Sort and keep index of a n-dimension array -- MATLAB

Question

I have a 12-D array and am using each dimension as an index value in an optimization problem.

A(:,:,i1,i2,i3,i4,i5,i6,i7,i8,i9,i10)

each index value i is a value from 1 to 5.

I want to sort A from greatest to least and keep track of the indices so I know which indices correspond to to what value of A.

So my ideal output would be a 2 column cell/array with one column being the value and the other other column being the index values.

For a simple 3D example: say I have a 3D array: A(:,:,i1).

Where:

A(:,:,1) =  2 
A(:,:,2) =  6 
A(:,:,3) =  13 
A(:,:,4) =  11 
A(:,:,5) =  5

I would like my output to be:

EDIT:

assume I have 1x1x3x3 sized input such that

A(1,1,1,1) = 3

A(1,1,2,1) = 1

A(1,1,3,1) = 23

A(1,1,1,2) = 12

A(1,1,2,2) = 9

A(1,1,3,2) = 8

A(1,1,1,3) = 33

A(1,1,2,3) = 14

A(1,1,3,3) = 6

the expected output would be:

33 [1,1,1,3]

23 [1,1,3,1]

14 [1,1,2,3]

12 [1,1,1,2]

9 [1,1,2,2]

8 [1,1,3,2]

6 [1,1,3,3]

3 [1,1,1,1]

1 [1,1,2,1]

So what would be the size of that output 2 column array? That is how many rows would it have? — Divakar, Oct 30 '14 at 19:39
Can you take a small 3D array instead of 12-D array as an example and show us the expected output? — Divakar, Oct 30 '14 at 19:46
Sorry to bother again, but not that simplified. Could you assume `2 x 2 x 2` sized input? Or do you mean you would always have `1 x 1 x M x ..` as input? — Divakar, Oct 30 '14 at 20:02
@OliverOliver By the way, in my solution, I give you something like `[1st dim, 2nd dim, ..., 12th dim]`. If you want indices, then don't use `ind2sub` — Autonomous, Oct 30 '14 at 20:05
Alright, so could you assume `1 x 1 x 5 x 2` sized input and tell us the expected output? — Divakar, Oct 30 '14 at 20:16
@OliverOliver see my edit and read the comment carefully. I would have loved to give you a better solution, but running out of time. — Autonomous, Oct 30 '14 at 20:34
@Parag S. Chandakkar thanks for your help Divakar's solution worked out for me — Oliver Oliver, Oct 30 '14 at 20:46
Consider accepting the solution that has best met the needs of the question, by clicking on the hollow checkmark at the top-left side of the solution. — Divakar, Oct 31 '14 at 09:11

score 2 · Accepted Answer · edited May 23 '17 at 12:06

2

This should be a generic code for any multi-dimensional input array -

%// Sort A and get the indices
[sorted_vals,sorted_idx] = sort(A(:),'descend'); 

%// Set storage for indices as a cell array and then store sorted indices into it
c = cell([1 numel(size(A))]); 
[c{:}] = ind2sub(size(A),sorted_idx);

%// Convert c to the requested format and concatenate with cell arary version of 
%// sorted values for the desired output
out = [num2cell(sorted_vals) mat2cell([c{:}],ones(1,numel(A)),numel(size(A)))];

The generic code owes its gratitude to this fine solution.

edited May 23 '17 at 12:06

Community

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answered Oct 30 '14 at 20:37

Divakar

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well that's the same problem for me. Is there any way we can make this code work for variable dimensionality? Since you also have to specify `[p1,...,p12]` – Autonomous Oct 30 '14 at 20:39
@Divakar Thanks so much this works perfectly!! Now I just to to figure out a way to visualize/display this data. – Oliver Oliver Oct 30 '14 at 20:45
@OliverOliver isn't the cell used to display your data, for example, in my answer, the cell `yourCell`? – Autonomous Oct 30 '14 at 20:49
@Parag S. Chandakkar Yes, it is. I was was just thinking out loud. My next step is to display this output in a plot or something to make it super easy to visualize. – Oliver Oliver Oct 30 '14 at 20:53
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@ParagS.Chandakkar Check out the edits on how to make it generic. – Divakar Oct 30 '14 at 20:56
@OliverOliver So that `out` would be used to get your plot I am assuming? – Divakar Oct 30 '14 at 20:56
@OliverOliver Also, check out the edits, as the code is now less "stretchy", compact and generic! Let us know how it goes with you? – Divakar Oct 30 '14 at 21:00

Autonomous · Answer 2 · 2014-10-30T20:34:28.400

1

I guess this is what you want:

b=A(:);
[sorted_b,ind]=sort(b,'descend');
[dim1,dim2,dim3,dim4]=ind2sub(size(A),ind);

%arranging in the form you want
yourCell=cell(size(b,1),2);
yourCell(:,1)=mat2cell(sorted_b,ones(size(b,1),1),1);

%arranging indices -> maybe vectorized way is there for putting values in "yourCell"
for i=1:size(b,1)
    yourCell{i,2}=[dim1(i) dim2(i) dim3(i) dim4(i)];
end

For the array A, given by you, my output looks like:

33  [1,1,1,3]
23  [1,1,3,1]
14  [1,1,2,3]
12  [1,1,1,2]
9   [1,1,2,2]
8   [1,1,3,2]
6   [1,1,3,3]
3   [1,1,1,1]
1   [1,1,2,1]

which matches with your output.

edited Oct 30 '14 at 20:34

answered Oct 30 '14 at 19:56

Autonomous

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Something does't work when trying to extract the indices back out. I i get this for [3,3,12,2420] for the indices output when trying a 11-D array – Oliver Oliver Oct 30 '14 at 20:12
tell exact size of your matrix, as in `m x n x p x...` – Autonomous Oct 30 '14 at 20:20
[1 x 1 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4 x 4] – Oliver Oliver Oct 30 '14 at 20:26
Now I understand, well my code works, but it requires that you specify as many no. of variables as your matrix dimensionality i.e. if your matrix is 4-D. Then you should change `[row,col,layer]=ind2sub(size(a),ind);` to `[dim1,dim2,dim3,dim4]=ind2sub(size(a),ind);` and change `yourCell{i,2}=[row(i) col(i) layer(i)];` to `yourCell{i,2}=[dim1(i) dim2(i) dim3(i) dim4(i)];`. So my code will not work, if you enter variable dimensionality arrays i.e. 12-D, 11-D etc. See the modified code. It works for a 4-D array and it will work for an 11-D array if you write `[dim1,dim2,...,dim11]` as I suggested. – Autonomous Oct 30 '14 at 20:32
+1 for you too already and you can use the generic-part if you need to. It's not really an essential part of my code. – Divakar Oct 30 '14 at 21:20
ya I know... our solutions are very similar, I just didn't have time to make it generic, nice job. @OliverOliver Please consider accepting the appropriate solution. – Autonomous Oct 30 '14 at 21:35
Comeon I skipped loops! :) – Divakar Oct 30 '14 at 21:37
ya, I didn't pay attention in optimizing that... I even wrote it in solution that "maybe vectorized way is there for putting values in "yourCell"" – Autonomous Oct 30 '14 at 21:38

Sort and keep index of a n-dimension array -- MATLAB

2 Answers2