Algorithms Exercise 2

Imports



In [3]:

    
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns
import numpy as np

Peak finding

Write a function find_peaks that finds and returns the indices of the local maxima in a sequence. Your function should:

Properly handle local maxima at the endpoints of the input array.
Return a Numpy array of integer indices.
Handle any Python iterable as input.



In [6]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""



In [5]:

    
p1 = find_peaks([2,0,1,0,2,0,1])
assert np.allclose(p1, np.array([0,2,4,6]))
p2 = find_peaks(np.array([0,1,2,3]))
assert np.allclose(p2, np.array([3]))
p3 = find_peaks([3,2,1,0])
assert np.allclose(p3, np.array([0]))

Here is a string with the first 10000 digits of $\pi$ (after the decimal). Write code to perform the following:

Convert that string to a Numpy array of integers.
Find the indices of the local maxima in the digits of $\pi$.
Use np.diff to find the distances between consequtive local maxima.
Visualize that distribution using an appropriately customized histogram.



In [8]:

    
from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]



In [13]:

    
w=pi_digits_str
r=[]
for x in w:
    r.append(int(x))
a=np.array(r)
m=find_peaks(a)
s=np.diff(m)
plt.hist(s,bins=50)
s









    Out[13]:





array([3, 2, 5, ..., 5, 2, 4])



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assert True # use this for grading the pi digits histogram