MAINT: avoid redundant evaluation of user-provided function in l-bfgs-b optimization

[argriffing]

closes #4076

[argriffing]

#3913

[larsmans]

Can't you make () the default value for args? Or does it actually get None passed in?

[argriffing]

I did it like that because I knew there was some gotcha for [] as default value, but I guess this would not apply to args that are not mutable, so I'll change the default to ().

[coveralls]

Coverage increased (+0.0%) when pulling 5668269 on argriffing:streamline-approx-fprime into 187cf14 on scipy:master.

[ewmoore]

I'd imagine that at least some of the other minimization routines are also effected by this. Its probably worth making this change to them as well.

[argriffing]

I'd imagine that at least some of the other minimization routines are also effected by this. Its probably worth making this change to them as well.

I agree that the other minimization functions should be similarly changed if they suffer from similar issues, but I'm not sure I'll be up for digging through that code any time soon. Should this be required as a condition for merging the PR?

[dlax]

Have you considered adding **kwargs to approx_fprime instead of adding this helper function?
I seems to me that somthing like that would work:

def approx_fprime(xk, f, epsilon, *args, **kwargs):
     f0 = kwargs.pop('f0', None)
     if kwargs:
         raise TypeError('unepected keyword arguments: %s' % ', '.join(kwargs.keys()))
     if f0 is None:
         f0 = f(*((xk,) + args))

[argriffing]

I'd rather not... if *args means 'user-supplied args to the user-supplied callback functions' then shouldn't **kwargs mean 'user-supplied kwargs to the user-supplied callback functions'? Of course as I mentioned I'd rather just get rid of user-supplied args altogether and make them use functools.partial or some other callable instead, but this is not realistic in terms of backward compatibility.

[pv]

I think it's easiest to not go changing approx_fprime.

[argriffing]

Just to be clear, I'm -1 to adding **kwargs for the purpose of including f0, and I'm also -1 to adding **kwargs for the purpose of allowing user-supplied **kwargs to the user functions. I'm also -1 to removing the *args but only because of backwards compatibility, otherwise I'd be +1. So I agree with not changing the interface of approx_fprime.