"""
=====================
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 pylab as pl

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...")
# The return_models parameter sets that lasso_path will return
# the alphas and the coefficients as output, instead of a list
# of models as it does by default. Returning the list of models
# is deprecated and will eventually be removed in 0.15
alphas_lasso, coefs_lasso, _ = lasso_path(X, y, eps, return_models=False,
                                          fit_intercept=False)

print("Computing regularization path using the positive lasso...")
alphas_positive_lasso, coefs_positive_lasso, _ = lasso_path(
    X, y, eps, positive=True, return_models=False, 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, return_models=False, 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, return_models=False,
    fit_intercept=False)

# Display results

pl.figure(1)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(-np.log10(alphas_lasso), coefs_lasso.T)
l2 = pl.plot(-np.log10(alphas_enet), coefs_enet.T, linestyle='--')

pl.xlabel('-Log(alpha)')
pl.ylabel('coefficients')
pl.title('Lasso and Elastic-Net Paths')
pl.legend((l1[-1], l2[-1]), ('Lasso', 'Elastic-Net'), loc='lower left')
pl.axis('tight')


pl.figure(2)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(-np.log10(alphas_lasso), coefs_lasso.T)
l2 = pl.plot(-np.log10(alphas_positive_lasso), coefs_positive_lasso.T,
              linestyle='--')

pl.xlabel('-Log(alpha)')
pl.ylabel('coefficients')
pl.title('Lasso and positive Lasso')
pl.legend((l1[-1], l2[-1]), ('Lasso', 'positive Lasso'), loc='lower left')
pl.axis('tight')


pl.figure(3)
ax = pl.gca()
ax.set_color_cycle(2 * ['b', 'r', 'g', 'c', 'k'])
l1 = pl.plot(-np.log10(alphas_enet), coefs_enet.T)
l2 = pl.plot(-np.log10(alphas_positive_enet), coefs_positive_enet.T,
              linestyle='--')

pl.xlabel('-Log(alpha)')
pl.ylabel('coefficients')
pl.title('Elastic-Net and positive Elastic-Net')
pl.legend((l1[-1], l2[-1]), ('Elastic-Net', 'positive Elastic-Net'),
          loc='lower left')
pl.axis('tight')
pl.show()