将这段代码转换为伪代码：算法函数3-2：LM 1: def levenberg_marquardt(fun, grad, jacobian, x0, iterations, tol): 2: while (gnorm > tol) and (k < iterations): 3: if updateJ == 1: 4: x_log = np.append(x_log, xk.T) 5: yk = fun(xk) 6: y_log = np.append(y_log, yk) 7: H_lm = H + (lamda * np.eye(9)) 8: gfk = grad(xk) 9: pk = - np.linalg.inv(H_lm).dot(gfk) 10: pk = pk.A.reshape(1, -1)[0] 11: xk = xk + pk 12: fval = fun(xk) 13: if fval < old_fval: 14: lamda = lamda / 10 15: old_fval = fval

算法函数3-2：LM
输入：目标函数 fun，目标函数的梯度 grad，雅可比矩阵 jacobian，起始点 x0，最大迭代次数 iterations，收敛精度 tol
输出：最优解 xk

1. k = 0, lamda = 0.01, H = jacobian(x0)，old_fval = fun(x0)
2. while (gnorm > tol) and (k < iterations) do
3. if updateJ == 1 then
4. x_log = append(x_log, xk.T)
5. yk = fun(xk)
6. y_log = append(y_log, yk)
7. end if
8. H_lm = H + (lamda * eye(9))
9. gfk = grad(xk)
10. pk = - inv(H_lm) · gfk
11. pk = pk.A.reshape(1, -1)[0]
12. xk = xk + pk
13. fval = fun(xk)
14. if fval < old_fval then
15. lamda = lamda / 10
16. old_fval = fval
17. else
18. lamda = lamda * 10
19. end if
20. H = jacobian(xk)
21. k = k + 1
22. end while

23. return xk