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 [10]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    # YOUR CODE HERE
    #raise NotImplementedError()
    ind=[]
    #next two if checks end points
    if a[0]> a[1]:
            ind.append(0)
    if a[len(a)-1]>a[len(a)-2]:
        ind.append(len(a)-1)
    #finds local maxima in string by comparing adjacent
    for i in range(1,len(a)-1):
        if a[i]>a[i-1] and a[i]>a[i+1]:
            ind.append(i)
    #sorts by increasing order
    return sorted(ind) 
find_peaks([2,0,1,0,2,0,1])









    Out[10]:





[0, 2, 4, 6]



In [11]:

    
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 [12]:

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



In [84]:

    
# YOUR CODE HERE
#raise NotImplementedError()
def pimax(x):
    '''uses find_peaks to find the local maxima then finds the space between the maxima and
    plots the distribution of space between local maxima'''
    pi=np.ones(10000)
    for i in range(len(x)):
        pi[i]=int(x[i])
    m = find_peaks(pi)
    dist = np.diff(m)
    p = plt.hist(dist,bins=17)
    plt.title('Distances Between Local Maxima in First 10000 digtis of $\pi$')
    plt.xlabel('Distance Between Local Maxima')
    plt.ylabel('Number of Times Occured')
    plt.grid(False)
    plt.xlim([1,19])
    a=range(2,19)
    plt.xticks(a[::2])
    plt.ylim(0,1100)
    plt.show()
pimax(pi_digits_str)



In [ ]:

    
assert True # use this for grading the pi digits histogram