random initialization of vectors

I have to generate random vectors for p^(0), u_l and v_l for l=1...L

Now I am confused about how to generate these vector as l=1..L is number of users, for example I have L=2 then generation of vectors should like p^(1) p^(2)

For u_1 u_2 v_1 v_2. and after that i have peform step 1 and 2 respectivly, for each l.

A picture is also attached of an algorithm.kindly guide me I am very confused.