How do I repetitively shuffle elements in my matrix column-wise?

Hello everyone,

I am new to MATLAB and have a question about how to randomly shuffle elements in a matrix column-wise. Specifically, I have a 582x255 matrix and I would like to shuffle the elements. However, it is important that the elements of one column stay in the same column, so a column-wise shuffle and that the every column is shuffled in a different way (so that the elements in one row are not all shuffled to the same row). So far, this is what I have come up with:

[m,n]=size(F); % F = 582x255 matrix 
nb_rows = n; %number of rows
C_1 = F(:,1); % select first column of matrix
C_1_s = C_1(randperm(length(C_1))); % randomly shuffle the elements of that column

This works. However, I would like to find a way to do it automatically for every column. I think I would need to create a loop that does the same thing column per column, so I have tried this:

for i=1:nb_rows;
    C_i = F(i,1);
    C_i_s = C_i(randperm(length(C_i)));
end

But it doesn't seem to work.

I would greatly appreciate it if someone could help me with this!

Answer 1

[Matt J]

F=magic(5)

F = 5×5

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

[m,n]=size(F);

[~,I]=sort(rand([m,n]));
J=repmat(1:n,m,1);

Fshuffle = F(sub2ind([m,n],I,J))

Fshuffle = 5×5

17 6 7 2 3 11 5 25 14 16 4 24 1 21 9 10 18 13 20 22 23 12 19 8 15

[Joyce Oerlemans]

Hello, Matt

This seems to work well, thank you very much for your quick response!

Can I trust that everytime I perform this function, the values are shuffles in a different random way (meaning that not the exact same shuffle is repeated every time)? I ask because I want to do a permutation analysis on this data and I have to repeat it at least 100 times.

Thanks!

[Matt J]

Can I trust that everytime I perform this function, the values are shuffles in a different random way

Yes. Did you try it?

[Joyce Oerlemans]

Yes, I did, thank you!

How would I need to change the script if I want to do it row-wise instead of columnwise? So if my matrix is now 255x582? Is it:

[m,n]=size(F);

[I,~]=sort(rand([m,n]));

J=repmat(1:m,n,1);

Fshuffle = F(sub2ind([m,n],I,J))

Thank you very much for all your help and quick response!

[Matt J]

You could transpose the input and output.

F=magic(5)

F = 5×5

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

F=F';

[m,n]=size(F);

[~,I]=sort(rand([m,n]));
J=repmat(1:n,m,1);

Fshuffle = F(sub2ind([m,n],I,J))' %rows shuffled

Fshuffle = 5×5

17 15 24 8 1 5 14 23 16 7 6 13 20 4 22 21 19 12 10 3 9 11 25 2 18

[Joyce Oerlemans]

That works perfectly, thank you very much! I have one last question: is there a way to repeat this loop a 100 times so that I get 100 variables each which a different shuffle of the matrix?

[Matt J]

That works perfectly, thank you very much!

You're welcome, but please Accept-click the answer to indicate that it worked.

I have one last question: is there a way to repeat this loop a 100 times so that I get 100 variables each which a different shuffle of the matrix?

As below:

F=magic(5)

F = 5×5

17 24 1 8 15 23 5 7 14 16 4 6 13 20 22 10 12 19 21 3 11 18 25 2 9

[m,n]=size(F);
p=100;

[~,I]=sort(rand([m,n,p]));
J=repmat(1:n,m,1,p);

Fshuffle = F(sub2ind([m,n],I,J))

Fshuffle = 
Fshuffle(:,:,1) =

    17    12     1    21    22
    10    18    19    20     3
     4     6     7     2    15
    11    24    13     8     9
    23     5    25    14    16


Fshuffle(:,:,2) =

    11    24    25     2    22
    23     6     7    21     3
     4    12     1     8     9
    10     5    13    20    16
    17    18    19    14    15


Fshuffle(:,:,3) =

     4     5    13    21    16
    17    18     1    14    22
    10    12    19    20    15
    23     6     7     8     9
    11    24    25     2     3


Fshuffle(:,:,4) =

    10    12     1    21    16
    17    18    19    20     3
    23     6     7    14    15
     4    24    13     2    22
    11     5    25     8     9


Fshuffle(:,:,5) =

     4    12    13    14    16
    10     5    25    20    15
    11    24     7     8    22
    17     6     1    21     9
    23    18    19     2     3


