How can I number each element of a matrix according to the corresponding ordered position, row by row?

For example, I have matrix A:

A = [9 15 1 16
       15 9 1 16
       1 6 2 4]

The sorted matrix is:

B= [1 9 15 16
      1 9 15 16
      1 2 4 6]

For each rows of A, I want to determine if each element corresponds to the first, second, third or fourth position, as follows:

A'= [2 3 1 4
       3 2 1 4
       1 4 2 3] 

Thanks for help

Answer 1

[Andrei Bobrov]

[~,ii] = sort(A,2);
[~,out] = sort(ii,2)

[Daniela Conforti]

It works! Thank you for help.

Answer 2

[madhan ravi]

Note: Your A' doesn't correspond to the exact position. See https://www.mathworks.com/help/matlab/ref/sort.html#bt8nojg-1-I

A =   [9  15 1 16 ;...
       15 9  1 16 ;...
       1  6  2 4 ];
   
Adash = [2 3 1 4 ;...
         3 2 1 4 ;...
         1 4 2 3];       
[B,I]=sort(A,2)  % B - sorted matrix , I - position of the original values --> see doc sort for explanation

Gives:

B =
     1     9    15    16
     1     9    15    16
     1     2     4     6
I =
     3     1     2     4
     3     2     1     4
     1     3     4     2
     

To compare A' you could do somethig like below:

Adash==I

Gives:

ans =
  3×4 logical array
   0   0   0   1
   1   1   1   1
   1   0   0   0

[Daniela Conforti]

This is not what I want to achieve. I need the opposite corrispondence. If we have, for example, only the vector A= [9 15 1 16] the sorted vector is B= [1 9 15 16]; If we look at B, 9 is the second element, 15 is the third, 1 is the first and 16 is the forth. I want to obtain A' --> [2 3 1 4], but for all rows.