nested loops in parfor, indexing

Hey

im trying to solove an equation system over a 4 dimensional grid of parameter values. Since the difference between neigbouring parameter-grid points is small, using the solution of a neigbouring parameter-grid point as a starting value speeds up computation a lot. See the code below.

Now i would like to use parallel computiong to further speed up computation. But Matlab doesnt allow the indexing i need (i3-1, i4-1). Now i understand this makes sense for the parfor index (i1), but for the nested loop indexes it seems an unneccessary restriction.

Is there a way around?

Many Thanks

Dominik

parfor i1=1:n1 % works with for, not with parfor
 for i2=1:n2
  for i3=1:n3
   for i4=1:n4
     if solution(i1,i2,max(1,i3-1),i4)~=0
      start=solution(i1,i2,max(1,i3-1),i4);
     else
      start=solution(i1,i2,i3,max(1,i4-1));
     end
      myparametrizedfun=@(x)myfun(x,parametergeneratingfun(i1,i2,i3,i4));
      solution(i1,i2,i3,i4)=fsolve(myparametrizedfun,start);
   end
  end
 end
end

Answer 1

[Edric Ellis]

Unfortunately, PARFOR's static analysis cannot tell that you are accessing 'solution' in an order-independent "sliced" manner. You can help it out by making a temporary partial solution, filling it out, and then sticking that pack into 'solution':

parfor i1=1:n1
    % Local temporary 'solution' for this value of i1.
    tmp_solution = zeros(n2, n3, n4);
    for i2=1:n2
        for i3=1:n3
            for i4=1:n4
                if tmp_solution(i2,max(1,i3-1),i4)~=0
                    start=tmp_solution(i2,max(1,i3-1),i4);
                else
                    start=tmp_solution(i2,i3,max(1,i4-1));
                end
                myparametrizedfun=@(x)myfun(x,parametergeneratingfun(i1,i2,i3,i4));
                tmp_solution(i2,i3,i4)=fsolve(myparametrizedfun,start);
            end
        end
    end
    % tmp_solution is now complete, paste back into solution.
    solution(i1, :, :, :) = tmp_solution;
end

[dominik]

Thats very helpful! Thanks a lot!