how to find common elements of two matrices considering also the repeated values?

Hello everybody, i would like to know how to find the position of elements of a matrix who are in another matrix. For example, letting i have two matrix A and B:

A= [2 1 2 
    3 2 5
    4 7 5
    4 8 10]

B= [4 7 5
    2 8 10
    4 1 2
    3 2 5]

I would like the output to provide the position of the elements of the B matrix that are present in the A matrix considering also repeated values.

For example "it finds in which position the element B (1,1) is present in the matrix A (:, 1), in which position the element B (2,1) is present in the matrix A (:, 1), in which position the element B (3,1) is present in the matrix A (:, 1) and so on ". So similarly for the other columns "find in which position the element B (1,2) is present in the matrix A (:, 2) etc"

Regarding the repetition I would like to make sure that if, for example, there are 3 repetitions in a column, each repetition will have an increasing order index, ie:

A= [ 2
4
4
4]

B=[4
2
4
4]

output=[2
1
3
4 ]

I tried to use the MATLAB function "intersect", but it give as outputs only the indexes of the columns whose values are not repeated.

for n=1:size(A,2)
      [C, idx1, idx2] = intersect( B(:,n), A(:,n), 'stable');
end

I do not know if I've been clear. Sorry.

Answer 1

[Stephen23]

This is easy with sort, assuming that both A and B contain exactly the same elements:

>> A = [2;4;4;4];
>> B = [4;2;4;4];
>> [~,ida] = sort(A);
>> [~,idb] = sort(B);
>> [~,ida] = sort(ida);
>> [~,idb] = sort(idb);
>> ida(idb)
ans =
     2
     1
     3
     4

EDIT: use a simple loop to do matrices of any size. This is simpler because C is preallocated so we can index into it using idb:

A = [2,1,2;3,2,5;4,7,5;4,8,10];
B = [4,7,5;2,8,10;4,1,2;3,2,5];
C = nan(size(A));
for k = 1:size(A,2)
    [~,ida] = sort(A(:,k));
    [~,idb] = sort(B(:,k));
    C(idb,k) = ida;
end

And checking the output:

>> C % my code
C =
     3     3     2
     1     4     4
     4     1     1
     2     2     3
>> [3 3 2; 1 4 4; 4 1 1; 2 2 3] % requested output
ans =
     3     3     2
     1     4     4
     4     1     1
     2     2     3

[Gessica Cos]

But the result is different if i consider the matrix A and B of [4x3]. I would like to obtain the indexs of elements of matrix B who are in matrix A.

[Stephen23]

@Gessica Cos: accepting Image Analyst's answer tells us that your question has been resolved. If their answer does not resolve your question, why did you accept it?

What output do you expect to get for the 4x3 matrices? Please show the example output.

[Gessica Cos]

Sorry, i made a mistcake. I'd like to have this output:

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

[Image Analyst]

You say "I would like the output to provide the position of the elements....." Now, since each number in B could show up a different number of times in A, won't you need a cell array to hold the different locations? Like 4 shows up in A 2 times: at (3,1) and (4,1). However 2 shows up 3 times: at (1,1), (1,3), and at (2,2). Please clarify why you think a 4 by 3 array would work to hold the positions.

[Gessica Cos]

I wanted to know if it was possible to do something like that:

"it finds in which position the element B (1,1) is present in the matrix A (:, 1), in which position the element B (2,1) is present in the matrix A (:, 1), in which position the element B (3,1) is present in the matrix A (:, 1) and so on ". So similarly for the other columns "find in which position the element B (1,2) is present in the matrix A (:, 2) etc"

I tried to use the MATLAB function "intersect", but it give as outputs only the indexes of the columns whose values are not repeated.

ps I thank you for the help you are giving me

[Stephen23]

@Gessica Cos: see my edited answer. Neither ismember nor interesect will do what you want.

[Gessica Cos]

Thanks so much. You've been really kind. You have been very helpful to me.

Answer 2

[Image Analyst]

Try ismember().

[Gessica Cos]

I tried to use "ismember" but I have not succeeded.Could you give me an idea of the code I should write?

Answer 3

[Image Analyst]

Try this:

A= [2 1 2
  3 2 5
  4 7 5
  4 8 10]

B= [4 7 5
  2 8 10
  4 1 2
  3 2 5]
% Find unique numbers in each of the two arrays.
ua = unique(A)
ub = unique(B)
% Check each number in B to see where it lives in A.
for k = 1 : length(ub)
  % Get this number from B
  thisB = ub(k);
  % Find out what rows and columns it shows up at in A
  [rows, columns] = find(A == thisB);
  % Save the number we were looking for into column 1 of the cell array.
  locations{k, 1} = thisB;
  % Save the locations that number was found into column 2 of the cell array.
  locations{k, 2} = [rows, columns];
end
celldisp(locations)

Be sure to read the FAQ https://matlab.wikia.com/wiki/FAQ#What_is_a_cell_array.3F so you understand what I did.