int32"), dtype="int64")
pm.Normal("size64", mu=0, sigma=1, size=size64, observed=obs)
pm.Normal("shape64", mu=0, sigma=1, shape=size64, observed=obs)
model.logp()
pm.Normal("size_cast64", mu=0, sigma=1, size=cast64, observed=obs)
pm.Normal("shape_cast64",
mu=0,
sigma=1,
shape=cast64,
observed=obs)
model.logp()
def rv_op(cls, dist, lower=None, upper=None, size=None, rngs=None):
lower = at.constant(
-np.inf) if lower is None else at.as_tensor_variable(lower)
upper = at.constant(
np.inf) if upper is None else at.as_tensor_variable(upper)
# When size is not specified, dist may have to be broadcasted according to lower/upper
dist_shape = size if size is not None else at.broadcast_shape(
dist, lower, upper)
dist = change_rv_size(dist, dist_shape)
# Censoring is achieved by clipping the base distribution between lower and upper
rv_out = at.clip(dist, lower, upper)
# Reference nodes to facilitate identification in other classmethods, without
# worring about possible dimshuffles
rv_out.tag.dist = dist
rv_out.tag.lower = lower
rv_out.tag.upper = upper
if rngs is not None:
rv_out = cls._change_rngs(rv_out, rngs)
return rv_out
def test_interval_transform_raises():
with pytest.raises(ValueError, match="Lower and upper interval bounds cannot both be None"):
tr.Interval(None, None)
with pytest.raises(ValueError, match="Interval bounds must be constant values"):
tr.Interval(at.constant(5) + 1, None)
assert tr.Interval(at.constant(5), None)
def __init__(self, name="", model=None):
super().__init__(name, model)
assert pm.modelcontext(None) is self
# 1) init variables with Var method
self.register_rv(pm.Normal.dist(), "v1")
self.v2 = pm.Normal("v2", mu=0, sigma=1)
# 2) Potentials and Deterministic variables with method too
# be sure that names will not overlap with other same models
pm.Deterministic("d", at.constant(1))
pm.Potential("p", at.constant(1))
def test_dtype_normal_uniform_687(self):
# Regression test for #687.
rng_R = random_state_type()
assert (uniform(rng_R,
low=tensor.constant(0, dtype="float64"),
dtype="float32")[1].dtype == "float32")
assert (normal(rng_R,
avg=tensor.constant(0, dtype="float64"),
dtype="float32")[1].dtype == "float32")
def test_constant(self):
# Get counter value
autoname_id = next(Variable.__count__)
Variable.__count__ = count(autoname_id)
r1 = at.constant(1.5)
assert r1.auto_name == "auto_" + str(autoname_id), (
r1.auto_name,
"auto_" + str(autoname_id),
)
r3 = at.constant(1.6)
assert r3.auto_name == "auto_" + str(autoname_id + 1)
def test_vals(self):
npt.assert_equal(draw_values([np.array([5, 6])])[0], [5, 6])
npt.assert_equal(draw_values([np.array(5.0)])[0], 5)
npt.assert_equal(draw_values([aet.constant([5.0, 6.0])])[0], [5, 6])
assert draw_values([aet.constant(5)])[0] == 5
npt.assert_equal(
draw_values([2 * aet.constant([5.0, 6.0])])[0], [10, 12])
val = aesara.shared(np.array([5.0, 6.0]))
npt.assert_equal(draw_values([val])[0], [5, 6])
npt.assert_equal(draw_values([2 * val])[0], [10, 12])
def mv_simple():
mu = floatX_array([-0.1, 0.5, 1.1])
p = floatX_array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]])
tau = np.dot(p, p.T)
with pm.Model() as model:
pm.MvNormal(
"x",
at.constant(mu),
tau=at.constant(tau),
initval=floatX_array([0.1, 1.0, 0.8]),
)
H = tau
C = np.linalg.inv(H)
return model.initial_point, model, (mu, C)
def test_constant(self):
x = tt.constant(np.random.rand(2, 3), dtype=config.floatX)
y = aesara.shared(np.random.rand(3, 6).astype(config.floatX), "y")
# should work
z = tt.dot(x, y)
assert hasattr(z.tag, "test_value")
f = aesara.function([], z)
assert _allclose(f(), z.tag.test_value)
# this test should fail
x = tt.constant(np.random.rand(2, 4), dtype=config.floatX)
