vectorization of comparison against several intervals

Hello,

I currently have the code below, which essentially checks if each element of the MainArray is within any of the intervals described in each row of CompArray; if yes, the corresponding position in ResultsArray is set to 0. In practice, I need to run this on mich bigger matrices and iteratively, so speed of execution becomes a problem. Is there a possibility to vectorize it? Note that CompArray can have a variable number of rows (comparison intervals), but always only two columns.

clc
clearvars

ResultsArray    = ones(10,10);
MainArray       = magic(10);
CompArray       = [ 20 30;...
                    40 50;...
                    60 70];
for Row = 1:10        
    for Col = 1:10
        if(any((MainArray(Row,Col) >= CompArray(:,1)) & (MainArray(Row,Col) <= CompArray(:,2))))
            ResultsArray(Row,Col) = 0;
        end  
    end
end

Best regards,

Cristian

[Jan]

What are typical sizes? It matters, if you want 100 intervals or millions.

[Cristian Berceanu]

Typical sizes for MainArray and ResultsArray would be 1000 x 1000 to 10.000 x 10.000.

CompArray could have anything between 20 and 200 rows.

Answer 1

[Jan]

Easier to run in the forum and maybe faster already:

N = 1000;
M = randi([1, 1000], N, N);
C = sort(randi([1, 1000], 100, 2), 2);

C1 = C(:, 1);
C2 = C(:, 2);

tic
R1 = ones(size(M));
for Row = 1:size(M, 1)        
    for Col = 1:size(M, 2)
        if(any((M(Row,Col) >= C(:,1)) & (M(Row,Col) <= C(:,2))))
            R1(Row,Col) = 0;
        end  
    end
end
toc

tic
R2 = ones(size(M));
for k = 1:numel(M)
   if any((M(k) >= C1) & (M(k) <= C2))
      R2(k) = 0;
   end  
end
toc

% Alternatively:
tic
R3 = ones(size(M));
for k = 1:numel(M)
    R3(k) = all((M(k) < C1) | (M(k) > C2));
end
toc

tic
R4 = true(size(M));
for k = 1:size(C1, 1)
   R4(R4 & (M >= C1(k)) & (M <= C2(k))) = false;
end
toc

tic
R5 = true(size(M));
for k = 1:size(C1, 1)
   R5 = R5 & (M < C1(k) | M > C2(k));
end
toc

isequal(R1, R2, R3, R4, R5)

% R2018b, Win10, i5 mobil:
% Elapsed time is 0.429244 seconds.    original
% Elapsed time is 0.335571 seconds.    simplilied
% Elapsed time is 0.351330 seconds.    no IF
% Elapsed time is 0.247861 seconds.    loop over intervals
% Elapsed time is 0.148806 seconds.    loop over intervals 2

[Cristian Berceanu]

Super, thanks!

I am not sure if this really counts as "vectorization" (since you still have to keep the "for" loop), but it most certainly gives much faster results!

Regards,

Cristian

[Jan]

The vectorized version are much slower, therefore I did not copy them. Vectorisation is not efficient, if large intermediate arrays are required, which do not match into the CPU cache.