
'''simple docstring'''







from __future__ import annotations

from typing import Any


class 			lowerCAmelCase :




		def __init__(				self					,						UpperCamelCase					,						UpperCamelCase					,						UpperCamelCase = 0      ):
								_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= row, column
								_SCREAMING_SNAKE_CASE				= [[default_value for c in range(UpperCamelCase      )] for r in range(UpperCamelCase      )]




		def __str__(				self      ):
								_SCREAMING_SNAKE_CASE				= F'Matrix consist of {self.row} rows and {self.column} columns\n'

								# Make string identifier
								_SCREAMING_SNAKE_CASE				= 0
								for row_vector in self.array:
														for obj in row_vector:
																				_SCREAMING_SNAKE_CASE				= max(UpperCamelCase					,						len(str(UpperCamelCase      )      )      )
								_SCREAMING_SNAKE_CASE				= F'%{max_element_length}s'

								# Make string and return
								def single_line(UpperCamelCase      ) -> str:
														nonlocal string_format_identifier
														_SCREAMING_SNAKE_CASE				= "["
														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      ):
								return str(self      )




		def     lowercase       (				self					,						UpperCamelCase      ):
								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					,						UpperCamelCase      ):
								assert self.validate_indicies(UpperCamelCase      )
								return self.array[loc[0]][loc[1]]




		def __setitem__(				self					,						UpperCamelCase					,						UpperCamelCase      ):
								assert self.validate_indicies(UpperCamelCase      )
								_SCREAMING_SNAKE_CASE				= value




		def __add__(				self					,						UpperCamelCase      ):
								assert isinstance(UpperCamelCase					,						UpperCamelCase      )
								assert self.row == another.row and self.column == another.column

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




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




		def __sub__(				self					,						UpperCamelCase      ):
								return self + (-another)




		def __mul__(				self					,						UpperCamelCase      ):

								if isinstance(UpperCamelCase					,						(int, float)      ):  # Scalar multiplication
														_SCREAMING_SNAKE_CASE				= Matrix(self.row					,						self.column      )
														for r in range(self.row      ):
																				for c in range(self.column      ):
																										_SCREAMING_SNAKE_CASE				= self[r, c] * another
														return result
								elif isinstance(UpperCamelCase					,						UpperCamelCase      ):  # Matrix multiplication
														assert self.column == another.row
														_SCREAMING_SNAKE_CASE				= 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:
														_SCREAMING_SNAKE_CASE				= F'Unsupported type given for another ({type(UpperCamelCase      )})'
														raise TypeError(UpperCamelCase      )




		def     lowercase       (				self      ):
								_SCREAMING_SNAKE_CASE				= Matrix(self.column					,						self.row      )
								for r in range(self.row      ):
														for c in range(self.column      ):
																				_SCREAMING_SNAKE_CASE				= self[r, c]
								return result




		def     lowercase       (				self					,						UpperCamelCase					,						UpperCamelCase      ):
								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
								_SCREAMING_SNAKE_CASE				= v.transpose()
								_SCREAMING_SNAKE_CASE				= (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		(	):
												# a^(-1)
												_SCREAMING_SNAKE_CASE				= Matrix(3	,			3	,			0  )
												for i in range(3  ):
																		_SCREAMING_SNAKE_CASE				= 1
												print(F'a^(-1) is {ainv}'  )
												# u, v
												_SCREAMING_SNAKE_CASE				= Matrix(3	,			1	,			0  )
												_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= 1, 2, -3
												_SCREAMING_SNAKE_CASE				= Matrix(3	,			1	,			0  )
												_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE,							_SCREAMING_SNAKE_CASE				= 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		(	):
												import doctest

												doctest.testmod()




						testa()

'''simple docstring'''







# tests directory-specific settings - this file is run automatically
# by pytest before any tests are run

import sys
import warnings
from os.path import abspath, dirname, join


# allow having multiple repository checkouts and not needing to remember to rerun
# 'pip install -e .[dev]' when switching between checkouts and running tests.
_snake_case				:   Optional[Any]     =				abspath(join(dirname(dirname(dirname(__file__))), """src"""))
sys.path.insert(1, git_repo_path)


# silence FutureWarning warnings in tests since often we can't act on them until
# they become normal warnings - i.e. the tests still need to test the current functionality
warnings.simplefilter(action="""ignore""", category=FutureWarning)



def 			_a		(	_SCREAMING_SNAKE_CASE		:   Tuple  ):
						from transformers.testing_utils import pytest_addoption_shared

						pytest_addoption_shared(_SCREAMING_SNAKE_CASE  )




def 			_a		(	_SCREAMING_SNAKE_CASE		:   Union[str, Any]  ):
						from transformers.testing_utils import pytest_terminal_summary_main

						_SCREAMING_SNAKE_CASE				= terminalreporter.config.getoption("--make-reports"  )
						if make_reports:
												pytest_terminal_summary_main(_SCREAMING_SNAKE_CASE	,			id=_SCREAMING_SNAKE_CASE  )