Parallel program required to be fixed for last couple of lines due to extensive time-consuming for saving variables in 3 by 3 matrix

parfor i=1:TotNu

a=(fy(i)*eye(3))+(Cyabs(i)*([cosa(i);cosb(i);cosc(i)]*[cosa(i) cosb(i) cosc(i)]));
b=a-Czabs(i)*([cosa(i);cosb(i);cosc(i)]*[cosa0(i) cosb0(i) cosc0(i)]);
xsj=(a*SAp(:,i)+b*[0;0;1]);
Ex=[Ex;xsj];
RondF_RondEta=[a RondF_RondEta];
RondF_RondZeta=[b RondF_RondZeta];

issues are with

RondF_RondEta=[a RondF_RondEta];
RondF_RondZeta=[b RondF_RondZeta];

where takes huge amount of time for saving. I tried to slice variable, and use parfor etc. I am looking for a solution to resolve that?

[James Tursa]

How large is TotNu? Is this the only thing you are doing inside the parfor loop?

It looks like this is basically some nD outer products and matrix-vector multiplies which could be done e.g. with the bsxfun and times functions. It will take more memory to store intermediate results (hence my question about TotNu) using the method I have in mind, but may be cleaner and faster overall than the parfor you are currently doing (parfor seems like overkill for what you have shown).

[Mohammad]

That is 1120000 iteration in each parfor loop

Answer 1

[Thorsten]

If is more efficient if you allocate Ex, RondF_RondEta and RondF_RondZeta before the loop:

Ex = nan(1, TotNu);
RondF_RondEta = nan(1, TotNu);
RondF_RondZeta = nan(1, TotNu);

for i=1:TotNu
  a = (fy(i)*eye(3))+(Cyabs(i)*([cosa(i);cosb(i);cosc(i)]*[cosa(i) cosb(i) cosc(i)]));
  b = a-Czabs(i)*([cosa(i);cosb(i);cosc(i)]*[cosa0(i) cosb0(i) cosc0(i)]);
  Ex(i) = (a*SAp(:,i)+b*[0;0;1]);
  RondF_RondEta(i) = a;
  RondF_RondZeta(i) = b;
end

[Mohammad]

This unfortunately increases time. This way does not work.

Answer 2

[James Tursa]

E.g., using nD operations without parfor:

cosabc = [cosa(:)'; cosb(:)'; cosc(:)'];
cos0abc = [cosa0(:)'; cosb0(:)'; cosc0(:)'];

a = bsxfun(@times,reshape(cosabc,3,1,TotNu),reshape(cosabc,1,3,TotNu));
a = bsxfun(@times,a,reshape(Cyabs,1,1,TotNu));
a = a + bsxfun(@times,eye(3),reshape(fy,1,1,TotNu));

b = bsxfun(@times,reshape(cosabc,3,1,TotNu),reshape(cos0abc,1,3,TotNu));
b = bsxfun(@times,b,reshape(Czabs,1,1,TotNu));
b = a - b;
Ex = zeros(3,TotNu);
for k=1:TotNu
    Ex(:,k) = a(:,:,k) * SAp(:,k) + b(:,3,k); % nD matrix multiply
end

RondF_RondEta = reshape(a(:,:,TotNu:-1:1),3,[]);
RondF_RondZeta = reshape(b(:,:,TotNu:-1:1),3,[]);
Ex = Ex(:);

[Mohammad]

That sounds good since I realized calculation time is shortened. However, I intend to add matrix "a" and "b" like as

       A(:,:,1)=a(:,:,1)+a(:,:,2)+......a(:,:,28)
      A(:,:,2)=a(:,:,29)+a(:,:,302)+......a(:,:,56)
          .
          .
          .
          .
      A(:,:,m1)=a(:,:,.........

and similarly for b

B(:,:,1)=b(:,:,1)+b(:,:,2)+......b(:,:,28)
B(:,:,2)=b(:,:,29)+b(:,:,302)+......b(:,:,56)
    .
    .
    .
    .
B(:,:,m1)=b(:,:,.........

so It seems I need to apply changes like this following

for k=1:m1

Ex(:,k) = A(:,:,k) * SAp(:,k) + B(:,3,k); % nD matrix multiply
end

TotNu=28*m1

I am looking for a way to do this summation but NOT WITH A LOOP! please let me know if you have any ideas.