






'''simple docstring'''




def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_)							->     bool:
		UpperCamelCase__				:					Dict					=					len(lowerCamelCase_)
		UpperCamelCase__				:					Dict					=					len(lowerCamelCase_)
		UpperCamelCase__				:					Dict					=					[[False for _ in range(m + 1)] for _ in range(n + 1)]
		UpperCamelCase__				:					List[Any]					=					True
		for i in range(lowerCamelCase_):
				for j in range(m + 1):
						if dp[i][j]:
								if j < m and a[i].upper() == b[j]:
										UpperCamelCase__				:					Tuple					=					True
								if a[i].islower():
										UpperCamelCase__				:					Any					=					True
		return dp[n][m]


if __name__ == "__main__":
		import doctest

		doctest.testmod()












'''simple docstring'''




import numpy as np
from PIL import Image







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)							->     np.ndarray:
		UpperCamelCase__				:					List[Any]					=					np.array(lowerCamelCase_)
		if arr.shape[0] != arr.shape[1]:
				raise ValueError('The input array is not a square matrix')
		UpperCamelCase__				:					Tuple					=					0
		UpperCamelCase__				:					int					=					0
		UpperCamelCase__				:					Optional[int]					=					0
		UpperCamelCase__				:					str					=					0

		# compute the shape of the output matrix
		UpperCamelCase__				:					int					=					(arr.shape[0] - size) // stride + 1
		# initialize the output matrix with zeros of shape maxpool_shape
		UpperCamelCase__				:					Dict					=					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
						UpperCamelCase__				:					Dict					=					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
				UpperCamelCase__				:					List[Any]					=					0
				UpperCamelCase__				:					Optional[int]					=					0

		return updated_arr







def       __UpperCAmelCase						(  lowerCamelCase_     ,      lowerCamelCase_     ,      lowerCamelCase_)							->     np.ndarray:
		UpperCamelCase__				:					Tuple					=					np.array(lowerCamelCase_)
		if arr.shape[0] != arr.shape[1]:
				raise ValueError('The input array is not a square matrix')
		UpperCamelCase__				:					Optional[int]					=					0
		UpperCamelCase__				:					int					=					0
		UpperCamelCase__				:					List[str]					=					0
		UpperCamelCase__				:					List[Any]					=					0

		# compute the shape of the output matrix
		UpperCamelCase__				:					str					=					(arr.shape[0] - size) // stride + 1
		# initialize the output matrix with zeros of shape avgpool_shape
		UpperCamelCase__				:					Union[str, Any]					=					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
						UpperCamelCase__				:					List[Any]					=					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
				UpperCamelCase__				:					Union[str, Any]					=					0
				UpperCamelCase__				:					Optional[Any]					=					0

		return updated_arr


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

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

		# Loading the image
		lowerCAmelCase__          =						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()




