MrAzzman already pointed out how to linearise nested loops. Here is a general solution to linearise n nested loops.
1) Assuming you have a simple nested loop structure like this:
%dummy function for demonstration purposes
f=@(a,b,c)([a,b,c]);
%three loops
X=cell(4,5,6);
for a=1:size(X,1);
for b=1:size(X,2);
for c=1:size(X,3);
X{a,b,c}=f(a,b,c);
end
end
end
2) Basic linearisation using a for loop:
%linearized conventional loop
X=cell(4,5,6);
iterations=size(X);
for ix=1:prod(iterations)
[a,b,c]=ind2sub(iterations,ix);
X{a,b,c}=f(a,b,c);
end
3) Linearisation using a parfor loop.
%linearized parfor loop
X=cell(4,5,6);
iterations=size(X);
parfor ix=1:prod(iterations)
[a,b,c]=ind2sub(iterations,ix);
X{ix}=f(a,b,c);
end
4) Using the second version with a conventional for loop, the order in which the iterations are executed is altered. If anything relies on this you have to reverse the order of the indices.
%linearized conventional loop
X=cell(4,5,6);
iterations=fliplr(size(X));
for ix=1:prod(iterations)
[c,b,a]=ind2sub(iterations,ix);
X{a,b,c}=f(a,b,c);
end
Reversing the order when using a parfor
loop is irrelevant. You can not rely on the order of execution at all. If you think it makes a difference, you can not use parfor
.