content: """
  =====================
  Lasso and Elastic Net
  =====================
  
  Lasso and elastic net (L1 and L2 penalisation) implemented using a
  coordinate descent.
  
  The coefficients can be forced to be positive.
  """
  print(__doc__)
  
  # Author: Alexandre Gramfort <alexandre.gramfort@inria.fr>
  # License: BSD 3 clause
  
  import numpy as np
  import matplotlib.pyplot as plt
  
  from sklearn.linear_model import lasso_path, enet_path
  from sklearn import datasets
  
  diabetes = datasets.load_diabetes()
  X = diabetes.data
  y = diabetes.target
  
  X /= X.std(axis=0)  # Standardize data (easier to set the l1_ratio parameter)
  
  # Compute paths
  
  eps = 5e-3  # the smaller it is the longer is the path
  
  print("Computing regularization path using the lasso...")
  alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, fit_intercept=False)
  
  print("Computing regularization path using the positive lasso...")
  alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
      X, y, eps, positive=True, fit_intercept=False)
  print("Computing regularization path using the elastic net...")
  alphas_enet, coefs_enet, _ = enet_path(
      X, y, eps=eps, l1_ratio=0.8, fit_intercept=False)
  
  print("Computing regularization path using the positve elastic net...")
  alphas_positive_enet, coefs_positive_enet, _ = enet_path(
      X, y, eps=eps, l1_ratio=0.8, positive=True, fit_intercept=False)
  
  # Display results
  
  plt.figure(1)
  ax = plt.gca()
  ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
  l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T)
  l2 = plt.plot(-np.log10(alphas_enet), coefs_enet.T, linestyle='--')
  
  plt.xlabel('-Log(alpha)')
  plt.ylabel('coefficients')
  plt.title('Lasso and Elastic-Net Paths')
  plt.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
  plt.axis('tight')
  
  
  plt.figure(2)
  ax = plt.gca()
  ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
  l1 = plt.plot(-np.log10(alphas_lasso), coefs_lasso.T)
  l2 = plt.plot(-np.log10(alphas_positive_lasso), coefs_positive_lasso.T,
                linestyle='--')
  
  plt.xlabel('-Log(alpha)')
  plt.ylabel('coefficients')
  plt.title('Lasso and positive Lasso')
  plt.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
  plt.axis('tight')
  
  
  plt.figure(3)
  ax = plt.gca()
  ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
  l1 = plt.plot(-np.log10(alphas_enet), coefs_enet.T)
  l2 = plt.plot(-np.log10(alphas_positive_enet), coefs_positive_enet.T,
                linestyle='--')
  
  plt.xlabel('-Log(alpha)')
  plt.ylabel('coefficients')
  plt.title('Elastic-Net and positive Elastic-Net')
  plt.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
             loc='lower left')
  plt.axis('tight')
  plt.show()
  