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

randperm

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 (i.e. ~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!

Best Answer

You're probably going to need a loop for this since the number of non-zero elements in a column is not constant across all the columns. For each column, use randperm on the non-zero elements. E.g., the process for one column:
A = your matrix
Ac = A(:,1); % a column
z = Ac ~= 0; % the non-zero element logical indexes
Az = Ac(z); % the non-zero elements
A(z,1) = Az(randperm(numel(Az))); % the shuffled elements replaced
Or, if you want a new matrix B as a result then copy A into B first and operate on B.
Related Question