Dynamically normalise 2D numpy array

Question

I have a 2D numpy array "signals" of shape (100000, 1024). Each row contains the traces of amplitude of a signal, which I want to normalise to be within 0-1.

The signals each have different amplitudes, so I can't just divide by one common factor, so I was wondering if there's a way to normalise each of the signals so that each value within them is between 0-1?

Let's say that the signals look something like [[0,1,2,3,5,8,2,1],[0,2,5,10,7,4,2,1]] and I want them to become [[0.125,0.25,0.375,0.625,1,0.25,0.125],[0,0.2,0.5,0.7,0.4,0.2,0.1]].

Is there a way to do it without looping over all 100,000 signals, as this will surely be slow?

Thanks!

Answer 1

Easy thing to do would be to generate a new numpy array with max values by axis and divide by it:

import numpy as np

a = np.array([[0,1,2,3,5,8,2,1],[0,2,5,10,7,4,2,1]])

b = np.max(a, axis = 1)

print(a / b[:,np.newaxis])

output:

[[0.    0.125 0.25  0.375 0.625 1.    0.25  0.125]
 [0.    0.2   0.5   1.    0.7   0.4   0.2   0.1  ]]

Answer 2

Adding a little benchmark to show just how significant is the performance difference between the two solutions:

import numpy as np
import timeit

arr = np.arange(1024).reshape(128,8)

def using_list_comp():
    return np.array([s/np.max(s) for s in arr])

def using_vectorized_max_div():
    return arr/arr.max(axis=1)[:, np.newaxis]

result1 = using_list_comp()
result2 = using_vectorized_max_div()

print("Results equal:", (result1==result2).all())

time1 = timeit.timeit('using_list_comp()', globals=globals(), number=1000)
time2 = timeit.timeit('using_vectorized_max_div()', globals=globals(), number=1000)

print(time1)
print(time2)
print(time1/time2)

On my machine the output is:

Results equal: True
0.9873569
0.010177099999999939
97.01750989967731

Almost a 100x difference!