

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  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__			)     ->     List[str]:
       A_		   = k_size // 2
       A_   ,     A_		   = mgrid[0 - center : k_size - center, 0 - center : k_size - center]
       A_		   = 1 / (2 * pi * sigma) * exp(-(square(UpperCAmelCase__			) + square(UpperCAmelCase__			)) / (2 * square(UpperCAmelCase__			))			)
       return g
def  UpperCAmelCase__      ( UpperCAmelCase__,    UpperCAmelCase__,    UpperCAmelCase__			)     ->     Optional[Any]:
       A_   ,     A_		   = image.shape[0], image.shape[1]
       # dst image height and width
       A_		   = height - k_size + 1
       A_		   = width - k_size + 1

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

       #  turn the kernel into shape(k*k, 1)
       A_		   = gen_gaussian_kernel(UpperCAmelCase__,    UpperCAmelCase__			)
       A_		   = ravel(UpperCAmelCase__			)

       # reshape and get the dst image
       A_		   = dot(UpperCAmelCase__,    UpperCAmelCase__			).reshape(UpperCAmelCase__,    UpperCAmelCase__			).astype(UpperCAmelCase__			)

       return dst


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

      # get values with two different mask size
      __lowerCamelCase						    =      gaussian_filter(gray, 3, sigma=1)
      __lowerCamelCase						    =      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()



'''simple docstring'''







def  UpperCAmelCase__      ( UpperCAmelCase__ = 1_00			)     ->     int:
       A_		   = n * (n + 1) * (2 * n + 1) / 6
       A_		   = (n * (n + 1) / 2) ** 2
       return int(square_of_sum - sum_of_squares			)


if __name__ == "__main__":
      print(f"""{solution() = }""")
