relabel the elements in each column according to the magnitude of these elements in an array

Hi, I have

 a=[4 5; 
    5 1;
    6 4; 
    7 7]

I want to relabel the elements in each column according to the magnitude of these elements in the column to become

   a=[1 3; 
      2 1;
      3 2; 
      4 4]

How can I do this? Thank you.

Answer 1

[Star Strider]

This works:

a=[4 5; 5 1;6 4; 7 7]
[as,ai] = sort(a,1);
b = [ai(ai(:,1),1)  ai(ai(:,2),2)]

produces:

b =

       1     3
       2     1
       3     2
       4     4

It sorts the first and second columns independently. Then, to get the column indices as you want them, it maps each set of column indices to its own sorted indices. A bit complicated to explain, but taking the reference to the columns of b apart and looking at its components will reveal how it works.

[Grace]

Hi Star,

as gives me the sorted array for the first and second column independently.

What is ai? I can't figure it out.

[Grace]

Here I've found it:

as=sorted array in ascending order

ai=position of the index

[Grace]

But Star, this can't apply to other arrays? For example:

 d=[6 4;
    4 5; 
    2 6; 
    7 7]

Relabel, and I want to get

 e=[3 1; 
    2 2; 
    1 3; 
    4 4]

If I used the code that u suggested,

 [as,ai] = sort(d,1);
 e = [ai(ai(:,1),1)  ai(ai(:,2),2)]

gives me

 e=[1 1; 
    2 2;
    3 3;
    4 4]

What's the problem? Did I misunderstand something? Thank you.

[Star Strider]

This works for both, plus some test matrices I created:

m = a;                      % Define ‘argument’ matrix
ms = sort(m,1);             % Sort
for k1 = 1:size(m,2)        % Column iterations
    for k2 = 1:ize(m,1)     % Row iterations
        mi(k2,k1) = find(m(k2,k1) == ms(:,k1));
    end
end

The ‘mi’ matrix is the matrix of indices that maps column sort order to position in the argument matrix.

Not quite as compact, but reasonably fast.

[Grace]

Thanks a lot, Star. Appreciate it :)

[Star Strider]

My pleasure!

[Grace]

Hi Star, I put my a and d in a big array,f which gives me:

 f=
    [4x2 double]    
    [4x2 double]

I want to run the code above in a time, then I did:

 [r c]=size(f);    
for col=1:c
for row=1:r
ff{row,col}=sort{f{row,col,1)   % To sort the two arrays in f and denote           the sorted arrays as ff

 end 
end 

 [rr cc]=size(f{r,c}); % to find the size for each array in f
for col=1:c
for row=1:r
for di=1:cc
for mi=1:rr
fff{utr,utc}(rr,cc)=find(f{utr,utc}(rr,cc)==ff{utr,utc}(:,cc));
end 
end
end
end

I can't get what i want in the end, what mistakes did i make in the code above?

[Star Strider]

My code was predicated on the elements in each row being unique with no repeats. If there are repeats, the code will fail. I didn’t anticipate that, since it wasn’t part of the original problem. I’ll see what I can do to make it work with repeats, since I understand how it works, but no promises. (I created the new array out of vertically concatenating ‘a’ and ‘d’.)

I can’t follow your code by inspection, and there are some obvious typos (probably inadvertent in pasting it to the Comment window) so I can’t run it.

[Grace]

Hope can get good news from you, Star :)

[Star Strider]

Apologise for the delay. It took a while to figure it out, but it turned out to be a surprisingly easy solution, using only a bulit-in MATLAB functon and one small loop:

a=[4 5; 5 1;6 4; 7 7];
 d=[6 4;
    4 5; 
    2 6; 
    7 7];
g = [a; d];

m = g;                      % Define ‘argument’ matrix
for k1 = 1:size(m,2)
    [mu(:,k1) ai(:,k1) mui(:,k1)] = unique(m(:,k1));
end
result = mui

The ‘result’ array should be what you want.

[Grace]

Really thanks a lot, Star :) This helps me a lot!! Thanks again!!

[Star Strider]

My pleasure!

It’s an unusual enough request that it took some time to come up with solution. When I was Answering another Question involving unique, it occurred to me that the unique function actually does exactly what you want.