import numpy as np
import matplotlib.pyplot as plt

r = 0.9
X = np.random.normal(size=100)
Y = r*X + np.sqrt(1-r**2)*np.random.normal(size=100)

ii = np.flatnonzero( (X>0) * (X<1) )

XR = np.argsort(np.argsort(X))
YR = np.argsort(np.argsort(Y))

def pearson(X,Y):
    cc = np.cov(X,Y)
    return cc[0,1]/np.sqrt(cc[0,0]*cc[1,1])

r1 = pearson(X, Y)
r2 = pearson(X[ii], Y[ii])

s1 = pearson(XR, YR)
s2 = pearson(XR[ii], YR[ii])

plt.clf()
plt.hold(True)
plt.figure(figsize=(5,4))
plt.axes([0.13,0.13,0.8,0.8])
plt.fill((0,1,1,0,0), (-3,-3,3,3,-3), 'lightgrey', ec='lightgrey')
a = plt.plot(X, Y, 'o', color='orange')
b = plt.plot(X[ii], Y[ii], 'o', color='lightblue')
plt.xlim(-3,3)
plt.ylim(-3,3)
plt.xlabel("X", size=18)
plt.ylabel("Y", size=18)
bx = plt.legend((a,b), ["%.2f/%.2f" % (r1,s1), "%.2f/%.2f" % (r2,s2)],\
                'upper left', numpoints=1, handletextpad=0.00001)
bx.draw_frame(False)
plt.savefig("correlation_range_dependence.pdf")
plt.savefig("correlation_range_dependence.svg")