def eval_mejora_m(f,xk,dk):
#modelo:
qk = lambda x: f(xk) + gradiente(f,xk).T@(x-xk) + 0.5*(x-xk).T@(hessiano(f,xk)@(x-xk))
mk = lambda d: qk(xk + d)
ared = f(xk) - f(xk + dk)
pred = mk(0) - mk(dk)
return ared/pred
def punto_cauchy(f,x,Dk):
gk = gradiente(f,x)
Bk = hessiano(f,x)
gkTBkgk = gk.T@(Bk@gk)
min_cuadratica = np.power(norm(gk),3)/(Dk*gkTBkgk)
tk = 1 if gkTBkgk <= 0 else np.min([min_cuadratica,1])
dk = -tk*(Dk*gk/norm(gk))
return dk
def metodo_de_newton(f, x0, e, kmax, metodo):
k = 0
x = x0
while (gradiente(f, x).all() > e and k < kmax):
d = solve(hessiano(f, x), -gradiente(f, x))
t = metodo(f, x, d)
x = x + t * d
k = k + 1
return x
def metodo_de_Levenberg_Marquardt(f, x0, e, kmax, g, metodo):
k = 0
x = x0
while (norm(gradiente(f, x)) > e and k < kmax):
B = hessiano(f, x)
mu = np.min(eigvals(B))
if (mu <= 0):
B += (-mu + g) * np.eye(B.shape[0])
d = solve(B, -gradiente(f, x))
t = metodo(f, x, d)
x = x + t * d
k = k + 1
return x