Shuffling elements within the rows of a matrix

Say I have a matrix, I would like to shuffle the elements within the rows randomly. For example,

A = randi(1000, 3,4)
A =

   815   279   958   793
   906   547   486   960
   127   958   801   656

I need to get the shuffled matrix like this

B =

   279   793   958   815
   960   547   486   906
   801   127   958   656

The most straightforward way I can think of achieving this is to use randperm to shuffle the indices of each row, and then loop over the number of rows to create the shuffled matrix. But I would like to get it all done in one go, preferably more elegantly than using a loop, because I need to do this for large matrices many times. So, alternatively, I tried this:

[nr,nc] = size(A);
P=perms(1:nc);
col_indx_mtrx = P(randi(size(P,1),nr,1),:);
ri = repmat((1:nr)',1,nc);

which gives me

ri =

       1     1     1     1
       2     2     2     2
       3     3     3     3

col_indx_mtrx =

       2     1     4     3
       3     4     1     2
       1     4     2     3

Now, after this, I thought if I simply do

B = A(ri,col_indx_mtrx)

I am done. But, I don't get the desired result, because when I give the row and column indices as matrices, MATLAB tries to create a matrix with all combinations of the row and column indices?

Essentially, what I need is to create the shuffled matrix B such that

B(1,1) = A(ri(1,1), col_indx_mtrx(1,1))

and so on. Is there an elegant way to achieve this last step? I tried to use arrayfun, but I could not get it done.

Or, better, is there a more elegant way of achieving the overall objective?

Any help would be greatly appreciated.

Answer 1

[the cyclist]

Here's one way:

% Original matrix
A = randi(1000, 3,4);
[M,N] = size(A);

% Preserve the row indices
rowIndex = repmat((1:M)',[1 N]);

% Get randomized column indices by sorting a second random array
[~,randomizedColIndex] = sort(rand(M,N),2);

% Need to use linear indexing to create B
newLinearIndex = sub2ind([M,N],rowIndex,randomizedColIndex);

B = A(newLinearIndex);

[Par]

Thanks for the answer! The main difference in my method and yours, I notice, is the way of generating the randomizedColIndex. I like yours better, and so have used it. If we use perms, instead, as I was doing, MATLAB is likely to go out of memory very quickly.

Thanks also to Thorsten below.

[Sahil Bansal]

And how can I shuffle the elements in the column randomly?

[Jan]

Sorting random indices is less efficient and has a tiny bias compared to the stable Fisher Yates shuffle: There is (and must be) the chance, that rand(1, 2) replies two equal numbers. Matlab's sort is stable, such that the first occurrence is preferred.

In older Matlab versions randperm used the sorting of random vectors also, but now the relation between data size and runtime looks like the faster Fisher Yates shuffle is used also, when it is called with 2 inputs:

tic;
v = randperm(1e6);
toc;
tic;
v = randperm(1e6, 1e6);
toc;

 Elapsed time is 0.204787 seconds.
 Elapsed time is 0.086091 seconds.

I've delivered a suggestion for improvements.

Answer 2

[Matt J]

    [m,n]=size(A);    
    T=perms(1:n);  %tabulate once only

    J=T(randi(m,m,1),:);

    B=A(  bsxfun(@plus,(1:m).', (J-1)*m)  );

Answer 3

[Thorsten]

To achieve the last step in your code, use sub2ind:

 B = A(sub2ind([nr nc], ri, col_indx_mtrx));

Answer 4

[Jan]

See https://www.mathworks.com/matlabcentral/fileexchange/27076-shuffle:

A  = randi(1000, 3,4);
A1 = Shuffle(A, 1);
A2 = Shuffle(A, 2);