optimization - Calculate Hessian & Gradient of a function using Python -

i'm implementing unconstrained minimization of 2d functions:

• for search direction, i'm using both steepest descent , newton descent.
• for step size, i'm using backtracking line search algorithm

the code simple (mainly future reference might find helpful): function optimize(f, df, hess_f, method) looks this:

# prepare contour plot fig = pt.figure() xmesh, ymesh = np.mgrid[-5:5:100j,-5:5:100j] fmesh = f(np.array([xmesh, ymesh]))  pt.axis("equal") pt.contour(xmesh, ymesh, fmesh) pt.contour(xmesh, ymesh, fmesh, 250)  # initial guess + first update of search direction guesses = [np.array([5, 0.1])] x = guesses[-1] s = search_direction(df, hess_f, x, method)  not_done = true  while not_done:     # calculate step size using backtracking line search:     alpha_opt = backtracking_alpha(f, df, 0.5, 0.5, x, s)      # update step     next_guess = x + alpha_opt * s     guesses.append(next_guess)      # plot current step our updating contour graph:     it_array = np.array(guesses)     pt.plot(it_array.t[-2], it_array.t[-1], "-")      # check stopping condition     if (np.linalg.norm(guesses[-2] - guesses[-1]) < 0.0001):         not_done = false      # prepare next guess according search direction method     x = guesses[-1]     s = search_direction(df, hess_f, x, method)  pt.show() print("method {2} converged to: {0}, in {1} iterations".format(x, len(guesses), method)) 

it works ok: example, function

we method 0 converged to: [ 1.37484167e-04 -8.24905001e-06], in 22 iterations method 1 converged to: [ 0. 0.], in 3 iterations

the thing bothers me if fact optimization functions explicitly requires not function i'm minimizing (which of course makes sense), gradient , hessian. right i'm "hard coding" these functions, so:

def f2(x): return 100*(x[0]-3)**2 + (x[1]-1)**2

def df2(x): return np.array([200*(x[0]-3), 2*(x[1]-1)])

def hess_f2(x): return np.array([200, 0, 0, 2]).reshape((2,2))

so question is, "pythonic" way generate functions calculate gradient , hessian of input function function, in way fit above implementation? i'm guessing it's simple main experience python scripting, haven't yet done this. thanks!