






def 	UpperCamelCase	(							snake_case__  : list						,snake_case__  : list						,snake_case__  : int	):




     '''simple docstring'''






     __snake_case      :List[Any] 							=    len(snake_case__	)
     __snake_case      :Optional[Any] 							=    [[0] * n for i in range(snake_case__	)]
     for i in range(snake_case__	):
          __snake_case      :List[Any] 							=    y_points[i]

     for i in range(2						,snake_case__	):
          for j in range(snake_case__						,snake_case__	):
               __snake_case      :List[Any] 							=    (
                   (xa - x_points[j - i + 1]) * q[j][i - 1]
                   - (xa - x_points[j]) * q[j - 1][i - 1]
               ) / (x_points[j] - x_points[j - i + 1])

     return [q[n - 1][n - 1], q]


if __name__ == "__main__":
     import doctest

     doctest.testmod()










from __future__ import annotations




class       snake_case__ :

       '''simple docstring'''



       def __init__(				self      ,    a__     )			->   None:






            '''simple docstring'''





            __snake_case      :str 							=    order

            # a_{0} ... a_{k}
            __snake_case      :int 							=    [1.0] + [0.0] * order
            # b_{0} ... b_{k}
            __snake_case      :Any 							=    [1.0] + [0.0] * order

            # x[n-1] ... x[n-k]
            __snake_case      :List[Any] 							=    [0.0] * self.order
            # y[n-1] ... y[n-k]
            __snake_case      :int 							=    [0.0] * self.order



       def        __lowercase    (				self      ,    a__      ,    a__     )			->   None:






            '''simple docstring'''





            if len(a__     ) < self.order:
                 __snake_case      :Optional[int] 							=    [1.0, *a_coeffs]

            if len(a__     ) != self.order + 1:
                 __snake_case      :Dict 							=    (
                     F'''Expected a_coeffs to have {self.order + 1} elements '''
                     F'''for {self.order}-order filter, got {len(a__     )}'''
                 )
                 raise ValueError(a__     )

            if len(a__     ) != self.order + 1:
                 __snake_case      :Optional[Any] 							=    (
                     F'''Expected b_coeffs to have {self.order + 1} elements '''
                     F'''for {self.order}-order filter, got {len(a__     )}'''
                 )
                 raise ValueError(a__     )

            __snake_case      :str 							=    a_coeffs
            __snake_case      :str 							=    b_coeffs



       def        __lowercase    (				self      ,    a__     )			->   float:






            '''simple docstring'''





            __snake_case      :List[Any] 							=    0.0

            # Start at index 1 and do index 0 at the end.
            for i in range(1      ,    self.order + 1     ):
                 result += (
                     self.b_coeffs[i] * self.input_history[i - 1]
                     - self.a_coeffs[i] * self.output_history[i - 1]
                 )

            __snake_case      :Dict 							=    (result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

            __snake_case      :Optional[int] 							=    self.input_history[:-1]
            __snake_case      :Optional[Any] 							=    self.output_history[:-1]

            __snake_case      :Union[str, Any] 							=    sample
            __snake_case      :Optional[Any] 							=    result

            return result


