

from itertools import product

from cva import COLOR_BGR2GRAY, cvtColor, imread, imshow, waitKey
from numpy import dot, exp, mgrid, pi, ravel, square, uinta, zeros

def       a__					(		UpperCAmelCase							:      Any    ,			UpperCAmelCase							:      List[Any]      )  ->						Optional[int]:
  UpperCAmelCase	:							Any						=			k_size // 2
  UpperCAmelCase	:							Optional[Any]						=			mgrid[0 - center : k_size - center, 0 - center : k_size - center]
  UpperCAmelCase	:							int						=			1 / (2 * pi * sigma) * exp(-(square(UpperCAmelCase      ) + square(UpperCAmelCase      )) / (2 * square(UpperCAmelCase      ))      )
  return g

def       a__					(		UpperCAmelCase							:      Any    ,			UpperCAmelCase							:      Dict    ,			UpperCAmelCase							:      List[Any]      )  ->						Any:
  UpperCAmelCase	:							Optional[Any]						=			image.shape[0], image.shape[1]
  # dst image height and width
  UpperCAmelCase	:							Tuple						=			height - k_size + 1
  UpperCAmelCase	:							Dict						=			width - k_size + 1

  # im2col, turn the k_size*k_size pixels into a row and np.vstack all rows
  UpperCAmelCase	:							Union[str, Any]						=			zeros((dst_height * dst_width, k_size * k_size)      )
  UpperCAmelCase	:							Dict						=			0
  for i, j in product(range(UpperCAmelCase      )    ,			range(UpperCAmelCase      )      ):
    UpperCAmelCase	:							str						=			ravel(image[i : i + k_size, j : j + k_size]      )
    UpperCAmelCase	:							Dict						=			window
    row += 1

  #  turn the kernel into shape(k*k, 1)
  UpperCAmelCase	:							Any						=			gen_gaussian_kernel(UpperCAmelCase    ,			UpperCAmelCase      )
  UpperCAmelCase	:							Optional[int]						=			ravel(UpperCAmelCase      )

  # reshape and get the dst image
  UpperCAmelCase	:							List[str]						=			dot(UpperCAmelCase    ,			UpperCAmelCase      ).reshape(UpperCAmelCase    ,			UpperCAmelCase      ).astype(UpperCAmelCase      )

  return dst


if __name__ == "__main__":
     # read original image
     _lowerCamelCase    :       int        =							imread(R"../image_data/lena.jpg")
     # turn image in gray scale value
     _lowerCamelCase    :       int        =							cvtColor(img, COLOR_BGR2GRAY)

     # get values with two different mask size
     _lowerCamelCase    :       List[str]        =							gaussian_filter(gray, 3, sigma=1)
     _lowerCamelCase    :       Union[str, Any]        =							gaussian_filter(gray, 5, sigma=0.8)

     # show result images
     imshow("gaussian filter with 3x3 mask", gaussianaxa)
     imshow("gaussian filter with 5x5 mask", gaussianaxa)
     waitKey()








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

def       a__					(		UpperCAmelCase							:      int      )  ->						Dict:

  # A local function to see if a dot lands in the circle.
  def is_in_circle(UpperCAmelCase							:      float    ,			UpperCAmelCase							:      float      ) -> bool:
    UpperCAmelCase	:							Dict						=			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
  UpperCAmelCase	:							List[str]						=			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.
  UpperCAmelCase	:							int						=			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

  UpperCAmelCase	:							int						=			area_under_curve_estimator(
      UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase    ,			UpperCAmelCase      )
  UpperCAmelCase	:							Tuple						=			(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      )

  UpperCAmelCase	:							Optional[int]						=			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()





