Inverse of sorting arrangement

[B,I] = sort(A) output is such that B = A(I). What would be the most efficient way to rather get B and J, such that A = B(J)?

Answer 1

[Stephen23]

Assuming that A is a vector:

[B,I] = sort(A);
[~,J] = sort(I);
B(J)

If you have a matrix/array, then you first need to define what the intended effect is: to sort elements along one dimension (e.g. separately sort each column or row of a matrix) or to sort the rows atomically (i.e. using SORTROWS).

[Mohamed Eldin]

Matlab returns the new matrix according only the first column, why? so the indices will be subtitute regarding the first column values

[Stephen23]

"Matlab returns the new matrix according only the first column, why? so the indices will be subtitute regarding the first column values"

My answer only applies to vector inputs.

The answer to your question is explained in the SORT documentation: "[B,I] = sort(___) also returns a collection of index vectors for any of the previous syntaxes. I is the same size as A and describes the arrangement of the elements of A into B along the sorted dimension" (bold added). This means that if you sort the up/down the columns (default for a matrix) that the indices will give the new row positions of the column elements. This means the indices are 1<=indices<=size(A,1), and if you (incorrectly) interpret them as linear indices then you will get combinations of the first column.

So for matrices ultimately you will need to loop over each row/column, and also decide if you want linear indices or to retain the indices along the dimension along the sorted dimension. Which do you want?

[Mohamed Eldin]

I used the command "sortrows" and it worked perfectly

as in the following example:

[Indata,id] = sortrows(InData,1); % sort InData

[~,ids] = sortrows(id,1); % sort the index

InData_returne = Indata(ids,:); % return InData again

[Stephen23]

@Mohamed Eldin: you do not need the 2nd SORTROWS, a simple SORT is quite sufficient:

[B,I] = sortrows(A,1);
[~,J] = sort(I);
A = B(J,:);

Also note that if you are only sorting one column instead of SORTROWS you could use indexing & SORT:

[B,I] = sort(A(:,1));

Answer 2

[Matt J]

 [B,I] = sort(A); 

 J=1:numel(I);

 J(I)=J;

[Robert]

Surprisingly, even this works:

 [B,I] = sort(A); 
 J(I) = 1:numel(I);

[Matt J]

Yes, but it can have unintended effects if J is a pre-existing variable in the workspace.

Answer 3

[Bruno Luong]

If A has distinct elements such as

A = rand(1,10)

A = 1×10

0.0113 0.2350 0.1021 0.4269 0.9673 0.4399 0.3871 0.0288 0.5912 0.1876

a single line command is

[B,~,J] = unique(A);

Check

J

J = 10×1

1 5 3 7 10 8 6 2 9 4

B(J)

ans = 1×10

0.0113 0.2350 0.1021 0.4269 0.9673 0.4399 0.3871 0.0288 0.5912 0.1876

[Bruno Luong]

If A has non distinct element, then the above method gives B that is shorter than A (and B has distinct elements) and

B(J) = A 

still hold.