

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_		(	SCREAMING_SNAKE_CASE    ):
       def __init__(		self		:      Optional[Any]       ,SCREAMING_SNAKE_CASE__		:      Distribution       ,SCREAMING_SNAKE_CASE__		:      Dict=None       ,SCREAMING_SNAKE_CASE__		:      Union[str, Any]=None       ,SCREAMING_SNAKE_CASE__		:      List[Any]=0):
        __lowerCamelCase    :    Optional[Any] 	=			1.0 if scale is None else scale
        __lowerCamelCase    :    int 	=			0.0 if loc is None else loc

        super().__init__(SCREAMING_SNAKE_CASE__       ,[AffineTransform(loc=self.loc       ,scale=self.scale       ,event_dim=SCREAMING_SNAKE_CASE__)])
       @property
       def    lowerCAmelCase					(		self		:      Any):
        return self.base_dist.mean * self.scale + self.loc
       @property
       def    lowerCAmelCase					(		self		:      List[str]):
        return self.base_dist.variance * self.scale**2


       @property
       def    lowerCAmelCase					(		self		:      Any):
        return self.variance.sqrt()






class 	A_		(	nn.Module    ):
       def __init__(		self		:      Optional[Any]       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      Dict[str, int]       ,SCREAMING_SNAKE_CASE__		:      Callable[..., Tuple[torch.Tensor]]       ,**SCREAMING_SNAKE_CASE__		:      Any):
        super().__init__(**SCREAMING_SNAKE_CASE__)
        __lowerCamelCase    :    List[str] 	=			args_dim
        __lowerCamelCase    :    str 	=			nn.ModuleList([nn.Linear(SCREAMING_SNAKE_CASE__       ,SCREAMING_SNAKE_CASE__) for dim in args_dim.values()])
        __lowerCamelCase    :    str 	=			domain_map


       def    lowerCAmelCase					(		self		:      Tuple       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        __lowerCamelCase    :    Any 	=			[proj(SCREAMING_SNAKE_CASE__) for proj in self.proj]

        return self.domain_map(*SCREAMING_SNAKE_CASE__)






class 	A_		(	nn.Module    ):
       def __init__(		self		:      Optional[int]       ,SCREAMING_SNAKE_CASE__		:      Optional[Any]):
        super().__init__()
        __lowerCamelCase    :    Optional[int] 	=			function


       def    lowerCAmelCase					(		self		:      Dict       ,SCREAMING_SNAKE_CASE__		:      Optional[int]       ,*SCREAMING_SNAKE_CASE__		:      Any):
        return self.function(SCREAMING_SNAKE_CASE__       ,*SCREAMING_SNAKE_CASE__)






class 	A_		:
       _UpperCAmelCase   :  type
       _UpperCAmelCase   :  int
       _UpperCAmelCase   :  Dict[str, int]
       def __init__(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int = 1):
        __lowerCamelCase    :    Tuple 	=			dim
        __lowerCamelCase    :    Any 	=			{k: dim * self.args_dim[k] for k in self.args_dim}
       def    lowerCAmelCase					(		self		:      str       ,SCREAMING_SNAKE_CASE__		:      List[str]):
        if self.dim == 1:
         return self.distribution_class(*SCREAMING_SNAKE_CASE__)
        else:
         return Independent(self.distribution_class(*SCREAMING_SNAKE_CASE__)       ,1)
       def    lowerCAmelCase					(		self		:      Dict       ,SCREAMING_SNAKE_CASE__		:      List[str]       ,SCREAMING_SNAKE_CASE__		:      Optional[torch.Tensor] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[torch.Tensor] = None       ,):
        __lowerCamelCase    :    str 	=			self._base_distribution(SCREAMING_SNAKE_CASE__)
        if loc is None and scale is None:
         return distr
        else:
         return AffineTransformed(SCREAMING_SNAKE_CASE__       ,loc=SCREAMING_SNAKE_CASE__       ,scale=SCREAMING_SNAKE_CASE__       ,event_dim=self.event_dim)
       @property
       def    lowerCAmelCase					(		self		:      Union[str, Any]):
        return () if self.dim == 1 else (self.dim,)
       @property
       def    lowerCAmelCase					(		self		:      Tuple):
        return len(self.event_shape)
       @property
       def    lowerCAmelCase					(		self		:      Optional[int]):
        return 0.0
       def    lowerCAmelCase					(		self		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      int):
        return ParameterProjection(
            in_features=SCREAMING_SNAKE_CASE__       ,args_dim=self.args_dim       ,domain_map=LambdaLayer(self.domain_map)       ,)
       def    lowerCAmelCase					(		self		:      Any       ,*SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        raise NotImplementedError()


