# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
# The implementation follows the design in PyTorch: torch.distributions.constraints.py
#
# Copyright (c) 2016- Facebook, Inc (Adam Paszke)
# Copyright (c) 2014- Facebook, Inc (Soumith Chintala)
# Copyright (c) 2011-2014 Idiap Research Institute (Ronan Collobert)
# Copyright (c) 2012-2014 Deepmind Technologies (Koray Kavukcuoglu)
# Copyright (c) 2011-2012 NEC Laboratories America (Koray Kavukcuoglu)
# Copyright (c) 2011-2013 NYU (Clement Farabet)
# Copyright (c) 2006-2010 NEC Laboratories America (Ronan Collobert, Leon Bottou, Iain Melvin, Jason Weston)
# Copyright (c) 2006 Idiap Research Institute (Samy Bengio)
# Copyright (c) 2001-2004 Idiap Research Institute (Ronan Collobert, Samy Bengio, Johnny Mariethoz)
#
# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
# ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
# LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
# CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
# SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
# INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
# CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
# ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
# POSSIBILITY OF SUCH DAMAGE.
__all__ = [
"boolean",
"circular",
"complex",
"corr_cholesky",
"corr_matrix",
"dependent",
"greater_than",
"greater_than_eq",
"integer_interval",
"integer_greater_than",
"interval",
"is_dependent",
"l1_ball",
"less_than",
"lower_cholesky",
"multinomial",
"nonnegative",
"nonnegative_integer",
"positive",
"positive_definite",
"positive_definite_circulant_vector",
"positive_semidefinite",
"positive_integer",
"real",
"real_vector",
"real_matrix",
"scaled_unit_lower_cholesky",
"simplex",
"sphere",
"softplus_lower_cholesky",
"softplus_positive",
"unit_interval",
"zero_sum",
"Constraint",
]
import math
from typing import Optional
import numpy as np
import jax.numpy
import jax.numpy as jnp
from jax.tree_util import register_pytree_node
from jax.typing import ArrayLike
from numpyro._typing import ConstraintT
class Constraint(object):
"""
Abstract base class for constraints.
A constraint object represents a region over which a variable is valid,
e.g. within which a variable can be optimized.
"""
is_discrete = False
event_dim = 0
def __init_subclass__(cls, **kwargs):
super().__init_subclass__(**kwargs)
register_pytree_node(cls, cls.tree_flatten, cls.tree_unflatten)
def __call__(self, x: ArrayLike) -> ArrayLike:
raise NotImplementedError
def __repr__(self) -> str:
return self.__class__.__name__[1:] + "()"
def check(self, value: ArrayLike) -> ArrayLike:
"""
Returns a byte tensor of `sample_shape + batch_shape` indicating
whether each event in value satisfies this constraint.
"""
return self(value)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
"""
Get a feasible value which has the same shape as dtype as `prototype`.
"""
raise NotImplementedError
@classmethod
def tree_unflatten(cls, aux_data, params):
params_keys, aux_data = aux_data
self = cls.__new__(cls)
for k, v in zip(params_keys, params):
setattr(self, k, v)
for k, v in aux_data.items():
setattr(self, k, v)
return self
class ParameterFreeConstraint(Constraint):
def tree_flatten(self):
return (), ((), dict())
class _SingletonConstraint(ParameterFreeConstraint):
"""
A constraint type which has only one canonical instance, like constraints.real,
and unlike constraints.interval.
