Speeding up a for loop

Hi,

I'm trying to speed up processing time of my code.

Can the next code be reduced to be processed using vectorization instead of using a for-loop? I usually manage fine with these things, but here there are some tricky matrix operations.

Give these inputs:

S1 = 5994;
S2 = 88;
S3 = 8;
A = 100*rand(S1,S3)-50;
B = 100*rand(S2,S3)-50;
C = 100*rand(S1,S2)-50;
Const1 = 1.1;

The loop:

for vv=1:size(A,1)
    temp1 = A(vv,:)-Const1*B;
    temp2 = C(vv,:).*(abs(temp1).^2).';
    Sum = Sum + sum(temp2,'all');
end
Sum = Sum/(S1*S3);

[Adam Danz]

I assume Sum is initialized as the following (or something similar), prior to the loop.

Sum = 0;

Answer 1

[Thiago Henrique Gomes Lobato]

If you don't mind having 3 dimensional arrays something like this can be used

rng(42)
S1 = 5994;
S2 = 88;
S3 = 8;
A = 100*rand(S1,S3)-50;
B = 100*rand(S2,S3)-50;
C = 100*rand(S1,S2)-50;
Const1 = 1.1;
Sum = 0;
tic
for vv=1:size(A,1)
    temp1 = A(vv,:)-Const1*B;
    temp2 = C(vv,:).*(abs(temp1).^2).';
    Sum = Sum + sum(temp2,'all');
end
timeLoop = toc

% Vector alternative
tic
temp1Vec = reshape(A',1,size(A,2),size(A,1) )-Const1*B;
temp2Vec = sum(reshape(C',size(C,2),1,size(C,1)).* ((abs(temp1Vec).^2)) ,'all');
timeVec = toc


SumVec   = sum(temp2Vec)/(S1*S3)
Sum = Sum/(S1*S3)

timeLoop =

    0.0424


timeVec =

    0.0228


SumVec =

   6.6553e+03


Sum =

   6.6553e+03

For your S1 I get sometimes faster results and some times slower ones, if I increase the S1 size I start to become consistent faster results.

[Alex Kozlov]

Thanks, that did the trick. I improved the speed further by replacing

((abs(temp1Vec).^2)),'all'); 

by:

((real(temp1Vec).^2+imag(temp1Vec).^2)),'all');

In the original code, which i couldn't share, temp1 could contain complex numbers.

Answer 2

[Adam Danz]

Idea 1

This single line does the same thing as the 2nd block of your code.

Sum2 =  sum(arrayfun(@(i)sum(C(i,:) .* (abs(A(i,:)-Const1*B).^2).','all'), 1:size(A,1)))/(S1*S3);

isequal(Sum,Sum2)  % Test that it matches the loop output (it does)

However, it's 0.01sec longer than your loop method.

Idea 2

Even if your loop is condensed by combining the variables, the improvement in speed is barely measurable and it comes at the expense of readability.

Sum2 = 0;
for vv=1:size(A,1)
    Sum2 = Sum2 + sum(C(vv,:) .* (abs(A(vv,:)-Const1*B).^2).', 'all');
end
Sum2 = Sum2/(S1*S3);

isequal(Sum,Sum2)  % Test that it matches the loop output (it does)