
"""simple docstring"""



from __future__ import annotations
class        _SCREAMING_SNAKE_CASE  :






				'''simple docstring'''



				def __init__(					self	:			Any				,     UpperCAmelCase_	:			list[list[int]]  )		->  int:







											"""simple docstring"""




											_lowerCAmelCase  	=			TypeError(
											    'Matrices must be formed from a list of zero or more lists containing at '
											    'least one and the same number of values, each of which must be of type '
											    'int or float.'  )
											if len(UpperCAmelCase_  ) != 0:
																		_lowerCAmelCase  	=			len(rows[0]  )
																		if cols == 0:
																									raise error
																		for row in rows:
																									if len(UpperCAmelCase_  ) != cols:
																																raise error
																									for value in row:
																																if not isinstance(UpperCAmelCase_				,     (int, float)  ):
																																							raise error
																		_lowerCAmelCase  	=			rows
											else:
																		_lowerCAmelCase  	=			[]


				def 				__lowerCamelCase	(					self	:			Optional[Any]  )		->  list[list[int]]:







											"""simple docstring"""




											return [[row[i] for row in self.rows] for i in range(len(self.rows[0]  )  )]


				@property
				def 				__lowerCamelCase	(					self	:			List[str]  )		->  int:







											"""simple docstring"""




											return len(self.rows  )


				@property
				def 				__lowerCamelCase	(					self	:			str  )		->  int:







											"""simple docstring"""




											return len(self.rows[0]  )


				@property
				def 				__lowerCamelCase	(					self	:			Optional[int]  )		->  tuple[int, int]:







											"""simple docstring"""




											return (self.num_rows, self.num_columns)


				@property
				def 				__lowerCamelCase	(					self	:			int  )		->  bool:







											"""simple docstring"""




											return self.order[0] == self.order[1]


				def 				__lowerCamelCase	(					self	:			int  )		->  Matrix:







											"""simple docstring"""




											_lowerCAmelCase  	=			[
											    [0 if column_num != row_num else 1 for column_num in range(self.num_rows  )]
											    for row_num in range(self.num_rows  )
											]
											return Matrix(UpperCAmelCase_  )


				def 				__lowerCamelCase	(					self	:			List[Any]  )		->  int:







											"""simple docstring"""




											if not self.is_square:
																		return 0
											if self.order == (0, 0):
																		return 1
											if self.order == (1, 1):
																		return int(self.rows[0][0]  )
											if self.order == (2, 2):
																		return int(
																		    (self.rows[0][0] * self.rows[1][1])
																		    - (self.rows[0][1] * self.rows[1][0])  )
											else:
																		return sum(
																		    self.rows[0][column] * self.cofactors().rows[0][column]
																		    for column in range(self.num_columns  )  )


				def 				__lowerCamelCase	(					self	:			str  )		->  bool:







											"""simple docstring"""




											return bool(self.determinant()  )


				def 				__lowerCamelCase	(					self	:			List[Any]				,     UpperCAmelCase_	:			int				,     UpperCAmelCase_	:			int  )		->  int:







											"""simple docstring"""




											_lowerCAmelCase  	=			[
											    [
											        self.rows[other_row][other_column]
											        for other_column in range(self.num_columns  )
											        if other_column != column
											    ]
											    for other_row in range(self.num_rows  )
											    if other_row != row
											]
											return Matrix(UpperCAmelCase_  ).determinant()


				def 				__lowerCamelCase	(					self	:			Union[str, Any]				,     UpperCAmelCase_	:			int				,     UpperCAmelCase_	:			int  )		->  int:







											"""simple docstring"""




											if (row + column) % 2 == 0:
																		return self.get_minor(UpperCAmelCase_				,     UpperCAmelCase_  )
											return -1 * self.get_minor(UpperCAmelCase_				,     UpperCAmelCase_  )


				def 				__lowerCamelCase	(					self	:			Optional[int]  )		->  Matrix:







											"""simple docstring"""




											return Matrix(
											    [
											        [self.get_minor(UpperCAmelCase_				,     UpperCAmelCase_  ) for column in range(self.num_columns  )]
											        for row in range(self.num_rows  )
											    ]  )


				def 				__lowerCamelCase	(					self	:			Optional[Any]  )		->  Matrix:







