





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        snake_case_		(			_A):







		def __init__(		self			,     __lowercase			,     __lowercase=None			,     __lowercase=None			,     __lowercase=0   )				->   List[Any]:
				lowerCamelCase   : int								=1.0 if scale is None else scale
				lowerCamelCase   : int								=0.0 if loc is None else loc

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







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







		@property
		def 			__lowercase   (		self   )				->   str:
				return self.base_dist.variance * self.scale**2







		@property
		def 			__lowercase   (		self   )				->   Optional[int]:
				return self.variance.sqrt()

class        snake_case_		(			nn.Module):







		def __init__(		self			,     __lowercase			,     __lowercase			,     __lowercase			,     **__lowercase   )				->   None:
				super().__init__(**__lowercase   )
				lowerCamelCase   : Tuple								=args_dim
				lowerCamelCase   : int								=nn.ModuleList([nn.Linear(__lowercase			,     __lowercase   ) for dim in args_dim.values()]   )
				lowerCamelCase   : str								=domain_map







		def 			__lowercase   (		self			,     __lowercase   )				->   Tuple[torch.Tensor]:
				lowerCamelCase   : List[str]								=[proj(__lowercase   ) for proj in self.proj]

				return self.domain_map(*__lowercase   )

class        snake_case_		(			nn.Module):







		def __init__(		self			,     __lowercase   )				->   int:
				super().__init__()
				lowerCamelCase   : List[str]								=function







		def 			__lowercase   (		self			,     __lowercase			,     *__lowercase   )				->   List[str]:
				return self.function(__lowercase			,     *__lowercase   )

class        snake_case_		:
		lowerCamelCase    :type
		lowerCamelCase    :int
		lowerCamelCase    :Dict[str, int]







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







		def 			__lowercase   (		self			,     __lowercase   )				->   Optional[Any]:
				if self.dim == 1:
						return self.distribution_class(*__lowercase   )
				else:
						return Independent(self.distribution_class(*__lowercase   )			,     1   )







		def 			__lowercase   (		self			,     __lowercase			,     __lowercase = None			,     __lowercase = None			,     )				->   Distribution:
				lowerCamelCase   : Tuple								=self._base_distribution(__lowercase   )
				if loc is None and scale is None:
						return distr
				else:
						return AffineTransformed(__lowercase			,     loc=__lowercase			,     scale=__lowercase			,     event_dim=self.event_dim   )







		@property
		def 			__lowercase   (		self   )				->   Tuple:
				return () if self.dim == 1 else (self.dim,)







		@property
		def 			__lowercase   (		self   )				->   int:
				return len(self.event_shape   )







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







		def 			__lowercase   (		self			,     __lowercase   )				->   nn.Module:
				return ParameterProjection(
				    in_features=__lowercase			,     args_dim=self.args_dim			,     domain_map=LambdaLayer(self.domain_map   )			,     )







		def 			__lowercase   (		self			,     *__lowercase   )				->   Optional[Any]:
				raise NotImplementedError()







		@staticmethod
		def 			__lowercase   (		__lowercase   )				->   torch.Tensor:
				return (x + torch.sqrt(torch.square(__lowercase   ) + 4.0   )) / 2.0

class        snake_case_		(			_A):
		lowerCamelCase    :Dict[str, int]						=     {"df": 1, "loc": 1, "scale": 1}
		lowerCamelCase    :type						=     StudentT







		@classmethod
		def 			__lowercase   (		cls			,     __lowercase			,     __lowercase			,     __lowercase   )				->   Dict:
				lowerCamelCase   : Tuple								=cls.squareplus(__lowercase   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
				lowerCamelCase   : List[Any]								=2.0 + cls.squareplus(__lowercase   )
				return df.squeeze(-1   ), loc.squeeze(-1   ), scale.squeeze(-1   )

class        snake_case_		(			_A):
		lowerCamelCase    :Dict[str, int]						=     {"loc": 1, "scale": 1}
		lowerCamelCase    :type						=     Normal







		@classmethod
		def 			__lowercase   (		cls			,     __lowercase			,     __lowercase   )				->   Optional[int]:
				lowerCamelCase   : List[Any]								=cls.squareplus(__lowercase   ).clamp_min(torch.finfo(scale.dtype   ).eps   )
				return loc.squeeze(-1   ), scale.squeeze(-1   )

class        snake_case_		(			_A):
		lowerCamelCase    :Dict[str, int]						=     {"total_count": 1, "logits": 1}
		lowerCamelCase    :type						=     NegativeBinomial







		@classmethod
		def 			__lowercase   (		cls			,     __lowercase			,     __lowercase   )				->   str:
				lowerCamelCase   : Dict								=cls.squareplus(__lowercase   )
				return total_count.squeeze(-1   ), logits.squeeze(-1   )







		def 			__lowercase   (		self			,     __lowercase   )				->   Distribution:
				lowerCamelCase   : Any								=distr_args
				if self.dim == 1:
						return self.distribution_class(total_count=__lowercase			,     logits=__lowercase   )
				else:
						return Independent(self.distribution_class(total_count=__lowercase			,     logits=__lowercase   )			,     1   )







		def 			__lowercase   (		self			,     __lowercase			,     __lowercase = None			,     __lowercase = None   )				->   Distribution:
				lowerCamelCase   : List[Any]								=distr_args

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

				return self._base_distribution((total_count, logits)   )








from __future__ import annotations


def 					A__	(       SCREAMING_SNAKE_CASE_		)   ->     bool:
		if len(SCREAMING_SNAKE_CASE_		) < 2:
				raise ValueError('''Monogons and Digons are not polygons in the Euclidean space'''		)
		if any(i <= 0 for i in nums		):
				raise ValueError('''All values must be greater than 0'''		)
		lowerCamelCase   : List[Any]								=nums.copy()
		copy_nums.sort()
		return copy_nums[-1] < sum(copy_nums[:-1]		)


if __name__ == "__main__":
				import doctest

				doctest.testmod()

