xref: /aosp_15_r20/external/pytorch/torch/distributions/gamma.py (revision da0073e96a02ea20f0ac840b70461e3646d07c45) 
1# mypy: allow-untyped-defs
2from numbers import Number
3
4import torch
5from torch.distributions import constraints
6from torch.distributions.exp_family import ExponentialFamily
7from torch.distributions.utils import broadcast_all
8from torch.types import _size
9
10
11__all__ = ["Gamma"]
12
13
14def _standard_gamma(concentration):
15    return torch._standard_gamma(concentration)
16
17
18class Gamma(ExponentialFamily):
19    r"""
20    Creates a Gamma distribution parameterized by shape :attr:`concentration` and :attr:`rate`.
21
22    Example::
23
24        >>> # xdoctest: +IGNORE_WANT("non-deterministic")
25        >>> m = Gamma(torch.tensor([1.0]), torch.tensor([1.0]))
26        >>> m.sample()  # Gamma distributed with concentration=1 and rate=1
27        tensor([ 0.1046])
28
29    Args:
30        concentration (float or Tensor): shape parameter of the distribution
31            (often referred to as alpha)
32        rate (float or Tensor): rate = 1 / scale of the distribution
33            (often referred to as beta)
34    """
35    arg_constraints = {
36        "concentration": constraints.positive,
37        "rate": constraints.positive,
38    }
39    support = constraints.nonnegative
40    has_rsample = True
41    _mean_carrier_measure = 0
42
43    @property
44    def mean(self):
45        return self.concentration / self.rate
46
47    @property
48    def mode(self):
49        return ((self.concentration - 1) / self.rate).clamp(min=0)
50
51    @property
52    def variance(self):
53        return self.concentration / self.rate.pow(2)
54
55    def __init__(self, concentration, rate, validate_args=None):
56        self.concentration, self.rate = broadcast_all(concentration, rate)
57        if isinstance(concentration, Number) and isinstance(rate, Number):
58            batch_shape = torch.Size()
59        else:
60            batch_shape = self.concentration.size()
61        super().__init__(batch_shape, validate_args=validate_args)
62
63    def expand(self, batch_shape, _instance=None):
64        new = self._get_checked_instance(Gamma, _instance)
65        batch_shape = torch.Size(batch_shape)
66        new.concentration = self.concentration.expand(batch_shape)
67        new.rate = self.rate.expand(batch_shape)
68        super(Gamma, new).__init__(batch_shape, validate_args=False)
69        new._validate_args = self._validate_args
70        return new
71
72    def rsample(self, sample_shape: _size = torch.Size()) -> torch.Tensor:
73        shape = self._extended_shape(sample_shape)
74        value = _standard_gamma(self.concentration.expand(shape)) / self.rate.expand(
75            shape
76        )
77        value.detach().clamp_(
78            min=torch.finfo(value.dtype).tiny
79        )  # do not record in autograd graph
80        return value
81
82    def log_prob(self, value):
83        value = torch.as_tensor(value, dtype=self.rate.dtype, device=self.rate.device)
84        if self._validate_args:
85            self._validate_sample(value)
86        return (
87            torch.xlogy(self.concentration, self.rate)
88            + torch.xlogy(self.concentration - 1, value)
89            - self.rate * value
90            - torch.lgamma(self.concentration)
91        )
92
93    def entropy(self):
94        return (
95            self.concentration
96            - torch.log(self.rate)
97            + torch.lgamma(self.concentration)
98            + (1.0 - self.concentration) * torch.digamma(self.concentration)
99        )
100
101    @property
102    def _natural_params(self):
103        return (self.concentration - 1, -self.rate)
104
105    def _log_normalizer(self, x, y):
106        return torch.lgamma(x + 1) + (x + 1) * torch.log(-y.reciprocal())
107
108    def cdf(self, value):
109        if self._validate_args:
110            self._validate_sample(value)
111        return torch.special.gammainc(self.concentration, self.rate * value)
112