generate random numbers among each non zero column elements

Given a=[0 1 1; 1 1 1; 1 0 1], the row index of first elements of 1st colomn is [2 3], 2nd colomn is [1 2] and 3rd colomn is [1 2 3].

Then I want to generate random numbers among each row index, e.g.:

generate 1 random number from 1st column index [2 3],

generate 1 random number from 2nd column [1 2],

generate 2 random numbers from 3rd column [1 2 3].

The following code is what I've written to do this. It works but it seems not efficient especially when a is huge. Currently, I am using for-loop, may I know if anyone could have more efficient ways like the vectorized version to do this?

Thank you!

a=[0 1 0 0; 1 1 1 0; 1 0 0 1];
  dind=1:3;
  [a1,a2]=find(a==1);
  e=[1 2 1 1];%define how many random numbers needed
  d=cell(length(e),1);
  for j=1:length(e)
      c=a1(a2==j);%read the random number row index of j-th colomn 
      d{j}=dind(1,c(1:e(j)));%read the row index
      a(c(1:e(j)),j)=0;%make the readed data into 0
  end

[jonas]

[r,c]=find(a==1)
r(randi(length(r(c==1))))

This will output a random index of a one in the first column, is that what you need but one number for every column?

[Chaoyang Jiang]

Yes, how to avoid for loop here, as I got 5021889 loops and the operation - find may take 5000s.

[KSSV]

Read about logical indexing......

[Chaoyang Jiang]

Thank you for your hint...