code: def test_load_balancing():
      check_optimality(
          60, np.array([0.25, 0.25, 0.25, 0.25]), [15, 15, 15, 15]
      )
      check_optimality(1024, np.array([0.3, 0.5, 0.9]), [0, 255, 769])
      check_optimality(60, np.array([0.44, 0.33, 0.22]), [42, 18, 0])
      check_optimality(60, np.array([0.55, 0.44, 0.40]), [35, 16, 9])
      check_optimality(
          1024 * 1024,
          np.array([0.3, 0.5, 0.9, 0.6]),
          [0, 169327, 602629, 276620],
      )
      check_optimality(
          1024 * 1024,
          np.array([0.0, 0.5, 0.0, 0.6]),
          [0, 428963, 0, 619613],
      )
      assert load_balance_peers(
          60, np.array([0.55, 0.44, 0.40]), min_size=10
      ) == (41, 19, 0)
      assert load_balance_peers(
          60, np.array([0.32, 0.55, 0.44]), min_size=10
      ) == (0, 40, 20)
      assert load_balance_peers(
          2, np.array([0.55, 0.20, 0.44]), min_size=10
      ) == (1, 0, 1)
      assert load_balance_peers(
          1, np.array([0.55, 0.20, 0.44]), min_size=10
      ) == (1, 0, 0)
  
      assert load_balance_peers(100, (None, None)) == (50, 50)
      assert load_balance_peers(
          100, (None, None, None, None, None)
      ) == (20, 20, 20, 20, 20)
      assert load_balance_peers(100, (0, 0, 0, None, None)) == (
          0,
          0,
          0,
          50,
          50,
      )
  
      with pytest.raises(AssertionError):
          load_balance_peers(100, (0, 0, 0))
  
      for i in range(10):
          vector_size = np.random.randint(1, 1024**3)
          num_peers = np.random.randint(1, 256)
          scale = 1e-9 + np.random.rand() * 1e5
          bandwidths = np.random.rand(num_peers) * scale + 1e-6
          min_size = np.random.choice(
              [0, np.random.randint(0, vector_size // 10)]
          )
          assignment = load_balance_peers(
              vector_size, bandwidths, min_size
          )
          assert np.sum(assignment) == vector_size
          assert np.min(assignment) >= 0
  
imports: import random
  import time
  import numpy
  import pytest
  import torch
  import hivemind
  from hivemind.averaging import DecentralizedAverager
  from hivemind.averaging.allreduce import AveragingMode
  from hivemind.averaging.control import AveragingStage
  from hivemind.averaging.key_manager import GroupKeyManager
  from hivemind.averaging.load_balancing import load_balance_peers
  from hivemind.averaging.partition import AllreduceException
  from hivemind.p2p import PeerID
  from test_utils.dht_swarms import launch_dht_instances
label_desc: Use image node_id 10 for calling a global function with example usage: test_load_balancing() without return types