You are an expert in writing code in many different languages. Your goal is to perform code completion for the following code, keeping in mind the rest of the code and the file meta data.
    Metadata details:
    filename: lansvd_d1.m
    path of file: ./repos/lrslibrary/algorithms/rpca/DUAL
    
    the code of the file until where you have to start completion: %this is a simplified version of lansvd that is specialized to compute
%the largest singular value and one principal singular vector of A
%
% Minming Chen, June 2009. Questions? v-minmch@microsoft.com ; 
% Arvind Ganesh (abalasu2@illinois.edu)
%
% Copyright: Perception and Decision Laboratory, University of Illinois, Urbana-Cham
    
function [S1] = lansvd_d1(A)

[m, n] = size(A);
K = min([m n 10]);
K0 = K;

stop = 0;
nrestart = 0;
p_j1 = rand(m,1) - 0.5;

while ~stop
    beta_j = sqrt(p_j1'*p_j1);
    u_j = p_j1/beta_j;
    v_j1 = zeros(n,1);

    j = 1;
    U = u_j;
    V = [];
    alpha = zeros(K + 1, 1);
    beta = zeros(K + 1, 1);
    beta(1) = beta_j;
    while j <= K %Lanczos bi-diagonalizaion
        r_j = A'*u_j - beta_j*v_j1;
    
%         for i = 1:j - 1 %full-orthogonalization for r_j
%             v_i = V(:,i);
%             t = v_i'*r_j;
%             r_j = r_j - t*v_i;
%         end