How can I faster matrix multiplication

Hello, first time here to ask

I have a 3 by 3 matrix, say G. And I also have a row vector, R.

What I need is finding R * G * R.'

but it is running very slow.

It used around 84.5s to have it call 26800 times.

Is that normal? Or how can I speed up since I have to do it inside a nested for loop?

I am currently using matlab R2019b version.

Thank you!

[James Tursa]

What are the actual sizes of the variables involved? Are you looping over a 3rd dimension to do the multiplies? Are any of the variables constant throughout the looping? Are all the variables real? What is done with the results downstream in your code? Etc. We need more details in order to help you.

[Paul]

Thank you for your reply.

First, for R, it is actually like [a b c], which a b c are looping integers, say 0 to 5.

And one thing may worth to mention is that G is constant while it is doing iteration on R.

Show you one of my G=[

-0.00101584090085100 -0.0373729264800720 0.00786581385357300

-0.0373729264800720 -0.284509289498308 0.0752540345065320

0.00786581385357300 0.0752540345065320 -0.0158385837800100]

All variables are real. Is that help?

[James Tursa]

So R is 1x3 and changing each iteration?

[Paul]

yes

G = [...; ...; ...]

for a=0 to 5

for b = 0 to 5

for c = 0 to 5

R= [a b c];

R*G*R.'

end

end

end

Answer 1

[KALYAN ACHARJYA]

Is it simmilar?

G=[-0.00101584090085100	-0.0373729264800720	0.00786581385357300
 -0.0373729264800720	-0.284509289498308	0.0752540345065320
 0.00786581385357300	0.0752540345065320	-0.0158385837800100];
tic
result=cell(1,26800);
for i=1:26800
    R=randi(10,[1,3]); % or Call the R here
    result{i}=R*G*R';
end 
toc

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Elapsed time is 0.194492 seconds. (Measuring Elapsed Time Using tic and toc)