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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def solve_dual(a, b, C, regul, method="L-BFGS-B", tol=1e-3, max_iter=500, verbose=False):
 """ Solve the "smoothed" dual objective. Parameters a: array, shape = len(a) b: array, shape = len(b) Input histograms (should be non-negative and sum to 1). C: array, shape = len(a) x len(b) Ground cost matrix. regul: Regularization object Should implement a delta_Omega(X) method. method: str Solver to be used (passed to `scipy.optimize.minimize`). tol: float Tolerance parameter. max_iter: int Maximum number of iterations. Returns ------- alpha: array, shape = len(a) beta: array, shape = len(b) Dual potentials. """


    def _func(params):
        # Unpack alpha and beta.
        alpha = params[:len(a)]
        beta = params[len(a):]

        obj, grad_alpha, grad_beta = dual_obj_grad(alpha, beta, a, b, C, regul)

        # Pack grad_alpha and grad_beta.
        grad = np.concatenate((grad_alpha, grad_beta))

        # We need to maximize the dual.
        return -obj, -grad

    # Unfortunately, `minimize` only supports functions whose argument is a
    # vector. So, we need to concatenate alpha and beta.
    alpha_init = np.zeros(len(a))
    beta_init = np.zeros(len(b))
    params_init = np.concatenate((alpha_init, beta_init))

    res = minimize(_func, params_init, method=method, jac=True,
                   tol=tol, options=dict(maxiter=max_iter, disp=verbose))

    alpha = res.x[:len(a)]
    beta = res.x[len(a):]

    return alpha, beta, res