Take mean value when elements inside array "clump up"

I have an Array,for example:

    r1 = rand(1000,1)
    sort(r1)

and have this sorted in ascending order. What Im trying to accomplish is: I want to take the mean value whenever the values inside the arrays clump up and are in between a specific threshold. Trying to explain this in an example:

    a = [1; 10; 15; 16; 16.1; 16.2; 16.3; 18]

Mean Value should always be taken when the number inside the array have a maximum difference of 0.5.

So here essentially this should be taken:

    a_sub = [16; 16.1; 16.2; 16.3]
    mean(a_sub)

I hope this is understandable. Any help is greatly appreciated.

[the cyclist]

So, in this case, you want the output to be

out = [1; 10; 15; 16.15; 18];

?

[Ko Fa]

Im actually only interested in the mean value, the array is non of my concern anymore.

[the cyclist]

Could there be more than one cluster in the same array? For example, could the input be something like

a = [0.1 0.2 0.3 5 6 7 0.8 0.9 1.0];

?

[Ko Fa]

yes

Answer 1

[the cyclist]

Assuming that my guess about the correct output is correct, then the following should work.

% Original (sorted) data
a = [1; 10; 15; 16; 16.1; 16.2; 16.3; 18];

% The difference threshold
d = 0.5;

% Identify which "cluster" each value belongs to. This part is slightly tricky.
% The diff command will result in a value of 1 if the prior value is more than the threshold.
% By taking the cumulative sum, the index will therefore move to the next value.
clusterIndex = cumsum(diff([a(1); a]) > d) + 1;

% According to the index, take the mean over values that belong to the same cluster
out = accumarray(clusterIndex,a,[],@mean);

[Ko Fa]

Thanks a lot for your anwer!

Is there a way to then extract all the mean values calculated?

[the cyclist]

a = [1; 2.1; 2.2; 10; 15; 16; 16.1; 16.2; 16.3; 18];

d = 0.5;

clusterIndex = cumsum(diff([a(1); a]) > d) + 1;
numberInCluster = histcounts(clusterIndex);

clusterMeans = accumarray(clusterIndex,a,[],@mean);

clusterMeansWithMoreThanOneValue = clusterMeans(numberInCluster>1);

[Ko Fa]

Thank you kind sir! I