# import necessary packages
from matplotlib import pyplot as plt
import numpy as np
from qpsolvers import solve_qp
from matplotlib.patches import Arc
from sklearn.svm import SVC

# enter our data
left_points = [2, 3]
right_points = [6, 6.5, 8.3]
addtl_points = [10.5]

# assign classifications
x = left_points + right_points + addtl_points
y = np.concatenate((np.full((len(left_points), 1), -1),
	np.full((len(right_points), 1), 1),
	np.full((len(addtl_points), 1), -1)))

# details of our naive transformation: subtract 7 and square
offset = np.average(7) 
def my_kernel(X, Y):
	return np.dot(X, Y.T) + np.dot((X - offset)**2, (Y.T - offset)**2)

# arrange data into a form suitable for the SVC package
X = np.reshape(x, (-1, 1))
Y = y.ravel()

# a collection of potential solution settings
model = SVC(C = 1, kernel = my_kernel) # matches the manual results
#model = SVC(C = 1e9, kernel = 'poly', degree=3, gamma = 'scale', coef0 = 1)
#model = SVC(C = 1, kernel = 'rbf')

# output the results
print('Model details: ', model.fit(X, Y))
print('Support vector indices: ', model.support_)
print('Number of support vectors in each class: ', model.n_support_)
print('Dual coefficients: ', model.dual_coef_)
print('Intercept (b): ', model.intercept_)

# plot the results
font = {'size':16}
tickfont = {'size':10}
fig, ax = plt.subplots()
plt.rcParams['savefig.facecolor'] = '#c0c0c0'
plt.rc('font', **font)
marker_style = dict(linestyle='none', markersize = 10, markeredgecolor = 'k')

ax.set_aspect(1)
ax.plot(left_points,np.zeros(len(left_points)),marker="^",
	markerfacecolor='red', **marker_style)
ax.plot(right_points,np.zeros(len(right_points)),marker="s",
	markerfacecolor='blue', **marker_style)
ax.plot(addtl_points,np.zeros(len(addtl_points)),marker="^",
	markerfacecolor='red', **marker_style)

# locate the classification thresholds
def classification(x):
	return model.predict([[x]])[0]
class_input_array = np.linspace(0, 12, 5000)
class_output = [classification(x) for x in class_input_array]
zero_crossings = np.where(np.diff(np.sign(class_output)))
(div_1, div_2)=class_input_array[zero_crossings] # expecting two divisions
print('Divisions: ', div_1, div_2)
print('Classification of far-right point: ', classification(addtl_points[0]))	

# plot the division points with associated graphics and labeling
for i in [div_1, div_2]:
	ax.annotate('', xy = (i, -0.6), xytext = (i, 0.6),
	arrowprops={'arrowstyle':'-', 'lw':5, 'color':'0'},
	va='center')
arc=Arc(((div_1 + div_2)/2, 0.6), div_2 - div_1, 3, linestyle = '--',
	angle = 0.0, theta1 = 0, theta2 = 180)		
ax.add_artist(arc)
plt.gca().axes.get_yaxis().set_visible(False)
ax.annotate('', xy = (0, 1.9), xytext = (0, -1.9),
arrowprops={'arrowstyle':'-', 'lw':1, 'facecolor':'k'},va = 'center')
fig.set_facecolor('#c0c0c0')
plt.xlim([-1, 13])
plt.ylim([-2.5, 2.5])
plt.xticks(np.arange(2, 11, 2), **tickfont)
ax.annotate('', xy = (12, 0), xytext = (-.05, 0),
	arrowprops = {'arrowstyle':'->', 'lw':1, 'facecolor':'k'},
	va = 'center', zorder = -1)
ax.annotate('$x$', xy = (0, 0), xytext = (12.2, 0), va = 'center') 
ax.text(1.4, 1, '-1 class', fontsize = '14')
ax.annotate('+1 class', xy=(0, 0), xytext = ((div_1 + div_2)/2, 0.8),
	ha = 'center', fontsize = '14')
plt.tick_params(axis = 'x', which='major', labelsize = 10)
for i in model.support_:
	ax.plot(x[i], 0, marker = "o", linestyle = 'none',
	markersize = 25, markerfacecolor = 'None', markeredgecolor = 'k')

plt.box(on = None)
ax.spines['bottom'].set_position('zero')
ax.spines['bottom'].set_color('none')
ax.spines['left'].set_position('zero')
ax.spines['left'].set_color('none')
ax.spines['left'].set_linewidth(1)
ax.spines['bottom'].set_linewidth(1)
plt.show()