
'''simple docstring'''


import math as m




def lowercase_		(				_lowercase     ,    _lowercase     ,    _lowercase=0.0_01			)       ->							List[Any]:
					'''simple docstring'''

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




def lowercase_		(				_lowercase     ,    _lowercase=0     ,    _lowercase=100     ,    _lowercase=0.00_01     ,    _lowercase=1e-6     ,    _lowercase=False			)       ->							str:
					'''simple docstring'''

					lowerCamelCase_   : str       =						xa  # set the initial guess
					lowerCamelCase_   : str       =						[a]
					lowerCamelCase_   : Any       =						abs(f(_lowercase			)			)
					lowerCamelCase_   : Union[str, Any]       =						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_   : Union[str, Any]       =						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

					__lowercase							:				Union[str, Any]					=       lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
					__lowercase			,						__lowercase			,						__lowercase							:				Any					=       newton_raphson(
					    f, xa=10, maxiter=1000, 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}}}')




'''simple docstring'''


def lowercase_		(				_lowercase			)       ->							int:
					'''simple docstring'''

					if not isinstance(_lowercase     ,    _lowercase			):
										raise TypeError('''recursive_lucas_number accepts only integer arguments.'''			)
					if n_th_number == 0:
										return 2
					if n_th_number == 1:
										return 1

					return recursive_lucas_number(n_th_number - 1			) + recursive_lucas_number(
					    n_th_number - 2			)




def lowercase_		(				_lowercase			)       ->							int:
					'''simple docstring'''

					if not isinstance(_lowercase     ,    _lowercase			):
										raise TypeError('''dynamic_lucas_number accepts only integer arguments.'''			)
					lowerCamelCase_, lowerCamelCase_   : List[Any]       =						2, 1
					for _ in range(_lowercase			):
										lowerCamelCase_, lowerCamelCase_   : Dict       =						b, a + b
					return a


if __name__ == "__main__":
					from doctest import testmod

					testmod()
					__lowercase							:				Any					=       int(input('''Enter the number of terms in lucas series:\n''').strip())
					print('''Using recursive function to calculate lucas series:''')
					print(''' '''.join(str(recursive_lucas_number(i)) for i in range(n)))
					print('''\nUsing dynamic function to calculate lucas series:''')
					print(''' '''.join(str(dynamic_lucas_number(i)) for i in range(n)))


