# Listing 3
def roc_curve(y, prob):
    tpr_list = []
    fpr_list = []
    threshold = np.linspace(1.1, 0, 10)
    for t in threshold:
        y_pred = np.zeros(y.shape[0])
        y_pred[prob >= t] = 1
        TN = y_pred[(y_pred == y) & (y == 0)].shape[0]
        TP = y_pred[(y_pred == y) & (y == 1)].shape[0]
        FP = y_pred[(y_pred != y) & (y == 0)].shape[0]
        FN = y_pred[(y_pred != y) & (y == 1)].shape[0]
        TPR = TP / (TP + FN)
        FPR = FP / (FP + TN)
        tpr_list.append(TPR)
        fpr_list.append(FPR)
    return fpr_list, tpr_list, threshold

prob = predict_proba(x)
fpr, tpr, threshold = roc_curve(y, prob)

plt.plot(fpr, tpr, 'b')
plt.plot([0,1],[0,1], 'r--')
plt.xlabel("False Positive Rate", fontsize=12)
plt.ylabel("True Positive Rate", fontsize=12)

plt.show()