"""
def __new__(cls):
if (not hasattr(cls, "_instance")) or (type(cls._instance) is not cls):
# Do not use the singleton instance of a superclass of cls.
cls._instance = super(_SingletonConstraint, cls).__new__(cls)
return cls._instance
class _Boolean(_SingletonConstraint):
is_discrete = True
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x == 0) | (x == 1)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.zeros_like(prototype)
class _CorrCholesky(_SingletonConstraint):
event_dim = 2
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
tril = jnp.tril(x)
lower_triangular = jnp.all(
jnp.reshape(tril == x, x.shape[:-2] + (-1,)), axis=-1
)
positive_diagonal = jnp.all(jnp.diagonal(x, axis1=-2, axis2=-1) > 0, axis=-1)
x_norm = jnp.linalg.norm(x, axis=-1)
tol = jnp.finfo(x.dtype).eps * x.shape[-1] * 10
unit_norm_row = jnp.all(jnp.abs(x_norm - 1) <= tol, axis=-1)
return lower_triangular & positive_diagonal & unit_norm_row
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]), prototype.shape
)
class _CorrMatrix(_SingletonConstraint):
event_dim = 2
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
# check for symmetric
symmetric = jnp.all(jnp.isclose(x, jnp.swapaxes(x, -2, -1)), axis=(-2, -1))
# check for the smallest eigenvalue is positive
positive = jnp.linalg.eigvalsh(x)[..., 0] > 0
# check for diagonal equal to 1
unit_variance = jnp.all(
jnp.abs(jnp.diagonal(x, axis1=-2, axis2=-1) - 1) < 1e-6, axis=-1
)
return symmetric & positive & unit_variance
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]), prototype.shape
)
class _Dependent(Constraint):
"""
Placeholder for variables whose support depends on other variables.
These variables obey no simple coordinate-wise constraints.
:param bool is_discrete: Optional value of ``.is_discrete`` in case this
can be computed statically. If not provided, access to the
``.is_discrete`` attribute will raise a NotImplementedError.
:param int event_dim: Optional value of ``.event_dim`` in case this can be
computed statically. If not provided, access to the ``.event_dim``
attribute will raise a NotImplementedError.
"""
def __init__(
self, *, is_discrete: bool = NotImplemented, event_dim: int = NotImplemented
):
self._is_discrete = is_discrete
self._event_dim = event_dim
super().__init__()
@property
def is_discrete(self):
if self._is_discrete is NotImplemented:
raise NotImplementedError(".is_discrete cannot be determined statically")
return self._is_discrete
@property
def event_dim(self) -> int:
if self._event_dim is NotImplemented:
raise NotImplementedError(".event_dim cannot be determined statically")
return self._event_dim
def __call__(
self,
x: Optional[ArrayLike] = None,
*,
is_discrete: bool = NotImplemented,
event_dim: int = NotImplemented,
):
if x is not None:
raise ValueError("Cannot determine validity of dependent constraint")
# Support for syntax to customize static attributes::
# constraints.dependent(is_discrete=True, event_dim=1)
if is_discrete is NotImplemented:
is_discrete = self._is_discrete
if event_dim is NotImplemented:
event_dim = self._event_dim
return _Dependent(is_discrete=is_discrete, event_dim=event_dim)
def __eq__(self, other: ConstraintT) -> bool:
return (
type(self) is type(other)
and self._is_discrete == other._is_discrete
and self._event_dim == other._event_dim
)
def tree_flatten(self):
return (), (
(),
dict(_is_discrete=self._is_discrete, _event_dim=self._event_dim),
)
class dependent_property(property, _Dependent):
# XXX: this should not need to be pytree-able since it simply wraps a method
# and thus is automatically present once the method's object is created
def __init__(
self, fn=None, *, is_discrete=NotImplemented, event_dim=NotImplemented
):
super().__init__(fn)
self._is_discrete = is_discrete
self._event_dim = event_dim
def __call__(self, x: ArrayLike) -> ArrayLike:
if not callable(x):
return super().__call__(x)
