# TODO: calculate the probability of a student being admitted with score of 45,85
# replace pred_prob = 0 with pred_prob = expression for that probability
pred_prob = theta_opt.dot(np.array([1, 45, 85]))
print "For a student with 45 on exam 1 and 85 on exam 2, the probability of admission = ", pred_prob
# compute accuracy on the training set
predy = log_reg1.predict(XX)
# TODO: calculate the accuracy of predictions on training set (hint: compare predy and y)
accuracy = 1. * sum([predy[i] == y[i] for i in xrange(len(y))]) / len(y)
print "Accuracy on the training set = ", accuracy
# plot the decision surface
plot_utils.plot_decision_boundary(X,y,theta_opt,'Exam 1 score', 'Exam 2 score',['Not Admitted','Admitted'])
plt.savefig('fig2.pdf')
# Compare with sklearn logistic regression
# note the parameters fed into the LogisticRegression call
from sklearn import linear_model
sk_logreg = linear_model.LogisticRegression(C=1e5,solver='lbfgs',fit_intercept=False)
sk_logreg.fit(XX,y)
print "Theta found by sklearn: ", sk_logreg.coef_
plot_utils.plot_decision_boundary_sklearn(X,y,sk_logreg,'Exam 1 score', 'Exam 2 score',['Not Admitted','Admitted'])
plt.savefig('fig2_sk.pdf')