newtonMethod_2variables.py

import math as m


def f1(x, y):
    return 2 * x * x - x * y - 5 * x + 1


def f2(x, y):
    return x + 3 * m.log10(x) - y * y


def df1x(x, y):
    return -y + 4 * x - 5


def df2x(x, y):
    return 3 / (m.log(10) * x) + 1


def df1y(x, y):
    return -x


def df2y(x, y):
    return -2 * y


def jacobian(x, y):
    return df1x(x, y) * df2y(x, y) - df1y(x, y) * df2x(x, y)


def newtonMethod_2(y0, x0):
    x = x0
    y = y0
    for i in range(20):
        x = x - (f1(x, y) * df2y(x, y) - df1y(x, y) * f2(x, y)) / jacobian(x, y)
        y = y - (df1x(x, y) * f2(x, y) - df2x(x, y) * f1(x, y)) / jacobian(x, y)
        print('n: {2}\t x: {0:.10f}\t y: {1:.10f}'.format(x, y, i))


newtonMethod_2(1, 2)