code: """
  Small helpers for code that is not shown in the notebooks
  """
  
  from sklearn import neighbors, datasets, linear_model
  import pylab as pl
  import numpy as np
  from matplotlib.colors import ListedColormap
  
  # Create color maps for 3-class classification problem, as with iris
  cmap_light = ListedColormap(['#FFAAAA', '#AAFFAA', '#AAAAFF'])
  cmap_bold = ListedColormap(['#FF0000', '#00FF00', '#0000FF'])
  
  def plot_iris_knn():
      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
  
      knn = neighbors.KNeighborsClassifier(n_neighbors=3)
      knn.fit(X, y)
  
      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.linspace(x_min, x_max, 100),
                           np.linspace(y_min, y_max, 100))
      Z = knn.predict(np.c_[xx.ravel(), yy.ravel()])
  
      # Put the result into a color plot
      Z = Z.reshape(xx.shape)
      pl.figure()
      pl.pcolormesh(xx, yy, Z, cmap=cmap_light)
  
      # Plot also the training points
      pl.scatter(X[:, 0], X[:, 1], c=y, cmap=cmap_bold)
      pl.xlabel('sepal length (cm)')
      pl.ylabel('sepal width (cm)')
      pl.axis('tight')
  
  
  def plot_polynomial_regression():
      rng = np.random.RandomState(0)
      x = 2*rng.rand(100) - 1
  
      f = lambda t: 1.2 * t**2 + .1 * t**3 - .4 * t **5 - .5 * t ** 9
      y = f(x) + .4 * rng.normal(size=100)
  
      x_test = np.linspace(-1, 1, 100)
  
      pl.figure()
      pl.scatter(x, y, s=4)
  
      X = np.array([x**i for i in range(5)]).T
      X_test = np.array([x_test**i for i in range(5)]).T
      regr = linear_model.LinearRegression()
      regr.fit(X, y)
      pl.plot(x_test, regr.predict(X_test), label='4th order')
  
      X = np.array([x**i for i in range(10)]).T
      X_test = np.array([x_test**i for i in range(10)]).T
      regr = linear_model.LinearRegression()
      regr.fit(X, y)
      pl.plot(x_test, regr.predict(X_test), label='9th order')
  
      pl.legend(loc='best')
      pl.axis('tight')
      pl.title('Fitting a 4th and a 9th order polynomial')
  
      pl.figure()
      pl.scatter(x, y, s=4)
      pl.plot(x_test, f(x_test), label="truth")
      pl.axis('tight')
      pl.title('Ground truth (9th order polynomial)')
apis: matplotlib.colors.ListedColormap sklearn.linear_model.LinearRegression numpy.random.RandomState sklearn.neighbors.KNeighborsClassifier numpy.linspace sklearn.datasets.load_iris