function row_sample(A,s)

Let à be an empty matrix

for t = 1 to s do

Randomly sample a row according to the distribution P

Let Ait, ⋆ be the sampled row, with corresponding probability pi

Set ${\tilde{A}}_{t,\star }=\frac{1}{\sqrt{s{p}_i}}{A}_{i_t,\star }$

end for

return à and row indices

end function