



"""simple docstring"""
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				(	snake_case__					):







 """simple docstring"""




 def __init__(				self					: Dict						, A_					: Optional[Any]						, A_					: Optional[Any]=None						, A_					: Tuple=None						, A_					: Union[str, Any]=0	)->	Union[str, Any]:
   __UpperCamelCase  						=							1.0 if scale is None else scale
   __UpperCamelCase  						=							0.0 if loc is None else loc

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





 @property
 def  A  (				self					: List[Any]	)->	int:
   return self.base_dist.mean * self.scale + self.loc





 @property
 def  A  (				self					: Union[str, Any]	)->	List[str]:
   return self.base_dist.variance * self.scale**2





 @property
 def  A  (				self					: List[str]	)->	int:
   return self.variance.sqrt()





class 		__UpperCAmelCase				(	nn.Module					):







 """simple docstring"""




 def __init__(				self					: List[Any]						, A_					: Any						, A_					: Optional[int]						, A_					: int						, **A_					: List[Any]	)->	None:
   super().__init__(**UpperCAmelCase_	)
   __UpperCamelCase  						=							args_dim
   __UpperCamelCase  						=							nn.ModuleList([nn.Linear(UpperCAmelCase_						, UpperCAmelCase_	) for dim in args_dim.values()]	)
   __UpperCamelCase  						=							domain_map





 def  A  (				self					: str						, A_					: int	)->	Tuple[torch.Tensor]:
   __UpperCamelCase  						=							[proj(UpperCAmelCase_	) for proj in self.proj]

   return self.domain_map(*UpperCAmelCase_	)





class 		__UpperCAmelCase				(	nn.Module					):







 """simple docstring"""




 def __init__(				self					: Any						, A_					: Tuple	)->	str:
   super().__init__()
   __UpperCamelCase  						=							function





 def  A  (				self					: Optional[int]						, A_					: str						, *A_					: Tuple	)->	Dict:
   return self.function(UpperCAmelCase_						, *UpperCAmelCase_	)





class 		__UpperCAmelCase				:







 """simple docstring"""




 _snake_case       :							type
 _snake_case       :							int
 _snake_case       :							Dict[str, int]





 def __init__(				self					: List[Any]						, A_					: int = 1	)->	None:
   __UpperCamelCase  						=							dim
   __UpperCamelCase  						=							{k: dim * self.args_dim[k] for k in self.args_dim}





 def  A  (				self					: Union[str, Any]						, A_					: int	)->	int:
   if self.dim == 1:
     return self.distribution_class(*UpperCAmelCase_	)
   else:
     return Independent(self.distribution_class(*UpperCAmelCase_	)						, 1	)





 def  A  (				self					: Optional[int]						, A_					: Optional[Any]						, A_					: Tuple = None						, A_					: Any = None						, )->	Distribution:
   __UpperCamelCase  						=							self._base_distribution(UpperCAmelCase_	)
   if loc is None and scale is None:
     return distr
   else:
     return AffineTransformed(UpperCAmelCase_						, loc=UpperCAmelCase_						, scale=UpperCAmelCase_						, event_dim=self.event_dim	)





 @property
 def  A  (				self					: Optional[int]	)->	Tuple:
   return () if self.dim == 1 else (self.dim,)





 @property
 def  A  (				self					: Optional[int]	)->	int:
   return len(self.event_shape	)





 @property
 def  A  (				self					: Dict	)->	float:
   return 0.0





 def  A  (				self					: str						, A_					: List[Any]	)->	nn.Module:
   return ParameterProjection(
       in_features=UpperCAmelCase_						, args_dim=self.args_dim						, domain_map=LambdaLayer(self.domain_map	)						, )





 def  A  (				self					: Tuple						, *A_					: Any	)->	int:
   raise NotImplementedError()





 @staticmethod
 def  A  (				A_					: Union[str, Any]	)->	torch.Tensor:
   return (x + torch.sqrt(torch.square(UpperCAmelCase_	) + 4.0	)) / 2.0





class 		__UpperCAmelCase				(	snake_case__					):







 """simple docstring"""




 _snake_case       :							Dict[str, int]      	=	{"df": 1, "loc": 1, "scale": 1}
 _snake_case       :							type      	=	StudentT





 @classmethod
 def  A  (				cls					: str						, A_					: Union[str, Any]						, A_					: Any						, A_					: int	)->	Union[str, Any]:
   __UpperCamelCase  						=							cls.squareplus(UpperCAmelCase_	).clamp_min(torch.finfo(scale.dtype	).eps	)
   __UpperCamelCase  						=							2.0 + cls.squareplus(UpperCAmelCase_	)
   return df.squeeze(-1	), loc.squeeze(-1	), scale.squeeze(-1	)





class 		__UpperCAmelCase				(	snake_case__					):







 """simple docstring"""




 _snake_case       :							Dict[str, int]      	=	{"loc": 1, "scale": 1}
 _snake_case       :							type      	=	Normal





 @classmethod
 def  A  (				cls					: List[Any]						, A_					: Tuple						, A_					: Tuple	)->	Union[str, Any]:
   __UpperCamelCase  						=							cls.squareplus(UpperCAmelCase_	).clamp_min(torch.finfo(scale.dtype	).eps	)
   return loc.squeeze(-1	), scale.squeeze(-1	)





class 		__UpperCAmelCase				(	snake_case__					):







 """simple docstring"""




 _snake_case       :							Dict[str, int]      	=	{"total_count": 1, "logits": 1}
 _snake_case       :							type      	=	NegativeBinomial





 @classmethod
 def  A  (				cls					: Optional[Any]						, A_					: Union[str, Any]						, A_					: Tuple	)->	List[Any]:
   __UpperCamelCase  						=							cls.squareplus(UpperCAmelCase_	)
   return total_count.squeeze(-1	), logits.squeeze(-1	)





 def  A  (				self					: Optional[Any]						, A_					: Optional[Any]	)->	Distribution:
   __UpperCamelCase						,   __UpperCamelCase  						=							distr_args
   if self.dim == 1:
     return self.distribution_class(total_count=UpperCAmelCase_						, logits=UpperCAmelCase_	)
   else:
     return Independent(self.distribution_class(total_count=UpperCAmelCase_						, logits=UpperCAmelCase_	)						, 1	)





 def  A  (				self					: Dict						, A_					: Optional[Any]						, A_					: List[Any] = None						, A_					: List[str] = None	)->	Distribution:
   __UpperCamelCase						,   __UpperCamelCase  						=							distr_args

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

   return self._base_distribution((total_count, logits)	)




'''simple docstring'''





from __future__ import annotations




def 							lowerCamelCase	(					_snake_case	:    list[int]							):





    '''simple docstring'''


    return len(set(_snake_case							)							) == len(_snake_case							)


if __name__ == "__main__":
 import doctest

 doctest.testmod()




