



"""simple docstring"""







from __future__ import annotations

from typing import Any






class       UpperCamelCase__			:

			"""simple docstring"""


			def __init__(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__ = 0		)      ->	None:
				A__							,							A__											=					row, column
				A__											=					[[default_value for c in range(SCREAMING_SNAKE_CASE__		)] for r in range(SCREAMING_SNAKE_CASE__		)]


			def __str__(      self		)      ->	str:
				A__											=					f"""Matrix consist of {self.row} rows and {self.column} columns\n"""

				# Make string identifier
				A__											=					0
				for row_vector in self.array:
					for obj in row_vector:
						A__											=					max(SCREAMING_SNAKE_CASE__						,	len(str(SCREAMING_SNAKE_CASE__		)		)		)
				A__											=					f"""%{max_element_length}s"""

				# Make string and return
				def single_line(SCREAMING_SNAKE_CASE__		) -> str:
					nonlocal string_format_identifier
					A__											=					"["
					line += ", ".join(string_format_identifier % (obj,) for obj in row_vector		)
					line += "]"
					return line

				s += "\n".join(single_line(SCREAMING_SNAKE_CASE__		) for row_vector in self.array		)
				return s


			def __repr__(      self		)      ->	str:
				return str(self		)


			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__		)      ->	bool:
				if not (isinstance(SCREAMING_SNAKE_CASE__						,	(list, tuple)		) and len(SCREAMING_SNAKE_CASE__		) == 2):
					return False
				elif not (0 <= loc[0] < self.row and 0 <= loc[1] < self.column):
					return False
				else:
					return True


			def __getitem__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Any:
				assert self.validate_indicies(SCREAMING_SNAKE_CASE__		)
				return self.array[loc[0]][loc[1]]


			def __setitem__(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	None:
				assert self.validate_indicies(SCREAMING_SNAKE_CASE__		)
				A__											=					value


			def __add__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:
				assert isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				assert self.row == another.row and self.column == another.column

				# Add
				A__											=					Matrix(self.row						,	self.column		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					self[r, c] + another[r, c]
				return result


			def __neg__(      self		)      ->	Matrix:
				A__											=					Matrix(self.row						,	self.column		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					-self[r, c]
				return result


			def __sub__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:
				return self + (-another)


			def __mul__(      self						,	SCREAMING_SNAKE_CASE__		)      ->	Matrix:

				if isinstance(SCREAMING_SNAKE_CASE__						,	(int, float)		):  # Scalar multiplication
					A__											=					Matrix(self.row						,	self.column		)
					for r in range(self.row		):
						for c in range(self.column		):
							A__											=					self[r, c] * another
					return result
				elif isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		):  # Matrix multiplication
					assert self.column == another.row
					A__											=					Matrix(self.row						,	another.column		)
					for r in range(self.row		):
						for c in range(another.column		):
							for i in range(self.column		):
								result[r, c] += self[r, i] * another[i, c]
					return result
				else:
					A__											=					f"""Unsupported type given for another ({type(SCREAMING_SNAKE_CASE__		)})"""
					raise TypeError(SCREAMING_SNAKE_CASE__		)


			def   snake_case__	(      self		)      ->	Matrix:
				A__											=					Matrix(self.column						,	self.row		)
				for r in range(self.row		):
					for c in range(self.column		):
						A__											=					self[r, c]
				return result







			def   snake_case__	(      self						,	SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)      ->	Any:
				assert isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		) and isinstance(SCREAMING_SNAKE_CASE__						,	SCREAMING_SNAKE_CASE__		)
				assert self.row == self.column == u.row == v.row  # u, v should be column vector
				assert u.column == v.column == 1  # u, v should be column vector

				# Calculate
				A__											=					v.transpose()
				A__											=					(v_t * self * u)[0, 0] + 1
				if numerator_factor == 0:
					return None  # It's not invertable
				return self - ((self * u) * (v_t * self) * (1.0 / numerator_factor))


# Testing
if __name__ == "__main__":

			def       _lowerCamelCase				(							)	-> None:






				"""simple docstring"""





				A__											=					Matrix(3,	3,	0     )
				for i in range(3     ):
					A__											=					1
				print(F"""a^(-1) is {ainv}"""     )
				# u, v
				A__											=					Matrix(3,	1,	0     )
				A__							,							A__							,							A__											=					1, 2, -3
				A__											=					Matrix(3,	1,	0     )
				A__							,							A__							,							A__											=					4, -2, 5
				print(F"""u is {u}"""     )
				print(F"""v is {v}"""     )
				print(F"""uv^T is {u * v.transpose()}"""     )
				# Sherman Morrison
				print(F"""(a + uv^T)^(-1) is {ainv.sherman_morrison(UpperCAmelCase_,	UpperCAmelCase_     )}"""     )

			def       _lowerCamelCase				(							)	-> None:






				"""simple docstring"""





				import doctest

				doctest.testmod()




			testa()









"""simple docstring"""







def       _lowerCamelCase				(							UpperCAmelCase_ :       int     )	-> int:






	"""simple docstring"""





	if not isinstance(UpperCAmelCase_,	UpperCAmelCase_     ):
		raise ValueError("Input must be an integer"     )
	if input_num <= 0:
		raise ValueError("Input must be positive"     )
	return sum(
	    divisor for divisor in range(1,	input_num // 2 + 1     ) if input_num % divisor == 0     )


if __name__ == "__main__":
			import doctest

			doctest.testmod()




