Shuffling non-zero elements of each column in a matrix

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!

Answer 1

[James Tursa]

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.

[Antonio]

@James Tursa It works for one column and I definitely need a loop. If you write it this way then how do you put the last two lines in a loop?

[James Tursa]

Put everything in the loop, not just the last two lines. Change the 1 to your loop index variable.

[Antonio]

@James Tursa Oh man .. since you didn't put it in a loop yourself I thought it is way more complicated than that lmao. Thanks a bunch anyway it works perfect!