import pandas as pd
from pandas import  DataFrame

d = DataFrame(columns=['xi','eta','x'])
d.x = np.random.rand(100)
d.xi = d.eval('2*x**2')
d.eta =1-abs(2*d.x-1)
d['h']=d[(d.x<0.5)].eval('eta**2/2')
d['h2']=d[(d.x>=0.5)].eval('(2-eta)**2/2')

%matplotlib inline

d = DataFrame(columns=['xi','eta','x','h','h1','h2'])
# 100 random samples
d.x = np.random.rand(100)
d.xi = d.eval('2*x**2')
d.eta =1-abs(2*d.x-1)
d.h1=d[(d.x<0.5)].eval('eta**2/2')
d.h2=d[(d.x>=0.5)].eval('(2-eta)**2/2')
d.fillna(0,inplace=True)
d.h = d.h1+d.h2

fig,ax=subplots()
ax.plot(d.xi,d.eta,'.',alpha=.3,label='$\eta$')
ax.plot(d.xi,d.h,'k.',label='$h(\eta)$')
ax.set_aspect(1)
ax.legend(loc=0,fontsize=18)
ax.set_xlabel('$2 x^2$',fontsize=18)
ax.set_ylabel('$h(\eta)$',fontsize=18)
fig.savefig('Conditional_expectation_MSE_Ex_005.png')

d = DataFrame(columns=['xi','eta','x','h','h1','h2'])
# 100 random samples
d.x = np.random.rand(100)
d.xi = d.eval('2*x**2')
d['eta']=(d.x<0.5)*(2*d.x)+(d.x>=0.5)*(2*d.x-1)
d.h1=d[(d.x<0.5)].eval('eta**2/2')
d.h2=d[(d.x>=0.5)].eval('(1+eta)**2/2')
d.fillna(0,inplace=True)
d.h = d.h1+d.h2

fig,ax=subplots()
ax.plot(d.xi,d.eta,'.',alpha=.3,label='$\eta$')
ax.plot(d.xi,d.h,'k.',label='$h(\eta)$')
ax.set_aspect(1)
ax.legend(loc=0,fontsize=18)
ax.set_xlabel('$2 x^2$',fontsize=18)
ax.set_ylabel('$h(\eta)$',fontsize=18)
fig.savefig('Conditional_expectation_MSE_Ex_005.png')