Newton-Raphson method for nonlinear functions

newton_raphson.py

"""
 （修正）牛顿拉夫逊迭代 求解非线性方程组
"""

import numpy as np
import sympy as sp


class NewtonRaphsonSolver:
    def __init__(self, p, x, f, tolerance=0.001):
        self.p = p
        self.x = x
        self.f = f
        self.k = p.jacobian(x)
        self.tolerance = tolerance
        self.k_inv = self.k.subs([(self.x[0], 1), (self.x[1], 2)]).inv()
        self.ans = self.iterate(sp.Matrix([1, 0]))

    def get_tangent(self, k, x):
        return k.subs([(self.x[0], x[0]), (self.x[1], x[1])])

    def iterate(self, x):
        r = self.f-self.p.subs([(self.x[0], x[0]), (self.x[1], x[1])])
        # Newton-Raphson iteration for nonlinear problem
        # k = self.get_tangent(self.k, x)
        # delta_x = k.inv()*r
        # modified Newton-Raphson
        delta_x = self.k_inv*r
        if (delta_x.T*delta_x)[0] < self.tolerance*((x.T*x)[0]):
            return delta_x+x
        return self.iterate(x+delta_x)


x1, x2 = sp.symbols('x1 x2')
x = sp.Matrix([x1, x2])
a = sp.Matrix([[1, 1], [x1, x2]])
p = a*x
f = sp.Matrix([3, 9])
solution = NewtonRaphsonSolver(p, x, f)
print(solution.ans)