Fshuffle(:,:,6) =

    11     6     7    14     9
    23    18    25    20     3
    10    24    13     2    16
    17     5    19     8    22
     4    12     1    21    15


Fshuffle(:,:,7) =

    23    18    19    20     3
    10    24     7    21    16
     4    12    13    14    15
    17     6    25     2    22
    11     5     1     8     9


Fshuffle(:,:,8) =

     4    18    13    21    16
    10     5     7     2    15
    23    12    19    20     9
    17    24     1    14    22
    11     6    25     8     3


Fshuffle(:,:,9) =

    11     6    25    20    15
    17     5    13    14     9
     4    12     7     8     3
    10    24     1    21    16
    23    18    19     2    22


Fshuffle(:,:,10) =

    11     5    13    14    15
    17    12     7    21     9
     4     6    25     8     3
    23    24     1    20    16
    10    18    19     2    22


Fshuffle(:,:,11) =

    23    24    13    20     9
    17     6     1     8     3
     4     5     7    21    15
    10    18    25     2    22
    11    12    19    14    16


Fshuffle(:,:,12) =

    10    24    13    21    22
     4     6    19     8     3
    11     5     7     2    16
    23    18     1    14     9
    17    12    25    20    15


Fshuffle(:,:,13) =

    10     5    13    14    15
     4    12    25    21    22
    11    24    19     8     9
    23     6     7     2    16
    17    18     1    20     3


Fshuffle(:,:,14) =

    17     5    19     8    16
    10    18    25     2    22
     4    24    13    20     3
    23    12     1    21     9
    11     6     7    14    15


Fshuffle(:,:,15) =

    17     5    19    21     9
    23    12    25    20     3
    10     6    13    14    15
     4    24     7     8    22
    11    18     1     2    16


Fshuffle(:,:,16) =

    10    12     7     2    15
    23    18    19     8     3
    11    24    25    21     9
    17     6     1    20    16
     4     5    13    14    22


Fshuffle(:,:,17) =

    17    12    13     8    16
    10    18     7    21     9
    23     6     1    20     3
     4    24    25     2    15
    11     5    19    14    22


Fshuffle(:,:,18) =

    17    18     1     2     3
     4    12    25    14    16
    23     6    19     8    22
    11     5     7    20     9
    10    24    13    21    15


Fshuffle(:,:,19) =

    10    18    19     8    15
    17    24     7    20     3
     4     5     1    21     9
    23     6    13     2    16
    11    12    25    14    22


Fshuffle(:,:,20) =

    23     5     1    20     9
     4     6    25     2     3
    17    24     7     8    16
    11    12    19    14    22
    10    18    13    21    15


Fshuffle(:,:,21) =

     4    12     7    21    16
    17     6    19     2     9
    23     5     1    20    15
    10    24    13     8    22
    11    18    25    14     3


Fshuffle(:,:,22) =

    11     6    19     2    15
    23    12    25    21    16
     4     5     7     8     3
    10    18    13    14     9
    17    24     1    20    22


Fshuffle(:,:,23) =

    23    18    25    20    16
     4     5    19    14    15
    11     6    13     8     9
    10    12     1     2    22
    17    24     7    21     3


Fshuffle(:,:,24) =

     4     6    19     8    16
    10     5    25     2     9
    17    18     7    20    22
    11    12    13    14    15
    23    24     1    21     3


Fshuffle(:,:,25) =

    10    12     1    20     3
     4     5    13     2    15
    23    18     7    14     9
    17    24    25     8    16
    11     6    19    21    22


Fshuffle(:,:,26) =

    11    24    13     8     3
    23     6     1    14    22
    10    12    25     2     9
     4     5    19    21    16
    17    18     7    20    15


Fshuffle(:,:,27) =

    10    24    19    20    16
    23    18    25    21    15
    11     5     7     8    22
    17     6     1    14     3
     4    12    13     2     9


Fshuffle(:,:,28) =

    10    12    13    21    16
    23    18    19     8     3
    17     6     1     2    15
     4     5    25    14     9
    11    24     7    20    22


Fshuffle(:,:,29) =

    17    18    25    20    22
    10     6     1    14    16
    23     5    19     8     9
    11    12    13     2    15
     4    24     7    21     3


Fshuffle(:,:,30) =

    11     5    13     8    16
    23    18    19     2     3
    10    12     1    21     9
     4    24     7    14    15
    17     6    25    20    22


