import numpy as np

import matplotlib.pyplot as plt

n = 200

a = np.linspace(0, np.pi, int(n / 2))

u = -10 * np.r_[np.cos(a) + 0.5, np.cos(a) - 0.5].reshape(-1, 1) + np.random.randn(n, 1)

v = 10 * np.r_[np.sin(a), -np.sin(a)].reshape(-1, 1) + np.random.randn(n, 1)

x = np.c_[u, v]

y = np.zeros((n, 1))

y[0] = 1

y[n - 1] = -1

x2 = (x ** 2).sum(axis=1).reshape(-1, 1)

hh = 2 * 1 ** 2

k = np.exp(-(x2 + x2.T - 2 * x.dot(x.T)) / hh)

w = k

t = np.linalg.lstsq((k ** 2) + np.eye(n) + 10 * k.dot(np.diagflat(w.sum(axis=1)) - w).dot(k), k.dot(y), rcond=-1)[0]

m = 100

X = np.linspace(-20, 20, m).reshape(-1, 1)

X2 = (X ** 2)

U = np.exp(-((u ** 2) + X2.T - 2 * u.dot(X.T)) / hh)

V = np.exp(-((v ** 2) + X2.T - 2 * v.dot(X.T)) / hh)

K = V.T.dot(U * t)

plt.contourf(X.reshape((-1, )), X.reshape((-1, )), np.sign(K))

plt.plot(x[np.where(y == 1)[0], 0], x[np.where(y == 1)[0], 1], 'bo')

plt.plot(x[np.where(y == -1)[0], 0], x[np.where(y == -1)[0], 1], 'rx')

plt.plot(x[np.where(y == 0)[0], 0], x[np.where(y == 0)[0], 1], 'k.')

plt.axis([-20, 20, -20, 20])

plt.show()