# Support for syntax to customize static attributes::
# @constraints.dependent_property(is_discrete=True, event_dim=1)
# def support(self):
# ...
return dependent_property(
x, is_discrete=self._is_discrete, event_dim=self._event_dim
)
def is_dependent(constraint):
return isinstance(constraint, _Dependent)
class _GreaterThan(Constraint):
def __init__(self, lower_bound):
self.lower_bound = lower_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return x > self.lower_bound
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(lower_bound={})".format(self.lower_bound)
return fmt_string
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(self.lower_bound + 1, jax.numpy.shape(prototype))
def tree_flatten(self):
return (self.lower_bound,), (("lower_bound",), dict())
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _GreaterThan):
return False
return jnp.array_equal(self.lower_bound, other.lower_bound)
class _GreaterThanEq(_GreaterThan):
def __call__(self, x: ArrayLike) -> ArrayLike:
return x >= self.lower_bound
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _GreaterThanEq):
return False
return jnp.array_equal(self.lower_bound, other.lower_bound)
class _Positive(_SingletonConstraint, _GreaterThan):
def __init__(self) -> None:
super().__init__(0.0)
class _Nonnegative(_SingletonConstraint, _GreaterThanEq):
def __init__(self) -> None:
super().__init__(0.0)
class _IndependentConstraint(Constraint):
"""
Wraps a constraint by aggregating over ``reinterpreted_batch_ndims``-many
dims in :meth:`check`, so that an event is valid only if all its
independent entries are valid.
"""
def __init__(self, base_constraint, reinterpreted_batch_ndims):
assert isinstance(base_constraint, Constraint)
assert isinstance(reinterpreted_batch_ndims, int)
assert reinterpreted_batch_ndims >= 0
if isinstance(base_constraint, _IndependentConstraint):
reinterpreted_batch_ndims = (
reinterpreted_batch_ndims + base_constraint.reinterpreted_batch_ndims
)
base_constraint = base_constraint.base_constraint
self.base_constraint = base_constraint
self.reinterpreted_batch_ndims = reinterpreted_batch_ndims
super().__init__()
@property
def event_dim(self) -> int:
return self.base_constraint.event_dim + self.reinterpreted_batch_ndims
def __call__(self, value: ArrayLike) -> ArrayLike:
result = self.base_constraint(value)
if self.reinterpreted_batch_ndims == 0:
return result
elif jax.numpy.ndim(result) < self.reinterpreted_batch_ndims:
expected = self.event_dim
raise ValueError(
f"Expected value.dim() >= {expected} but got {jax.numpy.ndim(value)}"
)
result = result.reshape(
jax.numpy.shape(result)[
: jax.numpy.ndim(result) - self.reinterpreted_batch_ndims
]
+ (-1,)
)
result = result.all(-1)
return result
def __repr__(self) -> str:
return "{}({}, {})".format(
self.__class__.__name__[1:],
repr(self.base_constraint),
self.reinterpreted_batch_ndims,
)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return self.base_constraint.feasible_like(prototype)
def tree_flatten(self):
return (self.base_constraint,), (
("base_constraint",),
{"reinterpreted_batch_ndims": self.reinterpreted_batch_ndims},
)
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _IndependentConstraint):
return False
return (self.base_constraint == other.base_constraint) & (
self.reinterpreted_batch_ndims == other.reinterpreted_batch_ndims
)
class _RealVector(_IndependentConstraint, _SingletonConstraint):
def __init__(self) -> None:
super().__init__(_Real(), 1)
class _RealMatrix(_IndependentConstraint, _SingletonConstraint):
def __init__(self) -> None:
super().__init__(_Real(), 2)
class _LessThan(Constraint):
def __init__(self, upper_bound: ArrayLike) -> None:
self.upper_bound = upper_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return x < self.upper_bound
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(upper_bound={})".format(self.upper_bound)
return fmt_string
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(self.upper_bound - 1, jax.numpy.shape(prototype))
def tree_flatten(self):
return (self.upper_bound,), (("upper_bound",), dict())
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _LessThan):
return False
return jnp.array_equal(self.upper_bound, other.upper_bound)
class _LessThanEq(_LessThan):
def __call__(self, x: ArrayLike) -> ArrayLike:
return x <= self.upper_bound
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _LessThanEq):
return False
return jnp.array_equal(self.upper_bound, other.upper_bound)
