In [2]:
%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 [7]:
a=[1,2,3,4,5,3]
for x in a:
print(x)
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def find_peaks(a):
"""Find the indices of the local maxima in a sequence."""
a=list(a)
index=[]
first=a[0]
if first>a[1]:
index.append(0)
start=1
for x in a[1:len(a)-1]:
prev=a[a.index(x)-1]
foll=a[a.index(x)+1]
if x> prev and x>foll:
index.append(a.index(x,start))
start+=1
last=a[len(a)-1]
if last>a[len(a)-2]:
index.append(len(a)-1)
return(np.array(index))
find_peaks([3,2,1,0])
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In [28]:
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.
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from sympy import pi, N
pi_digits_str = str(N(pi, 10001))[2:]
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pi_digits_list=np.array([int(x) for x in pi_digits_str])
pi_digits_list
x=np.diff(find_peaks(pi_digits_list))
plt.hist(x,20)
plt.title('Distance between local maxes in the digits of $\pi$')
plt.xlabel('Distance between Maxima')
plt.ylabel('Number of Maxima')
plt.xticks(range(0,30,2))
plt.xlim(right=22)
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assert True # use this for grading the pi digits histogram