



from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean






def 			lowerCAmelCase__	(					lowerCamelCase_	:	int):





    '''simple docstring'''

    def is_in_circle(lowerCamelCase_	:	float ,lowerCamelCase_	:	float) -> bool:
        lowerCAmelCase__  :       Any				=  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__  :       List[Any]				=  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__  :       int				=  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 			lowerCAmelCase__	(					lowerCamelCase_	:	int ,lowerCamelCase_	:	Callable[[float], float] ,lowerCamelCase_	:	float = 0.0 ,lowerCamelCase_	:	float = 1.0 ,):





    '''simple docstring'''

    return mean(
        function_to_integrate(uniform(lowerCamelCase_ ,lowerCamelCase_)) for _ in range(lowerCamelCase_)) * (max_value - min_value)






def 			lowerCAmelCase__	(					lowerCamelCase_	:	int ,lowerCamelCase_	:	float = 0.0 ,lowerCamelCase_	:	float = 1.0):





    '''simple docstring'''

    def identity_function(lowerCamelCase_	:	float) -> float:
        return x

    lowerCAmelCase__  :       Dict				=  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 			lowerCAmelCase__	(					lowerCamelCase_	:	int):





    '''simple docstring'''

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

    lowerCAmelCase__  :       Optional[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()






import copy

from ...configuration_utils import PretrainedConfig
from ...utils import logging


__snake_case       :	Any            =logging.get_logger(__name__)



class  lowerCamelCase__    (							lowerCamelCase__):




		'''simple docstring'''



		snake_case_			="""encoder-decoder"""
		snake_case_			=True



		def __init__(self	,**__lowerCamelCase				)  ->    Union[str, Any]:

						"""simple docstring"""






						super().__init__(**__lowerCamelCase				)
						assert (
						    "encoder" in kwargs and "decoder" in kwargs
						), "Config has to be initialized with encoder and decoder config"
						lowerCAmelCase__  :       Optional[Any]				=  kwargs.pop('''encoder'''				)
						lowerCAmelCase__  :       Any				=  encoder_config.pop('''model_type'''				)
						lowerCAmelCase__  :       str				=  kwargs.pop('''decoder'''				)
						lowerCAmelCase__  :       Tuple				=  decoder_config.pop('''model_type'''				)

						from ..auto.configuration_auto import AutoConfig

						lowerCAmelCase__  :       Tuple				=  AutoConfig.for_model(__lowerCamelCase	,**__lowerCamelCase				)
						lowerCAmelCase__  :       Any				=  AutoConfig.for_model(__lowerCamelCase	,**__lowerCamelCase				)
						lowerCAmelCase__  :       str				=  True



		@classmethod
		def 	lowerCAmelCase__   (cls	,__lowerCamelCase	,__lowerCamelCase	,**__lowerCamelCase				)  ->    PretrainedConfig:

						"""simple docstring"""






						logger.info('''Set `config.is_decoder=True` and `config.add_cross_attention=True` for decoder_config'''				)
						lowerCAmelCase__  :       Optional[int]				=  True
						lowerCAmelCase__  :       List[str]				=  True

						return cls(encoder=encoder_config.to_dict()	,decoder=decoder_config.to_dict()	,**__lowerCamelCase				)



		def 	lowerCAmelCase__   (self				)  ->    Tuple:

						"""simple docstring"""






						lowerCAmelCase__  :       int				=  copy.deepcopy(self.__dict__				)
						lowerCAmelCase__  :       Optional[Any]				=  self.encoder.to_dict()
						lowerCAmelCase__  :       str				=  self.decoder.to_dict()
						lowerCAmelCase__  :       Optional[int]				=  self.__class__.model_type
						return output

