print(__doc__)
from scipy import linalg
import numpy as np
import matplotlib.pyplot as plt
import matplotlib as mpl
from matplotlib import colors
from sklearn.discriminant_analysis import LinearDiscriminantAnalysis, QuadraticDiscriminantAnalysis

cmap = colors.LinearSegmentedColormap('red_blue_classes', {'red': [(0, 1, 1), (1, 0.7, 0.7)], 'green': [(0, 0.7, 0.7), (1, 0.7, 0.7)], 'blue': [(0, 0.7, 0.7), (1, 1, 1)]})
plt.cm.register_cmap(cmap=cmap)

def dataset_fixed_cov():
    n, dim = 300, 2
    np.random.seed(0)
    C = np.array([[0., -0.23], [0.83, .23]])
    X = np.r_[np.dot(np.random.randn(n, dim), C), np.dot(np.random.randn(n, dim), C) + np.array([1, 1])]
    y = np.hstack((np.zeros(n), np.ones(n)))
    return X, y

def dataset_cov():
    n, dim = 300, 2
    np.random.seed(0)
    C = np.array([[0., -1.], [2.5, .7]]) * 2.
    X = np.r_[np.dot(np.random.randn(n, dim), C), np.dot(np.random.randn(n, dim), C.T) + np.array([1, 4])]
    y = np.hstack((np.zeros(n), np.ones(n)))
    return X, y

def plot_data(lda, X, y, y_pred, fig_index, plot_cov):
    splot = plt.subplot(2, 2, fig_index)
    plt.title('Linear Discriminant Analysis' if fig_index == 1 else 'Quadratic Discriminant Analysis' if fig_index == 2 else '')
    plt.ylabel('Data with\n fixed covariance' if fig_index == 1 else 'Data with\n varying covariances' if fig_index == 3 else '')

    tp = (y == y_pred)
    colors_list = ['red', 'blue']
    markers_list = ['.', 'x']

    for i in range(2):
        tp_i, fp_i = tp[y == i], ~tp[y == i]
        X_i = X[y == i]
        X_tp, X_fp = X_i[tp_i], X_i[fp_i]
        plt.scatter(X_tp[:, 0], X_tp[:, 1], marker=markers_list[i], color=colors_list[i])
        plt.scatter(X_fp[:, 0], X_fp[:, 1], marker=markers_list[i], s=20, color='#990000' if i == 0 else '#000099')

    nx, ny = 200, 100
    x_min, x_max = plt.xlim()
    y_min, y_max = plt.ylim()
    xx, yy = np.meshgrid(np.linspace(x_min, x_max, nx), np.linspace(y_min, y_max, ny))
    Z = lda.predict_proba(np.c_[xx.ravel(), yy.ravel()])[:, 1].reshape(xx.shape)
    plt.pcolormesh(xx, yy, Z, cmap='red_blue_classes', norm=colors.Normalize(0., 1.), zorder=0)
    plt.contour(xx, yy, Z, [0.5], linewidths=2., colors='white')
    plt.plot(lda.means_[0][0], lda.means_[0][1], '*', color='yellow', markersize=15, markeredgecolor='grey')
    plt.plot(lda.means_[1][0], lda.means_[1][1], '*', color='yellow', markersize=15, markeredgecolor='grey')

    if plot_cov:
        plot_ellipse(splot, lda.means_[0], lda.covariance_, 'red')
        plot_ellipse(splot, lda.means_[1], lda.covariance_, 'blue') if fig_index != 1 else plot_ellipse(splot, qda.means_[1], qda.covariance_[1], 'blue')

    splot.set_xticks(())
    splot.set_yticks(())

plt.figure(figsize=(10, 8), facecolor='white')
plt.suptitle('Linear Discriminant Analysis vs Quadratic Discriminant Analysis', y=0.98, fontsize=15)

for i, (X, y) in enumerate([dataset_fixed_cov(), dataset_cov()]):
    lda = LinearDiscriminantAnalysis(solver="svd", store_covariance=True)
    y_pred = lda.fit(X, y).predict(X)
    plot_data(lda, X, y, y_pred, fig_index=2 * i + 1, plot_cov=True)

    qda = QuadraticDiscriminantAnalysis(store_covariance=True)
    y_pred = qda.fit(X, y).predict(X)
    plot_data(qda, X, y, y_pred, fig_index=2 * i + 2, plot_cov=(i == 1))

plt.tight_layout()
plt.subplots_adjust(top=0.92)
plt.show()