



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

def        __a			(   __lowerCAmelCase   )     ->     int:

					# A local function to see if a dot lands in the circle.
					def is_in_circle(__lowerCAmelCase      ,	__lowerCAmelCase   ) -> bool:
										SCREAMING_SNAKE_CASE							:     int						=				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
					SCREAMING_SNAKE_CASE							:     Tuple						=				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.
					SCREAMING_SNAKE_CASE							:     List[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        __a			(   __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        __a			(   __lowerCAmelCase      ,	__lowerCAmelCase = 0.0      ,	__lowerCAmelCase = 1.0   )     ->     None:

					def identity_function(__lowerCAmelCase   ) -> float:
										return x

					SCREAMING_SNAKE_CASE							:     str						=				area_under_curve_estimator(
					    __lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase      ,	__lowerCAmelCase   )
					SCREAMING_SNAKE_CASE							:     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        __a			(   __lowerCAmelCase   )     ->     None:

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

					SCREAMING_SNAKE_CASE							:     int						=				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()




from datetime import datetime

import matplotlib.pyplot as plt
import torch

def        __a			(   __lowerCAmelCase   )     ->     int:
					for param in module.parameters():
										SCREAMING_SNAKE_CASE							:     List[Any]						=				False

def        __a			(   )     ->     List[str]:
					SCREAMING_SNAKE_CASE							:     List[Any]						=				'cuda' if torch.cuda.is_available() else 'cpu'
					if torch.backends.mps.is_available() and torch.backends.mps.is_built():
										SCREAMING_SNAKE_CASE							:     List[str]						=				'mps'
					if device == "mps":
										print(
										    'WARNING: MPS currently doesn\'t seem to work, and messes up backpropagation without any visible torch'
										    ' errors. I recommend using CUDA on a colab notebook or CPU instead if you\'re facing inexplicable issues'
										    ' with generations.'   )
					return device

def        __a			(   __lowerCAmelCase   )     ->     List[Any]:
					SCREAMING_SNAKE_CASE							:     Optional[int]						=				plt.imshow(__lowerCAmelCase   )
					fig.axes.get_xaxis().set_visible(__lowerCAmelCase   )
					fig.axes.get_yaxis().set_visible(__lowerCAmelCase   )
					plt.show()



def        __a			(   )     ->     Optional[Any]:
					SCREAMING_SNAKE_CASE							:     str						=				datetime.now()
					SCREAMING_SNAKE_CASE							:     Optional[int]						=				current_time.strftime('%H:%M:%S'   )
					return timestamp