



'''simple docstring'''



from __future__ import annotations

from typing import Any
class 	lowerCamelCase_							:







						def __init__(  self   :      List[str]				,    lowerCAmelCase__   :      int				,    lowerCAmelCase__   :      int				,    lowerCAmelCase__   :      float = 0				):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE					,SCREAMING_SNAKE_CASE					:      Optional[int]     					=			row, column
													SCREAMING_SNAKE_CASE					:      Optional[int]     					=			[[default_value for c in range(lowerCAmelCase__				)] for r in range(lowerCAmelCase__				)]







						def __str__(  self   :      Dict				):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE					:      str     					=			F"""Matrix consist of {self.row} rows and {self.column} columns\n"""

													# Make string identifier
													SCREAMING_SNAKE_CASE					:      List[str]     					=			0
													for row_vector in self.array:
																				for obj in row_vector:
																											SCREAMING_SNAKE_CASE					:      Union[str, Any]     					=			max(lowerCAmelCase__				,    len(str(lowerCAmelCase__				)				)				)
													SCREAMING_SNAKE_CASE					:      Any     					=			F"""%{max_element_length}s"""

													# Make string and return
													def single_line(lowerCAmelCase__   :      list[float]				) -> str:
																				nonlocal string_format_identifier
																				SCREAMING_SNAKE_CASE					:      Union[str, Any]     					=			'''['''
																				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   :      Optional[Any]				):

													"""simple docstring"""
													return str(self				)







						def 					__lowercase    (  self   :      List[str]				,    lowerCAmelCase__   :      tuple[int, int]				):

													"""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   :      str				,    lowerCAmelCase__   :      tuple[int, int]				):

													"""simple docstring"""
													assert self.validate_indicies(lowerCAmelCase__				)
													return self.array[loc[0]][loc[1]]







						def __setitem__(  self   :      Optional[Any]				,    lowerCAmelCase__   :      tuple[int, int]				,    lowerCAmelCase__   :      float				):

													"""simple docstring"""
													assert self.validate_indicies(lowerCAmelCase__				)
													SCREAMING_SNAKE_CASE					:      str     					=			value







						def __add__(  self   :      Dict				,    lowerCAmelCase__   :      Matrix				):

													"""simple docstring"""
													assert isinstance(lowerCAmelCase__				,    lowerCAmelCase__				)
													assert self.row == another.row and self.column == another.column

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







						def __neg__(  self   :      int				):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE					:      Optional[int]     					=			Matrix(self.row				,    self.column				)
													for r in range(self.row				):
																				for c in range(self.column				):
																											SCREAMING_SNAKE_CASE					:      List[str]     					=			-self[r, c]
													return result







						def __sub__(  self   :      Any				,    lowerCAmelCase__   :      Matrix				):

													"""simple docstring"""
													return self + (-another)







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

													"""simple docstring"""

													if isinstance(lowerCAmelCase__				,    (int, float)				):  # Scalar multiplication
																				SCREAMING_SNAKE_CASE					:      Any     					=			Matrix(self.row				,    self.column				)
																				for r in range(self.row				):
																											for c in range(self.column				):
																																		SCREAMING_SNAKE_CASE					:      Tuple     					=			self[r, c] * another
																				return result
													elif isinstance(lowerCAmelCase__				,    lowerCAmelCase__				):  # Matrix multiplication
																				assert self.column == another.row
																				SCREAMING_SNAKE_CASE					:      Optional[int]     					=			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					:      Dict     					=			F"""Unsupported type given for another ({type(lowerCAmelCase__				)})"""
																				raise TypeError(lowerCAmelCase__				)







						def 					__lowercase    (  self   :      Any				):

													"""simple docstring"""
													SCREAMING_SNAKE_CASE					:      Any     					=			Matrix(self.column				,    self.row				)
													for r in range(self.row				):
																				for c in range(self.column				):
																											SCREAMING_SNAKE_CASE					:      Optional[Any]     					=			self[r, c]
													return result







						def 					__lowercase    (  self   :      Optional[int]				,    lowerCAmelCase__   :      Matrix				,    lowerCAmelCase__   :      Matrix				):

													"""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
													SCREAMING_SNAKE_CASE					:      Optional[int]     					=			v.transpose()
													SCREAMING_SNAKE_CASE					:      int     					=			(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 					UpperCAmelCase   (						):
														# a^(-1)
														SCREAMING_SNAKE_CASE					:      Optional[Any]     					=			Matrix(3					,		3					,		0				)
														for i in range(3				):
																					SCREAMING_SNAKE_CASE					:      Optional[int]     					=			1
														print(F"""a^(-1) is {ainv}"""				)
														# u, v
														SCREAMING_SNAKE_CASE					:      str     					=			Matrix(3					,		1					,		0				)
														SCREAMING_SNAKE_CASE					,SCREAMING_SNAKE_CASE					,SCREAMING_SNAKE_CASE					:      Tuple     					=			1, 2, -3
														SCREAMING_SNAKE_CASE					:      Tuple     					=			Matrix(3					,		1					,		0				)
														SCREAMING_SNAKE_CASE					,SCREAMING_SNAKE_CASE					,SCREAMING_SNAKE_CASE					:      Dict     					=			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 					UpperCAmelCase   (						):
														import doctest

														doctest.testmod()






							testa()









'''simple docstring'''



import os


# All paths are set with the intent you should run this script from the root of the repo with the command
# python utils/check_doctest_list.py
lowerCAmelCase_     :       Optional[Any]								=						'.'


if __name__ == "__main__":
							lowerCAmelCase_     :       Optional[Any]								=						os.path.join(REPO_PATH, 'utils/documentation_tests.txt')
							lowerCAmelCase_     :       Dict								=						[]
							lowerCAmelCase_     :       Any								=						[]
							with open(doctest_file_path) as fp:
														for line in fp:
																					lowerCAmelCase_     :       List[str]								=						line.strip()
																					lowerCAmelCase_     :       Optional[Any]								=						os.path.join(REPO_PATH, line)
																					if not (os.path.isfile(path) or os.path.isdir(path)):
																												non_existent_paths.append(line)
																					all_paths.append(path)
							if len(non_existent_paths) > 0:
														lowerCAmelCase_     :       Dict								=						'\n'.join(non_existent_paths)
														raise ValueError(f'`utils/documentation_tests.txt` contains non-existent paths:\n{non_existent_paths}')
							if all_paths != sorted(all_paths):
														raise ValueError('Files in `utils/documentation_tests.txt` are not in alphabetical order.')




