def mysteryf_mean(n):
x=5*rand(n)
y=mysteryf(x)
y_avg=mean(y)
return y_avg
plot(rr2[:-1], rr2[1:], 'b.', ms=2.5, alpha=.7)
title('random.rand Pair Wise Correlation');
# ### EX 2
# 1. Use Monte Carlo integration to average the function mysteryf in the mystery module by random sampling using numpy.random.rand over the interval [0, 5]. use numpy array operations to apply the mystery function f to all points xi and then use mean() use lots of point to get a good estimate.
#
# In[3]:
from mystery import mysteryf
# In[49]:
mysteryf(array([0,1,2,3,4,5]))
# In[44]:
trails = 10000
results = empty([trails])
for i in xrange(npts):
u = random.rand(100)*5 #array of size 100 in range (0->5)
d = mysteryf(u).mean() # mean of that
results[i] = d
print "Average output of Mystery Function: ",mean(results)
hist(results, bins=50);
title('Mystery Function Average Output')
hist(x_rand,50)
title('random.rand Histogram')
figure (6)
plot(x_rand[0::2],x_rand[1::2],'b.')
title('random.rand Pairwise Correlation')
xlabel('$x_i$')
ylabel('$x_{i+1}$')
#Part 2 - Finding the Mean of mysterf Using Monte Carlo Integration
print "PART 2"
from mystery import mysteryf
x=5*rand(1000)
y=mysteryf(x)
figure (7)
plot(x,y,'b.')
title('Plotting mysteryf Evaluated at Random Points')
xlabel('x')
ylabel('mysteryf(x)')
def mysteryf_mean(n):
x=5*rand(n)
y=mysteryf(x)
y_avg=mean(y)
return y_avg
y_avg=mysteryf_mean(n)
print "The mean of mysteryf in the range [0,5] is",y_avg
