Efficient Row x Collumn multiplication
1 view (last 30 days)
Show older comments
Hi all,
Consider the vectors: A of size; s x 4 B of size; 4 x s
Now, I am only interested in the product A(i,:)*B(:,i) of size s x 1
for i=1,..,s. I.e. only the row times the collumn with the same index.
The solution I found myself is: diag(A*B);
But I think there must be a faster solution, since I calculate many useless matrix elements if s>>4.
Do you guys have a suggestion?
0 Comments
Accepted Answer
More Answers (3)
Titus Edelhofer
on 20 Mar 2012
Hi,
don't know if it is really more efficient, give it a try:
x = dot(A',B)'
Titus
Daniel Shub
on 20 Mar 2012
Maybe I am missing something here, but it seems like you already have a solution ...
x = zeros(s, 1)
for i = 1:s
x(i) = A(i, :)*B(i, :);
end
Daniel Shub
on 20 Mar 2012
I am posting this as a separate answer. First when using timing, MATLAB has a hard time timing things that take only 0.000065 seconds, so you should put things in a loop. Second, The size of the matrices need to be established before discounting an answer as too slow.
t=linspace(0,1,1e4);
tf=[t'.^3 t'.^2 t' ones(size(t'))];
M=[-1 3 -3 1; 3 -6 3 0 ; -3 0 3 0; 1 4 1 0]; %Standard form for matrix uniform cubic spline evaluation
P=randn(4,length(t));
tic;
for ii = 1:10
x = diag(tf*M*P);
end;
toc
tic;
for ii = 1:10
x = sum((tf*M)'.*P)';
end;
toc
tic;
for ii = 1:10
x = dot((tf*M)', P)';
end;
toc
tic;
s = length(t);
x = zeros(s, 1);
A = (tf*M);
B = P;
for ii = 1:10
for i = 1:s
x(i) = A(i, :)*B(:, i);
end
end
toc
On my machine I get:
- Elapsed time is 7.584815 seconds.
- Elapsed time is 0.004872 seconds.
- Elapsed time is 0.004445 seconds.
- Elapsed time is 0.149892 seconds.
with the "too slow" loop being an order of magnitude faster than diag. With a large s, there is essentially no difference between the dot and sum method. For your example matrix sizes, the error checking in dot takes a significant portion of the time.
To really optimize your code you want to think about the order in which operations are occurring and memory access.
2 Comments
Daniel Shub
on 20 Mar 2012
Because I chose s to be very large (1e4) and I looped 10 times. If s ~4, then the diag method doesn't have that many useless calculations. It is only as s >> 4, that the number of useless calculations dominates.
See Also
Categories
Find more on Logical in Help Center and File Exchange
Products
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!