MATLAB: For loop to matrix calculation

for loopmatrixoptimization

Hello there,
I do not know how to optimize this calculation. It is very slow, since vector "my_vector" is made of 3 millions indeces.
I would like to perform the same calculation using matrices, but I really do not know how to do it!
Thank you!
Have a good one,
Andrea.
corr = zeros(1,n_A*p_A-1); % row vector of 3762799
v = residual(my_vector);
variance = mean(v.^2); 
index_corr = 0;
ref_length = 0;
for l = 1:(n_A*p_A-1)
    for j = 1:(n_A*p_A-l)
        corr(1,l) = corr(1,l)+v(1,j)*v(1,j+l);
    end
    corr(1,l) = corr(1,l)/((n_A*p_A-l)*variance);
    if (corr(1,l) < (1/exp(1)))
        if index_corr == 0
            ref_length = l;
        end
        index_corr = 1;
    end   
end

Best Answer

1/exp(1) is a very expensive calculation. Do this once before the loop.
The index "l" (lowercase L) looks like a "1", so I replaced it by "k".
corr = zeros(1, n_A*p_A-1); % row vector of 3762799
v = residual(my_vector);
variance = mean(v .^ 2); 
index_corr = 0;
ref_length = 0;
c = 1 / exp(1);
for k = 1:(n_A*p_A-1)
    n = n_A * p_A - k;
    % Use DOT product to calculate the sum:
    corr(1, k) = corr(1, k) + v(1, 1:n) * v(1, (1 + k):(n + k)).';
    % Alternative - assumed to be slower:
    % corr(1, k) = corr(1, k) + sum(v(1, 1:n) .* v(1, (1 + k):(n + k)));
    
    corr(1, k) = corr(1,k) / ((n_A*p_A-k) * variance);
    if corr(1,k) < c
        if index_corr == 0
            ref_length = k;
        end
        index_corr = 1;
    end
end
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