Algorithms Exercise 2

Imports



In [48]:

    
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns
import numpy as np
from IPython.display import display

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 [76]:

    
def find_peaks(a):
    """Find the indices of the local maxima in a sequence."""
    a = np.array()
    np.argmax(a)
    np.argmax(a)
    return()



In [77]:

    
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]))









    



---------------------------------------------------------------------------
TypeError                                 Traceback (most recent call last)
<ipython-input-77-e9503c7dbdc3> in <module>()
----> 1 p1 = find_peaks([2,0,1,0,2,0,1])
      2 assert np.allclose(p1, np.array([0,2,4,6]))
      3 p2 = find_peaks(np.array([0,1,2,3]))
      4 assert np.allclose(p2, np.array([3]))
      5 p3 = find_peaks([3,2,1,0])

<ipython-input-76-44056ea807d0> in find_peaks(a)
      1 def find_peaks(a):
      2     """Find the indices of the local maxima in a sequence."""
----> 3     a = np.array()
      4     np.argmax(a)
      5     np.argmax(a)

TypeError: Required argument 'object' (pos 1) not found

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 [13]:

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



In [24]:

    
n= np.fromstring(pi_digits_str, np.dtype(int))
n









    Out[24]:





array([3834307354039497777, 3617297835054609715, 3689633584008935475, ...,
       3474022643680228657, 3617856382531809584, 4050765992030320181])



In [25]:

    
np.argmax(n)









    Out[25]:





132



In [26]:

    
np.diff(n)









    Out[26]:





array([-217009518984888062,   72335748954325760, -215887987194527744, ...,
       -577024840473510148,  143833738851580927,  432909609498510597])



In [54]:

    
plt.hist(np.histogram(n))
plt.title('Distribution of local max. in $\pi$');



In [ ]:

    
assert True # use this for grading the pi digits histogram