




"""simple docstring"""




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



def 					a__				(       snake_case__       )		->      Optional[Any]:

			# A local function to see if a dot lands in the circle.
			def is_in_circle(snake_case__ ,				snake_case__       ) -> bool:
						lowerCamelCase       =      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       =      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.
			lowerCamelCase       =      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__				(       snake_case__ ,				snake_case__ ,				snake_case__ = 0.0 ,				snake_case__ = 1.0 ,				)		->      float:
			return mean(
			    function_to_integrate(uniform(snake_case__ ,				snake_case__       )       ) for _ in range(snake_case__       )       ) * (max_value - min_value)



def 					a__				(       snake_case__ ,				snake_case__ = 0.0 ,				snake_case__ = 1.0       )		->      None:

			def identity_function(snake_case__       ) -> float:
						return x

			lowerCamelCase       =      area_under_curve_estimator(
			    snake_case__ ,				snake_case__ ,				snake_case__ ,				snake_case__       )
			lowerCamelCase       =      (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__				(       snake_case__       )		->      None:

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

			lowerCamelCase       =      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 typing import TYPE_CHECKING

# rely on isort to merge the imports
from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


lowerCAmelCase							:    List[str]  							=							{
    """configuration_autoformer""": [
        """AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP""",
        """AutoformerConfig""",
    ],
}

try:
					if not is_torch_available():
										raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
					pass
else:
					lowerCAmelCase							:    Tuple  							=							[
					    """AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST""",
					    """AutoformerForPrediction""",
					    """AutoformerModel""",
					    """AutoformerPreTrainedModel""",
					]


if TYPE_CHECKING:
					from .configuration_autoformer import (
					    AUTOFORMER_PRETRAINED_CONFIG_ARCHIVE_MAP,
					    AutoformerConfig,
					)

					try:
										if not is_torch_available():
															raise OptionalDependencyNotAvailable()
					except OptionalDependencyNotAvailable:
										pass
					else:
										from .modeling_autoformer import (
										    AUTOFORMER_PRETRAINED_MODEL_ARCHIVE_LIST,
										    AutoformerForPrediction,
										    AutoformerModel,
										    AutoformerPreTrainedModel,
										)

else:
					import sys

					lowerCAmelCase							:    str  							=							_LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)



