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How can I index elements by their sorted positions?

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Daniel Drumm
Daniel Drumm on 4 Mar 2020
Commented: Daniel Drumm on 5 Mar 2020
I have a question regarding indexing vector elements according to their position in a sorted list. The usual query I have seen is more like this, where the secondary output of sort() is sufficient - but not for my purpose.
The problem (using R2019a in Windows 10):
I have a vector (which could be arbitrarily long, with an arbitrary number of sets of replicants, each of which could have an arbitrary number of elements).
A = [20 23 1 19 20 8 5 14 9 7];
and can happily sort it:
>>B = sort(A)
B =
[1 5 7 8 9 14 19 20 20 23]
I want to create another vector C whose ith element describes the index position within B of the ith element of A. Duplicates should be handled by their original appearance order.
i.e., the desired C = [8 10 1 7 9 4 2 6 5 3]
C therefore has the properties: sort(C) = 1:size(A), and size(unique(C)) = size(C).
for ii = 1:size(A,1)
C(ii) = find(B,A(ii))
end
almost works. It doesn't handle duplicate values though, and returns C(5) = 8 instead of 9. (It's also non-vectorised and therefore presumptively ugly.)
A nastier test selection would be
>>A = [42 23 23 7 9 7 8 1 10 23 9 9 1 2 23 23 16 18 7 9];
>>B = sort(A)
B =
[ 1 1 2 7 7 7 8 9 9 9 9 10 16 18 23 23 23 23 23 42];
with corresponding
C = [20 15 16 4 8 5 7 1 12 17 9 10 2 3 18 19 13 14 6 11]
I'd appreciate any ideas on how to handle duplicates - or direction to the appropriate question/answer/function if my GoogleFu isn't up to scratch.

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Accepted Answer

Aquatris
Aquatris on 4 Mar 2020
Edited: Aquatris on 5 Mar 2020
Sort has a second output that is the index;
[B,I] = sort(A);
such that A(I) = B;
From there, I is the C_ matrix you are looking for with non-unique elements shown as well. You can extract the unique element indeces using the [temp,index]=unique(B) function on B to obtain the indeces of B that are unique and equate C = C_(index).
Working Solution;
A = [20 23 1 19 20 8 5 14 9 7];
[B,idx] = sort(A) ;
indA = 1:length(A);
[temp,idB] = sort(idx);
C = indA(idB)

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Daniel Drumm
Daniel Drumm on 5 Mar 2020
Chapeau, Aquatris. Beautiful solution. Works perfectly on the nastier test case too.
Thanks!
Out of curiosity (and self-examination), why did you mention the [temp,index] = unique(B) function in the initial solution description?
Also, I want to accept the solution in your comment above. Could you please copy it into a new answer?
Aquatris
Aquatris on 5 Mar 2020
You mentioned you wanted only the unique values in B. With the unique function, you can identify the unique element indeces in B and extract those indeces from the "idB". This way you can assign the unique value indeces to the C instead of everything.
Daniel Drumm
Daniel Drumm on 5 Mar 2020
Ah, I see the confusion. I was trying to specify that C should not treat unique values within A the same as each other, since I wanted them counted in appearance order. It was a check that could be used to verify a solution.
Anyway, thanks again. I spotted the edit and accepted the answer.

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