Physicist Physicist - 9 days ago 5
Python Question

Selecting close matches from one array based on another reference array

I have an array

A
and a reference array
B
. Size of
A
is at least as big as
B
. e.g.

A = [2,100,300,793,1300,1500,1810,2400]
B = [4,305,789,1234,1890]


B
is in fact the position of peaks in a signal at a specified time, and
A
contains position of peaks at a later time. But some of the elements in
A
are actually not the peaks I want (might be due to noise, etc), and I want to find the 'real' one in
A
based on
B
. The 'real' elements in
A
should be close to those in
B
, and in the example given above, the 'real' ones in
A
should be
A'=[2,300,793,1300,1810]
. It should be obvious in this example that
100,1500,2400
are not the ones we want as they are quite far off from any of the elements in B. How can I code this in the most efficient/accurate way in python/matlab?

Answer

Approach #1: With NumPy broadcasting, we can look for absolute element-wise subtractions between the input arrays and use an appropriate threshold to filter out unwanted elements from A. It seems for the given sample inputs, a threshold of 90 works.

Thus, we would have an implementation, like so -

thresh = 90
Aout = A[(np.abs(A[:,None] - B) < thresh).any(1)]

Sample run -

In [69]: A
Out[69]: array([   2,  100,  300,  793, 1300, 1500, 1810, 2400])

In [70]: B
Out[70]: array([   4,  305,  789, 1234, 1890])

In [71]: A[(np.abs(A[:,None] - B) < 90).any(1)]
Out[71]: array([   2,  300,  793, 1300, 1810])

Approach #2: Based on this post, here's a memory efficient approach using np.searchsorted, which could be crucial for large arrays -

def searchsorted_filter(a, choices, thresh):
    lidx = np.searchsorted(choices, a, 'left').clip(max=choices.size-1)
    ridx = (np.searchsorted(choices, a, 'right')-1).clip(min=0)
    cl = np.take(choices,lidx) # Or choices[lidx]
    cr = np.take(choices,ridx) # Or choices[ridx]
    return A[np.minimum(np.abs(A - cl), np.abs(A - cr)) < thresh]

Sample run -

In [95]: searchsorted_filter(A,B, thresh = 90)
Out[95]: array([   2,  300,  793, 1300, 1810])

Runtime test

In [104]: A = np.sort(np.random.randint(0,100000,(1000)))

In [105]: B = np.sort(np.random.randint(0,100000,(400)))

In [106]: out1 = A[(np.abs(A[:,None] - B) < 10).any(1)]

In [107]: out2 = searchsorted_filter(A,B, thresh = 10)

In [108]: np.allclose(out1, out2)  # Verify results
Out[108]: True

In [109]: %timeit A[(np.abs(A[:,None] - B) < 10).any(1)]
100 loops, best of 3: 2.74 ms per loop

In [110]: %timeit searchsorted_filter(A,B, thresh = 10)
10000 loops, best of 3: 85.3 ┬Ás per loop
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