





'''simple docstring'''






from collections.abc import Callable
from math import pi, sqrt
from random import uniform
from statistics import mean
def        UpperCamelCase__				(		lowerCAmelCase  ):





      """simple docstring"""


      def is_in_circle(lowerCAmelCase							,     lowerCAmelCase  ) -> 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(lowerCAmelCase  )  )
      # 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        UpperCamelCase__				(		lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase = 0.0							,     lowerCAmelCase = 1.0							,     ):





      """simple docstring"""


      return mean(
          function_to_integrate(uniform(lowerCAmelCase							,     lowerCAmelCase  )  ) for _ in range(lowerCAmelCase  )  ) * (max_value - min_value)
def        UpperCamelCase__				(		lowerCAmelCase							,     lowerCAmelCase = 0.0							,     lowerCAmelCase = 1.0  ):





      """simple docstring"""


      def identity_function(lowerCAmelCase  ) -> float:
            return x

      _lowerCAmelCase												=							area_under_curve_estimator(
          lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase  )
      _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        UpperCamelCase__				(		lowerCAmelCase  ):





      """simple docstring"""


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

      _lowerCAmelCase												=							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()













'''simple docstring'''






from pathlib import Path

import cva
import numpy as np
from matplotlib import pyplot as plt
def        UpperCamelCase__				(		lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase							,     lowerCAmelCase  ):





      """simple docstring"""


      _lowerCAmelCase												=							cva.getAffineTransform(lowerCAmelCase							,     lowerCAmelCase  )
      return cva.warpAffine(lowerCAmelCase							,     lowerCAmelCase							,     (rows, cols)  )


if __name__ == "__main__":
      # read original image
      A__    :       Any              =cva.imread(
          str(Path(__file__).resolve().parent.parent / '''image_data''' / '''lena.jpg''')
      )
      # turn image in gray scale value
      A__    :       Any              =cva.cvtColor(image, cva.COLOR_BGR2GRAY)
      # get image shape
      A__       ,						A__    :       Tuple              =gray_img.shape

      # set different points to rotate image
      A__    :       Optional[int]              =np.array([[50, 50], [2_00, 50], [50, 2_00]], np.floataa)
      A__    :       Tuple              =np.array([[10, 1_00], [2_00, 50], [1_00, 2_50]], np.floataa)
      A__    :       List[str]              =np.array([[50, 50], [1_50, 50], [1_20, 2_00]], np.floataa)
      A__    :       Dict              =np.array([[10, 1_00], [80, 50], [1_80, 2_50]], np.floataa)

      # add all rotated images in a list
      A__    :       List[Any]              =[
          gray_img,
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
          get_rotation(gray_img, ptsa, ptsa, img_rows, img_cols),
      ]

      # plot different image rotations
      A__    :       Tuple              =plt.figure(1)
      A__    :       int              =['''Original''', '''Rotation 1''', '''Rotation 2''', '''Rotation 3''']
      for i, image in enumerate(images):
            plt.subplot(2, 2, i + 1), plt.imshow(image, '''gray''')
            plt.title(titles[i])
            plt.axis('''off''')
            plt.subplots_adjust(left=0.0, bottom=0.05, right=1.0, top=0.95)
      plt.show()






