CODEWITHSUNDEEP
performancematlabfor-loopvectorization
user2578152
user2578152

Reputation:

trying to improve the efficency of a triple for loop in matlab

I'm trying to vectorize or make this loop run faster (it's a minimal code):

n=1000;
L=100;
x=linspace(-L/2,L/2);
V1=rand(n);
for i=1:length(x)
    for k=1:n
        for j=1:n
            V2(j,k)=V1(j,k)*log(2/L)*tan(pi/L*(x(i)+L/2)*j);
        end
    end
    V3(i,:)=sum(V2);
end

would appreciate you help.

Upvotes: 1

Views: 219

Answers (2)

bla
bla

Reputation: 26069

here's a vectorized solution using meshgrid, bsxfun and repmat:

% fast preallocation
jj(n,n)=0; B(n,n,L)=0; V3(L,n)=0;
lg=log(2/L);

% the vectorizaion part
jj=meshgrid(1:n);
B=bsxfun(@times,ones(n),permute(x,[3 1 2]));
V3=squeeze(sum(lg*repmat(V1,1,1,numel(x)).*tan(bsxfun(@times,jj',pi/L*(B+L/2))),1)).';

Running your code at my computer using tic\toc took ~25 seconds. The bsxfun code took ~4.5 seconds...

Upvotes: 0

Geoff
Geoff

Reputation: 1603

An alternative to vectorization, is to recognize the expensive operations in the code and somehow reduce them. For instance, the log(2/L) is called 100*1000*1000 times with input that does not depend on any of the three for loops. If we calculate this value outside of the for loops, then we can use it instead:

logResult = log(2/L);

and

V2(j,k)=V1(j,k)*log(2/L)*tan(pi/L*(x(i)+L/2)*j);

becomes 

V2(j,k)=(V1(j,k)*logResult*tan(pi/L*(x(i)+L/2)*j));

Likewise, the code calls the tan function the same 100*1000*1000 times. Note how this calculation, tan(pi/L*(x(i)+L/2)*j) does not depend on k. And so if we calculate these values outside of the for loops, we can reduce this calculation by 1000 times:

tanValues = zeros(lenx,n);
for i=1:lenx
    for j=1:n
        tanValues(i,j) = tan(pi/L*(x(i)+L/2)*j);
    end
end

and the calculation for V2(j,k) becomes

V2(j,k)=V1(j,k)*logResult*tanValues(i,j);

Also, memory can be pre-allocated to the V2 and V3 matrices to avoid the internal resizing that occurs on each iteration. Just do the following outside the for loops

V2 = zeros(n,n);
V3 = zeros(lenx,n);

Using tic and toc reduces the original execution from ~14 seconds to ~6 on my workstation. This is still three times slower than natan's solution which is ~2 seconds for me.

Upvotes: 2

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