for loop to matrix calculation

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

[Jan]

It would be useful if you explain, what the code should do. Some meaningful comments in the code are required also to improve its quality. Please provide some meaningful inputs also, because this is more efficient than letting the readers guess the inputs.

Answer 1

[Jan]

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

[john_arle]

Okay, thak you for the advice!

There you go with teh comments!

corr = zeros(1, 3762799); % row vector of 3762799
v = residual(my_vector); % calculating the residual of a 'double' vector
variance = mean(v .^ 2); % calculating the variance of 'my_vector'
index_corr = 0;
ref_length = 0;
c = 1 / exp(1);
for k = 1:(n_A*p_A-1)  % calculates the correlation function of the set C(k)
    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

[john_arle]

Hello Jan,

thank you again for your kind response!

I get an error though (implementing dot product), and I do not know how to fix it!

Index in position 2 exceeds array bounds (must not exceed 1).

Error in example2 (line 67)
    corr(1, k) = corr(1, k) + v(1, 1:n) * v(1, (1 + k):(n + k)).';

[Jan]

@Andrea: Unfortunately I cannot run your code, because you did not provide the input arguments. Then you have to debug the code by your own. Perhaps one of the inputs is a column vector? Try this:

...
v = V(:).';
for k = 1:(n_A*p_A-1)
    n = n_A * p_A - k;
    corr(k) = corr(k) + v(1:n) * v((1 + k):(n + k)).';
    corr(k) = corr(k) / ((n_A*p_A-k) * variance);
    if corr(k) < c
        if index_corr == 0
            ref_length = k;
        end
        index_corr = 1;
    end
end