# Generate npoints randomly with importance sampling
npoints = 1000000
xg0 = xg00 = 0
for n1 in range(npoints):
#here do the calculation with importance sampling
x0 = xmin**gRandom.Uniform()
weight = x0*log(1/xmin)
# here do the calculation using linear sampling
# x0 = xmin+(1-xmin)*gRandom.Uniform()
# weight = 1-xmin
f = g0(x0)
ff = weight*f
xg0 += ff
xg00 += ff**2
# Calculate the MC integral
xg0 /= npoints
xg00 /= npoints
sigma2 = xg00 - xg0*xg0
error = sqrt(sigma2/npoints)
print " integral for g(x) = (1-x)**5/x is: ",xg0,"+/-", error
# Get the exact value using incomplete beta function [https://en.wikipedia.org/wiki/Beta_function]
x = 1-xmin
a = 5
b = -0.9999999999
print "Exact value ", TMath.BetaIncomplete(x, a+1, b+1) * TMath.Beta(a+1, b+1)
# Generate npoints randomly with importance sampling
xg0 = xg00 = 0
for n1 in range(npoints):
# here do the calculation with importance sampling
x0 = xmin**gRandom.Uniform()
weight = x0 * log(1 / xmin)
# here do the calculation using linear sampling
# x0 = xmin+(1-xmin)*gRandom.Uniform()
# weight = 1-xmin
f = g0(x0)
ff = weight * f
xg0 += ff
xg00 += ff**2
# Calculate the MC integral
xg0 /= npoints
xg00 /= npoints
sigma2 = xg00 - xg0 * xg0
error = sqrt(sigma2 / npoints)
print(" integral for g(x) = (1-x)**5/x is: ", xg0, "+/-", error)
# Get the exact value using incomplete beta function [https://en.wikipedia.org/wiki/Beta_function]
x = 1 - xmin
a = 5
b = -0.9999999999
print("Exact value ",
TMath.BetaIncomplete(x, a + 1, b + 1) * TMath.Beta(a + 1, b + 1))
