
'''simple docstring'''







from __future__ import annotations

from typing import Any


class 		__UpperCAmelCase   :


							def __init__( self					,     lowerCAmelCase_					,     lowerCAmelCase_					,     lowerCAmelCase_ = 0						):





								"""simple docstring"""






								_snake_case		,				_snake_case     		=	row, column
								_snake_case     		=	[[default_value for c in range(lowerCAmelCase_						)] for r in range(lowerCAmelCase_						)]


							def __str__( self						):





								"""simple docstring"""






								_snake_case     		=	F'Matrix consist of {self.row} rows and {self.column} columns\n'

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

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

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


							def __repr__( self						):





								"""simple docstring"""






								return str(self						)


							def 				lowerCamelCase       ( self					,     lowerCAmelCase_						):





								"""simple docstring"""






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


							def __getitem__( self					,     lowerCAmelCase_						):





								"""simple docstring"""






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


							def __setitem__( self					,     lowerCAmelCase_					,     lowerCAmelCase_						):





								"""simple docstring"""






								assert self.validate_indicies(lowerCAmelCase_						)
								_snake_case     		=	value


							def __add__( self					,     lowerCAmelCase_						):





								"""simple docstring"""






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

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


							def __neg__( self						):





								"""simple docstring"""






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


							def __sub__( self					,     lowerCAmelCase_						):





								"""simple docstring"""






								return self + (-another)


							def __mul__( self					,     lowerCAmelCase_						):





								"""simple docstring"""






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


							def 				lowerCamelCase       ( self						):





								"""simple docstring"""






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




							def 				lowerCamelCase       ( self					,     lowerCAmelCase_					,     lowerCAmelCase_						):





								"""simple docstring"""






								assert isinstance(lowerCAmelCase_					,     lowerCAmelCase_						) and isinstance(lowerCAmelCase_					,     lowerCAmelCase_						)
								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
								_snake_case     		=	v.transpose()
								_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        SCREAMING_SNAKE_CASE__			(     ) ->			None:
						# a^(-1)
						_snake_case     		=	Matrix(3    ,       3    ,       0			)
						for i in range(3			):
							_snake_case     		=	1
						print(F'a^(-1) is {ainv}'			)
						# u, v
						_snake_case     		=	Matrix(3    ,       1    ,       0			)
						_snake_case		,				_snake_case		,				_snake_case     		=	1, 2, -3
						_snake_case     		=	Matrix(3    ,       1    ,       0			)
						_snake_case		,				_snake_case		,				_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(__A    ,       __A			)}'			)







					def        SCREAMING_SNAKE_CASE__			(     ) ->			None:
						import doctest

						doctest.testmod()





					testa()



'''simple docstring'''







from ..utils import DummyObject, requires_backends


class 		__UpperCAmelCase   (      metaclass=_lowerCamelCase		):
							__lowercase   	= ["""torch""", """torchsde"""]


							def __init__( self					,     *lowerCAmelCase_					,     **lowerCAmelCase_						):





								"""simple docstring"""






								requires_backends(self					,     ['torch', 'torchsde']						)


							@classmethod
							def 				lowerCamelCase       ( cls					,     *lowerCAmelCase_					,     **lowerCAmelCase_						):





								"""simple docstring"""






								requires_backends(cls					,     ['torch', 'torchsde']						)




							@classmethod
							def 				lowerCamelCase       ( cls					,     *lowerCAmelCase_					,     **lowerCAmelCase_						):





								"""simple docstring"""






								requires_backends(cls					,     ['torch', 'torchsde']						)

