def pack_range(key, packing, grad_vars, rng):
    """Form the concatenation of a specified range of gradient tensors.

  Args:
    key: Value under which to store meta-data in packing that will be used
      later to restore the grad_var list structure.
    packing: Dict holding data describing packed ranges of small tensors.
    grad_vars: List of (grad, var) pairs for one tower.
    rng: A pair of integers giving the first, last indices of a consecutive
      range of tensors to be packed.

  Returns:
    A tensor that is the concatenation of all the specified small tensors.
  """
    to_pack = grad_vars[rng[0]:rng[1] + 1]
    members = []
    variables = []
    restore_shapes = []
    with tf.name_scope("pack"):
        for g, v in to_pack:
            variables.append(v)
            restore_shapes.append(g.shape)
            with tf.device(g.device):
                members.append(tf.reshape(g, [-1]))
        packing[key] = GradPackTuple(
            indices=range(rng[0], rng[1] + 1),
            vars=variables,
            shapes=restore_shapes)
        with tf.device(members[0].device):
            return tf.concat(members, 0)
Form the concatenation of a specified range of gradient tensors.

  Args:
    key: Value under which to store meta-data in packing that will be used
      later to restore the grad_var list structure.
    packing: Dict holding data describing packed ranges of small tensors.
    grad_vars: List of (grad, var) pairs for one tower.
    rng: A pair of integers giving the first, last indices of a consecutive
      range of tensors to be packed.

  Returns:
    A tensor that is the concatenation of all the specified small tensors.