

"""simple docstring"""


from __future__ import annotations

from typing import Any





class     snake_case	:

				def __init__(	self							:				Optional[int]     ,  UpperCamelCase__							:				int     ,  UpperCamelCase__							:				int     ,  UpperCamelCase__							:				float = 0)->   None:



						'''simple docstring'''


						__lowerCAmelCase      , __lowerCAmelCase:       Any          =			row, column
						__lowerCAmelCase:       List[Any]          =			[[default_value for c in range(UpperCAmelCase__)] for r in range(UpperCAmelCase__)]

				def __str__(	self							:				List[str])->   str:



						'''simple docstring'''


						__lowerCAmelCase:       List[str]          =			f"Matrix consist of {self.row} rows and {self.column} columns\n"

						# Make string identifier
						__lowerCAmelCase:       int          =			0
						for row_vector in self.array:
								for obj in row_vector:
										__lowerCAmelCase:       Tuple          =			max(UpperCAmelCase__     ,  len(str(UpperCAmelCase__)))
						__lowerCAmelCase:       Optional[int]          =			f"%{max_element_length}s"

						# Make string and return
						def single_line(UpperCamelCase__							:				list[float]) -> str:
								nonlocal string_format_identifier
								__lowerCAmelCase:       Optional[Any]          =			"["
								line += ", ".join(string_format_identifier % (obj,) for obj in row_vector)
								line += "]"
								return line

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

				def __repr__(	self							:				List[str])->   str:



						'''simple docstring'''


						return str(self)

				def 							lowercase_     (	self							:				Optional[int]     ,  UpperCamelCase__							:				tuple[int, int])->   bool:



						'''simple docstring'''


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

				def __getitem__(	self							:				Any     ,  UpperCamelCase__							:				tuple[int, int])->   Any:



						'''simple docstring'''


						assert self.validate_indicies(UpperCAmelCase__)
						return self.array[loc[0]][loc[1]]

				def __setitem__(	self							:				Dict     ,  UpperCamelCase__							:				tuple[int, int]     ,  UpperCamelCase__							:				float)->   None:



						'''simple docstring'''


						assert self.validate_indicies(UpperCAmelCase__)
						__lowerCAmelCase:       str          =			value

				def __add__(	self							:				Any     ,  UpperCamelCase__							:				Matrix)->   Matrix:



						'''simple docstring'''


						assert isinstance(UpperCAmelCase__     ,  UpperCAmelCase__)
						assert self.row == another.row and self.column == another.column

						# Add
						__lowerCAmelCase:       Union[str, Any]          =			Matrix(self.row     ,  self.column)
						for r in range(self.row):
								for c in range(self.column):
										__lowerCAmelCase:       List[Any]          =			self[r, c] + another[r, c]
						return result

				def __neg__(	self							:				int)->   Matrix:



						'''simple docstring'''


						__lowerCAmelCase:       Union[str, Any]          =			Matrix(self.row     ,  self.column)
						for r in range(self.row):
								for c in range(self.column):
										__lowerCAmelCase:       str          =			-self[r, c]
						return result

				def __sub__(	self							:				str     ,  UpperCamelCase__							:				Matrix)->   Matrix:



						'''simple docstring'''


						return self + (-another)

				def __mul__(	self							:				str     ,  UpperCamelCase__							:				int | float | Matrix)->   Matrix:



						'''simple docstring'''


						if isinstance(UpperCAmelCase__     ,  (int, float)):  # Scalar multiplication
								__lowerCAmelCase:       List[Any]          =			Matrix(self.row     ,  self.column)
								for r in range(self.row):
										for c in range(self.column):
												__lowerCAmelCase:       List[str]          =			self[r, c] * another
								return result
						elif isinstance(UpperCAmelCase__     ,  UpperCAmelCase__):  # Matrix multiplication
								assert self.column == another.row
								__lowerCAmelCase:       Dict          =			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:
								__lowerCAmelCase:       Union[str, Any]          =			f"Unsupported type given for another ({type(UpperCAmelCase__)})"
								raise TypeError(UpperCAmelCase__)

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



						'''simple docstring'''


						__lowerCAmelCase:       str          =			Matrix(self.column     ,  self.row)
						for r in range(self.row):
								for c in range(self.column):
										__lowerCAmelCase:       Any          =			self[r, c]
						return result




				def 							lowercase_     (	self							:				List[str]     ,  UpperCamelCase__							:				Matrix     ,  UpperCamelCase__							:				Matrix)->   Any:



						'''simple docstring'''


						assert isinstance(UpperCAmelCase__     ,  UpperCAmelCase__) and isinstance(UpperCAmelCase__     ,  UpperCAmelCase__)
						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
						__lowerCAmelCase:       Union[str, Any]          =			v.transpose()
						__lowerCAmelCase:       Any          =			(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     a__    (    )	->	Union[str, Any]:
					# a^(-1)
					__lowerCAmelCase:       List[str]          =			Matrix(3					, 3					, 0 )
					for i in range(3 ):
							__lowerCAmelCase:       Dict          =			1
					print(F"a^(-1) is {ainv}" )
					# u, v
					__lowerCAmelCase:       Any          =			Matrix(3					, 1					, 0 )
					__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase:       Optional[Any]          =			1, 2, -3
					__lowerCAmelCase:       Tuple          =			Matrix(3					, 1					, 0 )
					__lowerCAmelCase      , __lowerCAmelCase      , __lowerCAmelCase:       Tuple          =			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(__SCREAMING_SNAKE_CASE					, __SCREAMING_SNAKE_CASE )}" )






			def     a__    (    )	->	int:
					import doctest

					doctest.testmod()


			testa()






'''simple docstring'''




print((lambda quine: quine % quine)("""print((lambda quine: quine %% quine)(%r))"""))





