from tensorflow.python.ops import array_ops

    grads, variables = zip(*grads_and_vars)

    norm = clip_ops.global_norm(grads)

    max_norm, log_mean = _adaptive_max_norm(norm, std_factor, decay,
                                            global_step, epsilon, name)

    # reports the max gradient norm for debugging
    if report_summary:
      summary.scalar("global_norm/adaptive_max_gradient_norm", max_norm)

    # factor will be 1. if norm is smaller than max_norm
    factor = array_ops.where(norm < max_norm, array_ops.ones_like(norm),
                             math_ops.exp(log_mean) / norm)

    if static_max_norm is not None:
      factor = math_ops.minimum(static_max_norm / norm, factor)

    # apply factor
    clipped_grads = []
    for grad in grads:
      if grad is None:
        clipped_grads.append(None)
      elif isinstance(grad, ops.IndexedSlices):
