
"""simple docstring"""





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



def 				lowerCamelCase__		(      __snake_case     )							->		int:


					"""simple docstring"""





					def is_in_circle(__snake_case,					__snake_case     ) -> bool:
										_UpperCamelCase										=  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
					_UpperCamelCase										=  mean(
					    int(is_in_circle(uniform(-1.0,					1.0     ),					uniform(-1.0,					1.0     )     )     )
					    for _ in range(snake_case__     )     )
					# The ratio of the area for circle to square is pi/4.
					_UpperCamelCase										=  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__		(      __snake_case,					__snake_case,					__snake_case = 0.0,					__snake_case = 1.0,					)							->		float:


					"""simple docstring"""





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



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


					"""simple docstring"""





					def identity_function(__snake_case     ) -> float:
										return x

					_UpperCamelCase										=  area_under_curve_estimator(
					    snake_case__,					snake_case__,					snake_case__,					snake_case__     )
					_UpperCamelCase										=  (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__		(      __snake_case     )							->		None:


					"""simple docstring"""





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

					_UpperCamelCase										=  area_under_curve_estimator(
					    snake_case__,					snake_case__,					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()








"""simple docstring"""





from ...utils import is_torch_available, is_transformers_available


if is_transformers_available() and is_torch_available():
				from .pipeline_vq_diffusion import LearnedClassifierFreeSamplingEmbeddings, VQDiffusionPipeline






