import numpy as np
import matplotlib.pyplot as plt

from sklearn.decomposition import PCA, KernelPCA
from sklearn.datasets import make_circles
from mpl_toolkits.mplot3d import Axes3D
from sklearn import decomposition
import time

np.random.seed(0)

X, y = make_circles(n_samples=400, factor=.3, noise=.05)

plt.figure(1)
 
plt.title("Original space")
reds = y == 0
blues = y == 1


plt.scatter(X[reds, 0], X[reds, 1], c="red",
            s=20, edgecolor='k')
plt.scatter(X[blues, 0], X[blues, 1], c="blue",
            s=20, edgecolor='k')




#PCA 2d -> 1d original points 

points_orig=np.zeros((X.shape[0],2))

points_orig[:,0]=X[:,0]
points_orig[:,1]=X[:,1]

print("Calculating PCA 2d -> 1d, orig. points ", end="", flush=True)
start_time = time.time()		
pca1_orig = decomposition.PCA(n_components=1) 
pca1_orig.fit(points_orig)
points_pca1_orig_reduced = pca1_orig.transform(points_orig)
print("\t\t took %s seconds " % round((time.time() - start_time),5))



plt.figure(14)
plt.title("Original 2d points -> 1d")
plt.scatter(points_pca1_orig_reduced[reds, 0], np.zeros((points_pca1_orig_reduced[reds, 0]).shape[0]), c="red",
            s=20, edgecolor='k')
            
            
plt.scatter(points_pca1_orig_reduced[blues, 0], np.zeros((points_pca1_orig_reduced[blues, 0]).shape[0]), c="blue",
            s=20, edgecolor='k')
                      



fig2 = plt.figure(2)

ax2 = fig2.add_subplot(111, projection='3d')
ax2.set_title("2d points -> 3d points")



# \phi(x) = (x1^2, x_2^2, \sqrt(2) x1x2)
#Z=np.sqrt(2)*X[:,0]*X[:,1]
#X[:,0]=X[:,0]**2;
#X[:,1]=X[:,1]**2;

# \phi(x) = (x1, x_2,  exp((x1^2+x2^2)/1.25))
Z=np.exp( ((X[:,0]**2)+X[:,1]**2)/1.25)




ax2.scatter(X[reds,0],X[reds,1],Z[reds],s=20, color='red')
ax2.scatter(X[blues,0],X[blues,1],Z[blues],s=20, color='blue')


points=np.zeros((X.shape[0],3))

points[:,0]=X[:,0]
points[:,1]=X[:,1]
points[:,2]=Z


print("Calculating PCA to 2d...", end="", flush=True)
start_time = time.time()		
pca2 = decomposition.PCA(n_components=2) 
pca2.fit(points)
points_pca2_reduced = pca2.transform(points)
print("\t\t took %s seconds " % round((time.time() - start_time),5))

plt.figure(13)
plt.title("3d points -> PCA to 2d")
plt.scatter(points_pca2_reduced[reds, 0], points_pca2_reduced[reds, 1], c="red",
            s=140, edgecolor='k')
plt.scatter(points_pca2_reduced[blues, 0], points_pca2_reduced[blues, 1], c="blue",
            s=20, edgecolor='k')

 
 



print("Calculating PCA to 1d...", end="", flush=True)
start_time = time.time()		
pca1 = decomposition.PCA(n_components=2) 
pca1.fit(points)
points_pca1_reduced = pca1.transform(points)
print("\t\t took %s seconds " % round((time.time() - start_time),5))





plt.figure(4)
plt.title("3d points -> PCA to 1d")
plt.scatter(points_pca1_reduced[reds, 0], np.zeros((points_pca1_reduced[reds, 0]).shape[0]), c="red",
            s=20, edgecolor='k')
plt.scatter(points_pca1_reduced[blues, 0], np.zeros((points_pca1_reduced[blues, 0]).shape[0]), c="blue",
            s=20, edgecolor='k')
                      




plt.show()