content: """
  ======================
  SVM with custom kernel
  ======================
  
  Simple usage of Support Vector Machines to classify a sample. It will
  plot the decision surface and the support vectors.
  
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  from sklearn import svm, datasets
  
  # import some data to play with
  iris = datasets.load_iris()
  X = iris.data[:, :2]  # we only take the first two features. We could
                        # avoid this ugly slicing by using a two-dim dataset
  Y = iris.target
  
  
  def my_kernel(X, Y):
      """
      We create a custom kernel:
  
                   (2  0)
      k(X, Y) = X  (    ) Y.T
                   (0  1)
      """
      M = np.array([[2, 0], [0, 1.0]])
      return np.dot(np.dot(X, M), Y.T)
  
  
  h = .02  # step size in the mesh
  
  # we create an instance of SVM and fit out data.
  clf = svm.SVC(kernel=my_kernel)
  clf.fit(X, Y)
  
  # Plot the decision boundary. For that, we will assign a color to each
  # point in the mesh [x_min, m_max]x[y_min, y_max].
  x_min, x_max = X[:, 0].min() - 1, X[:, 0].max() + 1
  y_min, y_max = X[:, 1].min() - 1, X[:, 1].max() + 1
  xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))
  Z = clf.predict(np.c_[xx.ravel(), yy.ravel()])
  
  # Put the result into a color plot
  Z = Z.reshape(xx.shape)
  plt.pcolormesh(xx, yy, Z, cmap=plt.cm.Paired)
  
  # Plot also the training points
  plt.scatter(X[:, 0], X[:, 1], c=Y, cmap=plt.cm.Paired)
  plt.title('3-Class classification using Support Vector Machine with custom'
            ' kernel')
  plt.axis('tight')
  plt.show()
  