






"""simple docstring"""


def    lowerCAmelCase							(       __UpperCamelCase					):




  """simple docstring"""







  if not isinstance(__UpperCamelCase						,			__UpperCamelCase					):
    raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''					)
  if len(__UpperCamelCase					) == 0:
    raise ValueError('''Input list must be a non empty list'''					)
  if len(__UpperCamelCase					) == 1:
    return True
  try:
    __A		     =					series[1] / series[0]
    for index in range(len(__UpperCamelCase					) - 1					):
      if series[index + 1] / series[index] != common_ratio:
        return False
  except ZeroDivisionError:
    return False
  return True



def    lowerCAmelCase							(       __UpperCamelCase					):




  """simple docstring"""







  if not isinstance(__UpperCamelCase						,			__UpperCamelCase					):
    raise ValueError('''Input series is not valid, valid series - [2, 4, 8]'''					)
  if len(__UpperCamelCase					) == 0:
    raise ValueError('''Input list must be a non empty list'''					)
  __A		     =					1
  for value in series:
    answer *= value
  return pow(__UpperCamelCase						,			1 / len(__UpperCamelCase					)					)


if __name__ == "__main__":
       import doctest

       doctest.testmod()






"""simple docstring"""






import math as m






def 		_snake_case			(      lowercase__						:    Any ,	lowercase__						:    Any ,	lowercase__						:    Optional[int]=0.001						)    ->							Tuple:


			'''simple docstring'''





			return (f(a + h						) - f(a - h						)) / (2 * h)






def 		_snake_case			(      lowercase__						:    Optional[Any] ,	lowercase__						:    List[str]=0 ,	lowercase__						:    Union[str, Any]=1_0_0 ,	lowercase__						:    Any=0.0001 ,	lowercase__						:    List[str]=1E-6 ,	lowercase__						:    str=False						)    ->							List[str]:


			'''simple docstring'''





			lowerCAmelCase_       :Dict     	=    xa  # set the initial guess
			lowerCAmelCase_       :int     	=    [a]
			lowerCAmelCase_       :int     	=    abs(f(lowercase__						)						)
			lowerCAmelCase_       :Optional[int]     	=    lambda lowercase__						: calc_derivative(lowercase__ ,	lowercase__ ,	h=lowercase__						)  # noqa: E731  Derivative of f(x)
			for _ in range(lowercase__						):
						if fa(lowercase__						) == 0:
									raise ValueError("""No converging solution found"""						)
						lowerCAmelCase_       :Tuple     	=    a - f(lowercase__						) / fa(lowercase__						)  # Calculate the next estimate
						if logsteps:
									steps.append(lowercase__						)
						if error < maxerror:
									break
			else:
						raise ValueError("""Iteration limit reached, no converging solution found"""						)
			if logsteps:
						# If logstep is true, then log intermediate steps
						return a, error, steps
			return a, error


if __name__ == "__main__":
				from matplotlib import pyplot as plt

				__UpperCAmelCase 					=    lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				__UpperCAmelCase					,					__UpperCAmelCase					,					__UpperCAmelCase 					=    newton_raphson(
				    f, xa=10, maxiter=10_00, step=1e-6, logsteps=True
				)
				plt.plot([abs(f(x)) for x in steps])
				plt.xlabel('step')
				plt.ylabel('error')
				plt.show()
				print(F"""solution = {{{solution:f}}}, error = {{{error:f}}}""")






