





'''simple docstring'''
from __future__ import annotations

from typing import Any
def     lowercase__       (       *__lowercase						:  list[list[int]]					)			->				list[list[int]]:



       """simple docstring"""






       if all(_check_not_integer(__lowercase					) for m in matrix_s					):
              for i in matrix_s[1:]:
                     _verify_matrix_sizes(matrix_s[0]    ,  __lowercase					)
              return [[sum(__lowercase					) for t in zip(*__lowercase					)] for m in zip(*__lowercase					)]
       raise TypeError('Expected a matrix, got int/list instead'					)
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  list[list[int]]					)			->				list[list[int]]:



       """simple docstring"""






       if (
           _check_not_integer(__lowercase					)
           and _check_not_integer(__lowercase					)
           and _verify_matrix_sizes(__lowercase    ,  __lowercase					)
       ):
              return [[i - j for i, j in zip(*__lowercase					)] for m in zip(__lowercase    ,  __lowercase					)]
       raise TypeError('Expected a matrix, got int/list instead'					)
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  int | float					)			->				list[list[float]]:



       """simple docstring"""






       return [[x * n for x in row] for row in matrix]
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  list[list[int]]					)			->				list[list[int]]:



       """simple docstring"""






       if _check_not_integer(__lowercase					) and _check_not_integer(__lowercase					):
              __UpperCamelCase	,						__UpperCamelCase	=  _verify_matrix_sizes(__lowercase    ,  __lowercase					)

       if cols[0] != rows[1]:
              __UpperCamelCase	=  (
                  'Cannot multiply matrix of dimensions '
                  F'''({rows[0]},{cols[0]}) and ({rows[1]},{cols[1]})'''
              )
              raise ValueError(__lowercase					)
       return [
           [sum(m * n for m, n in zip(__lowercase    ,  __lowercase					)					) for j in zip(*__lowercase					)] for i in matrix_a
       ]
def     lowercase__       (       __lowercase						:  int					)			->				list[list[int]]:



       """simple docstring"""






       __UpperCamelCase	=  int(__lowercase					)
       return [[int(row == column					) for column in range(__lowercase					)] for row in range(__lowercase					)]
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  bool = True					)			->				list[list[int]] | map[list[int]]:



       """simple docstring"""






       if _check_not_integer(__lowercase					):
              if return_map:
                     return map(__lowercase    ,  zip(*__lowercase					)					)
              else:
                     return list(map(__lowercase    ,  zip(*__lowercase					)					)					)
       raise TypeError('Expected a matrix, got int/list instead'					)
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  int    ,  __lowercase						:  int					)			->				list[list[int]]:



       """simple docstring"""






       __UpperCamelCase	=  matrix[:row] + matrix[row + 1 :]
       return [row[:column] + row[column + 1 :] for row in minor]
def     lowercase__       (       __lowercase						:  list[list[int]]					)			->				Any:



       """simple docstring"""






       if len(__lowercase					) == 1:
              return matrix[0][0]

       return sum(
           x * determinant(minor(__lowercase    ,  0    ,  __lowercase					)					) * (-1) ** i
           for i, x in enumerate(matrix[0]					)					)
def     lowercase__       (       __lowercase						:  list[list[int]]					)			->				list[list[float]] | None:



       """simple docstring"""






       __UpperCamelCase	=  determinant(__lowercase					)
       if det == 0:
              return None

       __UpperCamelCase	=  [
           [determinant(minor(__lowercase    ,  __lowercase    ,  __lowercase					)					) for j in range(len(__lowercase					)					)]
           for i in range(len(__lowercase					)					)
       ]

       __UpperCamelCase	=  [
           [x * (-1) ** (row + col) for col, x in enumerate(matrix_minor[row]					)]
           for row in range(len(__lowercase					)					)
       ]
       __UpperCamelCase	=  list(transpose(__lowercase					)					)
       return scalar_multiply(__lowercase    ,  1 / det					)
def     lowercase__       (       __lowercase						:  list[list[int]]					)			->				bool:



