content: import numpy as np
  from numpy.testing import assert_array_almost_equal
  
  from sklearn.manifold import mds
  from sklearn.utils.testing import assert_raises
  
  
  def test_smacof():
      # test metric smacof using the data of "Modern Multidimensional Scaling",
      # Borg & Groenen, p 154
      sim = np.array([[0, 5, 3, 4],
                      [5, 0, 2, 2],
                      [3, 2, 0, 1],
                      [4, 2, 1, 0]])
      Z = np.array([[-.266, -.539],
                    [.451, .252],
                    [.016, -.238],
                    [-.200, .524]])
      X, _ = mds.smacof(sim, init=Z, n_components=2, max_iter=1, n_init=1)
      X_true = np.array([[-1.415, -2.471],
                         [1.633, 1.107],
                         [.249, -.067],
                         [-.468, 1.431]])
      assert_array_almost_equal(X, X_true, decimal=3)
  
  
  def test_smacof_error():
      # Not symmetric similarity matrix:
      sim = np.array([[0, 5, 9, 4],
                      [5, 0, 2, 2],
                      [3, 2, 0, 1],
                      [4, 2, 1, 0]])
  
      assert_raises(ValueError, mds.smacof, sim)
  
      # Not squared similarity matrix:
      sim = np.array([[0, 5, 9, 4],
                      [5, 0, 2, 2],
                      [4, 2, 1, 0]])
  
      assert_raises(ValueError, mds.smacof, sim)
  
      # init not None and not correct format:
      sim = np.array([[0, 5, 3, 4],
                      [5, 0, 2, 2],
                      [3, 2, 0, 1],
                      [4, 2, 1, 0]])
  
      Z = np.array([[-.266, -.539],
                    [.016, -.238],
                    [-.200, .524]])
      assert_raises(ValueError, mds.smacof, sim, init=Z, n_init=1)
  
  
  def test_MDS():
      sim = np.array([[0, 5, 3, 4],
                      [5, 0, 2, 2],
                      [3, 2, 0, 1],
                      [4, 2, 1, 0]])
      mds_clf = mds.MDS(metric=False, n_jobs=3, dissimilarity="precomputed")
      mds_clf.fit(sim)
  