
"""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 				A__ (			UpperCamelCase_):

		def __init__(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE=None ,	_SCREAMING_SNAKE_CASE=None ,	_SCREAMING_SNAKE_CASE=0				):
			__lowerCAmelCase    :		Dict		    =   1.0 if scale is None else scale
			__lowerCAmelCase    :		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 							__lowerCamelCase							(   self				):
			return self.base_dist.mean * self.scale + self.loc

		@property
		def 							__lowerCamelCase							(   self				):
			return self.base_dist.variance * self.scale**2







		@property
		def 							__lowerCamelCase							(   self				):
			return self.variance.sqrt()




class 				A__ (			nn.Module):

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







		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		Any		    =   [proj(UpperCamelCase__				) for proj in self.proj]

			return self.domain_map(*UpperCamelCase__				)




class 				A__ (			nn.Module):

		def __init__(   self ,	_SCREAMING_SNAKE_CASE				):
			super().__init__()
			__lowerCAmelCase    :		Union[str, Any]		    =   function







		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	*_SCREAMING_SNAKE_CASE				):
			return self.function(UpperCamelCase__ ,	*UpperCamelCase__				)




class 				A__ :
		A_		: Any            =			4_2
		A_		: str            =			4_2
		A_		: List[str]            =			4_2

		def __init__(   self ,	_SCREAMING_SNAKE_CASE = 1				):
			__lowerCAmelCase    :		Tuple		    =   dim
			__lowerCAmelCase    :		List[str]		    =   {k: dim * self.args_dim[k] for k in self.args_dim}

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):





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

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = None ,	):
			__lowerCAmelCase    :		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 							__lowerCamelCase							(   self				):
			return () if self.dim == 1 else (self.dim,)

		@property
		def 							__lowerCamelCase							(   self				):
			return len(self.event_shape				)

		@property
		def 							__lowerCamelCase							(   self				):
			return 0.0

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
			return ParameterProjection(
			    in_features=UpperCamelCase__ ,	args_dim=self.args_dim ,	domain_map=LambdaLayer(self.domain_map				) ,	)

		def 							__lowerCamelCase							(   self ,	*_SCREAMING_SNAKE_CASE				):
			raise NotImplementedError()







		@staticmethod
		def 							__lowerCamelCase							(   _SCREAMING_SNAKE_CASE				):
			return (x + torch.sqrt(torch.square(UpperCamelCase__				) + 4.0				)) / 2.0




class 				A__ (			UpperCamelCase_):
		A_		: Optional[int]            =			{'df': 1, 'loc': 1, 'scale': 1}
		A_		: Union[str, Any]            =			StudentT

		@classmethod
		def 							__lowerCamelCase							(   cls ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		Optional[Any]		    =   cls.squareplus(UpperCamelCase__				).clamp_min(torch.finfo(scale.dtype				).eps				)
			__lowerCAmelCase    :		Any		    =   2.0 + cls.squareplus(UpperCamelCase__				)
			return df.squeeze(-1				), loc.squeeze(-1				), scale.squeeze(-1				)




class 				A__ (			UpperCamelCase_):
		A_		: List[str]            =			{'loc': 1, 'scale': 1}
		A_		: List[Any]            =			Normal

		@classmethod
		def 							__lowerCamelCase							(   cls ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		int		    =   cls.squareplus(UpperCamelCase__				).clamp_min(torch.finfo(scale.dtype				).eps				)
			return loc.squeeze(-1				), scale.squeeze(-1				)




class 				A__ (			UpperCamelCase_):
		A_		: Dict            =			{'total_count': 1, 'logits': 1}
		A_		: List[str]            =			NegativeBinomial

		@classmethod
		def 							__lowerCamelCase							(   cls ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		List[str]		    =   cls.squareplus(UpperCamelCase__				)
			return total_count.squeeze(-1				), logits.squeeze(-1				)

		def 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE				):
			__lowerCAmelCase    :		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 							__lowerCamelCase							(   self ,	_SCREAMING_SNAKE_CASE ,	_SCREAMING_SNAKE_CASE = None ,	_SCREAMING_SNAKE_CASE = None				):
			__lowerCAmelCase    :		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"""







def 					__lowerCAmelCase       (_UpperCamelCase ,						_UpperCamelCase	):

	if density <= 0:
		raise ValueError('Impossible fluid density'	)
	if bulk_modulus <= 0:
		raise ValueError('Impossible bulk modulus'	)

	return (bulk_modulus / density) ** 0.5


if __name__ == "__main__":
							import doctest

							doctest.testmod()