





from typing import Callable, Dict, Optional, Tuple

import torch
from torch import nn
from torch.distributions import (
    AffineTransform,
    Distribution,
    Independent,
    NegativeBinomial,
    Normal,
    StudentT,
    TransformedDistribution,
)





class UpperCAmelCase_				( _SCREAMING_SNAKE_CASE ):


  def __init__(							self ,__snake_case ,__snake_case=None ,__snake_case=None ,__snake_case=0 ):



       """simple docstring"""





       A_          =       1.0 if scale is None else scale
       A_          =       0.0 if loc is None else loc

       super().__init__(__snake_case ,[AffineTransform(loc=self.loc ,scale=self.scale ,event_dim=__snake_case )] )


  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return self.base_dist.mean * self.scale + self.loc


  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return self.base_dist.variance * self.scale**2




  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return self.variance.sqrt()





class UpperCAmelCase_				( nn.Module ):


  def __init__(							self ,__snake_case ,__snake_case ,__snake_case ,**__snake_case ):



       """simple docstring"""





       super().__init__(**__snake_case )
       A_          =       args_dim
       A_          =       nn.ModuleList([nn.Linear(__snake_case ,__snake_case ) for dim in args_dim.values()] )
       A_          =       domain_map




  def 						__UpperCAmelCase     (							self ,__snake_case ):



       """simple docstring"""





       A_          =       [proj(__snake_case ) for proj in self.proj]

       return self.domain_map(*__snake_case )





class UpperCAmelCase_				( nn.Module ):


  def __init__(							self ,__snake_case ):



       """simple docstring"""





       super().__init__()
       A_          =       function




  def 						__UpperCAmelCase     (							self ,__snake_case ,*__snake_case ):



       """simple docstring"""





       return self.function(__snake_case ,*__snake_case )





class UpperCAmelCase_				:
  __lowerCAmelCase   :						type
  __lowerCAmelCase   :						int
  __lowerCAmelCase   :						Dict[str, int]


  def __init__(							self ,__snake_case = 1 ):



       """simple docstring"""





       A_          =       dim
       A_          =       {k: dim * self.args_dim[k] for k in self.args_dim}


  def 						__UpperCAmelCase     (							self ,__snake_case ):



       """simple docstring"""





       if self.dim == 1:
            return self.distribution_class(*__snake_case )
       else:
            return Independent(self.distribution_class(*__snake_case ) ,1 )


  def 						__UpperCAmelCase     (							self ,__snake_case ,__snake_case = None ,__snake_case = None ,):



       """simple docstring"""





       A_          =       self._base_distribution(__snake_case )
       if loc is None and scale is None:
            return distr
       else:
            return AffineTransformed(__snake_case ,loc=__snake_case ,scale=__snake_case ,event_dim=self.event_dim )


  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return () if self.dim == 1 else (self.dim,)


  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return len(self.event_shape )


  @property
  def 						__UpperCAmelCase     (							self ):



       """simple docstring"""





       return 0.0


  def 						__UpperCAmelCase     (							self ,__snake_case ):



       """simple docstring"""





       return ParameterProjection(
           in_features=__snake_case ,args_dim=self.args_dim ,domain_map=LambdaLayer(self.domain_map ) ,)


  def 						__UpperCAmelCase     (							self ,*__snake_case ):



       """simple docstring"""





       raise NotImplementedError()




  @staticmethod
  def 						__UpperCAmelCase     (							__snake_case ):



       """simple docstring"""





       return (x + torch.sqrt(torch.square(__snake_case ) + 4.0 )) / 2.0





class UpperCAmelCase_				( _SCREAMING_SNAKE_CASE ):
  __lowerCAmelCase   :						Dict[str, int]							=   {"df": 1, "loc": 1, "scale": 1}
  __lowerCAmelCase   :						type							=   StudentT


  @classmethod
  def 						__UpperCAmelCase     (							cls ,__snake_case ,__snake_case ,__snake_case ):



       """simple docstring"""





       A_          =       cls.squareplus(__snake_case ).clamp_min(torch.finfo(scale.dtype ).eps )
       A_          =       2.0 + cls.squareplus(__snake_case )
       return df.squeeze(-1 ), loc.squeeze(-1 ), scale.squeeze(-1 )





class UpperCAmelCase_				( _SCREAMING_SNAKE_CASE ):
  __lowerCAmelCase   :						Dict[str, int]							=   {"loc": 1, "scale": 1}
  __lowerCAmelCase   :						type							=   Normal


  @classmethod
  def 						__UpperCAmelCase     (							cls ,__snake_case ,__snake_case ):



       """simple docstring"""





       A_          =       cls.squareplus(__snake_case ).clamp_min(torch.finfo(scale.dtype ).eps )
       return loc.squeeze(-1 ), scale.squeeze(-1 )





class UpperCAmelCase_				( _SCREAMING_SNAKE_CASE ):
  __lowerCAmelCase   :						Dict[str, int]							=   {"total_count": 1, "logits": 1}
  __lowerCAmelCase   :						type							=   NegativeBinomial


  @classmethod
  def 						__UpperCAmelCase     (							cls ,__snake_case ,__snake_case ):



       """simple docstring"""





       A_          =       cls.squareplus(__snake_case )
       return total_count.squeeze(-1 ), logits.squeeze(-1 )


  def 						__UpperCAmelCase     (							self ,__snake_case ):



       """simple docstring"""





       A_   ,    A_          =       distr_args
       if self.dim == 1:
            return self.distribution_class(total_count=__snake_case ,logits=__snake_case )
       else:
            return Independent(self.distribution_class(total_count=__snake_case ,logits=__snake_case ) ,1 )




  def 						__UpperCAmelCase     (							self ,__snake_case ,__snake_case = None ,__snake_case = None ):



       """simple docstring"""





       A_   ,    A_          =       distr_args

       if scale is not None:
            # See scaling property of Gamma.
            logits += scale.log()

       return self._base_distribution((total_count, logits) )










def      UpperCAmelCase_    (    _UpperCAmelCase							:Any  ,						_UpperCAmelCase							:Dict				)	->				Union[str, Any]:
     '''simple docstring'''


     A_          =       [1]
     for i in range(2  ,						_UpperCAmelCase				):
          factorials.append(factorials[-1] * i				)
     assert 0 <= k < factorials[-1] * n, "k out of bounds"

     A_          =       []
     A_          =       list(range(_UpperCAmelCase				)				)

     # Find permutation
     while factorials:
          A_          =       factorials.pop()
          A_   ,    A_          =       divmod(_UpperCAmelCase  ,						_UpperCAmelCase				)
          permutation.append(elements[number]				)
          elements.remove(elements[number]				)
     permutation.append(elements[0]				)

     return permutation


if __name__ == "__main__":
      import doctest

      doctest.testmod()



