newton_method

from math import fabs

e = 10e-3


def newton_method(x0, f, df):
    x1 = x0 - f(x0) / df(x0)
    iteration = 1
    print('k | x(k) | F(x(k)) | dF(x(k)) | -F/dF')
    print('iter: {} | {} | {} | {} | '.format(iteration, x1, f(x1), df(x1), -f(x1)/df(x1)))
    while fabs(x1 - x0) >= e:
        iteration += 1
        x0 = x1
        x1 = x1 - f(x1) / df(x1)
        print('iter: {} | {} | {} | {} | '.format(iteration, x1, f(x1), df(x1), -f(x1)/df(x1)))
    return x1, iteration


def main():
    intervals = [(-2, -1), (-1, 0), (0, 1)]
    def function(x): return x ** 3 + x ** 2 - x - 0.5
    def dfunction(x): return 3 * x ** 2 + 2 * x - 1

    # newton method
    print('Newton method')

    res, iterations = newton_method(intervals[0][0], function, dfunction)
    print('Root = {}, {} iterations'.format(res, iterations))

    res, iterations = newton_method(intervals[1][1], function, dfunction)
    print('Root = {}, {} iterations'.format(res, iterations))

    res, iterations = newton_method(intervals[2][1], function, dfunction)
    print('Root = {}, {} iterations'.format(res, iterations))


if __name__ == '__main__':
    main()