Question

I found this post: Python: finding an element in an array

and it’s about returning the index of an array through matching the values.

On the other hand, what I am thinking of doing is similar but different. I would like to find the nearest value for the target value. For example I am looking for 4.2 but I know in the array there is no 4.2 but I want to return the index of the value 4.1 instead of 4.4.

What would be the fastest way of doing it?

I am thinking of doing it the old way like how I used to do it with Matlab, which is using the array A where I want to get the index from to minus the target value and take the absolute of it, then select the min. Something like this:-

[~,idx] = min(abs(A - target))

That is Matlab code but I am newbie in Python so I am thinking, is there a fast way of doing it in Python?

Thank you so much for your help!

Answer 1

This is similar to using bisect_left, but it’ll allow you to pass in an array of targets

def find_closest(A, target):
    #A must be sorted
    idx = A.searchsorted(target)
    idx = np.clip(idx, 1, len(A)-1)
    left = A[idx-1]
    right = A[idx]
    idx -= target - left < right - target
    return idx

Some explanation:

First the general case: idx = A.searchsorted(target) returns an index for each target such that target is between A[index - 1] and A[index]. I call these left and right so we know that left < target <= right. target - left < right - target is True (or 1) when target is closer to left and False (or 0) when target is closer to right.

Now the special case: when target is less than all the elements of A, idx = 0. idx = np.clip(idx, 1, len(A)-1) replaces all values of idx < 1 with 1, so idx=1. In this case left = A[0], right = A[1] and we know that target <= left <= right. Therefor we know that target - left <= 0 and right - target >= 0 so target - left < right - target is True unless target == left == right and idx - True = 0.

There is another special case if target is greater than all the elements of A, In that case idx = A.searchsorted(target) and np.clip(idx, 1, len(A)-1)
replaces len(A) with len(A) - 1 so idx=len(A) -1 and target - left < right - target ends up False so idx returns len(A) -1. I’ll let you work though the logic on your own.

For example:

In [163]: A = np.arange(0, 20.)

In [164]: target = np.array([-2, 100., 2., 2.4, 2.5, 2.6])

In [165]: find_closest(A, target)
Out[165]: array([ 0, 19,  2,  2,  3,  3])