#GDA
#author:Xiaolewen
import matplotlib.pyplot as plt
from numpy import *

#Randomly generate two cluster data of Gaussian distributions
mean0=[2,3]
cov=mat([[1,0],[0,2]])
x0=random.multivariate_normal(mean0,cov,500).T #The first class point which labael equal 0
y0=zeros(shape(x0)[1])
#print x0,y0
mean1=[7,8]
cov=mat([[1,0],[0,2]])
x1=random.multivariate_normal(mean1,cov,300).T
y1=ones(shape(x1)[1]) #The second class point which label equals 1
#print x1,y1

x=array([concatenate((x0[0],x1[0])),concatenate((x0[1],x1[1]))])
y=array([concatenate((y0,y1))])
m=shape(x)[1]
#print x,y,m
#Caculate the parameters:\phi,\u0,\u1,\Sigma
phi=(1.0/m)*len(y1)
#print phi
u0=mean(x0,axis=1) 
#print u0
u1=mean(x1,axis=1)
#print u1

xplot0=x0;xplot1=x1 #save the original data to plot 
x0=x0.T;x1=x1.T;x=x.T
#print x0,x1,x
x0_sub_u0=x0-u0
x1_sub_u1=x1-u1
#print x0_sub_u0
#print x1_sub_u1
x_sub_u=concatenate([x0_sub_u0,x1_sub_u1])
#print x_sub_u

x_sub_u=mat(x_sub_u)
#print x_sub_u

sigma=(1.0/m)*(x_sub_u.T*x_sub_u)
#print sigma

#plot the discriminate boundary ,use the u0_u1's midnormal
midPoint=[(u0[0]+u1[0])/2.0,(u0[1]+u1[1])/2.0]
#print midPoint
k=(u1[1]-u0[1])/(u1[0]-u0[0])
#print k
x=range(-2,11)
y=[(-1.0/k)*(i-midPoint[0])+midPoint[1] for i in x]



#plot contour for two gaussian distributions
def gaussian_2d(x, y, x0, y0, sigmaMatrix):
 return exp(-0.5*((x-x0)**2+0.5*(y-y0)**2))
delta = 0.025
xgrid0=arange(-2, 6, delta)
ygrid0=arange(-2, 6, delta)
xgrid1=arange(3,11,delta)
ygrid1=arange(3,11,delta)
X0,Y0=meshgrid(xgrid0, ygrid0) #generate the grid
X1,Y1=meshgrid(xgrid1,ygrid1)
Z0=gaussian_2d(X0,Y0,2,3,cov)
Z1=gaussian_2d(X1,Y1,7,8,cov)

#plot the figure and add comments
plt.figure(1)
plt.clf()
plt.plot(xplot0[0],xplot0[1],'ko')
plt.plot(xplot1[0],xplot1[1],'gs')
plt.plot(u0[0],u0[1],'rx',markersize=20)
plt.plot(u1[0],u1[1],'y*',markersize=20)
plt.plot(x,y)
CS0=plt.contour(X0, Y0, Z0)
plt.clabel(CS0, inline=1, fontsize=10)
CS1=plt.contour(X1,Y1,Z1)
plt.clabel(CS1, inline=1, fontsize=10)
plt.title("Gaussian discriminat analysis")
plt.xlabel('Feature Dimension (0)')
plt.ylabel('Feature Dimension (1)')
plt.show(1)