# parallel computation for a for loop

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Maryam on 12 Apr 2019
Commented: Maryam on 12 Apr 2019
Below is the part of the code I have written, in which I am trying to use parallel computation. But it does give me an error as below:
"Error: The variable k_1 in a parfor cannot be classified."
In each parfor iteration some specific rows of "k_1" matrix will be updated irrelavant to the rest, so I cannot see why I get this message. Any help in this regard will be highly appreciated. Please find the parallel portion of my code below:
k_1 = k;
M_1 = M;
% pi = 0;
parfor ppi=1:NP
for pii=1:kkk
% pi= pi + 1;
pi = (ppi-1)*kkk+pii;
Tempo1 = zeros(1,1);
Tempo1_M = zeros(1,1);
Tempo2 = zeros(1,1);
Tempo2_M = zeros(1,1);
for irow = 1:p(pi)
[xx,inside_angle] = find(irow==[p;q]);
Tempo1(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[k(p(inside_angle),p(pi))+lambda(pi)*k(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[k(q(inside_angle),p(pi))+lambda(pi)*k(q(inside_angle),q(pi))];
Tempo1_M(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[M(p(inside_angle),p(pi))+lambda(pi)*M(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[M(q(inside_angle),p(pi))+lambda(pi)*M(q(inside_angle),q(pi))];
end
for irow = 1:q(pi)
[xx,inside_angle] = find(irow==[p;q]);
Tempo2(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[alpha(pi)*k(p(inside_angle),p(pi))+k(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[alpha(pi)*k(q(inside_angle),p(pi))+k(q(inside_angle),q(pi))];
Tempo2_M(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[alpha(pi)*M(p(inside_angle),p(pi))+M(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[alpha(pi)*M(q(inside_angle),p(pi))+M(q(inside_angle),q(pi))];
end
%Assign tempos to k
for irow = 1:p(pi)
k_1(irow,p(pi)) = Tempo1(irow);
k_1(p(pi),irow) = Tempo1(irow);
M_1(irow,p(pi)) = Tempo1_M(irow);
M_1(p(pi),irow) = Tempo1_M(irow);
end
for irow = 1:q(pi)
k_1(irow,q(pi)) = Tempo2(irow);
k_1(q(pi),irow) = Tempo2(irow);
M_1(irow,q(pi)) = Tempo2_M(irow);
M_1(q(pi),irow) = Tempo2_M(irow);
end
end
end
k=k_1;
M=M_1;
Please note that k and M matrices are defined by me at the start of the code!
Maryam on 12 Apr 2019
Well, the reason I think it's parallel is that in each iteration (over ppi) I produce 4 arrays, which are independant. Then I assign the arrays to the columns of k_1 and M_1, which the array numbers are not the same. For example for a 6x6 matrix, if "NP" will be equal 3 (which means I want to use 3 processors to do the job independantly from each other), then processor one will override 2 specific columns of k_1 (lets say 2 and 3), processor 2 override another 2 columns (1 and 4 for example), and the last processor should override the last two columns (5 and 6). These pairs have computed at the start of my code (which is not mention here), and it is prooved that there aren't any repeated number in pairs!
So by the explanation I provided, would you please tel me in what part I am making the mistake? In another words, what part of my explanation is wrong based on the parallel computation concept?
Again thank you so much for your time and considerations.

Catalytic on 12 Apr 2019
parfor pi=1:NP*kkk
Tempo1 = zeros( p(pi) ,1 );
Tempo1_M = zeros( p(pi) ,1);
Tempo2 = zeros(q(pi) ,1);
Tempo2_M = zeros(q(pi) ,1);
pSubs = zeros( p(pi) ,2 ); %new
qSubs = zeros(q(pi) ,2);
for irow = 1:p(pi)
[xx,inside_angle] = find(irow==[p;q]);
Tempo1(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[k(p(inside_angle),p(pi))+lambda(pi)*k(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[k(q(inside_angle),p(pi))+lambda(pi)*k(q(inside_angle),q(pi))];
Tempo1_M(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[M(p(inside_angle),p(pi))+lambda(pi)*M(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[M(q(inside_angle),p(pi))+lambda(pi)*M(q(inside_angle),q(pi))];
pSubs(irow,:)=[irow,p(pi)]; %new
end
for irow = 1:q(pi)
[xx,inside_angle] = find(irow==[p;q]);
Tempo2(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[alpha(pi)*k(p(inside_angle),p(pi))+k(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[alpha(pi)*k(q(inside_angle),p(pi))+k(q(inside_angle),q(pi))];
Tempo2_M(irow) = [(xx-1)*alpha(inside_angle)+(2-xx)]* ...
[alpha(pi)*M(p(inside_angle),p(pi))+M(p(inside_angle),q(pi))] + ...
[(2-xx)*lambda(inside_angle)+(xx-1)]* ...
[alpha(pi)*M(q(inside_angle),p(pi))+M(q(inside_angle),q(pi))];
qSubs(irow,:)=[irow,q(pi)]; %new
end
subsCell{pi}=[pSubs;qSubs]; %new
kValCell{pi}=[Tempo1;Tempo2];
MValCell{pi}=[Tempo1_M;Tempo2_M];
end
subs=cell2mat(subsCell);
kVal=cell2mat(kValCell);
MVal=cell2mat(MValCell);
k_1=accumarray(subs,kVal,size(k));
M_1=accumarray(subs,MVal,size(M));
k=k_1 + tril(k_1.',-1); %make symmetric
M=M_1 + tril(M_1.',-1);
Maryam on 12 Apr 2019
I understand! Well I wasn't aware of that. Thank you so much for clarification and your help.