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| from numbers import Number | |
| import torch | |
| from torch.distributions import constraints | |
| from torch.distributions.distribution import Distribution | |
| from torch.distributions.utils import broadcast_all | |
| __all__ = ["Laplace"] | |
| class Laplace(Distribution): | |
| r""" | |
| Creates a Laplace distribution parameterized by :attr:`loc` and :attr:`scale`. | |
| Example:: | |
| >>> # xdoctest: +IGNORE_WANT("non-deterministic") | |
| >>> m = Laplace(torch.tensor([0.0]), torch.tensor([1.0])) | |
| >>> m.sample() # Laplace distributed with loc=0, scale=1 | |
| tensor([ 0.1046]) | |
| Args: | |
| loc (float or Tensor): mean of the distribution | |
| scale (float or Tensor): scale of the distribution | |
| """ | |
| arg_constraints = {"loc": constraints.real, "scale": constraints.positive} | |
| support = constraints.real | |
| has_rsample = True | |
| def mean(self): | |
| return self.loc | |
| def mode(self): | |
| return self.loc | |
| def variance(self): | |
| return 2 * self.scale.pow(2) | |
| def stddev(self): | |
| return (2**0.5) * self.scale | |
| def __init__(self, loc, scale, validate_args=None): | |
| self.loc, self.scale = broadcast_all(loc, scale) | |
| if isinstance(loc, Number) and isinstance(scale, Number): | |
| batch_shape = torch.Size() | |
| else: | |
| batch_shape = self.loc.size() | |
| super().__init__(batch_shape, validate_args=validate_args) | |
| def expand(self, batch_shape, _instance=None): | |
| new = self._get_checked_instance(Laplace, _instance) | |
| batch_shape = torch.Size(batch_shape) | |
| new.loc = self.loc.expand(batch_shape) | |
| new.scale = self.scale.expand(batch_shape) | |
| super(Laplace, 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) | |
| finfo = torch.finfo(self.loc.dtype) | |
| if torch._C._get_tracing_state(): | |
| # [JIT WORKAROUND] lack of support for .uniform_() | |
| u = torch.rand(shape, dtype=self.loc.dtype, device=self.loc.device) * 2 - 1 | |
| return self.loc - self.scale * u.sign() * torch.log1p( | |
| -u.abs().clamp(min=finfo.tiny) | |
| ) | |
| u = self.loc.new(shape).uniform_(finfo.eps - 1, 1) | |
| # TODO: If we ever implement tensor.nextafter, below is what we want ideally. | |
| # u = self.loc.new(shape).uniform_(self.loc.nextafter(-.5, 0), .5) | |
| return self.loc - self.scale * u.sign() * torch.log1p(-u.abs()) | |
| def log_prob(self, value): | |
| if self._validate_args: | |
| self._validate_sample(value) | |
| return -torch.log(2 * self.scale) - torch.abs(value - self.loc) / self.scale | |
| def cdf(self, value): | |
| if self._validate_args: | |
| self._validate_sample(value) | |
| return 0.5 - 0.5 * (value - self.loc).sign() * torch.expm1( | |
| -(value - self.loc).abs() / self.scale | |
| ) | |
| def icdf(self, value): | |
| term = value - 0.5 | |
| return self.loc - self.scale * (term).sign() * torch.log1p(-2 * term.abs()) | |
| def entropy(self): | |
| return 1 + torch.log(2 * self.scale) | |