MATLAB: How to improve the code speed (for loop)

for loopperformance

T = clasval.T;
Gamma_x = clasval.Gamma_x;
Gamma_xy = clasval.Gamma_xy;
Gamma_y = clasval.Gamma_y;
ut = clasval.ut;
[nsamples,dim]=size(trainingsset);
scorematrix=zeros(nsamples,nsamples);
for i=1:nsamples
    for j=1:nsamples
        probe=trainingsset(i,:);
        gallery=trainingsset(j,:);
        llr_score;
        scorematrix(j,i)=score;
        if i == j
            break;
        end
    end
end
I would like to improve the speed f the following code. I already tried preallocating scoreamatrix, but it is still very slow. The code llr_score.m contains the following:
x=T*(probe-ut)';
y=T*(gallery-ut)';
score=x'*Gamma_x*x + x'*Gamma_xy*y+y'*Gamma_y*y;

Best Answer

By profiling, the most computational intensive operations are
x=T*(probe-ut)';
y=T*(gallery-ut)';
That calculation is inside the nested loop and repeated for the same values multiple times. I moved that calculation out of the loop
clear all, close all
%% original code
% dimensions
N1 = 5;
N2 = 1672; % dim
N3 = 500;  % nsamples
% dummy values
T = rand(N1,N2);
Gamma_x = rand(N1,N1);
Gamma_xy = rand(N1,N1);
Gamma_y = rand(N1,N1);
ut = rand(1,N2);
trainingsset = rand(N3,N2);
[nsamples,dim]=size(trainingsset);
scorematrix=zeros(nsamples,nsamples);
tic
for i=1:nsamples
    for j=1:nsamples
        probe=trainingsset(i,:);
        gallery=trainingsset(j,:);
        
        % llr_score
        x=T*(probe-ut)';
        y=T*(gallery-ut)';
        score=x'*Gamma_x*x + x'*Gamma_xy*y+y'*Gamma_y*y;
        
        scorematrix(j,i)=score;
        if i == j
            break;
        end
    end
end
toc
%% new code
scorematrix2=zeros(nsamples,nsamples);
tic
xy = T*bsxfun(@minus,trainingsset,ut).';
for i=1:nsamples
    for j=1:nsamples
        
        x = xy(:,i);
        y = xy(:,j);
        score=x'*Gamma_x*x + x'*Gamma_xy*y+y'*Gamma_y*y;
        
        scorematrix2(j,i)=score;
        if i == j
            break;
        end
    end
end
toc
% check
norm(scorematrix-scorematrix2,'fro')/norm(scorematrix,'fro')
On my computer the new version is 30x faster with relative error of oder 10^-16 on the output
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