Support for external function call

[kalosu]

Hi @Nicholaswogan,

I am interested in using your NumbaMinPack implementation for finding the roots of a non-linear problem.

At the moment I am using scipy's root function for doing this but the thing is I need to apply this root finding routine while iterating over a sequence of points.

For a small number of points, I do not have that much of a problem but once the number is increased, scipy's standard root finding is not feasible anymore.

I was then searching for an alternative and found your project. The thing that I was wondering about is: How can I pass an argument which is a scipy function to the function for which I want to find the root.

The problem that I am trying to solve is somehow described as:

In where $\nabla H(\xi,\eta)$ is in fact a RectBivariateSpline function.

Right now I am doing the following:

        for i in range(0,self.N_total,1):
            sol = optimize.root(xi_np1_3,x0=xi_n[i],args=(eta_n[i],h,xi_n[i],self.H_initial_sp))
            self.xi_np1_eval[i] = sol.x

in where xi_np1_3 is given as:

def xi_np1_3(xi,eta,h,xi_n,H):
    H_grad_y = H.ev(eta,xi,dx=1)
    return (xi - xi_n + h*H_grad_y)

So in this case, everything would be a float (supported by Numba) except the Spline object (not supported by Numba) which is evaluated internally within the root finding calls.

Do you know what could I do in this case? Is there any way in which I can have a callback to the Spline ev method and return directly a float to your root finding routine? I guess this could work and would be supported by Numba right?