Calculate the average gradient for a shared variable across all towers.

  Note that this function provides a synchronization point across all towers.

  Args:
    grad_and_vars: A list or tuple of (gradient, variable) tuples. Each
      (gradient, variable) pair within the outer list represents the gradient
      of the variable calculated for a single tower, and the number of pairs
      equals the number of towers.
    use_mean: if True, mean is taken, else sum of gradients is taken.
    check_inf_nan: check grads for nans and infs.

  Returns:
    The tuple ([(average_gradient, variable),], has_nan_or_inf) where the
      gradient has been averaged across all towers. The variable is chosen from
      the first tower. The has_nan_or_inf indicates the grads has nan or inf.

def aggregate_single_gradient(grad_and_vars, use_mean, check_inf_nan):
    """Calculate the average gradient for a shared variable across all towers.

  Note that this function provides a synchronization point across all towers.

  Args:
    grad_and_vars: A list or tuple of (gradient, variable) tuples. Each
      (gradient, variable) pair within the outer list represents the gradient
      of the variable calculated for a single tower, and the number of pairs
      equals the number of towers.
    use_mean: if True, mean is taken, else sum of gradients is taken.
    check_inf_nan: check grads for nans and infs.

  Returns:
    The tuple ([(average_gradient, variable),], has_nan_or_inf) where the
      gradient has been averaged across all towers. The variable is chosen from
      the first tower. The has_nan_or_inf indicates the grads has nan or inf.
  """
    grads = [g for g, _ in grad_and_vars]
    grad = tf.add_n(grads)

    if use_mean and len(grads) > 1:
        grad = tf.multiply(grad, 1.0 / len(grads))

    v = grad_and_vars[0][1]
    if check_inf_nan:
        has_nan_or_inf = tf.logical_not(tf.reduce_all(tf.is_finite(grads)))
        return (grad, v), has_nan_or_inf
    else:
        return (grad, v), None