






'''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_					(    UpperCamelCase_				):




      """simple docstring"""




      def __init__( self			:		Tuple     ,      UpperCAmelCase			:		Distribution     ,      UpperCAmelCase			:		Optional[Any]=None     ,      UpperCAmelCase			:		str=None     ,      UpperCAmelCase			:		Optional[Any]=0		)  ->  Union[str, Any]:


       '''simple docstring'''

       lowercase					:   Dict				  =1.0 if scale is None else scale
       lowercase					:   Optional[int]				  =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			:		Union[str, Any]		)  ->  Optional[Any]:


       '''simple docstring'''

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






      @property
      def 				A__      ( self			:		List[Any]		)  ->  str:


       '''simple docstring'''

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






      @property
      def 				A__      ( self			:		int		)  ->  Dict:


       '''simple docstring'''

       return self.variance.sqrt()





class UpperCAmelCase_					(    nn.Module				):




      """simple docstring"""




      def __init__( self			:		Optional[Any]     ,      UpperCAmelCase			:		int     ,      UpperCAmelCase			:		Dict[str, int]     ,      UpperCAmelCase			:		Callable[..., Tuple[torch.Tensor]]     ,      **UpperCAmelCase			:		int		)  ->  List[str]:


       '''simple docstring'''

       super().__init__(**UpperCamelCase__		)
       lowercase					:   Union[str, Any]				  =args_dim
       lowercase					:   List[Any]				  =nn.ModuleList([nn.Linear(UpperCamelCase__     ,      UpperCamelCase__		) for dim in args_dim.values()]		)
       lowercase					:   Dict				  =domain_map






      def 				A__      ( self			:		List[str]     ,      UpperCAmelCase			:		torch.Tensor		)  ->  List[Any]:


       '''simple docstring'''

       lowercase					:   Any				  =[proj(UpperCamelCase__		) for proj in self.proj]

       return self.domain_map(*UpperCamelCase__		)





class UpperCAmelCase_					(    nn.Module				):




      """simple docstring"""




      def __init__( self			:		str     ,      UpperCAmelCase			:		Tuple		)  ->  List[str]:


       '''simple docstring'''

       super().__init__()
       lowercase					:   Union[str, Any]				  =function






      def 				A__      ( self			:		List[str]     ,      UpperCAmelCase			:		Optional[Any]     ,      *UpperCAmelCase			:		List[Any]		)  ->  Any:


       '''simple docstring'''

       return self.function(UpperCamelCase__     ,      *UpperCamelCase__		)





class UpperCAmelCase_					:




      """simple docstring"""




      UpperCamelCase_								=			42
      UpperCamelCase_								=			42
      UpperCamelCase_								=			42






      def __init__( self			:		str     ,      UpperCAmelCase			:		int = 1		)  ->  Optional[Any]:


       '''simple docstring'''

       lowercase					:   Tuple				  =dim
       lowercase					:   List[str]				  ={k: dim * self.args_dim[k] for k in self.args_dim}






      def 				A__      ( self			:		Tuple     ,      UpperCAmelCase			:		Union[str, Any]		)  ->  Dict:


       '''simple docstring'''

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






      def 				A__      ( self			:		Any     ,      UpperCAmelCase			:		List[Any]     ,      UpperCAmelCase			:		Optional[torch.Tensor] = None     ,      UpperCAmelCase			:		Optional[torch.Tensor] = None     ,      )  ->  int:


       '''simple docstring'''

       lowercase					:   Union[str, Any]				  =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]		)  ->  int:


       '''simple docstring'''

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






      @property
      def 				A__      ( self			:		str		)  ->  List[Any]:


       '''simple docstring'''

       return len(self.event_shape		)






      @property
      def 				A__      ( self			:		int		)  ->  Optional[Any]:


       '''simple docstring'''

       return 0.0






      def 				A__      ( self			:		Union[str, Any]     ,      UpperCAmelCase			:		int		)  ->  Union[str, Any]:


       '''simple docstring'''

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






      def 				A__      ( self			:		List[str]     ,      *UpperCAmelCase			:		torch.Tensor		)  ->  Tuple:


       '''simple docstring'''

       raise NotImplementedError()






