Obtaining different results when using parfor in matlab - matlab

Question

I am trying to parallelize the code below in matlab:
%reduce the size of A if necessary.
A=rand(100,60);
B=int8(rand(size(A,1),size(A,2))>0.5);
N=10;
G=15;
lambda_tol_vector= zeros(G,1);
conto = 1;
for h=-G:0.1:G
lambda_tol_vector(conto)=2^(h);
conto = conto+1;
end
M=4;
tol = 1e-9;
CompletedMat_nopar1={};
tic
for RIPETIZIONE = 1:10
%using normal for loop CompletedMat is saved
for k = 1:size(lambda_tol_vector,1)
%fprintf('Completion using nuclear norm regularization... \n');
%sequential code:
[CompletedMat34,flag] = matrix_completion_nuclear_GG_vec(A.*double(B),double(B),N,lambda_tol_vector(k),tol);
%parallel code thread-based:
if flag==1
CompletedMat_nopar1{RIPETIZIONE,k}=zeros(size(A));
end
CompletedMat_nopar1{RIPETIZIONE,k}=CompletedMat34;
end
end
toc
After having vectorized whereby possible I ended up with the following code:
A = parallel.pool.Constant(A);
lambda_tol_vector=parallel.pool.Constant(lambda_tol_vector);
R=10;
K=size(lambda_tol_vector.Value,1);
CompletedMat_parvec=cell(R,K);
idx=cellfun('isempty', CompletedMat_parvec);
CompletedMat_parvec(idx)={zeros(size(A.Value))};
B=double(B);
tic
parfor n=1:R*K
[~,k]=ind2sub([R,K],n);
%fprintf('Completion using nuclear norm regularization... \n');
[CompletedMat,flag] = matrix_completion_nuclear_GG_vec( ...
A.Value.*B,B, N, lambda_tol_vector.Value(k), tol);
if flag~=0
CompletedMat_parvec{n}=CompletedMat;
end
end
toc
The problem here is that CompletedMat_parvec and CompletedMat_nopar1 provide totally different results while they are expected to give the same result.
How is this possible?
For the sake of completeness I will provide matrix_completion_nuclear_GG_vec below:
%%
% We need a functional environment so that the MAtimesVec subfunction can
% access variables in workspace
function [Anew,objective,flag,iteration] = matrix_completion_nuclear_GG_vec(A,B,N,lambda_tol,tol)
%%
%This code ttries to vectorize and make more efficient the code in
%matrix_completion_nuclear_GG_alt
%% Singular value thresholding for structured (sparse + low rank) matrix
%clear;
%tol=10^-7;
%lambda_tol=0.5;
%%
% Read in sparse matrices downloaded from The University of Florida Sparse
% Matrix Collection
%data = load('mhd4800b.mat');
%A = data.mhd4800b;
%A=A(1:100,1:100);
%A=rand(100,5)*rand(5,100);
%[sA,vA,dA]=svd(A)
%%
% initialization
%B = rand(size(A))<0.3; % remove 10% of the entries
mat=A.*B;
m = size(mat,1);
n = size(mat,2);
L = zeros(m,1);
R = zeros(n,1);
iteration=0;
criterion=0;
flag=0;
Anew=L*R';
objective=zeros();
while (criterion==0 && iteration<N && flag==0)
Aold=Anew;
iteration=iteration+1;
%iteration
%%
% Generation of structured matrix (sparse plus low rank)
%LR = L*R'; % generation of low rank matrix
%Amat = mat + LR; % sparse + low rank
%%
% Find all singular values >= lambda_tol by svt (deflation method). Function
% MAtimesVec is defined at end of this file.
%tic;
%[u,s,v] = svt(#MAtimesVec,'m',m,'n',n,'lambda',lambda_tol);
[u,s,v] = svd(mat+Anew);
%toc;
%display(size(s));
if size(s,1)==0
Anew=NaN*A;
objective=NaN;
flag=1;
return
elseif max(max(s))<=lambda_tol
Anew=NaN*A;
objective=NaN;
flag=1;
return
else
for k=1:min(size(s,1),size(s,2))
if s(k,k)<lambda_tol
s(k,k)=0;
else
s(k,k)=s(k,k)-lambda_tol;
end
end
%size(s,1)
%s=s-lambda_tol*eye(size(s,1));
L=u*s;
R=v;
mat=(A-u*s*v').*B;
Anew=L*R';
objective(iteration)=1/2*(norm(mat,'Fro'))^2+lambda_tol*(sum(diag(s)));
%objective(iteration)
if (norm(Anew-Aold,'Fro')^2/(norm(Aold,'Fro')^2))<tol
criterion=1;
end
%norm(A-Anew,'Fro')
end
end
if flag==1
Anew=[];
objective=[];
end
%%
% Subfunction for exploiting matrix structure of sparse plus low rank
%function MAvec = MAtimesVec(vec, trans)
% if trans
% MAvec = (vec'*mat)' + R*(vec'*L)';
% else
% MAvec = mat*vec + L*(R'*vec);
% end
%end
end