code: def test_normalize_real():
      a = Real(2.0, 30.0, transform="normalize")
      for i in range(50):
          check_limits(a.rvs(random_state=i), 2, 30)
  
      rng = np.random.RandomState(0)
      X = rng.randn(100)
      X = 28 * (X - X.min()) / (X.max() - X.min()) + 2
  
      # Check transformed values are in [0, 1]
      assert np.all(a.transform(X) <= np.ones_like(X))
      assert np.all(np.zeros_like(X) <= a.transform(X))
  
      # Check inverse transform
      assert_array_almost_equal(a.inverse_transform(a.transform(X)), X)
  
      # log-uniform prior
      a = Real(
          10**2.0,
          10**4.0,
          prior="log-uniform",
          transform="normalize",
      )
      for i in range(50):
          check_limits(a.rvs(random_state=i), 10**2, 10**4)
  
      rng = np.random.RandomState(0)
      X = np.clip(10**3 * rng.randn(100), 10**2.0, 10**4.0)
  
      # Check transform
      assert np.all(a.transform(X) <= np.ones_like(X))
      assert np.all(np.zeros_like(X) <= a.transform(X))
  
      # Check inverse transform
      assert_array_almost_equal(a.inverse_transform(a.transform(X)), X)
  
      a = Real(0, 1, transform="normalize", dtype=float)
      for i in range(50):
          check_limits(a.rvs(random_state=i), 0, 1)
      assert_array_equal(a.transformed_bounds, (0, 1))
  
      X = rng.rand()
      # Check transformed values are in [0, 1]
      assert np.all(a.transform(X) <= np.ones_like(X))
      assert np.all(np.zeros_like(X) <= a.transform(X))
  
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, float)
      assert_array_equal(X_orig, X)
  
      a = Real(0, 1, transform="normalize", dtype="float64")
      X = np.float64(rng.rand())
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, np.float64)
  
      a = Real(0, 1, transform="normalize", dtype=np.float64)
      X = np.float64(rng.rand())
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, np.float64)
  
      a = Real(0, 1, transform="normalize", dtype="float64")
      X = np.float64(rng.rand())
      # Check inverse transform
      X_orig = a.inverse_transform(a.transform(X))
      assert isinstance(X_orig, np.float64)
  
imports: import pytest
  import numbers
  import numpy
  import os
  import yaml
  from tempfile import NamedTemporaryFile
  from numpy.testing import assert_array_almost_equal
  from numpy.testing import assert_array_equal
  from numpy.testing import assert_equal
  from numpy.testing import assert_raises_regex
  from skopt import Optimizer
  from skopt.space import Space
  from skopt.space import Real
  from skopt.space import Integer
  from skopt.space import Categorical
  from skopt.space import check_dimension
  from skopt.utils import normalize_dimensions
label_desc: Use image node_id 19 for calling a global function with example usage: test_normalize_real() without return types