											"""simple docstring"""




											return Matrix(
											    [
											        [
											            self.minors().rows[row][column]
											            if (row + column) % 2 == 0
											            else self.minors().rows[row][column] * -1
											            for column in range(self.minors().num_columns  )
											        ]
											        for row in range(self.minors().num_rows  )
											    ]  )


				def 				__lowerCamelCase	(					self	:			Any  )		->  Matrix:







											"""simple docstring"""




											_lowerCAmelCase  	=			[
											    [self.cofactors().rows[column][row] for column in range(self.num_columns  )]
											    for row in range(self.num_rows  )
											]
											return Matrix(UpperCAmelCase_  )


				def 				__lowerCamelCase	(					self	:			int  )		->  Matrix:







											"""simple docstring"""




											_lowerCAmelCase  	=			self.determinant()
											if not determinant:
																		raise TypeError('Only matrices with a non-zero determinant have an inverse'  )
											return self.adjugate() * (1 / determinant)


				def __repr__(					self	:			Any  )		->  str:







											"""simple docstring"""




											return str(self.rows  )


				def __str__(					self	:			Tuple  )		->  str:







											"""simple docstring"""




											if self.num_rows == 0:
																		return "[]"
											if self.num_rows == 1:
																		return "[[" + ". ".join(str(self.rows[0]  )  ) + "]]"
											return (
											    "["
											    + "\n ".join(
											        [
											            '[' + '. '.join([str(UpperCAmelCase_  ) for value in row]  ) + '.]'
											            for row in self.rows
											        ]  )
											    + "]"
											)


				def 				__lowerCamelCase	(					self	:			Tuple				,     UpperCAmelCase_	:			list[int]				,     UpperCAmelCase_	:			int | None = None  )		->  None:







											"""simple docstring"""




											_lowerCAmelCase  	=			TypeError('Row must be a list containing all ints and/or floats'  )
											if not isinstance(UpperCAmelCase_				,     UpperCAmelCase_  ):
																		raise type_error
											for value in row:
																		if not isinstance(UpperCAmelCase_				,     (int, float)  ):
																									raise type_error
											if len(UpperCAmelCase_  ) != self.num_columns:
																		raise ValueError(
																		    'Row must be equal in length to the other rows in the matrix'  )
											if position is None:
																		self.rows.append(UpperCAmelCase_  )
											else:
																		_lowerCAmelCase  	=			self.rows[0:position] + [row] + self.rows[position:]


				def 				__lowerCamelCase	(					self	:			str				,     UpperCAmelCase_	:			list[int]				,     UpperCAmelCase_	:			int | None = None  )		->  None:







											"""simple docstring"""




											_lowerCAmelCase  	=			TypeError(
											    'Column must be a list containing all ints and/or floats'  )
											if not isinstance(UpperCAmelCase_				,     UpperCAmelCase_  ):
																		raise type_error
											for value in column:
																		if not isinstance(UpperCAmelCase_				,     (int, float)  ):
																									raise type_error
											if len(UpperCAmelCase_  ) != self.num_rows:
																		raise ValueError(
																		    'Column must be equal in length to the other columns in the matrix'  )
											if position is None:
																		_lowerCAmelCase  	=			[self.rows[i] + [column[i]] for i in range(self.num_rows  )]
											else:
																		_lowerCAmelCase  	=			[
																		    self.rows[i][0:position] + [column[i]] + self.rows[i][position:]
																		    for i in range(self.num_rows  )
																		]


				def __eq__(					self	:			Dict				,     UpperCAmelCase_	:			object  )		->  bool:







											"""simple docstring"""




											if not isinstance(UpperCAmelCase_				,     UpperCAmelCase_  ):
																		return NotImplemented
											return self.rows == other.rows


				def __ne__(					self	:			Dict				,     UpperCAmelCase_	:			object  )		->  bool:







											"""simple docstring"""




											return not self == other


				def __neg__(					self	:			Optional[int]  )		->  Matrix:







											"""simple docstring"""




											return self * -1


				def __add__(					self	:			Union[str, Any]				,     UpperCAmelCase_	:			Matrix  )		->  Matrix:







