# mypy: allow-untyped-defs

import torch

from torch import nan, Tensor

from torch.distributions import constraints

from torch.distributions.distribution import Distribution

from torch.distributions.utils import lazy_property, logits_to_probs, probs_to_logits

__all__ = ["Categorical"]

class Categorical(Distribution):

r"""

Creates a categorical distribution parameterized by either :attr:`probs` or

:attr:`logits` (but not both).

.. note::

It is equivalent to the distribution that :func:`torch.multinomial`

samples from.

Samples are integers from :math:`\{0, \ldots, K-1\}` where `K` is ``probs.size(-1)``.

If `probs` is 1-dimensional with length-`K`, each element is the relative probability

of sampling the class at that index.

If `probs` is N-dimensional, the first N-1 dimensions are treated as a batch of

relative probability vectors.

.. note:: The `probs` argument must be non-negative, finite and have a non-zero sum,

and it will be normalized to sum to 1 along the last dimension. :attr:`probs`

will return this normalized value.

The `logits` argument will be interpreted as unnormalized log probabilities

and can therefore be any real number. It will likewise be normalized so that

the resulting probabilities sum to 1 along the last dimension. :attr:`logits`

will return this normalized value.

See also: :func:`torch.multinomial`

Example::

>>> # xdoctest: +IGNORE_WANT("non-deterministic")

>>> m = Categorical(torch.tensor([ 0.25, 0.25, 0.25, 0.25 ]))

>>> m.sample() # equal probability of 0, 1, 2, 3

tensor(3)

Args:

probs (Tensor): event probabilities

logits (Tensor): event log probabilities (unnormalized)

"""

# pyrefly: ignore [bad-override]

arg_constraints = {"probs": constraints.simplex, "logits": constraints.real_vector}

has_enumerate_support = True

def __init__(

self,

probs: Tensor | None = None,

logits: Tensor | None = None,

validate_args: bool | None = None,

) -> None:

if (probs is None) == (logits is None):

raise ValueError(

"Either `probs` or `logits` must be specified, but not both."

)

if probs is not None:

if probs.dim() < 1:

raise ValueError("`probs` parameter must be at least one-dimensional.")

# pyrefly: ignore [read-only]

self.probs = probs / probs.sum(-1, keepdim=True)

else:

if logits is None:

raise AssertionError("logits is unexpectedly None")

if logits.dim() < 1:

raise ValueError("`logits` parameter must be at least one-dimensional.")

# Normalize

# pyrefly: ignore [read-only]

self.logits = logits - logits.logsumexp(dim=-1, keepdim=True)

self._param = self.probs if probs is not None else self.logits

self._num_events = self._param.size()[-1]

batch_shape = (

self._param.size()[:-1] if self._param.ndimension() > 1 else torch.Size()

)

# pyrefly: ignore [bad-argument-type]

super().__init__(batch_shape, validate_args=validate_args)

def expand(self, batch_shape, _instance=None):

new = self._get_checked_instance(Categorical, _instance)

batch_shape = torch.Size(batch_shape)

param_shape = batch_shape + torch.Size((self._num_events,))

if "probs" in self.__dict__:

new.probs = self.probs.expand(param_shape)

new._param = new.probs

if "logits" in self.__dict__:

new.logits = self.logits.expand(param_shape)

new._param = new.logits

new._num_events = self._num_events

super(Categorical, new).__init__(batch_shape, validate_args=False)

new._validate_args = self._validate_args

return new

def _new(self, *args, **kwargs):

return self._param.new(*args, **kwargs)

@constraints.dependent_property(is_discrete=True, event_dim=0)

# pyrefly: ignore [bad-override]

def support(self):

return constraints.integer_interval(0, self._num_events - 1)

@lazy_property

def logits(self) -> Tensor:

return probs_to_logits(self.probs)

@lazy_property

def probs(self) -> Tensor:

return logits_to_probs(self.logits)

@property

def param_shape(self) -> torch.Size:

return self._param.size()

@property

def mean(self) -> Tensor:

return torch.full(

self._extended_shape(),

nan,

dtype=self.probs.dtype,

device=self.probs.device,

)

@property

def mode(self) -> Tensor:

return self.probs.argmax(dim=-1)

@property

def variance(self) -> Tensor:

return torch.full(

self._extended_shape(),

nan,

dtype=self.probs.dtype,

device=self.probs.device,

)

def sample(self, sample_shape=torch.Size()):

if not isinstance(sample_shape, torch.Size):

sample_shape = torch.Size(sample_shape)

probs_2d = self.probs.reshape(-1, self._num_events)

samples_2d = torch.multinomial(probs_2d, sample_shape.numel(), True).T

return samples_2d.reshape(self._extended_shape(sample_shape))

def log_prob(self, value):

if self._validate_args:

self._validate_sample(value)

value = value.long().unsqueeze(-1)

value, log_pmf = torch.broadcast_tensors(value, self.logits)

value = value[..., :1]

return log_pmf.gather(-1, value).squeeze(-1)

def entropy(self):

min_real = torch.finfo(self.logits.dtype).min

logits = torch.clamp(self.logits, min=min_real)

p_log_p = logits * self.probs

return -p_log_p.sum(-1)

def enumerate_support(self, expand=True):

num_events = self._num_events

values = torch.arange(num_events, dtype=torch.long, device=self._param.device)

values = values.view((-1,) + (1,) * len(self._batch_shape))

if expand:

values = values.expand((-1,) + self._batch_shape)

return values