with pytest.raises(ValueError):
tt.dot(x, y)
def mv_simple_very_coarse():
mu = floatX_array([-0.3, 0.7, 1.3])
p = floatX_array([[2.0, 0, 0], [0.05, 0.1, 0], [1.0, -0.05, 5.5]])
tau = np.dot(p, p.T)
with pm.Model() as model:
pm.MvNormal(
"x",
at.constant(mu),
tau=at.constant(tau),
shape=3,
testval=floatX_array([0.1, 1.0, 0.8]),
)
H = tau
C = np.linalg.inv(H)
return model.test_point, model, (mu, C)
def test_vector_components(self):
nd = 3
npop = 4
# [[0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3]]
mus = at.constant(np.full((nd, npop), np.arange(npop)))
with Model(rng_seeder=self.get_random_state()) as model:
m = Mixture(
"m",
w=np.ones(npop) / npop,
# MvNormal distribution with squared sigma diagonal covariance should
# be equal to vector of Normals from latent_m
comp_dists=[MvNormal.dist(mus[:, i], np.eye(nd) * 1e-5**2) for i in range(npop)],
)
z = Categorical("z", p=np.ones(npop) / npop)
latent_m = Normal("latent_m", mu=mus[..., z], sigma=1e-5, shape=nd)
size = 100
m_val = draw(m, draws=size)
latent_m_val = draw(latent_m, draws=size)
assert m_val.shape == latent_m_val.shape
# Test that each element in axis = -1 comes from the same mixture
# component
assert np.all(np.diff(m_val) < 1e-3)
assert np.all(np.diff(latent_m_val) < 1e-3)
# TODO: The following statistical test appears to be more flaky than expected
# even though the distributions should be the same. Seeding should make it
# stable but might be worth investigating further
self.samples_from_same_distribution(m_val, latent_m_val)
# Check that mixing of values in the last axis leads to smaller logp
logp_fn = model.compile_logp(vars=[m])
assert logp_fn({"m": [0, 0, 0]}) > logp_fn({"m": [0, 1, 0]}) > logp_fn({"m": [0, 1, 2]})
self.logp_matches(m, latent_m, z, npop, model=model)
def test_scalar_components(self):
nd = 3
npop = 4
# [[0, 1, 2, 3], [0, 1, 2, 3], [0, 1, 2, 3]]
mus = at.constant(np.full((nd, npop), np.arange(npop)))
with Model(rng_seeder=self.get_random_state()) as model:
m = NormalMixture(
"m",
w=np.ones(npop) / npop,
mu=mus,
sigma=1e-5,
comp_shape=(nd, npop),
shape=nd,
)
z = Categorical("z", p=np.ones(npop) / npop, shape=nd)
mu = at.as_tensor_variable([mus[i, z[i]] for i in range(nd)])
latent_m = Normal("latent_m", mu=mu, sigma=1e-5, shape=nd)
size = 100
m_val = draw(m, draws=size)
latent_m_val = draw(latent_m, draws=size)
assert m_val.shape == latent_m_val.shape
# Test that each element in axis = -1 can come from independent
# components
assert not all(np.all(np.diff(m_val) < 1e-3, axis=-1))
assert not all(np.all(np.diff(latent_m_val) < 1e-3, axis=-1))
self.samples_from_same_distribution(m_val, latent_m_val)
# Check that logp is the same whether elements of the last axis are mixed or not
logp_fn = model.compile_logp(vars=[m])
assert np.isclose(logp_fn({"m": [0, 0, 0]}), logp_fn({"m": [0, 1, 2]}))
self.logp_matches(m, latent_m, z, npop, model=model)
def __init__(self, mean=0, sigma=1, name="", model=None):
super().__init__(name, model)
self.Var("v1", Normal.dist(mu=mean, sigma=sigma))
Normal("v2", mu=mean, sigma=sigma)
Normal("v3", mu=mean, sigma=HalfCauchy("sd", beta=10, testval=1.0))
Deterministic("v3_sq", self.v3 ** 2)
Potential("p1", aet.constant(1))
def _replace_shared_variables(
graph: List[TensorVariable]) -> List[TensorVariable]:
"""Replace shared variables in graph by their constant values
Raises
------
ValueError
If any shared variable contains default_updates
"""
shared_variables = [
var for var in graph_inputs(graph) if isinstance(var, SharedVariable)
]
if any(hasattr(var, "default_update") for var in shared_variables):
raise ValueError(
"Graph contains shared variables with default_update which cannot "
"be safely replaced.")
