In [1]:

    

from math import factorial
from math import log
import matplotlib.pyplot as plt
%matplotlib inline


    

In [2]:

    

comb = lambda a, b: factorial(a)/factorial(b)/factorial(a-b)
def fn(d):
    r = comb(1000, d)
    for _ in xrange(1000):
        r /= 2.0
    return r


    

In [3]:

    

d = range(1001)


    

In [4]:

    

p = [fn(x) for x in d]


    

In [5]:

    

intp = [0]
for idx, x in enumerate(p):
    intp.append(intp[idx] + x)
intp = intp[1:]


    

In [24]:

    

list(enumerate(intI))


    

    
Out[24]:





[(0, 1000.0000000000001),
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In [14]:

    

I = [-log(x)/log(2) for x in p]


    

In [15]:

    

intI = [-log(x)/log(2) for x in intp]


    

In [16]:

    

I[425], I[451]


    

    
Out[16]:





(21.58433363061018, 12.240997780509938)

In [29]:

    

plt.figure(figsize=(8, 6), dpi=100)
d_max = 451
#plt.plot(d[425:d_max+1], [int(x) for x in intI][425:d_max+1], 'k')
plt.plot(d[400:600], [int(x) for x in intI][400:600], 'k')
plt.grid()
plt.xlabel('Distance')
plt.ylabel('Information');
#plt.axis([0, 1000, 0, 1000]);


    

In [ ]: