






"""simple docstring"""





import numpy as np
from numpy import floataa
from numpy.typing import NDArray






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__  ,     lowercase__:    str        =      np.shape(_A		)

       lowercase__:    int        =      np.zeros((rows, 1)						,       dtype=_A		)
       for row in reversed(range(_A		)		):
              lowercase__:    Dict        =      0
              for col in range(row + 1						,       _A		):
                     total += coefficients[row, col] * x[col]

              lowercase__:    List[str]        =      (vector[row] - total) / coefficients[row, row]

       return x






def     A(  snake_case_						,       snake_case_		):
       """simple docstring"""





       lowercase__  ,     lowercase__:    Tuple        =      np.shape(_A		)
       if rows != columns:
              return np.array(()						,       dtype=_A		)

       # augmented matrix
       lowercase__:    Dict        =      np.concatenate((coefficients, vector)						,       axis=1		)
       lowercase__:    int        =      augmented_mat.astype("float64"		)

       # scale the matrix leaving it triangular
       for row in range(rows - 1		):
              lowercase__:    Dict        =      augmented_mat[row, row]
              for col in range(row + 1						,       _A		):
                     lowercase__:    List[Any]        =      augmented_mat[col, row] / pivot
                     augmented_mat[col, :] -= factor * augmented_mat[row, :]

       lowercase__:    List[Any]        =      retroactive_resolution(
           augmented_mat[:, 0:columns]						,       augmented_mat[:, columns : columns + 1]		)

       return x


if __name__ == "__main__":
  import doctest

  doctest.testmod()














"""simple docstring"""





class 		_a       :





   '''simple docstring'''






   def __init__(   self			,				UpperCAmelCase_=None)	-> List[Any]:




          '''simple docstring'''




          lowercase__:    str        =      data
          lowercase__:    Any        =      None





   def __repr__(   self)	-> Optional[Any]:




          '''simple docstring'''




          lowercase__:    Any        =      ""
          lowercase__:    Dict        =      self
          while temp:
                 string_rep += F"""<{temp.data}> ---> """
                 lowercase__:    Tuple        =      temp.next
          string_rep += "<END>"
          return string_rep







def     A(  snake_case_		):
       """simple docstring"""





       if not elements_list:
              raise Exception("The Elements List is empty"		)

       # Set first element as Head
       lowercase__:    Any        =      Node(elements_list[0]		)
       lowercase__:    Optional[int]        =      head
       # Loop through elements from position 1
       for data in elements_list[1:]:
              lowercase__:    Dict        =      Node(snake_case_		)
              lowercase__:    Dict        =      current.next
       return head


UpperCamelCase			=      [1, 3, 5, 32, 44, 12, 43]
print(F"List: {list_data}")
print("""Creating Linked List from List.""")
UpperCamelCase			=      make_linked_list(list_data)
print("""Linked List:""")







print(linked_list)






