


'''simple docstring'''
from sympy import diff, lambdify, symbols
from sympy.functions import *  # noqa: F403


def 			_lowercase       (				UpperCamelCase__       :					str,				UpperCamelCase__       :					complex,				UpperCamelCase__       :					str = "x",				UpperCamelCase__       :					float = 10**-10,				UpperCamelCase__       :					int = 1,				):
 __A  :		Optional[int]       =			symbols(UpperCamelCase__			)
 __A  :		Tuple       =			lambdify(UpperCamelCase__,				UpperCamelCase__			)
 __A  :		int       =			lambdify(UpperCamelCase__,				diff(UpperCamelCase__,				UpperCamelCase__			)			)

 __A  :		Any       =			starting_point

 while True:
  if diff_function(UpperCamelCase__			) != 0:
   __A  :		Optional[Any]       =			prev_guess - multiplicity * func(UpperCamelCase__			) / diff_function(
       UpperCamelCase__			)
  else:
   raise ZeroDivisionError('Could not find root'			) from None

  # Precision is checked by comparing the difference of consecutive guesses
  if abs(next_guess - prev_guess			) < precision:
   return next_guess

  __A  :		List[str]       =			next_guess


# Let's Execute
if __name__ == "__main__":
 # Find root of trigonometric function
 # Find value of pi
 print(f'''The root of sin(x) = 0 is {newton_raphson("sin(x)", 2)}''')

 # Find root of polynomial
 # Find fourth Root of 5
 print(f'''The root of x**4 - 5 = 0 is {newton_raphson("x**4 -5", 0.4 +5J)}''')

 # Find value of e
 print(
     'The root of log(y) - 1 = 0 is ',
     f'''{newton_raphson("log(y) - 1", 2, variable="y")}''',
 )

 # Exponential Roots
 print(
     'The root of exp(x) - 1 = 0 is',
     f'''{newton_raphson("exp(x) - 1", 1_0, precision=0.0_05)}''',
 )

 # Find root of cos(x)
 print(f'''The root of cos(x) = 0 is {newton_raphson("cos(x)", 0)}''')










'''simple docstring'''
from __future__ import annotations

class 						_lowerCamelCase					:




 '''simple docstring'''


 def __init__(      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Dict       =			order

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

  # x[n-1] ... x[n-k]
  __A  :		Optional[int]       =			[0.0] * self.order
  # y[n-1] ... y[n-k]
  __A  :		Dict       =			[0.0] * self.order


 def  snake_case__   (      self      ,      __lowercase      ,      __lowercase						):

  """simple docstring"""







  if len(__lowercase						) < self.order:
   __A  :		List[Any]       =			[1.0, *a_coeffs]

  if len(__lowercase						) != self.order + 1:
   __A  :		Tuple       =			(
       F"""Expected a_coeffs to have {self.order + 1} elements """
       F"""for {self.order}-order filter, got {len(__lowercase						)}"""
   )
   raise ValueError(__lowercase						)

  if len(__lowercase						) != self.order + 1:
   __A  :		List[Any]       =			(
       F"""Expected b_coeffs to have {self.order + 1} elements """
       F"""for {self.order}-order filter, got {len(__lowercase						)}"""
   )
   raise ValueError(__lowercase						)

  __A  :		Optional[int]       =			a_coeffs
  __A  :		Optional[int]       =			b_coeffs







 def  snake_case__   (      self      ,      __lowercase						):

  """simple docstring"""







  __A  :		Union[str, 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]
   )

  __A  :		Optional[int]       =			(result + self.b_coeffs[0] * sample) / self.a_coeffs[0]

  __A  :		List[str]       =			self.input_history[:-1]
  __A  :		Optional[int]       =			self.output_history[:-1]

  __A  :		Optional[int]       =			sample
  __A  :		Dict       =			result

  return result






