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(x):
    a = np.array(x)
    l = []    
    for i in range(len(a)):
        if i == 0 and a[i] > a[i+1]:
            l.append(i)
        elif i == len(a)-1 and a[i]> a[i-1]:
            l.append(i)
        elif i > 0 and i < len(a)-1:
            if a[i]>a[i-1] and a[i] > a[i+1]:
                l.append(i)
    return l



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]:

    
a = [i for i in pi_digits_str]
b = find_peaks(a)
plt.hist(np.diff(b),10, align = 'left')
plt.title("Local Max");
plt.xlabel("Difference");
plt.ylabel("Freq");



In [6]:

    
assert True # use this for grading the pi digits histogram