#Libraries
from sklearn.mixture import GaussianMixture
from matplotlib.patches import Ellipse

#------Just To visualise the results----#
def draw_ellipse(position, covariance, ax=None, **kwargs):
    """Draw an ellipse with a given position and covariance"""
    ax = ax or plt.gca()

    # Convert covariance to principal axes
    if covariance.shape == (2, 2):
        U, s, Vt = np.linalg.svd(covariance)
        angle = np.degrees(np.arctan2(U[1, 0], U[0, 0]))
        width, height = 2 * np.sqrt(s)
    else:
        angle = 0
        width, height = 2 * np.sqrt(covariance)

    # Draw the Ellipse
    for nsig in range(1, 4):
        ax.add_patch(Ellipse(position, nsig * width, nsig * height,
                             angle, **kwargs))

def plot_gmm(gmm, X, label=True, ax=None):
    ax = ax or plt.gca()
    labels = gmm.fit(X).predict(X)
    if label=='r':
        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2, c=label,marker='+')
    else:
        ax.scatter(X[:, 0], X[:, 1], s=40, zorder=2,c=label,marker='_')
    ax.axis('equal')

    w_factor = 0.2 / gmm.weights_.max()
    for pos, covar, w in zip(gmm.means_, gmm.covariances_, gmm.weights_):
        draw_ellipse(pos, covar, alpha=w * w_factor)

#Segragating the positive and negative class
positive_class = df[df['Class']=='+'][['f1','f2']]
negative_class = df[df['Class']=='-'][['f1','f2']]

#Fiting the Gaussian curve
gmm_positive = GaussianMixture(n_components=1).fit(positive_class)
gmm_negative = GaussianMixture(n_components=1).fit(negative_class)

#Visualising the results
plot_gmm(gmm_positive, np.array(positive_class),label = 'r')
plot_gmm(gmm_negative, np.array(negative_class),label = 'b')