How can to compute the following case?

If there is a cell D and its size 6*9 and this cell contains matrices. (Attached)

in this line: svd(D{1,1}.'*D{1,2});

how can I change the indices of D to do the multiplication of all combinations of D but without repeat the similar combinations such as:

D{1,1}.'*D{1,2} and D{1,2}.'*D{1,1}

and exclude the similar indicies such as

D{1,1}.'*D{1,1} and so on ...

Then store all the results in "distance"

                [U,S,V]  = svd(D{1,1}.'*D{1,2});
                distance = sqrt(sum(arrayfun(@(i)acos(S(i,i))^2,1:4)))
          

[Chunru]

Can you give an example of your data D?

[M]

@Chunru I attached the file

Answer 1

[Torsten]

  D = load("D.mat");
  D = D.D;
  n = size(D,1);
  m = size(D,2);
  distance = zeros(n,m,n,m);
  for i=1:n
    for j=1:m
        for i1=1:n
            for j1=1:m
                [~,S,~]  = svd(D{i,j}.'*D{i1,j1});
                distance(i,j,i1,j1) = sqrt(sum(arrayfun(@(k)acos(S(k,k))^2,1:size(S,1))));
            end
        end
    end
  end
 [M,I] = max(distance,[],'All')

M = 1.5695

I = 2592

 [i,j,i1,j1] = ind2sub([n,m,n,m],I)

i = 6

j = 9

i1 = 6

j1 = 8

 distance(6,9,6,8)

ans = 1.5695

 distance(6,8,6,9)

ans = 1.5695

Answer 2

[Chunru]

load(websave("D.mat", "https://www.mathworks.com/matlabcentral/answers/uploaded_files/1436693/D.mat"));
for i=1:size(D, 1)
    for j=1:size(D, 2)
        for i1=1:size(D, 1)
            for j1=1:size(D, 2)
                S{i,j,i1,j1} = D{i,j} - D{i1,j1};
            end
        end
    end
end

whos

  Name        Size                Bytes  Class     Attributes

  D           6x9                 15984  cell                
  S           6x9x6x9            863136  cell                
  cmdout      1x33                   66  char                
  i           1x1                     8  double              
  i1          1x1                     8  double              
  j           1x1                     8  double              
  j1          1x1                     8  double              

S{1, 2, 3, 4}       % for example: D{1,2}-D{3,4}

ans = 6×4

-0.0068 0.1359 0.2272 0.2585 -0.5386 0.0657 0.4552 0.5899 0.2370 0.1540 0.0995 0.0803 0.1061 0.0122 -0.0485 -0.0696 0.0210 -0.0793 -0.1435 -0.1655 -0.0087 -0.1109 -0.1761 -0.1985

[M]

@Chunru thanks, but I have a question please I used your code for multiplication all the combinations then I used it to compute 'distnace' and distance should give one value, but I have a problem how can I store all the distance values in a right way. can you please check?

also I am not getting only single values.

for i=1:size(D, 1)
    for j=1:size(D, 2)
        for i1=1:size(D, 1)
            for j1=1:size(D, 2)
                [U,S,V]  = svd(D{i,j}.'*D{i+1,j+1});
                distance{i,j,i1,j1} = sqrt(sum(arrayfun(@(i)acos(S(i,i))^2,1:4)))
            end
        end
    end
end

[Torsten]

@M

[U,S,V]  = svd(directions{i,j}.'*directions{i,j});

This makes no sense. If you use identical directions to compare, you'll of course get a distance of 0 for every pair.

[M]

@Torsten I will ignore the zero value, I want to get all the distance between the other combinations

[Torsten]

Are you sure all cell matrices directions{i,j} have the same number of columns ? The distance formula only applies under this condition.

[M]

Hi @Torsten, I edited the question, could you please suggest a solution