class _IntegerInterval(Constraint):
is_discrete = True
def __init__(self, lower_bound: ArrayLike, upper_bound: ArrayLike) -> None:
self.lower_bound = lower_bound
self.upper_bound = upper_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x >= self.lower_bound) & (x <= self.upper_bound) & (x % 1 == 0)
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(lower_bound={}, upper_bound={})".format(
self.lower_bound, self.upper_bound
)
return fmt_string
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(self.lower_bound, jax.numpy.shape(prototype))
def tree_flatten(self):
return (self.lower_bound, self.upper_bound), (
("lower_bound", "upper_bound"),
dict(),
)
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _IntegerInterval):
return False
return jnp.array_equal(self.lower_bound, other.lower_bound) & jnp.array_equal(
self.upper_bound, other.upper_bound
)
class _IntegerGreaterThan(Constraint):
is_discrete = True
def __init__(self, lower_bound: ArrayLike) -> None:
self.lower_bound = lower_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x % 1 == 0) & (x >= self.lower_bound)
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(lower_bound={})".format(self.lower_bound)
return fmt_string
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(self.lower_bound, jax.numpy.shape(prototype))
def tree_flatten(self):
return (self.lower_bound,), (("lower_bound",), dict())
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _IntegerGreaterThan):
return False
return jnp.array_equal(self.lower_bound, other.lower_bound)
class _IntegerPositive(_SingletonConstraint, _IntegerGreaterThan):
def __init__(self) -> None:
super().__init__(1)
class _IntegerNonnegative(_SingletonConstraint, _IntegerGreaterThan):
def __init__(self) -> None:
super().__init__(0)
class _Interval(Constraint):
def __init__(self, lower_bound: ArrayLike, upper_bound: ArrayLike) -> None:
self.lower_bound = lower_bound
self.upper_bound = upper_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x >= self.lower_bound) & (x <= self.upper_bound)
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(lower_bound={}, upper_bound={})".format(
self.lower_bound, self.upper_bound
)
return fmt_string
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
(self.lower_bound + self.upper_bound) / 2, jax.numpy.shape(prototype)
)
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _Interval):
return False
return jnp.array_equal(self.lower_bound, other.lower_bound) & jnp.array_equal(
self.upper_bound, other.upper_bound
)
def tree_flatten(self):
return (self.lower_bound, self.upper_bound), (
("lower_bound", "upper_bound"),
dict(),
)
class _Circular(_SingletonConstraint, _Interval):
def __init__(self) -> None:
super().__init__(-math.pi, math.pi)
class _UnitInterval(_SingletonConstraint, _Interval):
def __init__(self) -> None:
super().__init__(0.0, 1.0)
class _OpenInterval(_Interval):
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x > self.lower_bound) & (x < self.upper_bound)
def __repr__(self) -> str:
fmt_string = self.__class__.__name__[1:]
fmt_string += "(lower_bound={}, upper_bound={})".format(
self.lower_bound, self.upper_bound
)
return fmt_string
class _LowerCholesky(_SingletonConstraint):
event_dim = 2
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
tril = jnp.tril(x)
lower_triangular = jnp.all(
jnp.reshape(tril == x, x.shape[:-2] + (-1,)), axis=-1
)
positive_diagonal = jnp.all(jnp.diagonal(x, axis1=-2, axis2=-1) > 0, axis=-1)
return lower_triangular & positive_diagonal
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]), prototype.shape
)
class _Multinomial(Constraint):
is_discrete = True
event_dim = 1
def __init__(self, upper_bound: ArrayLike) -> None:
self.upper_bound = upper_bound
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x >= 0).all(axis=-1) & (x.sum(axis=-1) == self.upper_bound)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
pad_width = ((0, 0),) * jax.numpy.ndim(self.upper_bound) + (
(0, prototype.shape[-1] - 1),
)
value = jax.numpy.pad(jax.numpy.expand_dims(self.upper_bound, -1), pad_width)
return jax.numpy.broadcast_to(value, prototype.shape)
def tree_flatten(self):
return (self.upper_bound,), (("upper_bound",), dict())
def __eq__(self, other: ConstraintT) -> bool:
if not isinstance(other, _Multinomial):
return False
return jnp.array_equal(self.upper_bound, other.upper_bound)
class _L1Ball(_SingletonConstraint):
"""
Constrain to the L1 ball of any dimension.
