content: """
  ========================================
  Lasso and Elastic Net for Sparse Signals
  ========================================
  
  Estimates Lasso and Elastic-Net regression models on a manually generated
  sparse signal corrupted with an additive noise. Estimated coefficients are
  compared with the ground-truth.
  
  """
  print(__doc__)
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  from sklearn.metrics import r2_score
  
  ###############################################################################
  # generate some sparse data to play with
  np.random.seed(42)
  
  n_samples, n_features = 50, 200
  X = np.random.randn(n_samples, n_features)
  coef = 3 * np.random.randn(n_features)
  inds = np.arange(n_features)
  np.random.shuffle(inds)
  coef[inds[10:]] = 0  # sparsify coef
  y = np.dot(X, coef)
  
  # add noise
  y += 0.01 * np.random.normal((n_samples,))
  
  # Split data in train set and test set
  n_samples = X.shape[0]
  X_train, y_train = X[:n_samples / 2], y[:n_samples / 2]
  X_test, y_test = X[n_samples / 2:], y[n_samples / 2:]
  
  ###############################################################################
  # Lasso
  from sklearn.linear_model import Lasso
  
  alpha = 0.1
  lasso = Lasso(alpha=alpha)
  
  y_pred_lasso = lasso.fit(X_train, y_train).predict(X_test)
  r2_score_lasso = r2_score(y_test, y_pred_lasso)
  print(lasso)
  print("r^2 on test data : %f" % r2_score_lasso)
  
  ###############################################################################
  # ElasticNet
  from sklearn.linear_model import ElasticNet
  
  enet = ElasticNet(alpha=alpha, l1_ratio=0.7)
  
  y_pred_enet = enet.fit(X_train, y_train).predict(X_test)
  r2_score_enet = r2_score(y_test, y_pred_enet)
  print(enet)
  print("r^2 on test data : %f" % r2_score_enet)
  
  plt.plot(enet.coef_, label='Elastic net coefficients')
  plt.plot(lasso.coef_, label='Lasso coefficients')
  plt.plot(coef, '--', label='original coefficients')
  plt.legend(loc='best')
  plt.title("Lasso R^2: %f, Elastic Net R^2: %f"
            % (r2_score_lasso, r2_score_enet))
  plt.show()
  