Shuffling non-zero elements of each column in a matrix in MATLAB

Question

I want to shuffle non-zero elements of each column in a matrix but keep the zero elements at the same place. Like I have this:

A = 
 [10    0     30    40    50    60
  11    0     31    41    0     61
  0     22    32    42    0     62
  13    23    0     43    0     63
  0     24    34    44    54    64
  15    0     35    0     0     65
  16    26    36    46    56    66]

And I want this:

B =
   [13    0     32    44    54    64
    11    0     35    42    0     63
    0     24    36    40    0     61
    16    23    0     43    0     62
    0     22    31    41    56    60
    10    0     30    0     0     66
    15    26    34    46    50    65]

So herein I have the zeros at the exact same place (ie ~A = ~B) and the non-zero elements are shuffled. Obviously shuffling the columns using 'randperm' does not work as it does not allow me to keep zeroes at the same place!

Answer 1

Here's an alternative to the explicit loop-over-columns approach:

[~, jj, vv] = find(A);
s = accumarray(jj, vv, [], @(x){x(randperm(numel(x)))});
B = A;
B(B~=0) = cell2mat(s);

Answer 2

This is a solution that works for one column: Making a new vector C containing the nonzero entries, shuffling those, and pasting them back into the nonzero entries of B should do exactly that. Now you can adjust this to work for matrices by looping over all columns.

A =  [10, 11, 0, 13, 0, 15, 16];
B = A;
C = A(A~=0);
B(A~=0) = C(randperm(numel(C)));
A
B

Try it online!

Answer 3

I wrote a function for you

function a=shuffle(src) 

[rows, cols] = size(src);
a = zeros(rows,cols);

for c = 1:cols
    lastIndex = 1;
    col = [];
    for r = 1:rows
        if(src(r,c) ~= 0)
            col(lastIndex) = src(r,c);
            lastIndex = lastIndex + 1;
        end
    end

    indexes = randperm(length(col));
    lastIndex = 1;

    for r = 1:rows
        if(src(r,c) == 0)
            a(r,c) = 0;
        else
            a(r,c) = col(indexes(lastIndex));
            lastIndex = lastIndex + 1;
        end
    end
end
end

It's not optimized, I leave it to You. It extracts the non-zeros to a vector, and takes randperm values from this vector to the new matrix, if the old matrix didnt have 0 there.