def scree_plot(S, n_components=10):
    """
    Plot proportion of variance contained in each individual component
    """
    components = np.arange(n_components) + 1
    S = S ** 2
    total_var = np.sum(S[:n_components])
    proportions = S / total_var
    plt.bar(components, proportions[:n_components])
    plt.title("Variance Proportions across Principal Components")
    plt.xlabel("Principal Component")
    plt.ylabel("Proportion")
    plt.show()
	# raise NotImplementedError

def plot_component_vector(V):
	#     raise NotImplementedError
    col = np.abs(V[0,:])
	#     print("col:", col)
    xvals = np.arange(V.shape[1])
    plt.bar(xvals, col)
    plt.title("Breakdown of First Principal Component into Features")
    plt.xlabel("Feature")
    plt.ylabel("Value")
    plt.show()