"""
event_dim = 1
reltol = 10.0 # Relative to finfo.eps.
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
eps = jnp.finfo(x.dtype).eps
return jnp.abs(x).sum(axis=-1) < 1 + self.reltol * eps
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.zeros_like(prototype)
class _OrderedVector(_SingletonConstraint):
event_dim = 1
def __call__(self, x: ArrayLike) -> ArrayLike:
return (x[..., 1:] > x[..., :-1]).all(axis=-1)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.arange(float(prototype.shape[-1])), prototype.shape
)
class _PositiveDefinite(_SingletonConstraint):
event_dim = 2
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
# check for symmetric
symmetric = jnp.all(jnp.isclose(x, jnp.swapaxes(x, -2, -1)), axis=(-2, -1))
# check for the smallest eigenvalue is positive
positive = jnp.linalg.eigh(x)[0][..., 0] > 0
return symmetric & positive
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]), prototype.shape
)
class _PositiveDefiniteCirculantVector(_SingletonConstraint):
event_dim = 1
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
tol = 10 * jnp.finfo(x.dtype).eps
rfft = jnp.fft.rfft(x)
return (jnp.abs(rfft.imag) < tol) & (rfft.real > -tol)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jnp.zeros_like(prototype).at[..., 0].set(1.0)
class _PositiveSemiDefinite(_SingletonConstraint):
event_dim = 2
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
# check for symmetric
symmetric = jnp.all(jnp.isclose(x, jnp.swapaxes(x, -2, -1)), axis=(-2, -1))
# check for the smallest eigenvalue is nonnegative
nonnegative = jnp.linalg.eigh(x)[0][..., 0] >= 0
return symmetric & nonnegative
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]), prototype.shape
)
class _PositiveOrderedVector(_SingletonConstraint):
"""
Constrains to a positive real-valued tensor where the elements are monotonically
increasing along the `event_shape` dimension.
"""
event_dim = 1
def __call__(self, x: ArrayLike) -> ArrayLike:
return ordered_vector.check(x) & independent(positive, 1).check(x)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.exp(jax.numpy.arange(float(prototype.shape[-1]))), prototype.shape
)
class _Complex(_SingletonConstraint):
def __call__(self, x: ArrayLike) -> ArrayLike:
# XXX: consider to relax this condition to [-inf, inf] interval
return (x == x) & (x != float("inf")) & (x != float("-inf"))
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.zeros_like(prototype)
class _Real(_SingletonConstraint):
def __call__(self, x: ArrayLike) -> ArrayLike:
# XXX: consider to relax this condition to [-inf, inf] interval
return (x == x) & (x != float("inf")) & (x != float("-inf"))
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.zeros_like(prototype)
class _Simplex(_SingletonConstraint):
event_dim = 1
def __call__(self, x: ArrayLike) -> ArrayLike:
x_sum = x.sum(axis=-1)
return (x >= 0).all(axis=-1) & (x_sum < 1 + 1e-6) & (x_sum > 1 - 1e-6)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.full_like(prototype, 1 / prototype.shape[-1])
class _SoftplusPositive(_SingletonConstraint, _GreaterThan):
def __init__(self) -> None:
super().__init__(lower_bound=0.0)
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.full(jax.numpy.shape(prototype), np.log(2))
class _SoftplusLowerCholesky(_LowerCholesky):
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.broadcast_to(
jax.numpy.eye(prototype.shape[-1]) * np.log(2), prototype.shape
)
class _ScaledUnitLowerCholesky(_LowerCholesky):
pass
class _Sphere(_SingletonConstraint):
"""
Constrain to the Euclidean sphere of any dimension.
