In [1]:
%matplotlib inline
from matplotlib import pyplot as plt
import seaborn as sns
import numpy as np
Write a function find_peaks
that finds and returns the indices of the local maxima in a sequence. Your function should:
In [2]:
def find_peaks(a):
"""Find the indices of the local maxima in a sequence."""
peaks = []
for i in range(len(a)):
if i == 0 and a[i] > a[i+1]:
peaks.append(i)
elif i == (len(a)-1) and a[i] > a[i-1]:
peaks.append(i)
elif a[i] > a[i-1] and a[i] > a[i+1]:
peaks.append(i)
return np.array(peaks)
In [3]:
find_peaks([2,0,1,0,2,0,1])
Out[3]:
In [4]:
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:
np.diff
to find the distances between consequtive local maxima.
In [5]:
from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]
In [6]:
a = pi_digits_str
b = np.array([int(a[i]) for i in range(len(a))])
In [8]:
plt.figure(figsize=(12,6))
plt.hist(np.diff(find_peaks(b)), bins=50)
plt.xlim(0,18)
plt.xlabel("Distance")
plt.ylabel("Occurences")
plt.title("Distance Between Consecutive Maxima for First 10,000 Decimals of Pi")
plt.show()
In [ ]:
assert True # use this for grading the pi digits histogram