




'''simple docstring'''





from __future__ import annotations

from collections.abc import Iterator
from typing import Generic, TypeVar

_SCREAMING_SNAKE_CASE							:       Optional[int]						=			TypeVar("T")




class 			_snake_case		(     Generic[T]							):




			def __init__( self    ,							a__							)    ->    Dict:

										'''simple docstring'''




										snake_case_      =				data
										snake_case_      =				None




			def __str__( self							)    ->    str:

										'''simple docstring'''




										return F'{self.data}'




class 			_snake_case		(     Generic[T]							):




			def __init__( self							)    ->    None:

										'''simple docstring'''




										snake_case_      =				None




			def __iter__( self							)    ->    Iterator[T]:

										'''simple docstring'''




										snake_case_      =				self.top
										while node:
																	yield node.data
																	snake_case_      =				node.next




			def __str__( self							)    ->    str:

										'''simple docstring'''




										return "->".join([str(a__							) for item in self]							)




			def __len__( self							)    ->    int:

										'''simple docstring'''




										return len(tuple(iter(self							)							)							)




			def        lowerCAmelCase__    ( self							)    ->    bool:

										'''simple docstring'''




										return self.top is None




			def        lowerCAmelCase__    ( self    ,							a__							)    ->    None:

										'''simple docstring'''




										snake_case_      =				Node(a__							)
										if not self.is_empty():
																	snake_case_      =				self.top
										snake_case_      =				node




			def        lowerCAmelCase__    ( self							)    ->    T:

										'''simple docstring'''




										if self.is_empty():
																	raise IndexError("pop from empty stack"							)
										assert isinstance(self.top    ,							a__							)
										snake_case_      =				self.top
										snake_case_      =				self.top.next
										return pop_node.data




			def        lowerCAmelCase__    ( self							)    ->    T:

										'''simple docstring'''




										if self.is_empty():
																	raise IndexError("peek from empty stack"							)

										assert self.top is not None
										return self.top.data




			def        lowerCAmelCase__    ( self							)    ->    None:

										'''simple docstring'''




										snake_case_      =				None


if __name__ == "__main__":
		from doctest import testmod

		testmod()










'''simple docstring'''





from __future__ import annotations

import numpy as np


def 					UpperCamelCase_(     snake_case							:	np.ndarray					):

							'''simple docstring'''






							snake_case_ ,				snake_case_      =				np.shape(snake_case					)
							if rows != columns:
														snake_case_      =				(
														    "'table' has to be of square shaped array but got a "
														    f'{rows}x{columns} array:\n{table}'
														)
														raise ValueError(snake_case					)

							snake_case_      =				np.zeros((rows, columns)					)
							snake_case_      =				np.zeros((rows, columns)					)
							for i in range(snake_case					):
														for j in range(snake_case					):
																					snake_case_      =				sum(lower[i][k] * upper[k][j] for k in range(snake_case					)					)
																					if upper[j][j] == 0:
																												raise ArithmeticError("No LU decomposition exists"					)
																					snake_case_      =				(table[i][j] - total) / upper[j][j]
														snake_case_      =				1
														for j in range(snake_case							,    snake_case					):
																					snake_case_      =				sum(lower[i][k] * upper[k][j] for k in range(snake_case					)					)
																					snake_case_      =				table[i][j] - total
							return lower, upper


if __name__ == "__main__":
		import doctest

		doctest.testmod()