"""
event_dim = 1
reltol = 10.0 # Relative to finfo.eps.
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
eps = jnp.finfo(x.dtype).eps
norm = jnp.linalg.norm(x, axis=-1)
error = jnp.abs(norm - 1)
return error < self.reltol * eps * x.shape[-1] ** 0.5
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.full_like(prototype, prototype.shape[-1] ** (-0.5))
class _ZeroSum(Constraint):
def __init__(self, event_dim: int = 1) -> None:
self.event_dim = event_dim
super().__init__()
def __call__(self, x: ArrayLike) -> ArrayLike:
jnp = np if isinstance(x, (np.ndarray, np.generic)) else jax.numpy
tol = jnp.finfo(x.dtype).eps * x.shape[-1] * 10
zerosum_true = True
for dim in range(-self.event_dim, 0):
zerosum_true = zerosum_true & jnp.allclose(x.sum(dim), 0, atol=tol)
return zerosum_true
def __eq__(self, other: ConstraintT) -> bool:
return type(self) is type(other) and self.event_dim == other.event_dim
def feasible_like(self, prototype: ArrayLike) -> ArrayLike:
return jax.numpy.zeros_like(prototype)
def tree_flatten(self):
return (self.event_dim,), (("event_dim",), dict())
# TODO: Make types consistent
# See https://github.com/pytorch/pytorch/issues/50616
boolean: ConstraintT = _Boolean()
circular: ConstraintT = _Circular()
complex: ConstraintT = _Complex()
corr_cholesky: ConstraintT = _CorrCholesky()
corr_matrix: ConstraintT = _CorrMatrix()
dependent: ConstraintT = _Dependent()
greater_than: ConstraintT = _GreaterThan
greater_than_eq: ConstraintT = _GreaterThanEq
less_than: ConstraintT = _LessThan
less_than_eq: ConstraintT = _LessThanEq
independent: ConstraintT = _IndependentConstraint
integer_interval: ConstraintT = _IntegerInterval
integer_greater_than: ConstraintT = _IntegerGreaterThan
interval: ConstraintT = _Interval
l1_ball: ConstraintT = _L1Ball()
lower_cholesky: ConstraintT = _LowerCholesky()
scaled_unit_lower_cholesky: ConstraintT = _ScaledUnitLowerCholesky()
multinomial: ConstraintT = _Multinomial
nonnegative: ConstraintT = _Nonnegative()
nonnegative_integer: ConstraintT = _IntegerNonnegative()
ordered_vector: ConstraintT = _OrderedVector()
positive: ConstraintT = _Positive()
positive_definite: ConstraintT = _PositiveDefinite()
positive_definite_circulant_vector: ConstraintT = _PositiveDefiniteCirculantVector()
positive_semidefinite: ConstraintT = _PositiveSemiDefinite()
positive_integer: ConstraintT = _IntegerPositive()
positive_ordered_vector: ConstraintT = _PositiveOrderedVector()
real: ConstraintT = _Real()
real_vector: ConstraintT = _RealVector()
real_matrix: ConstraintT = _RealMatrix()
simplex: ConstraintT = _Simplex()
softplus_lower_cholesky: ConstraintT = _SoftplusLowerCholesky()
softplus_positive: ConstraintT = _SoftplusPositive()
sphere: ConstraintT = _Sphere()
unit_interval: ConstraintT = _UnitInterval()
open_interval: ConstraintT = _OpenInterval
zero_sum: ConstraintT = _ZeroSum
