def sum_grad_and_var_all_reduce(grad_and_vars,
                                num_workers,
                                alg,
                                gpu_indices,
                                aux_devices=None,
                                num_shards=1):
    """Apply all-reduce algorithm over specified gradient tensors."""
    with tf.name_scope("allreduce"):
        # Note that each grad_and_vars looks like the following:
        #   ((grad0_gpu0, var0_gpu0), ... , (grad0_gpuN, var0_gpuN))
        scaled_grads = [g for g, _ in grad_and_vars]
        if alg == "nccl":
            from tensorflow.python.ops import nccl_ops
            summed_grads = nccl_ops.all_sum(scaled_grads)
        elif alg == "simple":
            summed_grads = build_reduce_sum(scaled_grads)
        elif alg == "trivial":
            summed_grads = build_trivial_sum(scaled_grads)
        elif alg == "xring":
            summed_grads = all_reduce.build_ring_all_reduce(
                scaled_grads, num_workers, num_shards, gpu_indices, tf.add)
        elif alg == "nccl/xring":
            summed_grads = all_reduce.build_nccl_then_ring(
                scaled_grads, num_shards, tf.add)
        elif alg == "nccl/rechd":
            summed_grads = all_reduce.build_nccl_then_recursive_hd(
                scaled_grads, tf.add)
        elif alg == "nccl/pscpu":
            summed_grads = all_reduce.build_nccl_then_shuffle(
                scaled_grads, aux_devices, tf.add, tf.add_n)
        elif alg == "pscpu/pscpu":
            summed_grads = all_reduce.build_shuffle_then_shuffle(
                scaled_grads,
                aux_devices,
                # TODO(tucker): devise a way of better specifying the device
                # for the second level.
                [aux_devices[0]],
                tf.add_n)
        elif alg in ["pscpu", "psgpu"]:
            summed_grads = all_reduce.build_shuffle_all_reduce(
                scaled_grads, aux_devices, tf.add_n)
        else:
            raise ValueError("unsupported all_reduce alg: ", alg)

        result = []
        for (_, v), g in zip(grad_and_vars, summed_grads):
            result.append([g, v])
        return result
Apply all-reduce algorithm over specified gradient tensors.