如何在 scipy.optimize.least_squares 中同时返回 fun 和 jac

Question

I am using scipy.optimize.least_squares to minimise a function of >40 parameters and for my particular problem I can express the jacobian of my function analytically. However, the function I minimize and the jacobian share a lot of the same calculations. Is there a way to return both fun and jac from a single function? I know this can be done when using scipy.optimize.minimize but haven't figured out a way to do it with scipy.optimize.least_squares .

Answer 1

There is no direct analog of fun_and_jac , it seems. A workaround is to refactor a common part of a calculation and use it in both callables. For instance (here's a deliberately simplied example):

In [8]: class F(object):
   ...:     def fun(self, x):
   ...:         return fun_rosenbrock(x)
   ...:     def jac(self, x):
   ...:         return jac_rosenbrock(x)
   ...:     

In [9]: x0_rosenbrock = np.array([2, 2])
   ...: f = F()
   ...: res_3 = least_squares(f.fun, x0_rosenbrock, f.jac)
   ...: res_3.x, res_3.cost
   ...: 
   ...: 
Out[9]: (array([1., 1.]), 0.0)

Here *_rosenbrock are taken from the docstring example of least_squares :

def fun_rosenbrock(x):
     return np.array([10 * (x[1] - x[0]**2), (1 - x[0])])

def jac_rosenbrock(x):
    return np.array([
        [-20 * x[0], 10],
        [-1, 0]])