      @staticmethod
      def 				A__      ( UpperCAmelCase			:		torch.Tensor		)  ->  Optional[int]:


       '''simple docstring'''

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





class UpperCAmelCase_					(    UpperCamelCase_				):




      """simple docstring"""




      UpperCamelCase_								=			{'''df''': 1, '''loc''': 1, '''scale''': 1}
      UpperCamelCase_								=			StudentT






      @classmethod
      def 				A__      ( cls			:		Optional[Any]     ,      UpperCAmelCase			:		torch.Tensor     ,      UpperCAmelCase			:		torch.Tensor     ,      UpperCAmelCase			:		torch.Tensor		)  ->  List[str]:


       '''simple docstring'''

       lowercase					:   Optional[Any]				  =cls.squareplus(UpperCamelCase__		).clamp_min(torch.finfo(scale.dtype		).eps		)
       lowercase					:   Any				  =2.0 + cls.squareplus(UpperCamelCase__		)
       return df.squeeze(-1		), loc.squeeze(-1		), scale.squeeze(-1		)





class UpperCAmelCase_					(    UpperCamelCase_				):




      """simple docstring"""




      UpperCamelCase_								=			{'''loc''': 1, '''scale''': 1}
      UpperCamelCase_								=			Normal






      @classmethod
      def 				A__      ( cls			:		str     ,      UpperCAmelCase			:		torch.Tensor     ,      UpperCAmelCase			:		torch.Tensor		)  ->  List[Any]:


       '''simple docstring'''

       lowercase					:   int				  =cls.squareplus(UpperCamelCase__		).clamp_min(torch.finfo(scale.dtype		).eps		)
       return loc.squeeze(-1		), scale.squeeze(-1		)





class UpperCAmelCase_					(    UpperCamelCase_				):




      """simple docstring"""




      UpperCamelCase_								=			{'''total_count''': 1, '''logits''': 1}
      UpperCamelCase_								=			NegativeBinomial






      @classmethod
      def 				A__      ( cls			:		Optional[int]     ,      UpperCAmelCase			:		torch.Tensor     ,      UpperCAmelCase			:		torch.Tensor		)  ->  str:


       '''simple docstring'''

       lowercase					:   List[str]				  =cls.squareplus(UpperCamelCase__		)
       return total_count.squeeze(-1		), logits.squeeze(-1		)






      def 				A__      ( self			:		Dict     ,      UpperCAmelCase			:		List[Any]		)  ->  str:


       '''simple docstring'''

       lowercase					:   Tuple				  =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			:		Union[str, Any]     ,      UpperCAmelCase			:		Dict     ,      UpperCAmelCase			:		Optional[torch.Tensor] = None     ,      UpperCAmelCase			:		Optional[torch.Tensor] = None		)  ->  Tuple:


       '''simple docstring'''

       lowercase					:   str				  =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

SCREAMING_SNAKE_CASE						=	8.988E9  # units = N * m^s * C^-2


def 							lowercase_				(    __A :       float					,      __A :       float					,      __A :       float					,      __A :       float			)       ->      dict[str, float]:



 """simple docstring"""




 lowercase					:   Dict				  =abs(chargea * chargea			)

 if (force, chargea, chargea, distance).count(0			) != 1:
  raise ValueError('''One and only one argument must be 0'''			)
 if distance < 0:
  raise ValueError('''Distance cannot be negative'''			)
 if force == 0:
  lowercase					:   Union[str, Any]				  =COULOMBS_CONSTANT * charge_product / (distance**2)
  return {"force": force}
 elif chargea == 0:
  lowercase					:   int				  =abs(__A			) * (distance**2) / (COULOMBS_CONSTANT * chargea)
  return {"charge1": chargea}
 elif chargea == 0:
  lowercase					:   int				  =abs(__A			) * (distance**2) / (COULOMBS_CONSTANT * chargea)
  return {"charge2": chargea}
 elif distance == 0:
  lowercase					:   Tuple				  =(COULOMBS_CONSTANT * charge_product / abs(__A			)) ** 0.5
  return {"distance": distance}
 raise ValueError('''Exactly one argument must be 0'''			)


if __name__ == "__main__":
      import doctest

      doctest.testmod()



