Finding a random non-zero location in a vector

I have a vector (Rs, size n x 1) which has few zeros and rest nonzero values. I need to randomly find a index to a nonzero valued location in the vector. This need to be done in a loop where every loop will change the number of zeros and nonzeros in the vector.

I have been attempting to do this in following fashion:

loop start
   toPick = find(Rs);
   rand_pick = toPick(randi(numel(toPick)));
   - Do something which changes the no. of zeros and nonzeros in Rd -
end

This method works. However the issue is the size of toPick changes which can result in significant overhead in terms of performance. Is there a way to change the code to increase the performance?

Answer 1

[Walter Roberson]

When the probability of "success" is not too small, sometimes the fastest is the rejection method.

numRs = size(Rs,1);    %can be done before any looping

while true
  rand_pick = Rs(randi(numRs));
  if rand_pick > 0; break; end
end

You can also increase the speed of this by choosing the random numbers ahead of time:

num_repeats = 1000;    %supposing the code loop as a whole is to be executed 1000 times

ridx = randi(numRs, [2*num_repeats, 1]);   %if you know the average fill rate you can adjust the "2*" using statistical techniques

num_left = size(ridx,1);

for K = 1 : num_repeats

    while num_left > 0
      rand_pick = Rs(ridx(num_left));
      num_left = num_left - 1;
      if rand_pick > 0; break; end
    end

    if num_left <= 0; error('need a bigger random buffer'); end

    do something with rand_pick
  end

[Amit]

Thank you, but I suspect that this will result in probably more poor performance in my case as first Rs is a growing vector (which grows to significantly larger size) and the ratio of zeros to nonzeros changes with every loop.

[Walter Roberson]

If Rs is a growing vector then you need to be careful because growing vectors can be slow.