replacements = {
var: at.constant(var.get_value(borrow=True))
for var in shared_variables
}
new_graph = clone_replace(graph, replace=replacements)
return new_graph
def _filter_grad_var(grad, inp):
# Returns (filtered_var, overrider_var)
# Args:
# grad: gradient Variable
# inp: the corresponding input of gradient Variable
#
# a grad() call could return instance of NullType() or DisconnectedType()
# which cannot be directly used in OfG
#
# Since we always use an OfG instance as self._lop_op, the current
# workaround is to "remember" the special cases of the gradient and
# replace them after self._lop_op is called.
#
# This helper function changes invalid types into a filtered_var,
# and provides a overrider_var to be replaced at grad() call
#
# For now, this converts NullType or DisconnectedType into zeros_like.
# other types are unmodified: overrider_var -> None
if isinstance(grad.type, (NullType, DisconnectedType)):
if hasattr(inp, "zeros_like"):
return inp.zeros_like(), grad
else:
return at.constant(0.0), grad
else:
return grad, None
def test_composite_elemwise_float16(self):
w = bvector()
x = vector(dtype="float16")
y = fvector()
cz = tanh(x + aet.cast(y, "float16"))
o = (
cz
- cz ** 2
+ aet.cast(x, "int16")
+ aet.cast(x, "float32")
+ aet.cast(w, "float16")
- aet.constant(np.float16(1.0))
)
aesara.function([w, x, y], o, mode=mode_with_gpu)
v = vector(dtype="uint8")
w = vector(dtype="float16")
x = vector(dtype="float16")
y = vector(dtype="float16")
z = vector(dtype="float16")
o = aet.switch(v, mul(w, x, y), z)
aesara.function([v, w, x, y, z], o, mode=mode_with_gpu)
def check_vectortransform_elementwise_logp(self, model):
x = model.free_RVs[0]
x_val_transf = x.tag.value_var
pt = model.initial_point(0)
test_array_transf = floatX(
np.random.randn(*pt[x_val_transf.name].shape))
transform = x_val_transf.tag.transform
test_array_untransf = transform.backward(test_array_transf,
*x.owner.inputs).eval()
# Create input variable with same dimensionality as untransformed test_array
x_val_untransf = at.constant(test_array_untransf).type()
jacob_det = transform.log_jac_det(test_array_transf, *x.owner.inputs)
# Original distribution is univariate
if x.owner.op.ndim_supp == 0:
assert joint_logpt(
x, sum=False)[0].ndim == x.ndim == (jacob_det.ndim + 1)
# Original distribution is multivariate
else:
assert joint_logpt(
x, sum=False)[0].ndim == (x.ndim - 1) == jacob_det.ndim
a = joint_logpt(x, x_val_transf,
jacobian=False).eval({x_val_transf: test_array_transf})
b = joint_logpt(x, x_val_untransf, transformed=False).eval(
{x_val_untransf: test_array_untransf})
# Hack to get relative tolerance
close_to(a, b, np.abs(0.5 * (a + b) * tol))
def choice(random_state,
size=None,
a=2,
replace=True,
p=None,
ndim=None,
dtype="int64"):
"""
Choose values from `a` with or without replacement. `a` can be a 1-D array
or a positive scalar. If `a` is a scalar, the samples are drawn from the
range 0,...,a-1.
