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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 backward(self, grad_output):
 r"""Apply the adjoint of the derivative at ``grad_output``. This method is usually not called explicitly but as a part of the ``cost.backward()`` pass of a backpropagation step. Parameters grad_output : `torch.tensor._TensorBase` Tensor to which the Jacobian should be applied. See Notes for details. Returns ------- result : `torch.autograd.variable.Variable` Variable holding the result of applying the Jacobian to ``grad_output``. See Notes for details. Examples -------- Compute the Jacobian adjoint of the matrix operator, which is the operator of the transposed matrix. We compose with the ``sum`` functional to be able to evaluate ``grad``: Variable containing: 1 1 2 [torch.FloatTensor of size 3] Compute the gradient of a custom functional: Variable containing: 14 [torch.FloatTensor of size 1] Variable containing: 2 4 6 [torch.FloatTensor of size 3] Notes ----- This method applies the contribution of this node, i.e., the transpose of the Jacobian of its outputs with respect to its inputs, to the gradients of some cost function with respect to the outputs of this node. Example: Assume that this node computes :math:`x \mapsto C(f(x))`, where :math:`x` is a tensor variable and :math:`C` is a scalar-valued function. In ODL language, what ``backward`` should compute is .. math:: \nabla(C \circ f)(x) = f'(x)^*\big(\nabla C (f(x))\big) according to the chain rule. In ODL code, this corresponds to :: f.derivative(x).adjoint(C.gradient(f(x))). Hence, the parameter ``grad_output`` is a tensor variable containing :math:`y = \nabla C(f(x))`. Then, ``backward`` boils down to computing ``[f'(x)^*(y)]`` using the input ``x`` stored during the previous `forward` pass. """

        # TODO: implement directly for GPU data
        if not self.operator.is_linear:
            input_arr = self.saved_variables[0].data.cpu().numpy()
            if any(s == 0 for s in input_arr.strides):
                # TODO: remove when Numpy issue #9165 is fixed
                # https://github.com/numpy/numpy/pull/9177
                input_arr = input_arr.copy()

        grad = None

        # ODL weights spaces, pytorch doesn't, so we need to handle this
        try:
            dom_weight = self.operator.domain.weighting.const
        except AttributeError:
            dom_weight = 1.0

        try:
            ran_weight = self.operator.range.weighting.const
        except AttributeError:
            ran_weight = 1.0

        scaling = dom_weight / ran_weight

        if self.needs_input_grad[0]:
            grad_output_arr = grad_output.cpu().numpy()
            if any(s == 0 for s in grad_output_arr.strides):
                # TODO: remove when Numpy issue #9165 is fixed
                # https://github.com/numpy/numpy/pull/9177
                grad_output_arr = grad_output_arr.copy()

            if self.operator.is_linear:
                adjoint = self.operator.adjoint
            else:
                adjoint = self.operator.derivative(input_arr).adjoint

            grad_odl = adjoint(grad_output_arr)

            if scaling != 1.0:
                grad_odl *= scaling

            grad = torch.from_numpy(np.array(grad_odl, copy=False, ndmin=1))
            grad = grad.to(grad_output.device)

        return grad