





import math as m


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_=0.0_0_1		) ->  Union[str, Any]:
		return (f(a + h		) - f(a - h		)) / (2 * h)


def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_=0				,							SCREAMING_SNAKE_CASE_=1_0_0				,							SCREAMING_SNAKE_CASE_=0.0_0_0_1				,							SCREAMING_SNAKE_CASE_=1E-6				,							SCREAMING_SNAKE_CASE_=False		) ->  Optional[int]:
		lowerCamelCase :			Tuple    		=xa  # set the initial guess
		lowerCamelCase :			Optional[Any]    		=[a]
		lowerCamelCase :			Any    		=abs(f(SCREAMING_SNAKE_CASE_		)		)
		lowerCamelCase :			List[str]    		=lambda SCREAMING_SNAKE_CASE_		: calc_derivative(SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_				,							h=SCREAMING_SNAKE_CASE_		)  # noqa: E731  Derivative of f(x)
		for _ in range(SCREAMING_SNAKE_CASE_		):
				if fa(SCREAMING_SNAKE_CASE_		) == 0:
						raise ValueError('''No converging solution found'''		)
				lowerCamelCase :			int    		=a - f(SCREAMING_SNAKE_CASE_		) / fa(SCREAMING_SNAKE_CASE_		)  # Calculate the next estimate
				if logsteps:
						steps.append(SCREAMING_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

				snake_case_				=      lambda x: m.tanh(x) ** 2 - m.exp(3 * x)  # noqa: E731
				snake_case_,							snake_case_,							snake_case_				=      newton_raphson(
				    f, xa=1_0, maxiter=1_0_0_0, 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}}}""")








import pytest

from datasets.utils.version import Version


@pytest.mark.parametrize(
    '''other, expected_equality'''				,							[
        (Version('''1.0.0'''		), True),
        ('''1.0.0''', True),
        (Version('''2.0.0'''		), False),
        ('''2.0.0''', False),
        ('''1''', False),
        ('''a''', False),
        (1, False),
        (None, False),
    ]				,							)
def        A__						(							SCREAMING_SNAKE_CASE_				,							SCREAMING_SNAKE_CASE_		) ->  Optional[int]:
		lowerCamelCase :			str    		=Version('''1.0.0'''		)
		assert (version == other) is expected_equality
		assert (version != other) is not expected_equality
		assert (hash(SCREAMING_SNAKE_CASE_		) == hash(SCREAMING_SNAKE_CASE_		)) is expected_equality

