Python：Scipy.optimize Levenberg-marquardt 方法

Question

我有一个关于如何在 Python 中使用 Levenberg-Marquardt 优化方法的问题。在 SCIPY 图书馆里有很多optimization methods。

我尝试了两种方法（Nelder-Mead 和 Basin-hopping），都可以很好地使用以下命令：

# Nelder-Mead
res0_10 = optimize.minimize(f0_10, x0, method='Nelder-Mead', options={'disp': True, 'maxiter': 2000})

# Basin-hopping
res0_10 = optimize.basinhopping(f0_10, x0, niter=100, disp=True)

使用Levenberg-Marquardt时出现问题（我只复制了错误的部分，因为程序很长）

def f0_10(x):
    m, u, z, s = x 
    for i in range(alt_max):
         if i==alt_min: suma=0
         if i > alt_min:
         suma = suma + (B(x, i)-b0_10(x, i))**2
    return np.sqrt(suma/alt_max)

x0 = np.array([40., 0., 500., 50.])

res0_10 = root(f0_10, x0, jac=True, method='lm')

我只改了最后一句（res0_10 = root...）。程序编译得很好，但是当我执行程序时：

Exception in Tkinter callback

Traceback (most recent call last):

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\App\appdata\canopy-1.7.4.3348.win-x86_64\lib\lib-tk\Tkinter.py", line 1536, in __call__
return self.func(*args)

File "C:\Users\Quini SB\Desktop\tfg\Steyn - levmar.py", line 384, in askopenfilename
res0_10 = root(f0_10, x0, jac=True, method='lm')

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\User\lib\site-packages\scipy\optimize\_root.py", line 188, in root
sol = _root_leastsq(fun, x0, args=args, jac=jac, **options)

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\User\lib\site-packages\scipy\optimize\_root.py", line 251, in _root_leastsq
factor=factor, diag=diag)

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\User\lib\site-packages\scipy\optimize\minpack.py", line 377, in leastsq
shape, dtype = _check_func('leastsq', 'func', func, x0, args, n)

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\User\lib\site-packages\scipy\optimize\minpack.py", line 26, in _check_func
res = atleast_1d(thefunc(*((x0[:numinputs],) + args)))

File "C:\Users\Quini SB\AppData\Local\Enthought\Canopy\User\lib\site-packages\scipy\optimize\optimize.py", line 64, in __call__
self.jac = fg[1]

IndexError: invalid index to scalar variable.

为什么会出现这个错误？

Answer 1

来自文档：

jac : bool or callable, optional

    If jac is a Boolean and is True, fun is assumed to return the value
    of Jacobian along with the objective function. If False, the 
    Jacobian will be estimated numerically. jac can also be a callable 
    returning the Jacobian of fun. In this case, it must accept the
    same arguments as fun.

因此，您的函数“f0_10”需要返回两个值，因为您将 jac 设置为 True