



'''simple docstring'''





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





def   a_   (		_UpperCAmelCase    :      int				)    ->  Tuple:

      # A local function to see if a dot lands in the circle.
      def is_in_circle(_UpperCAmelCase    :      float ,_UpperCAmelCase    :      float				) -> bool:
            __snake_case :   List[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
      __snake_case :   int													=    mean(
          int(is_in_circle(uniform(-1.0 ,1.0				) ,uniform(-1.0 ,1.0				)				)				)
          for _ in range(_UpperCAmelCase				)				)
      # The ratio of the area for circle to square is pi/4.
      __snake_case :   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_   (		_UpperCAmelCase    :      int ,_UpperCAmelCase    :      Callable[[float], float] ,_UpperCAmelCase    :      float = 0.0 ,_UpperCAmelCase    :      float = 1.0 ,)    ->  float:
      return mean(
          function_to_integrate(uniform(_UpperCAmelCase ,_UpperCAmelCase				)				) for _ in range(_UpperCAmelCase				)				) * (max_value - min_value)





def   a_   (		_UpperCAmelCase    :      int ,_UpperCAmelCase    :      float = 0.0 ,_UpperCAmelCase    :      float = 1.0				)    ->  None:

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

      __snake_case :   str													=    area_under_curve_estimator(
          _UpperCAmelCase ,_UpperCAmelCase ,_UpperCAmelCase ,_UpperCAmelCase				)
      __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_   (		_UpperCAmelCase    :      int				)    ->  None:

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

      __snake_case :   Tuple													=    area_under_curve_estimator(
          _UpperCAmelCase ,_UpperCAmelCase ,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

from ...utils import OptionalDependencyNotAvailable, _LazyModule, is_torch_available


A__    :   List[Any]           =					{
    '''configuration_luke''': ['''LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP''', '''LukeConfig'''],
    '''tokenization_luke''': ['''LukeTokenizer'''],
}

try:
    if not is_torch_available():
        raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
    pass
else:
    A__    :   Union[str, Any]           =					[
        '''LUKE_PRETRAINED_MODEL_ARCHIVE_LIST''',
        '''LukeForEntityClassification''',
        '''LukeForEntityPairClassification''',
        '''LukeForEntitySpanClassification''',
        '''LukeForMultipleChoice''',
        '''LukeForQuestionAnswering''',
        '''LukeForSequenceClassification''',
        '''LukeForTokenClassification''',
        '''LukeForMaskedLM''',
        '''LukeModel''',
        '''LukePreTrainedModel''',
    ]


if TYPE_CHECKING:
    from .configuration_luke import LUKE_PRETRAINED_CONFIG_ARCHIVE_MAP, LukeConfig
    from .tokenization_luke import LukeTokenizer

    try:
        if not is_torch_available():
            raise OptionalDependencyNotAvailable()
    except OptionalDependencyNotAvailable:
        pass
    else:
        from .modeling_luke import (
            LUKE_PRETRAINED_MODEL_ARCHIVE_LIST,
            LukeForEntityClassification,
            LukeForEntityPairClassification,
            LukeForEntitySpanClassification,
            LukeForMaskedLM,
            LukeForMultipleChoice,
            LukeForQuestionAnswering,
            LukeForSequenceClassification,
            LukeForTokenClassification,
            LukeModel,
            LukePreTrainedModel,
        )

else:
    import sys

    A__    :   List[str]           =					_LazyModule(__name__, globals()['''__file__'''], _import_structure, module_spec=__spec__)