If the size argument is ambiguous on the number of dimensions, ndim
may be a plain integer to supplement the missing information.
If size is None, a scalar will be returned.
"""
a = tensor.as_tensor_variable(a)
if isinstance(replace, bool):
replace = tensor.constant(replace, dtype="int8")
else:
replace = tensor.as_tensor_variable(replace)
# encode p=None as an empty vector
p = tensor.as_tensor_variable(p or [])
ndim, size, bcast = _infer_ndim_bcast(ndim, size)
op = RandomFunction(choice_helper,
tensor.TensorType(dtype=dtype, broadcastable=bcast))
return op(random_state, size, a, replace, p)
def test_scan(self):
x = vector("x")
# we will insert a subgraph involving these variables into the inner
# graph of scan. since they were not previously in the inner graph,
# they are like non_sequences to scan(). scan() infers these and
# imports them into the inner graph properly, and map_variables()
# should do this as well.
outer = scalar("outer")
shared = aesara.shared(np.array(1.0, dtype=aesara.config.floatX),
name="shared")
constant = at.constant(1, name="constant")
# z will equal 1 so multiplying by it doesn't change any values
z = outer * (shared + constant)
def step(x, a):
r = a + x
r.tag.replacement = z * (a - x)
return r
s, _ = aesara.scan(step, sequences=x, outputs_info=[np.array(0.0)])
# ensure z is owned by the outer graph so map_variables() will need to
# jump through additional hoops to placate FunctionGraph.
t = z * s
(s2, ) = map_variables(self.replacer, [t])
t2 = z * s2
f = aesara.function([x, outer], [t, t2])
rval = f(x=np.array([1, 2, 3], dtype=np.float32), outer=0.5)
assert np.array_equal(rval, [[1, 3, 6], [-1, -3, -6]])
def test_sparseblockgemv_grad(self):
W_val, h_val, iIdx_val, b_val, oIdx_val = self.gemv_data()
iIdx = at.constant(iIdx_val)
oIdx = at.constant(oIdx_val)
def metaop(b, h, W):
return sparse_block_dot(W, h, iIdx, b, oIdx)
def op(b, h, W):
return self.gemv_op(b.take(oIdx, axis=0), W, h, iIdx, oIdx)
eps = 3e-3
utt.verify_grad(metaop, [b_val, h_val, W_val], mode=self.mode, eps=eps)
utt.verify_grad(op, [b_val, h_val, W_val], mode=self.mode, eps=eps)
def test_opfromgraph(self):
