






"""simple docstring"""


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




def      snake_case    (A_ :NDArray[floataa]      ,     A_ :NDArray[floataa] ):







  '''simple docstring'''

  a,	a	:     Optional[Any]							=  np.shape(A_ )

  a	:     NDArray[floataa]							=  np.zeros((rows, 1)      ,     dtype=A_ )
  for row in reversed(range(A_ ) ):
    a	:     Tuple							=  0
    for col in range(row + 1      ,     A_ ):
      total += coefficients[row, col] * x[col]

    a	:     int							=  (vector[row] - total) / coefficients[row, row]

  return x




def      snake_case    (A_ :NDArray[floataa]      ,     A_ :NDArray[floataa] ):







  '''simple docstring'''

  a,	a	:     List[str]							=  np.shape(A_ )
  if rows != columns:
    return np.array(()      ,     dtype=A_ )

  # augmented matrix
  a	:     NDArray[floataa]							=  np.concatenate((coefficients, vector)      ,     axis=1 )
  a	:     List[str]							=  augmented_mat.astype('float64' )

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

  a	:     Optional[Any]							=  retroactive_resolution(
      augmented_mat[:, 0:columns]      ,     augmented_mat[:, columns : columns + 1] )

  return x


if __name__ == "__main__":
   import doctest

   doctest.testmod()












"""simple docstring"""


from __future__ import annotations




def      snake_case    (A_ :int ):







  '''simple docstring'''

  assert (
      isinstance(A_      ,     A_ ) and mask > 0
  ), f'''mask needs to be positive integer, your input {mask}'''
  a	:     Any							=  []
  a	:     Union[str, Any]							=  mask

  while submask:
    all_submasks.append(A_ )
    a	:     Any							=  (submask - 1) & mask

  return all_submasks


if __name__ == "__main__":
   import doctest

   doctest.testmod()




