



"""simple docstring"""







def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		_lowercase				: List[Any]     =   []
		_lowercase				: List[str]     =   1

		for i in range(len(snake_case_      )      ):
				if i + 1 < len(snake_case_      ) and text[i] == text[i + 1]:
						count += 1
				else:
						encoded.append((text[i], count)      )
						_lowercase				: str     =   1

		return encoded


def  __SCREAMING_SNAKE_CASE (  __UpperCAmelCase      ):
		return "".join(char * length for char, length in encoded      )


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

		testmod(name="""run_length_encode""", verbose=True)
		testmod(name="""run_length_decode""", verbose=True)








'''simple docstring'''






import math as m





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Union[str, Any] ,       snake_case_    :     int ,       snake_case_    :     Optional[Any]=0.0_0_1  )		->Tuple:






							'''simple docstring'''
							return (f(a + h  ) - f(a - h  )) / (2 * h)





def 				_SCREAMING_SNAKE_CASE(					snake_case_    :     Dict ,       snake_case_    :     List[Any]=0 ,       snake_case_    :     Dict=1_00 ,       snake_case_    :     List[str]=0.0_0_0_1 ,       snake_case_    :     str=1E-6 ,       snake_case_    :     Tuple=False  )		->List[Any]:






							'''simple docstring'''
							_lowercase							:		Tuple				=   xa  # set the initial guess
							_lowercase							:		List[str]				=   [a]
							_lowercase							:		str				=   abs(f(snake_case_  )  )
							_lowercase							:		Dict				=   lambda snake_case_  : calc_derivative(snake_case_ ,       snake_case_ ,       h=snake_case_  )  # noqa: E731  Derivative of f(x)
							for _ in range(snake_case_  ):
														if fa(snake_case_  ) == 0:
																					raise ValueError('''No converging solution found'''  )
														_lowercase							:		Tuple				=   a - f(snake_case_  ) / fa(snake_case_  )  # Calculate the next estimate
														if logsteps:
																					steps.append(snake_case_  )
														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

						lowerCamelCase__	  =		lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
						lowerCamelCase__  ,      lowerCamelCase__  ,      lowerCamelCase__	  =		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}}}''')