											"""simple docstring"""




											if self.order != other.order:
																		raise ValueError('Addition requires matrices of the same order'  )
											return Matrix(
											    [
											        [self.rows[i][j] + other.rows[i][j] for j in range(self.num_columns  )]
											        for i in range(self.num_rows  )
											    ]  )


				def __sub__(					self	:			int				,     UpperCAmelCase_	:			Matrix  )		->  Matrix:







											"""simple docstring"""




											if self.order != other.order:
																		raise ValueError('Subtraction requires matrices of the same order'  )
											return Matrix(
											    [
											        [self.rows[i][j] - other.rows[i][j] for j in range(self.num_columns  )]
											        for i in range(self.num_rows  )
											    ]  )


				def __mul__(					self	:			Union[str, Any]				,     UpperCAmelCase_	:			Matrix | int | float  )		->  Matrix:







											"""simple docstring"""




											if isinstance(UpperCAmelCase_				,     (int, float)  ):
																		return Matrix(
																		    [[int(element * other  ) for element in row] for row in self.rows]  )
											elif isinstance(UpperCAmelCase_				,     UpperCAmelCase_  ):
																		if self.num_columns != other.num_rows:
																									raise ValueError(
																									    'The number of columns in the first matrix must '
																									    'be equal to the number of rows in the second'  )
																		return Matrix(
																		    [
																		        [Matrix.dot_product(UpperCAmelCase_				,     UpperCAmelCase_  ) for column in other.columns()]
																		        for row in self.rows
																		    ]  )
											else:
																		raise TypeError(
																		    'A Matrix can only be multiplied by an int, float, or another matrix'  )


				def __pow__(					self	:			Union[str, Any]				,     UpperCAmelCase_	:			int  )		->  Matrix:







											"""simple docstring"""




											if not isinstance(UpperCAmelCase_				,     UpperCAmelCase_  ):
																		raise TypeError('A Matrix can only be raised to the power of an int'  )
											if not self.is_square:
																		raise ValueError('Only square matrices can be raised to a power'  )
											if other == 0:
																		return self.identity()
											if other < 0:
																		if self.is_invertable():
																									return self.inverse() ** (-other)
																		raise ValueError(
																		    'Only invertable matrices can be raised to a negative power'  )
											_lowerCAmelCase  	=			self
											for _ in range(other - 1  ):
																		result *= self
											return result







				@classmethod
				def 				__lowerCamelCase	(					cls	:			Optional[int]				,     UpperCAmelCase_	:			list[int]				,     UpperCAmelCase_	:			list[int]  )		->  int:







											"""simple docstring"""




											return sum(row[i] * column[i] for i in range(len(UpperCAmelCase_  )  )  )


if __name__ == "__main__":
	import doctest

	doctest.testmod()








"""simple docstring"""



from pathlib import Path

import numpy as np
from PIL import Image






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					np.ndarray						):






							"""simple docstring"""



							_lowerCAmelCase	,		_lowerCAmelCase	,		_lowerCAmelCase  	=			rgb[:, :, 0], rgb[:, :, 1], rgb[:, :, 2]
							return 0.29_89 * r + 0.58_70 * g + 0.11_40 * b






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					np.ndarray						):






							"""simple docstring"""



							return (gray > 127) & (gray <= 255)






def 	__snake_case  (    SCREAMING_SNAKE_CASE:					np.ndarray     ,  SCREAMING_SNAKE_CASE:					np.ndarray						):






							"""simple docstring"""



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

							# Copy image to padded image
							_lowerCAmelCase  	=			image

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


if __name__ == "__main__":
	# read original image
	_snake_case          =						Path(__file__).resolve().parent / '''image_data''' / '''lena.jpg'''
	_snake_case          =						np.array(Image.open(lena_path))
	# kernel to be applied
	_snake_case          =						np.array([[0, 1, 0], [1, 1, 1], [0, 1, 0]])
	_snake_case          =						dilation(gray_to_binary(rgb_to_gray(lena)), structuring_element)
	# Save the output image
	_snake_case          =						Image.fromarray(output).convert('''RGB''')
	pil_img.save('''result_dilation.png''')






