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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 adam(f, x, learning_rate=1e-3, beta1=0.9, beta2=0.999, eps=1e-8, maxiter=1000, tol=1e-16, callback=None):
 r"""ADAM method to minimize an objective function. General implementation of ADAM for solving .. math:: \min f(x) where :math:`f` is a differentiable functional. The algorithm is described in [KB2015] (`arxiv <https://arxiv.org/abs/1412.6980>`_). All parameter names and default valuesare taken from the article. Parameters f : `Functional` Goal functional. Needs to have ``f.gradient``. x : ``f.domain`` element Starting point of the iteration, updated in place. learning_rate : positive float, optional Step length of the method. beta1 : float in [0, 1), optional Update rate for first order moment estimate. beta2 : float in [0, 1), optional Update rate for second order moment estimate. eps : positive float, optional A small constant for numerical stability. maxiter : int, optional Maximum number of iterations. tol : positive float, optional Tolerance that should be used for terminating the iteration. callback : callable, optional Object executing code per iteration, e.g. plotting each iterate. See Also -------- odl.solvers.smooth.gradient.steepest_descent : Simple gradient descent. odl.solvers.iterative.iterative.landweber : Optimized solver for the case ``f(x) = ||Ax - b||_2^2``. odl.solvers.iterative.iterative.conjugate_gradient : Optimized solver for the case ``f(x) = x^T Ax - 2 x^T b``. References [KB2015] Kingma, D P and Ba, J. *Adam: A Method for Stochastic Optimization*, ICLR 2015. """

    grad = f.gradient
    if x not in grad.domain:
        raise TypeError('`x` {!r} is not in the domain of `grad` {!r}'
                        ''.format(x, grad.domain))

    m = grad.domain.zero()
    v = grad.domain.zero()

    grad_x = grad.range.element()
    for _ in range(maxiter):
        grad(x, out=grad_x)

        if grad_x.norm() < tol:
            return

        m.lincomb(beta1, m, 1 - beta1, grad_x)
        v.lincomb(beta2, v, 1 - beta2, grad_x ** 2)

        step = learning_rate * np.sqrt(1 - beta2) / (1 - beta1)

        x.lincomb(1, x, -step, m / (np.sqrt(v) + eps))

        if callback is not None:
            callback(x)