code: def test_mixed_spaces(optimizer):
      space = [("-2", "-1", "0", "1", "2"), (-2.0, 2.0)]
      x0 = [["0", 2.0], ["1", 1.0], ["2", 1.0]]
      n_calls = 5
      check_init_vals(optimizer, bench5, space, x0, n_calls)
  
imports: from functools import partial
  from itertools import product
  import numpy
  from scipy.optimize import OptimizeResult
  import pytest
  from numpy.testing import assert_almost_equal
  from numpy.testing import assert_array_less
  from numpy.testing import assert_array_equal
  from numpy.testing import assert_array_almost_equal
  from numpy.testing import assert_equal
  from numpy.testing import assert_raises
  from skopt import dummy_minimize
  from skopt import gp_minimize
  from skopt import forest_minimize
  from skopt import gbrt_minimize
  from skopt.benchmarks import branin
  from skopt.benchmarks import bench1
  from skopt.benchmarks import bench4
  from skopt.benchmarks import bench5
  from skopt.callbacks import DeltaXStopper
  from skopt.space import Space
label_desc: Use image node_id 15 for calling a global function with example usage: test_mixed_spaces(optimizer) without return types