Fshuffle(:,:,31) =

    10    24    25     8    15
    17     6    13    14    16
     4     5     7    21    22
    11    12     1     2     3
    23    18    19    20     9


Fshuffle(:,:,32) =

    17     6    25     8    22
    23    24     1    21    16
    11     5     7     2     3
     4    18    13    20    15
    10    12    19    14     9


Fshuffle(:,:,33) =

     4    24     7     2     9
    11    18    13     8    16
    10    12    25    20     3
    23     6     1    14    15
    17     5    19    21    22


Fshuffle(:,:,34) =

    23    12     1     2    16
    10    24    13    14    15
     4     6    19    20     9
    11    18     7    21    22
    17     5    25     8     3


Fshuffle(:,:,35) =

    11     6     1    21    22
     4     5     7    20     9
    10    18    13     2    15
    23    24    25    14     3
    17    12    19     8    16


Fshuffle(:,:,36) =

     4    12     7     8    15
    23     6    13    20     9
    17    24    19    21     3
    11    18    25    14    16
    10     5     1     2    22


Fshuffle(:,:,37) =

    10    12     7     8    22
     4     5    13    21     9
    17    18    19     2    15
    23     6     1    20    16
    11    24    25    14     3


Fshuffle(:,:,38) =

    17    18     1    21     9
    10     5    13     8    22
     4    24    25    14     3
    23    12    19     2    16
    11     6     7    20    15


Fshuffle(:,:,39) =

    10     6    13     8    16
     4    18     1    20     9
    17    12    19    21    22
    23     5     7    14    15
    11    24    25     2     3


Fshuffle(:,:,40) =

    23     5     1    21    15
    10     6    19     8     9
    11    18     7    14    16
    17    12    25     2    22
     4    24    13    20     3


Fshuffle(:,:,41) =

     4     6     1     8    22
    10    18    13    20    15
    11    24    19     2     3
    23     5     7    21     9
    17    12    25    14    16


Fshuffle(:,:,42) =

     4    24     1     8     3
    10    12    19    21    22
    17    18    25     2     9
    23     6     7    20    15
    11     5    13    14    16


Fshuffle(:,:,43) =

     4     6    13    14     9
    17    12    19    20     3
    23    18     1     2    22
    11     5     7    21    16
    10    24    25     8    15


Fshuffle(:,:,44) =

     4    12     1     8    22
    23    24     7     2     9
    17     5    13    14    16
    10     6    19    21     3
    11    18    25    20    15


Fshuffle(:,:,45) =

    23     6    25     2     3
    17    18    19    20    16
    11    24     1    21    22
     4    12     7     8    15
    10     5    13    14     9


Fshuffle(:,:,46) =

    11     5     7    20     3
    17    24    19     8     9
    10     6    13     2    16
    23    18     1    21    22
     4    12    25    14    15


Fshuffle(:,:,47) =

    23    12     1     2     3
    10     6    19    21    15
    11    24    25     8     9
    17     5    13    20    16
     4    18     7    14    22


Fshuffle(:,:,48) =

    23    12     7    20     9
    10     6    19    21    16
    17    24    25     2    22
    11     5    13    14     3
     4    18     1     8    15


Fshuffle(:,:,49) =

     4     5    19     8    22
    11    18    25    21    15
    23    24    13     2     3
    10    12     1    20    16
    17     6     7    14     9


Fshuffle(:,:,50) =

    11     6     7    20    16
     4    12    19     2     9
    10    18    25    14     3
    17    24    13    21    15
    23     5     1     8    22


Fshuffle(:,:,51) =

    11     5     7     8    16
     4    24    19    21    22
    23    18    13    14     3
    10     6     1     2     9
    17    12    25    20    15


Fshuffle(:,:,52) =

    11     5     7     2    15
     4    12     1    14     9
    17     6    25     8    16
    10    18    13    21    22
    23    24    19    20     3


Fshuffle(:,:,53) =

    23    12    25    21    22
     4     5    19     8    16
    11    18     1    14    15
    17     6    13     2     9
    10    24     7    20     3


Fshuffle(:,:,54) =

    10     6     7    21     3
     4     5    19    20    15
    17    24    25     8    16
    23    12     1     2     9
    11    18    13    14    22


Fshuffle(:,:,55) =

    17    18    19    14     3
     4    24    13     2    15
    10     6    25    21    16
    23    12     1     8    22
    11     5     7    20     9


