import numpy as np
def broyden(f, x, eps=1e-5):
it = 0
e = np.eye(len(x)) * eps
J = (f(x-e) - f(x+e)) / (-2*eps)
x = np.array(x).reshape(len(x), 1)
fx = f(x)
while np.linalg.norm(fx) >= eps:
dx = -np.linalg.inv(J) @ fx
x = x + dx
fx = f(x)
J = J + (fx @ dx.T) / (dx.T @ dx)
it += 1
return x.flatten(), fx.flatten(), it
# Новая система уравнений
def f(x):
return np.array([
np.cos(x[0]) + x[1] - 0.5, # cos(x1)+x2-0.5=0
1.0/(x[0] + 1.5) - x[1] - 1.0 # 1/(x1+1.5)-x2-1=0
])
x, y, it = broyden(f, [0.3, 0.3])
print(x, it, sep="\n")