MATLAB: Vectorized code slower than loops

column-majorloopsMATLABmemory allocationnested loopsslowerspeedvectorization

This question is a bit an offspring from an other one, but I have the following two codes:
maxN = 100;
levels = maxN+1;
xElements = 101;
umn = complex(zeros(levels, levels)); % cleaning 
bessels = ones(1201, 1201, 101);    % 1.09 GB
negMcontainer = ones(1201, 1201, 100);
posMcontainer = negMcontainer;
tic
for j = 1 : xElements
    for i = 1 : xElements
        for n = 1 : 2 : maxN
            nn = n + 1;
            mm = 1;
            m = 1:2:n;
            numOfEl = ceil(n/2);
            umn(nn, mm:mm+numOfEl-1) = bessels(i, j, nn) * posMcontainer(i, j, m);
        end
    end
end
toc
tic
for j = 1 : xElements
    for i = 1 : xElements
        for n = 1 : 2 : maxN
            nn = n + 1;
            mm = 1;
            for m = 1 : 2 : n
                umn(nn, mm) = bessels(i, j, nn) * posMcontainer(i, j, m);
                mm = mm + 1;
            end
        end
    end
end
toc
And it tourns out, that loops version is faste >2x. Why is that so? I know that i happens if vectorization requiers large temporary variables, but (it seems) it is not true here.
And generally, what (other than parfor) can I do to speed up this code?
Best regards, Alex

Best Answer

Given
  • Matlab stores matrices in column-major order.
  • bessels and posMcontainer are both large
Possibly the transport of data between the memory and the cpu will be more efficient (the caches will work better) if
umn(nn, mm:mm+numOfEl-1) = bessels(i, j, nn) * posMcontainer(i, j, m);
was replaced by
umn(mm:mm+numOfEl-1,nn) = bessels(nn, i, j) * posMcontainer(m, i, j);
The same should apply to the "all-for-loop-case".
See Columns and Rows are not the same
&nbsp
And finally the test from Columns and Rows are not the same with an additional case. (R2016a,
result =runperf('NestedLoops.m');
fullTable = vertcat(result.Samples);   
varfun(@mean,fullTable,'InputVariables'         ...
      ,'MeasuredTime','GroupingVariables','Name')
ans = 
           Name           GroupCount    mean_MeasuredTime
    __________________    __________    _________________
    NestedLoops/test      4             1.3266          
    NestedLoops/test_1    4             0.88148          
    NestedLoops/test_2    4             0.49775
where NestedLoops.m contains
X=rand(100,100,2000);
for ii=1:100
    for jj=1:100
        X(ii,jj,:)=10*X(ii,jj,:);
    end
end
X=rand(100,100,2000);
for jj=1:100
    for ii=1:100
        X(ii,jj,:)=10*X(ii,jj,:);
    end
end
X=rand(2000,100,100);
for jj=1:100
    for ii=1:100
        X(:,ii,jj)=10*X(:,ii,jj);
    end
end
The "differences" between the "cases" are actually larger, since
>> tic, X=rand(100,100,2000);, toc
Elapsed time is 0.355542 seconds.
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