Fshuffle(:,:,56) =

    23     5    19    14     3
    10     6     1    21    16
    11    12    25     2    15
     4    24    13     8     9
    17    18     7    20    22


Fshuffle(:,:,57) =

    17    24    13    20     9
    11     5     7    21    16
     4    18    25     2    15
    23    12     1    14    22
    10     6    19     8     3


Fshuffle(:,:,58) =

    10    12    25     2     3
    17     6    19    21    22
    11    24     1     8     9
    23     5    13    14    16
     4    18     7    20    15


Fshuffle(:,:,59) =

     4     5    25     8    22
    17     6     7    21     3
    11    24     1    20    15
    10    18    13     2     9
    23    12    19    14    16


Fshuffle(:,:,60) =

     4    18    13    20    16
    23     5    19    21    15
    11    12    25     8     9
    17     6     7     2     3
    10    24     1    14    22


Fshuffle(:,:,61) =

    10    18    13     2     9
    23     5     1    21    22
    17    12     7     8    15
     4     6    19    14     3
    11    24    25    20    16


Fshuffle(:,:,62) =

    17    24     1     2    22
     4    12    25    14     3
    23     6     7    20    15
    10    18    13     8     9
    11     5    19    21    16


Fshuffle(:,:,63) =

    10    12    25    20    15
    11    24    13     8    16
     4     5     1     2    22
    23     6    19    21     9
    17    18     7    14     3


Fshuffle(:,:,64) =

    17    18    19     2     9
    11    12    25    21     3
     4     5    13    14    16
    23     6     1    20    15
    10    24     7     8    22


Fshuffle(:,:,65) =

    10    18     7     8    16
    23     5     1    20    22
    11     6    25    14    15
     4    24    13     2     9
    17    12    19    21     3


Fshuffle(:,:,66) =

     4    24     1    21     9
    10     5    13     8    15
    17     6    25    20     3
    11    18     7    14    16
    23    12    19     2    22


Fshuffle(:,:,67) =

    23     5    13    21    16
     4    18    19    20    22
    17    12     1     8    15
    10     6    25    14     9
    11    24     7     2     3


Fshuffle(:,:,68) =

    11    18    19    20    22
    23     5    13    14     9
     4    24    25     8     3
    10    12     7    21    15
    17     6     1     2    16


Fshuffle(:,:,69) =

    11    18     7    21    15
    17     5    19     2    22
     4    12    25    20    16
    23     6    13     8     9
    10    24     1    14     3


Fshuffle(:,:,70) =

    10     5    13     2     9
    23    24    25    20    22
    17    18     1    14    15
     4    12     7    21     3
    11     6    19     8    16


Fshuffle(:,:,71) =

    11    12    25    21     9
    17     6    19    14    15
     4    18    13     8    22
    23    24     7     2     3
    10     5     1    20    16


Fshuffle(:,:,72) =

    23    12     7    14    16
    11    18    25     2    15
    10     6    19     8    22
     4    24     1    20     3
    17     5    13    21     9


Fshuffle(:,:,73) =

    23     6     7    20    16
     4    18    25     2     3
    11    12    19    14    22
    10    24    13    21     9
    17     5     1     8    15


Fshuffle(:,:,74) =

    11    12     1     2    16
    23    24    19    21    15
     4     5    25    20     3
    17     6     7    14    22
    10    18    13     8     9


Fshuffle(:,:,75) =

    11     6     1    20    22
    10    24    25    21    15
    23    18    19     2     9
     4    12    13    14     3
    17     5     7     8    16


Fshuffle(:,:,76) =

    23     5     1    20     9
    17     6     7     2     3
    10    24    25    21    22
     4    18    19    14    15
    11    12    13     8    16


Fshuffle(:,:,77) =

     4    18    25     2     3
    11     5    13    21    16
    10    12     7     8    15
    17     6    19    14     9
    23    24     1    20    22


Fshuffle(:,:,78) =

    10    18    19     2     3
    11     5    13    21    22
     4    12     1    20    15
    17     6    25     8    16
    23    24     7    14     9


Fshuffle(:,:,79) =

    10     6    25    20     3
    11     5     7    14    15
    23    18    13     8    22
     4    24     1     2    16
    17    12    19    21     9


