Algorithms Exercise 2

Imports



In [1]:

    
%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 [2]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    c = []
    for n in range(0,len(a)):
        if n >= 1 and n <= len(a)-2:
            if a[n] > a[n+1] and a[n] > a[n-1]: 
                c.append(n)
        elif n == 0:
            if a[n] > a[n+1]:
                c.append(n)
        elif n == len(a)-1:
            if a[n] > a[n-1]:
                c.append(n)
    d = np.array(c)
    return d



In [3]:

    
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 [4]:

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



In [5]:

    
z = []
for n in pi_digits_str:
    z.append(int(n))
x = np.array(z)



In [6]:

    
y = find_peaks(x)



In [7]:

    
dif = np.diff(y)



In [12]:

    
f = plt.figure(figsize=(7,8))
plt.hist(dif,bins=15)
plt.title('Distance between local maxima of first 10000 digits of pi')
plt.ylabel('count')
plt.xlabel('distance')









    Out[12]:





<matplotlib.text.Text at 0x7ff8fee9b550>



In [ ]:

    
assert True # use this for grading the pi digits histogram