Difference Between Scipy.optimize.least_squares and Scipy.optimize.curve_fit

Question

I'm trying to understand the difference between these two methods.

Both seem to be able to be used to find optimal parameters for an non-linear function using constraints and using least squares.

However, they are evidently not the same because curve_fit results do not correspond to a third solver whereas least_squares does.

Can someone explain the difference?

Answer 1

There is no fundamental difference between curve_fit and least_squares. Moreover, if you don't use method = 'lm'they do exactly the same thing. You can check it in a source code of curve_fit fucntion on a Github:

if method == 'lm':
    ...
    res = leastsq(func, p0, Dfun=jac, full_output=1, **kwargs)
    ...
else:
   ...
    res = least_squares(func, p0, jac=jac, bounds=bounds, method=method,
                        **kwargs)
   ...

So, curve_fit is just a wrapper around least_squares. I've just checked them out and I've got the same results from both.