Fshuffle(:,:,80) =

    11    12    19     2    15
    10    24     1    21     3
    17     6     7     8     9
     4     5    13    20    22
    23    18    25    14    16


Fshuffle(:,:,81) =

    11     5    13     2     9
    17    24    25     8    15
    10    12     7    20     3
     4    18    19    14    22
    23     6     1    21    16


Fshuffle(:,:,82) =

     4    24     1    14     9
    11     6    13    21    16
    23    12    19     8     3
    17     5    25     2    22
    10    18     7    20    15


Fshuffle(:,:,83) =

    17    18    25    20    22
    11     6     7     8    15
    23     5    19     2     9
    10    24    13    14     3
     4    12     1    21    16


Fshuffle(:,:,84) =

    11    12    19    14    15
    10    18     7    21    22
    17    24    25     8    16
    23     5    13     2     3
     4     6     1    20     9


Fshuffle(:,:,85) =

    10    24    13    21     3
    17     5     7    20    22
     4    12     1     2    15
    11     6    19     8    16
    23    18    25    14     9


Fshuffle(:,:,86) =

    11     6    19     8     9
     4    24    25    14     3
    10     5    13     2    15
    23    12     7    20    22
    17    18     1    21    16


Fshuffle(:,:,87) =

    11     5    13    20    16
    23    12     1     2    15
    10    18     7    21     3
     4    24    25     8     9
    17     6    19    14    22


Fshuffle(:,:,88) =

    23    12    13     8     9
     4     6     1    14    15
    10    24     7     2    16
    17    18    25    20     3
    11     5    19    21    22


Fshuffle(:,:,89) =

     4    24    19    20     9
    23     5     1    21    22
    11     6     7    14     3
    10    12    25     2    15
    17    18    13     8    16


Fshuffle(:,:,90) =

    11    12    19     2     9
    10    24     1     8     3
    17     5    13    14    16
    23     6     7    20    22
     4    18    25    21    15


Fshuffle(:,:,91) =

    17     6    19     2     9
    10    12    25    21    22
    23    18     1    14     3
    11    24    13    20    15
     4     5     7     8    16


Fshuffle(:,:,92) =

    10    24     7     8     3
    23    12    25    20    15
    11     6     1    21    22
    17    18    13     2    16
     4     5    19    14     9


Fshuffle(:,:,93) =

    23     5    19    14     9
    17    24    13     8    16
     4     6     7    20    15
    10    12    25    21    22
    11    18     1     2     3


Fshuffle(:,:,94) =

    17     5     7    20    15
    10    18    13     8    16
    23     6    25    14     9
    11    24     1    21     3
     4    12    19     2    22


Fshuffle(:,:,95) =

    11    12    19    21     3
    17     5     7     8    16
    23     6     1    20    15
    10    18    13     2    22
     4    24    25    14     9


Fshuffle(:,:,96) =

    10    18     1    20     3
    23     5    19    14    22
    11     6    25     2    15
    17    24    13    21     9
     4    12     7     8    16


Fshuffle(:,:,97) =

     4     6    13    14    16
    23     5    19    20     3
    10    18     7     2     9
    17    12    25     8    15
    11    24     1    21    22


Fshuffle(:,:,98) =

    11     5     7     8    15
    23    24    19    21     3
    10     6     1     2     9
     4    12    25    14    16
    17    18    13    20    22


Fshuffle(:,:,99) =

    17    24    13    20     9
    11    12     7    14     3
    10     5    19     2    16
     4    18     1     8    22
    23     6    25    21    15


Fshuffle(:,:,100) =

     4    18     1    20    22
    23    24    13     8    16
    17    12     7     2     3
    10     6    19    14    15
    11     5    25    21     9

Answer 2

[Voss]

Looks like this is what you are going for:

[m,n]=size(F); % F = 582x255 matrix 
for i = 1:n
    C_i = F(:,i);
    C_i_s = C_i(randperm(m));
    F(:,i) = C_i_s;
end

And it can be written more succinctly wihout the temporary variables:

[m,n]=size(F); % F = 582x255 matrix 
for i = 1:n
    F(:,i) = F(randperm(m),i);
end

[Joyce Oerlemans]

Hallo Voss,

thank you very much for your quick response. Could you elaborate a little bit more how I should interpret the output? Is it one possible matrix or does this give all possible matrices at once?

Thank you very much!

[Voss]

It is one matrix. Each column of F is shuffled separately one time and stored back in F.