       """simple docstring"""






       return not isinstance(__lowercase    ,  __lowercase					) and not isinstance(matrix[0]    ,  __lowercase					)
def     lowercase__       (       __lowercase						:  list[list[int]]					)			->				tuple[int, int]:



       """simple docstring"""






       return len(__lowercase					), len(matrix[0]					)
def     lowercase__       (       __lowercase						:  list[list[int]]    ,  __lowercase						:  list[list[int]]					)			->				tuple[tuple[int, int], tuple[int, int]]:



       """simple docstring"""






       __UpperCamelCase	=  _shape(__lowercase					) + _shape(__lowercase					)
       if shape[0] != shape[3] or shape[1] != shape[2]:
              __UpperCamelCase	=  (
                  'operands could not be broadcast together with shape '
                  F'''({shape[0], shape[1]}), ({shape[2], shape[3]})'''
              )
              raise ValueError(__lowercase					)
       return (shape[0], shape[2]), (shape[1], shape[3])
def     lowercase__       (       )			->				None:



       """simple docstring"""






       __UpperCamelCase	=  [[12, 10], [3, 9]]
       __UpperCamelCase	=  [[3, 4], [7, 4]]
       __UpperCamelCase	=  [[11, 12, 13, 14], [21, 22, 23, 24], [31, 32, 33, 34], [41, 42, 43, 44]]
       __UpperCamelCase	=  [[3, 0, 2], [2, 0, -2], [0, 1, 1]]
       print(F'''Add Operation, {add(__lowercase    ,  __lowercase					) = } \n'''					)
       print(
           F'''Multiply Operation, {multiply(__lowercase    ,  __lowercase					) = } \n'''    ,  )
       print(F'''Identity: {identity(5					)}\n'''					)
       print(F'''Minor of {matrix_c} = {minor(__lowercase    ,  1    ,  2					)} \n'''					)
       print(F'''Determinant of {matrix_b} = {determinant(__lowercase					)} \n'''					)
       print(F'''Inverse of {matrix_d} = {inverse(__lowercase					)}\n'''					)


if __name__ == "__main__":
    import doctest

    doctest.testmod()
    main()







'''simple docstring'''
import numpy as np
from PIL import Image
def     lowercase__       (       __lowercase						:  np.array					)			->				np.array:



       """simple docstring"""






       __UpperCamelCase	,						__UpperCamelCase	,						__UpperCamelCase	=  rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
       return 0.2_9_8_9 * r + 0.5_8_7_0 * g + 0.1_1_4_0 * b
def     lowercase__       (       __lowercase						:  np.array					)			->				np.array:



       """simple docstring"""






       return (gray > 127) & (gray <= 255)
def     lowercase__       (       __lowercase						:  np.array    ,  __lowercase						:  np.array					)			->				np.array:



       """simple docstring"""






       __UpperCamelCase	=  np.zeros_like(__lowercase					)
       __UpperCamelCase	=  np.zeros(
           (image.shape[0] + kernel.shape[0] - 1, image.shape[1] + kernel.shape[1] - 1)					)

       # Copy image to padded image
       __UpperCamelCase	=  image

       # Iterate over image & apply kernel
       for x in range(image.shape[1]					):
              for y in range(image.shape[0]					):
                     __UpperCamelCase	=  (
                         kernel * image_padded[y : y + kernel.shape[0], x : x + kernel.shape[1]]
                     ).sum()
                     __UpperCamelCase	=  int(summation == 5					)
       return output


# kernel to be applied
a__							:							Dict			=np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])

if __name__ == "__main__":
    # read original image
    a__							:							Any			=np.array(Image.open(r'''..\image_data\lena.jpg'''))
    # Apply erosion operation to a binary image
    a__							:							Union[str, Any]			=erosion(grayabinary(rgbagray(image)), structuring_element)
    # Save the output image
    a__							:							Tuple			=Image.fromarray(output).convert('''RGB''')
    pil_img.save('''result_erosion.png''')
