"""simple docstring"""






import numpy as np
from PIL import Image


def 			UpperCAmelCase__       (				lowerCAmelCase__     :np.ndarray					,		lowerCAmelCase__     :int					,		lowerCAmelCase__     :int		) ->    Union[str, Any]:
      '''simple docstring'''


      lowercase														=	np.array(__snake_case		)
      if arr.shape[0] != arr.shape[1]:
            raise ValueError("""The input array is not a square matrix"""		)
      lowercase														=	0
      lowercase														=	0
      lowercase														=	0
      lowercase														=	0

      # compute the shape of the output matrix
      lowercase														=	(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape maxpool_shape
      lowercase														=	np.zeros((maxpool_shape, maxpool_shape)		)

      while i < arr.shape[0]:
            if i + size > arr.shape[0]:
                  # if the end of the matrix is reached, break
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the maximum of the pooling matrix
                  lowercase														=	np.max(arr[i : i + size, j : j + size]		)
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1

            # reset the column index to 0
            lowercase														=	0
            lowercase														=	0

      return updated_arr


def 			UpperCAmelCase__       (				lowerCAmelCase__     :np.ndarray					,		lowerCAmelCase__     :int					,		lowerCAmelCase__     :int		) ->    List[Any]:
      '''simple docstring'''


      lowercase														=	np.array(__snake_case		)
      if arr.shape[0] != arr.shape[1]:
            raise ValueError("""The input array is not a square matrix"""		)
      lowercase														=	0
      lowercase														=	0
      lowercase														=	0
      lowercase														=	0

      # compute the shape of the output matrix
      lowercase														=	(arr.shape[0] - size) // stride + 1
      # initialize the output matrix with zeros of shape avgpool_shape
      lowercase														=	np.zeros((avgpool_shape, avgpool_shape)		)

      while i < arr.shape[0]:
            # if the end of the matrix is reached, break
            if i + size > arr.shape[0]:
                  break
            while j < arr.shape[1]:
                  # if the end of the matrix is reached, break
                  if j + size > arr.shape[1]:
                        break
                  # compute the average of the pooling matrix
                  lowercase														=	int(np.average(arr[i : i + size, j : j + size]		)		)
                  # shift the pooling matrix by stride of column pixels
                  j += stride
                  mat_j += 1

            # shift the pooling matrix by stride of row pixels
            i += stride
            mat_i += 1
            # reset the column index to 0
            lowercase														=	0
            lowercase														=	0

      return updated_arr


# Main Function
if __name__ == "__main__":
       from doctest import testmod

       testmod(name="""avgpooling""", verbose=True)

       # Loading the image
       __lowerCAmelCase    :       List[Any]					     =Image.open("""path_to_image""")

       # Converting the image to numpy array and maxpooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(maxpooling(np.array(image), size=3, stride=2)).show()

       # Converting the image to numpy array and averagepooling, displaying the result
       # Ensure that the image is a square matrix

       Image.fromarray(avgpooling(np.array(image), size=3, stride=2)).show()











"""simple docstring"""



def 						lowercase    (				__snake_case				: Optional[int]	):
		lowercase_ : int							       =   0
		lowercase_ : Optional[Any]							       =   len(__snake_case	)

		for i in range(n - 1	):
				for j in range(i + 1		,					__snake_case	):
						if arr[i] > arr[j]:
								num_inversions += 1

		return num_inversions



def 						lowercase    (				__snake_case				: str	):
		if len(__snake_case	) <= 1:
				return arr, 0
		lowercase_ : Optional[Any]							       =   len(__snake_case	) // 2
		lowercase_ : List[Any]							       =   arr[0:mid]
		lowercase_ : Union[str, Any]							       =   arr[mid:]

		lowercase_       ,					lowercase_ : Tuple							       =   count_inversions_recursive(__snake_case	)
		lowercase_       ,					lowercase_ : List[Any]							       =   count_inversions_recursive(__snake_case	)
		lowercase_       ,					lowercase_ : List[Any]							       =   _count_cross_inversions(__snake_case		,					__snake_case	)

		lowercase_ : List[Any]							       =   inversion_p + inversions_q + cross_inversions
		return c, num_inversions



def 						lowercase    (				__snake_case				: str		,					__snake_case				: Optional[int]	):
		lowercase_ : Optional[Any]							       =   []
		lowercase_ : Any							       =   0
		while i < len(__snake_case	) and j < len(__snake_case	):
				if p[i] > q[j]:
						# if P[1] > Q[j], then P[k] > Q[k] for all  i < k <= len(P)
						# These are all inversions. The claim emerges from the
						# property that P is sorted.
						num_inversion += len(__snake_case	) - i
						r.append(q[j]	)
						j += 1
				else:
						r.append(p[i]	)
						i += 1

		if i < len(__snake_case	):
				r.extend(p[i:]	)
		else:
				r.extend(q[j:]	)

		return r, num_inversion



def 						lowercase    (				):
		lowercase_ : Union[str, Any]							       =   [1_0, 2, 1, 5, 5, 2, 1_1]

		# this arr has 8 inversions:
		# (10, 2), (10, 1), (10, 5), (10, 5), (10, 2), (2, 1), (5, 2), (5, 2)

		lowercase_ : int							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : Dict							       =   count_inversions_recursive(__snake_case	)

		assert num_inversions_bf == num_inversions_recursive == 8

		print('''number of inversions = '''		,					__snake_case	)

		# testing an array with zero inversion (a sorted arr_1)

		arr_a.sort()
		lowercase_ : Dict							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : Dict							       =   count_inversions_recursive(__snake_case	)

		assert num_inversions_bf == num_inversions_recursive == 0
		print('''number of inversions = '''		,					__snake_case	)

		# an empty list should also have zero inversions
		lowercase_ : List[Any]							       =   []
		lowercase_ : Any							       =   count_inversions_bf(__snake_case	)
		lowercase_       ,					lowercase_ : List[str]							       =   count_inversions_recursive(__snake_case	)

		assert num_inversions_bf == num_inversions_recursive == 0
		print('''number of inversions = '''		,					__snake_case	)


if __name__ == "__main__":
						main()



