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| from numbers import Number | |
| import torch | |
| from torch.distributions import constraints | |
| from torch.distributions.exp_family import ExponentialFamily | |
| from torch.distributions.utils import broadcast_all | |
| __all__ = ["Gamma"] | |
| def _standard_gamma(concentration): | |
| return torch._standard_gamma(concentration) | |
| class Gamma(ExponentialFamily): | |
| r""" | |
| Creates a Gamma distribution parameterized by shape :attr:`concentration` and :attr:`rate`. | |
| Example:: | |
| >>> # xdoctest: +IGNORE_WANT("non-deterministic") | |
| >>> m = Gamma(torch.tensor([1.0]), torch.tensor([1.0])) | |
| >>> m.sample() # Gamma distributed with concentration=1 and rate=1 | |
| tensor([ 0.1046]) | |
| Args: | |
| concentration (float or Tensor): shape parameter of the distribution | |
| (often referred to as alpha) | |
| rate (float or Tensor): rate = 1 / scale of the distribution | |
| (often referred to as beta) | |
| """ | |
| arg_constraints = { | |
| "concentration": constraints.positive, | |
| "rate": constraints.positive, | |
| } | |
| support = constraints.nonnegative | |
| has_rsample = True | |
| _mean_carrier_measure = 0 | |
| def mean(self): | |
| return self.concentration / self.rate | |
| def mode(self): | |
| return ((self.concentration - 1) / self.rate).clamp(min=0) | |
| def variance(self): | |
| return self.concentration / self.rate.pow(2) | |
| def __init__(self, concentration, rate, validate_args=None): | |
| self.concentration, self.rate = broadcast_all(concentration, rate) | |
| if isinstance(concentration, Number) and isinstance(rate, Number): | |
| batch_shape = torch.Size() | |
| else: | |
| batch_shape = self.concentration.size() | |
| super().__init__(batch_shape, validate_args=validate_args) | |
| def expand(self, batch_shape, _instance=None): | |
| new = self._get_checked_instance(Gamma, _instance) | |
| batch_shape = torch.Size(batch_shape) | |
| new.concentration = self.concentration.expand(batch_shape) | |
| new.rate = self.rate.expand(batch_shape) | |
| super(Gamma, new).__init__(batch_shape, validate_args=False) | |
| new._validate_args = self._validate_args | |
| return new | |
| def rsample(self, sample_shape=torch.Size()): | |
| shape = self._extended_shape(sample_shape) | |
| value = _standard_gamma(self.concentration.expand(shape)) / self.rate.expand( | |
| shape | |
| ) | |
| value.detach().clamp_( | |
| min=torch.finfo(value.dtype).tiny | |
| ) # do not record in autograd graph | |
| return value | |
| def log_prob(self, value): | |
| value = torch.as_tensor(value, dtype=self.rate.dtype, device=self.rate.device) | |
| if self._validate_args: | |
| self._validate_sample(value) | |
| return ( | |
| torch.xlogy(self.concentration, self.rate) | |
| + torch.xlogy(self.concentration - 1, value) | |
| - self.rate * value | |
| - torch.lgamma(self.concentration) | |
| ) | |
| def entropy(self): | |
| return ( | |
| self.concentration | |
| - torch.log(self.rate) | |
| + torch.lgamma(self.concentration) | |
| + (1.0 - self.concentration) * torch.digamma(self.concentration) | |
| ) | |
| def _natural_params(self): | |
| return (self.concentration - 1, -self.rate) | |
| def _log_normalizer(self, x, y): | |
| return torch.lgamma(x + 1) + (x + 1) * torch.log(-y.reciprocal()) | |
| def cdf(self, value): | |
| if self._validate_args: | |
| self._validate_sample(value) | |
| return torch.special.gammainc(self.concentration, self.rate * value) | |