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."""
    # standard local maxima checking, not much explanation needed
    d=[]
    if a[0]>a[1]:
        d.append(0)
    for i in range(1,len(a)-1):
        if a[i]>a[i-1] and a[i]>a[i+1]:
            d.append(i)
    if a[-1]>a[-2]:
        d.append(len(a)-1)
    p=np.array(d)
    return p



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 [9]:

    
plt.figure(figsize=(10,6))
bins=range(0,15,1)
plt.hist(np.diff(find_peaks(pi_digits_str)),bins);
plt.xlim(left=2), plt.title('Differences between local maxima'),plt.xlabel('Difference'),plt.ylabel('Occurrance');



In [6]:

    
assert True # use this for grading the pi digits histogram