Replace the empty output of find() by the closest element

Hello everyone,

I have two arrays

a1 = [t1, t2, t3, t4, t5];
a2 = [t1, t1 + d, t1 + 2 * d, t1 + 3 * d];

I use find()

for i = 1:length(a1)
    indices(i) = find( a1 == a2(i) );          
end

If some elements of a2 are not contained in a1, some of the find() outputs are empty. How to replace these empty elemenets by the indices of the next closest number?

I have tried

for i = 1:length(a1)
    indices(i) = find( a1 == a2(i) );
    
    if isempty(indices(i))
       indices(i) = indices(i + 1);
             
end
end

but apparently it does not work.

Your help is highly acknowledged.

Answer 1

[John D'Errico]

You are trying to use the wrong tool (i.e., find) to solve this. Well, you could use find, I suppose, with some significant effort. But instead, just use a tool designed to solve that problem.

You apparently want to locate the index of the closest element in a2 to each element in a1. If there is an exact match, that is a great thing, but otherwise, you want the closest match. I'm not sure how you would resolve the case where there are two elements of a2 that are equidistant. I would think that logically, you would choose the first such match from equals.

Regardless, This is a problem solved by knnsearch.

a1 = [2, 3, 4, 5];
a2 = [1, 3, 5, 7, 9, 11];

[idx,D] = knnsearch(a2',a1')
idx =
     1
     2
     2
     3
D =
     1
     0
     1
     0

As you can see, knnsearch did exactly that.

[John D'Errico]

Note that in the time it took me to answer your question, I see you changed the example. No matter, as I think I am still solving your question in what I wrote.

[Asatur Khurshudyan]

Thank you very much, John. It was exactly what I was searching for.

[Guillaume]

find is a function that for some reason people tend to use too much. It's actually rare that find is needed or the correct tool. I'll blame it on the way people are taught to use matlab.

The most common misuse is when the output of find is used straight-up to index something. The find can just be removed:

A(find(expression))

is exactly the same as

A(expression)

find in a loop is also rarely useful. As demonstrated by John, for finding the nearest value, knnsearch is a lot simpler, and if it's for finding exact match, ismember would be the correct tool. For example, your first loop could be replaced by

isina2 = ismember(a1, a2);  %return a logical vector. Depending on what you do afterward you could indeed use find on that vector to get actual indices

Another issue with find is that people often forget that it can return more than one index. Your loop would fail (with a unable to perform assignment error) if find finds more than one match.

[John D'Errico]

I might blame it on the name - find. You want to find something? Use find. What are the odds someone would think to look for a name like knnsearch? This is why lookfor can be such a useful utility, since if the writers of a tool were good at the task of writing an H1 line, then you will find knnsearch by a careful choice of keywords. I'm running MATLAB flat out right now on a problem, so I will not test this claim, but I'd bet that

lookfor distance

might pop knnsearch up as one of the options. As it turns out, distance did not find knnsearch, but

lookfor nearest

will do so well enough.

Another important idea is something that I often like to do - just just help on a toolbox directory. For example, if you have the symbolic toolbox, then

help symbolic

will give you a long list of functions, with one line descriptions of what they do. A great way to learn what tools exist is to do exactly that sort of thing. Read the H1 lines shown, then look at the help for any function that happens to catch your eye as something of interest.

[John D'Errico]

Oh, by the way, interp1 would also have worked for this problem, though there is no reason why someone would have thought to use it.

That is, to find the index of the closest point in a2, for every point in a1?

ind = interp1(a2,1:numel(a2),a1,'nearest');

That should work. As long as the elements of a2 are sorted in an increasing order, and there are no replicates in a2, no problem.

Should you use interp1 for that? Well, it is a bit of a hack, using a tool to solve a problem it is not designed to solve, but it just happens to do what you want anyway.

Better is to just use knnsearch, a tool designed for the purpose.

[Asatur Khurshudyan]

Thank you for your comment. I will test it, because knnsearch works very slowly.