





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





def      lowerCAmelCase_ (       __a		)     ->		Union[str, Any]:







  """simple docstring"""





  def is_in_circle(__a	,    __a		) -> bool:
    lowerCamelCase__:      Tuple			  =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(__a		)		)
  # The ratio of the area for circle to square is pi/4.
  lowerCamelCase__:      Dict			  =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_ (       __a	,    __a	,    __a = 0.0	,    __a = 1.0	,    )     ->		float:







  """simple docstring"""





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





def      lowerCAmelCase_ (       __a	,    __a = 0.0	,    __a = 1.0		)     ->		None:







  """simple docstring"""





  def identity_function(__a		) -> float:
    return x

  lowerCamelCase__:      Dict			  =area_under_curve_estimator(
      __a	,    __a	,    __a	,    __a		)
  lowerCamelCase__:      Union[str, Any]			  =(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_ (       __a		)     ->		None:







  """simple docstring"""





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

  lowerCamelCase__:      List[Any]			  =area_under_curve_estimator(
      __a	,    __a	,    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_flax_available,
    is_torch_available,
    is_vision_available,
)


A__		:					List[str]												=  {"""configuration_beit""": ["""BEIT_PRETRAINED_CONFIG_ARCHIVE_MAP""", """BeitConfig""", """BeitOnnxConfig"""]}

try:
      if not is_vision_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__		:					str												=  ["""BeitFeatureExtractor"""]
      A__		:					List[str]												=  ["""BeitImageProcessor"""]

try:
      if not is_torch_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__		:					Optional[int]												=  [
          """BEIT_PRETRAINED_MODEL_ARCHIVE_LIST""",
          """BeitForImageClassification""",
          """BeitForMaskedImageModeling""",
          """BeitForSemanticSegmentation""",
          """BeitModel""",
          """BeitPreTrainedModel""",
      ]


try:
      if not is_flax_available():
            raise OptionalDependencyNotAvailable()
except OptionalDependencyNotAvailable:
      pass
else:
      A__		:					Any												=  [
          """FlaxBeitForImageClassification""",
          """FlaxBeitForMaskedImageModeling""",
          """FlaxBeitModel""",
          """FlaxBeitPreTrainedModel""",
      ]

if TYPE_CHECKING:
      from .configuration_beit import BEIT_PRETRAINED_CONFIG_ARCHIVE_MAP, BeitConfig, BeitOnnxConfig

      try:
            if not is_vision_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .feature_extraction_beit import BeitFeatureExtractor
            from .image_processing_beit import BeitImageProcessor

      try:
            if not is_torch_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_beit import (
                BEIT_PRETRAINED_MODEL_ARCHIVE_LIST,
                BeitForImageClassification,
                BeitForMaskedImageModeling,
                BeitForSemanticSegmentation,
                BeitModel,
                BeitPreTrainedModel,
            )

      try:
            if not is_flax_available():
                  raise OptionalDependencyNotAvailable()
      except OptionalDependencyNotAvailable:
            pass
      else:
            from .modeling_flax_beit import (
                FlaxBeitForImageClassification,
                FlaxBeitForMaskedImageModeling,
                FlaxBeitModel,
                FlaxBeitPreTrainedModel,
            )


else:
      import sys

      A__		:					Optional[Any]												=  _LazyModule(__name__, globals()["""__file__"""], _import_structure, module_spec=__spec__)






