



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



def __lowerCAmelCase       (   SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_     ):
			lowercase__         = np.shape(SCREAMING_SNAKE_CASE__     )

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

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

			return x



def __lowerCAmelCase       (   SCREAMING_SNAKE_CASE_  ,     SCREAMING_SNAKE_CASE_     ):
			lowercase__         = np.shape(SCREAMING_SNAKE_CASE__     )
			if rows != columns:
						return np.array(()  ,     dtype=SCREAMING_SNAKE_CASE__     )

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

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

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

			return x


if __name__ == "__main__":
							import doctest

							doctest.testmod()








class        A_					:




      '''simple docstring'''


      def __init__(				self:       Tuple						,      a:       Dict=None				):
       __lowerCamelCase		:							List[Any]							=						data
       __lowerCamelCase		:							Optional[Any]							=						None




      def __repr__(				self:       Optional[int]				):
       __lowerCamelCase		:							Any							=						''
       __lowerCamelCase		:							List[Any]							=						self
       while temp:
        string_rep += F'<{temp.data}> ---> '
        __lowerCamelCase		:							Any							=						temp.next
       string_rep += "<END>"
       return string_rep



def       UpperCamelCase__     (  SCREAMING_SNAKE_CASE__						):

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

 # Set first element as Head
 __lowerCamelCase		:							Optional[int]							=						Node(elements_list[0]						)
 __lowerCamelCase		:							List[str]							=						head
 # Loop through elements from position 1
 for data in elements_list[1:]:
  __lowerCamelCase		:							str							=						Node(SCREAMING_SNAKE_CASE__						)
  __lowerCamelCase		:							Tuple							=						current.next
 return head


lowercase_           =	[1, 3, 5, 3_2, 4_4, 1_2, 4_3]
print(F"""List: {list_data}""")
print('Creating Linked List from List.')
lowercase_           =	make_linked_list(list_data)
print('Linked List:')



print(linked_list)

