# Map X onto polynomial features and normalize
p = 6
poly = sklearn.preprocessing.PolynomialFeatures(degree=p,include_bias=False)
X_poly = poly.fit_transform(X)
# set up the data matrix (expanded basis functions) with the column of ones as intercept
XX = np.vstack([np.ones((X_poly.shape[0],)),X_poly.T]).T
# set up a regularized logistic regression model
from logistic_regressor import RegLogisticRegressor
reg_lr1 = RegLogisticRegressor()
# run fmin on the loss function and gradient implemented in logistic_regressor.py
reg = 1.0
theta_opt = reg_lr1.train(XX,y,reg=reg,num_iters=1000,norm=False)
# print the theta found and the final loss
print 'Theta found by fmin_bfgs: ',theta_opt
print "Final loss = ", reg_lr1.loss(theta_opt,XX,y,0.0)
# plot the decision boundary
plot_utils.plot_decision_boundary_poly(X,y,theta_opt,reg,p,'Chip Test 1', 'Chip Test 2',['y = 0','y = 1'])
plt.savefig('fig4.pdf')
