How to implement a parfor in place of a for loop?

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I understand the idea behind what is and isn't allowed in a parfor loop, but I do not understand the practical application. I have the following segment of code. It works great, but it only uses 1 core and takes hours to complete. It should be trivial to parallelize but I don't see how to do it.
By the way, the preallocations are merely for the purpose of presenting it to you in a way that it will work.
numfiles = 3249;
LABTnum = 61;
for i=1:LABTnum
adjusted_La{i} = rand(10,numfiles);
adjusted_Sm{i} = rand(10,numfiles);
adjusted_Yb{i} = rand(10,numfiles);
end
chem_LaSm = repmat(rand(10,1),1,numfiles);
pcoefs = repmat([0.2 1.0 3.0],numfiles,1)';
h = 2;
Mi = repmat(pcoefs(:,1),1,h+1);
polys = zeros(h+1,numfiles);
M = bsxfun(@power,Mi,0:h);
for i=1:LABTnum
bestCm_LaSm{i} = zeros(numfiles,numfiles);
curSm_LaSm = adjusted_Sm{i}; % for La/Sm
for k=1:numfiles
curLa = repmat(adjusted_La{i}(:,k),1,numfiles);
LaSm = curLa./curSm_LaSm;
difs = [mean((LaSm*0.2-chem_LaSm).^2)' mean((LaSm-chem_LaSm).^2)' mean((LaSm*3-chem_LaSm).^2)']';
for j=1:numfiles;
polys(:,j) = M\difs(:,j);
end
bestCm_LaSm{i}(:,k) = -0.5*polys(2,:)./polys(3,:);
end
end
I do not understand how to modify a code like this in a way that is acceptable for parfor. Any help is appreciated.
EDIT:
I've found that I may rewrite the active part of the code as:
for i=1:LABTnum
bestCm_LaSm{i} = zeros(numfiles,numfiles);
curSm_LaSm = adjusted_Sm{i}; % for La/Sm
parfor k=1:numfiles
polys{k} = zeros(h+1,numfiles);
curLa = repmat(adjusted_La{i}(:,k),1,numfiles);
LaSm = curLa./curSm_LaSm;
difs = [mean((LaSm*0.2-chem_LaSm).^2)' mean((LaSm-chem_LaSm).^2)' mean((LaSm*3-chem_LaSm).^2)']';
for j=1:numfiles;
polys{k}(:,j) = M\difs(:,j);
end
end
for k=1:numfiles
bestCm_LaSm{i}(:,k) = -0.5*polys{k}(2,:)./polys{k}(3,:);
end
end
Is there a better way?

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