scipy fmin操作数不能与形状一起广播

Question

i'm trying to learn about optimization in Python so i've written some code to test out the fmin function.

However i keep receiving the following error:

ValueError: operands could not be broadcast together with shapes (1,2) (100,)

I can tell the issue is to do with the dimensions of my arguments but I'm not sure how to rectify it. Rather than a lambda function I also tried to def a function but I still get the same error.

I'm sure it's something pretty basic but I can't seem to understand it. Any help wold be greatly appreciated!

import numpy as np
import pandas as pd
from scipy.stats.distributions import norm
from scipy.optimize import fmin

x = np.random.normal(size=100)

norm_1 = lambda theta,x: -(np.log(norm.pdf(x,theta[0],theta[1]))).sum()

def norm_2(theta,x):
    mu = theta[0]
    sigma = theta[1]
    ll = np.log(norm.pdf(x,mu,sigma)).sum()
    return -ll

fmin(norm_1,np.array([0,1]),x)

fmin(norm_2,np.array([0,1]),x)

Answer 1

The docs for fmin say:

Definition: fmin(func, x0, args=(), xtol=0.0001, ftol=0.0001, maxiter=None, maxfun=None, full_output=0, disp=1, retall=0, callback=None)
...
    args : tuple, optional
        Extra arguments passed to func, i.e. ``f(x,*args)``.

Therefore, the third argument, args , should be a tuple:

In [45]: fmin(norm_1,np.array([0,1]),(x,))
Warning: Maximum number of function evaluations has been exceeded.
Out[45]: array([-0.02405078,  1.0203125 ])

(x, ) is a tuple containing one element, x . The docs say f(x, *args) gets called. Which mean in your case

norm_1(np.array([0,1]), *(x,))

will get called, which is equivalent to

norm_1(np.array([0,1]), x)