# as with the scan tests above, insert foreign inputs into the
# inner graph.
outer = scalar("outer")
shared = aesara.shared(np.array(1.0, dtype=aesara.config.floatX),
name="shared")
constant = at.constant(1.0, name="constant")
z = outer * (shared + constant)
# construct the inner graph
a = scalar()
b = scalar()
r = a + b
r.tag.replacement = z * (a - b)
# construct the outer graph
c = scalar()
d = scalar()
u = aesara.compile.builders.OpFromGraph([a, b], [r])(c, d)
t = z * u
(v, ) = map_variables(self.replacer, [t])
t2 = z * v
f = aesara.function([c, d, outer], [t, t2])
for m, n in itertools.combinations(range(10), 2):
assert f(m, n, outer=0.5) == [m + n, m - n]
# test that the unsupported case of replacement with a shared
# variable with updates crashes
shared.update = shared + 1
with pytest.raises(NotImplementedError):
map_variables(self.replacer, [t])
def __init__(self, mean=0, sigma=1, name="", model=None):
super().__init__(name, model)
self.register_rv(Normal.dist(mu=mean, sigma=sigma), "v1")
Normal("v2", mu=mean, sigma=sigma)
Normal("v3", mu=mean, sigma=Normal("sd", mu=10, sigma=1, initval=1.0))
Deterministic("v3_sq", self.v3**2)
Potential("p1", at.constant(1))
def test_reshape(self):
new_shape = tensor.constant(
np.asarray([self.mat_in_shape[0] * self.mat_in_shape[1]], dtype="int64")
)
self.check_mat_rop_lop(
self.mx.reshape(new_shape), (self.mat_in_shape[0] * self.mat_in_shape[1],)
)
def make_node(self, x, index, toInsert):
assert isinstance(x.type, TypedListType)
assert x.ttype == toInsert.type
if not isinstance(index, Variable):
index = at.constant(index, ndim=0, dtype="int64")
else:
assert index.dtype == "int64"
assert isinstance(index, TensorVariable) and index.ndim == 0
return Apply(self, [x, index, toInsert], [x.type()])
def test_sparseblockgemv_grad_1(self):
# Test that we correctly handle cases where dimensions are 1.
h_val = randn(1, 1, 1).astype("float32")
iIdx_val = np.random.permutation(1)[:1][None, :]
oIdx_val = np.random.permutation(1)[:1][None, :]
W_val = randn(1, 1, 1, 1).astype("float32")
b_val = randn(1, 1).astype("float32")
iIdx = at.constant(iIdx_val)
oIdx = at.constant(oIdx_val)
def metaop(b, h, W):
return sparse_block_dot(W, h, iIdx, b, oIdx)
def op(b, h, W):
return self.gemv_op(b.take(oIdx, axis=0), W, h, iIdx, oIdx)
utt.verify_grad(metaop, [b_val, h_val, W_val], mode=self.mode)
utt.verify_grad(op, [b_val, h_val, W_val], mode=self.mode)
def make_node(self, o, x, y, xIdx, yIdx, alpha=None):
ctx = infer_context_name(o, x, y)
one = aet.constant(np.asarray(1.0, dtype="float32"))
o = as_gpuarray_variable(o, ctx)
x = as_gpuarray_variable(x, ctx)
y = as_gpuarray_variable(y, ctx)
xIdx = as_tensor_variable(xIdx)
yIdx = as_tensor_variable(yIdx)
if alpha is None:
alpha = one
return Apply(self, [o, x, y, xIdx, yIdx, alpha], [o.type()])
def _check_size(size):
"""
Canonicalise inputs to get valid output sizes for Aesara tensors.
Parameters
----------
size : int_vector_like
Some variable that could serve as the shape for an Aesara tensor.
This can be an int, a tuple of ints, a list of ints
or an Aesara Variable with similar properties.
Returns
-------
size_var : int_vector
A one-dimensional Aesara variable encapsulating the given size.
Raises
------
ValueError
If this method can not build a valid size from the input.
"""
# non-tuple checks and scalar-to-tuple transform
if isinstance(size, Variable):
if size.ndim == 1:
return size
elif size.ndim == 0:
return at.stack([size], ndim=1)
else:
raise ValueError(
"Aesara variable must have 1 dimension to be a valid size.",
size)
elif isinstance(size, (np.integer, int)):
return at.constant([size], ndim=1)
elif not isinstance(size, (tuple, list)):
raise ValueError("Size must be a int, tuple, list or Aesara variable.",
size)
# check entries of list or tuple
for i in size:
if isinstance(i, Variable):
if i.ndim != 0:
raise ValueError("Non-scalar Aesara variable in size", size, i)
elif isinstance(i, (np.integer, int)):
if i <= 0:
raise ValueError(
"Non-positive dimensions not allowed in size.", size, i)
else:
raise ValueError(
"Only Aesara variables and integers are allowed in a size-tuple.",
size,
i,
)
return at.as_tensor_variable(size, ndim=1)