ANI Z4 - WTF

# nachfolgend Ihre Nebenrechnungen
import numpy as np

x = [[  8.6,   -9.71,  -2.1,   -6.07,   5.62, -13.95,   4.31,
        3.39,   1.46, -11.37,  -8.93,  -3.55,  17.21,   7.82,
       18.33,  16.77,  13.15,  16.91,  10.52,  20.74,  -8.99,
        6.28, -13.24,   7.52, -15.17,  13.27,  -7.35,   7.41,
       -9.98,   8.62, -16.13,   1.16,  -3.52,  12.76,   1.98,
       -2.8,    8.56,   6.48,   4.4                           ],
     [ 28.1,  -25.94,  -2.15, -16.83,  21.83, -38.05,  16.29,
       13.61,   9.74, -34.68, -28.27, -13.0,   47.69,  20.33,
       54.12,  48.53,  36.8,   46.49,  28.13,  61.36, -28.61,
       16.37, -43.61,  19.38, -46.38,  38.03, -24.7,   17.99,
      -33.37,  31.18, -43.37,   8.09,  -6.48,  41.99,   9.32,
       -5.25,  28.19,  23.27,  16.85                          ],
     [  8.84,  -8.96,  -0.9,   -6.34,   7.3,  -12.9,    5.3,
        4.62,   3.32, -10.92,  -8.78,  -3.76,  16.46,   7.34,
       17.88,  16.02,  12.04,  15.26,   9.14,  21.04,  -9.14,
        5.62, -14.74,   6.44, -16.52,  11.62,  -9.36,   4.86,
      -12.26,  10.72, -13.94,   3.38,  -1.36,  14.98,   4.2,
       -0.46,  10.78,   8.34,   5.9                           ]]

label = [0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,
         1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3]

x_array = np.asarray(x)
y_array = np.asarray(label)

x_mean = np.mean(x_array, axis=1).reshape(3,1)

S_B = None
S_W = None
for cls in range(4):
    x_cls = x_array[:,y_array==cls]
    x_cls_mean = np.mean(x_cls, axis=1).reshape(3,1)
    x_cls_minus = x_cls_mean - x_mean

    if type(S_B) == type(None):
        S_B = x_cls_minus * x_cls_minus.transpose()
    else:
        S_B += x_cls_minus * x_cls_minus.transpose()

    for k in range(len(x_cls)):
        x_k = x_cls[:,k].reshape(3,1)
        x_cls_k_minus = x_k - x_cls_mean

        if type(S_W) == type(None):
            S_W = x_cls_k_minus * x_cls_k_minus.transpose()
        else:
            S_W += x_cls_k_minus * x_cls_k_minus.transpose()


# print(S_B)
# print(S_W)

S_B_sqrt = np.sqrt(S_B)
S_W_inv = np.linalg.inv(S_W)

# print(S_B_sqrt)
# print(S_W_inv)

A = np.dot(S_B_sqrt, np.dot(S_W_inv, S_B_sqrt))
# print(A)

ew, ev = np.linalg.eig(A)
# print(ev)

S_B_sqrt_inv = np.linalg.inv(S_B_sqrt)

W = S_B_sqrt_inv * ev
W_T = W.transpose()
# print(W_T)

p = np.dot(W_T, x_array)

# print(p)

p_best = p[:2,:]

# print(p_best)

p_best_T = p_best.transpose()
# print(p_best_T)

%matplotlib inline
import numpy
import scipy
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D # used in 3D-plot: projection='3d'

def plot_2D(x, label):
    """Visualisierung des Ausgangsproblems"""
    x_2D = numpy.matrix(x)
    color = ['b', 'g', 'r', 'c']
    fig = plt.figure()
    ax = fig.add_subplot(111)
    for i in range(len(label)):
        c = color[label[i]]
        ax.scatter(x_2D[0, i], x_2D[1, i], c=c, marker='o')
    ax.set_xlabel('$x_0$')
    ax.set_ylabel('$x_1$')
    plt.title('Klassifikationsproblem im $R^2$ mit 4 Klassen')
    plt.show()

plot_2D(p_best, label)


y_9_transformiert  = p_best_T[9-1] # Zahlen ersetzen durch Ihre berechneten Werte
y_10_transformiert = p_best_T[10-1]
y_13_transformiert = p_best_T[13-1]
y_14_transformiert = p_best_T[14-1]
y_18_transformiert = p_best_T[18-1]
y_20_transformiert = p_best_T[20-1]


# Ergebnisse überprüfen
import test_z_ip
result = [[y_9_transformiert[0], y_10_transformiert[0], y_13_transformiert[0],
           y_14_transformiert[0], y_18_transformiert[0], y_20_transformiert[0]],
          [y_9_transformiert[1], y_10_transformiert[1], y_13_transformiert[1],
           y_14_transformiert[1], y_18_transformiert[1], y_20_transformiert[1]]]
test_z_ip.loesung_z4(result)