       @staticmethod
       def    lowerCAmelCase					(		SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        return (x + torch.sqrt(torch.square(SCREAMING_SNAKE_CASE__) + 4.0)) / 2.0






class 	A_		(	SCREAMING_SNAKE_CASE    ):
       _UpperCAmelCase   :  Dict[str, int]										=				{"df": 1, "loc": 1, "scale": 1}
       _UpperCAmelCase   :  type										=				StudentT
       @classmethod
       def    lowerCAmelCase					(		cls		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        __lowerCamelCase    :    Union[str, Any] 	=			cls.squareplus(SCREAMING_SNAKE_CASE__).clamp_min(torch.finfo(scale.dtype).eps)
        __lowerCamelCase    :    str 	=			2.0 + cls.squareplus(SCREAMING_SNAKE_CASE__)
        return df.squeeze(-1), loc.squeeze(-1), scale.squeeze(-1)






class 	A_		(	SCREAMING_SNAKE_CASE    ):
       _UpperCAmelCase   :  Dict[str, int]										=				{"loc": 1, "scale": 1}
       _UpperCAmelCase   :  type										=				Normal
       @classmethod
       def    lowerCAmelCase					(		cls		:      List[Any]       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        __lowerCamelCase    :    int 	=			cls.squareplus(SCREAMING_SNAKE_CASE__).clamp_min(torch.finfo(scale.dtype).eps)
        return loc.squeeze(-1), scale.squeeze(-1)






class 	A_		(	SCREAMING_SNAKE_CASE    ):
       _UpperCAmelCase   :  Dict[str, int]										=				{"total_count": 1, "logits": 1}
       _UpperCAmelCase   :  type										=				NegativeBinomial
       @classmethod
       def    lowerCAmelCase					(		cls		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor       ,SCREAMING_SNAKE_CASE__		:      torch.Tensor):
        __lowerCamelCase    :    Tuple 	=			cls.squareplus(SCREAMING_SNAKE_CASE__)
        return total_count.squeeze(-1), logits.squeeze(-1)
       def    lowerCAmelCase					(		self		:      Union[str, Any]       ,SCREAMING_SNAKE_CASE__		:      str):
        __lowerCamelCase    :    List[Any] 	=			distr_args
        if self.dim == 1:
         return self.distribution_class(total_count=SCREAMING_SNAKE_CASE__       ,logits=SCREAMING_SNAKE_CASE__)
        else:
         return Independent(self.distribution_class(total_count=SCREAMING_SNAKE_CASE__       ,logits=SCREAMING_SNAKE_CASE__)       ,1)


       def    lowerCAmelCase					(		self		:      int       ,SCREAMING_SNAKE_CASE__		:      int       ,SCREAMING_SNAKE_CASE__		:      Optional[torch.Tensor] = None       ,SCREAMING_SNAKE_CASE__		:      Optional[torch.Tensor] = None):
        __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 collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					List[Any]:

	# A local function to see if a dot lands in the circle.
	def is_in_circle(lowerCamelCase__     ,			lowerCamelCase__      ) -> bool:
		__lowerCamelCase    :    Dict 	=			sqrt((x**2) + (y**2)      )
		# Our circle has a radius of 1, so a distance
		# greater than 1 would land outside the circle.
		return distance_from_centre <= 1

	# The proportion of guesses that landed in the circle
	__lowerCamelCase    :    Optional[int] 	=			mean(
	    int(is_in_circle(uniform(-1.0     ,			1.0      )     ,			uniform(-1.0     ,			1.0      )      )      )
	    for _ in range(lowerCamelCase__      )      )
	# The ratio of the area for circle to square is pi/4.
	__lowerCamelCase    :    Any 	=			proportion * 4
	print(F"The estimated value of pi is {pi_estimate}"      )
	print(F"The numpy value of pi is {pi}"      )
	print(F"The total error is {abs(pi - pi_estimate      )}"      )






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0     ,			)  ->					float:
	return mean(
	    function_to_integrate(uniform(lowerCamelCase__     ,			lowerCamelCase__      )      ) for _ in range(lowerCamelCase__      )      ) * (max_value - min_value)






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__     ,			lowerCamelCase__ = 0.0     ,			lowerCamelCase__ = 1.0      )  ->					None:

	def identity_function(lowerCamelCase__      ) -> float:
		return x

	__lowerCamelCase    :    str 	=			area_under_curve_estimator(
	    lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__     ,			lowerCamelCase__      )
	__lowerCamelCase    :    int 	=			(max_value * max_value - min_value * min_value) / 2

	print('******************'      )
	print(F"Estimating area under y=x where x varies from {min_value} to {max_value}"      )
	print(F"Estimated value is {estimated_value}"      )
	print(F"Expected value is {expected_value}"      )
	print(F"Total error is {abs(estimated_value - expected_value      )}"      )
	print('******************'      )






def        SCREAMING_SNAKE_CASE__	(  lowerCamelCase__      )  ->					None:

	def function_to_integrate(lowerCamelCase__      ) -> float:
		return sqrt(4.0 - x * x      )

	__lowerCamelCase    :    Any 	=			area_under_curve_estimator(
	    lowerCamelCase__     ,			lowerCamelCase__     ,			0.0     ,			2.0      )

	print('******************'      )
	print('Estimating pi using area_under_curve_estimator'      )
	print(F"Estimated value is {estimated_value}"      )
	print(F"Expected value is {pi}"      )
	print(F"Total error is {abs(estimated_value - pi      )}"      )
	print('******************'      )


if __name__ == "__main__":
					import doctest

					doctest.testmod()




