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 [60]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    n = 0
    x = []
    if a[n] > a[n+1]:
        x.append(n)
    while n < len(a) - 2:
        n = n + 1
        if a[n] > a[n+1] and a[n] > a[n-1]:
            x.append(n)
    if a[n+1] > a[n]:
        x.append(n+1)
    y = np.asarray(x)
    return y
print(find_peaks([2,0,1,0,2,0,1]))



In [61]:

    
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 [63]:

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



In [72]:

    
w = []
for ints in pi_digits_str:
    w.append(ints)
x = find_peaks(w)
plt.hist(np.diff(x), bins = 20)
plt.show()



In [ ]:

    
assert True # use this for grading the pi digits histogram