How to vectorize a product of a tensor and a vector.

3 次查看（过去 30 天）
Moslem Zamani
Moslem Zamani 2019-2-3
评论： David Goodmanson 2019-2-8
How could I vectorize the following loop?
A=randn(10,10,40);
b=randn(10,1);
a=zeros(40,1);
for i=1:40
a(i)=b'*A(:,:,i)*b;
end
  3 个评论
显示 1更早的评论
madhan ravi
madhan ravi 2019-2-4
Another possiblity:
A=randn(10,10,40);
[m,n,p]=size(A);
b=randn(10,1);
AA=reshape(A,m,[],1)';
B=mat2cell(AA,repmat(n,1,size(AA,1)/n));
R=cellfun(@(x)b'*x*b,B);
Test result:
Elapsed time is 0.001497 seconds. % using a simple loop
Elapsed time is 0.062664 seconds. % using cellfun
From the test it's quite clear that the loop you have is at it's best shape and is by nature the fastest in this case , so why bother?

请先登录，再进行评论。

请先登录，再回答此问题。

采纳的回答

David Goodmanson
David Goodmanson 2019-2-4
编辑：David Goodmanson 2019-2-4
Hi Moslem
Here is one way, and it does test out faster than the for loop. How much faster depends on the sizes of what I called m and n, which in your example are 10 and 40. But 2 - 80 times faster, using the method of total tic and toc elapsed time on a lot of repetitions of the same code, and around 15 times faster in the 10 and 40 case. (I know some people on this site are down on tic and toc, but total time for a lot of repetitions seems to me to be a valid real world test). There is more of an advantage the larger n is, which is the length of the for loop.
The code uses reshape, which can be pretty time consuming. [ I thought. See Guillaume's comment ]. There are any number of situations where reshapes and transposes take significantly more time than just using a for loop, but this seems to be a case where matrix manipulation wins out. (There is a transpose at the end, but it's only on a vector).
I tried in on complex to make sure it checked out vs the original.
m = 10;
n = 40;
% A=rand(m,m,n);
% b=rand(m,1);
A = 2*(rand(m,m,n) + i*rand(m,m,n)) - (1+i);
b = 2*(rand(m,1) + i*rand(m,1)) - (1+i);
B = reshape(A,m,m*n);
bB = reshape(b'*B,m,n);
anew = b.'*bB;
anew = anew(:);
  3 个评论
显示 1更早的评论
David Goodmanson
David Goodmanson 2019-2-8
Hi Moslem,
You're welcome. And thanks to Guillaume for pointing out the reason behind why reshape is quick.

请先登录，再进行评论。

更多回答（0 个）

类别

在 Help Center 和 File Exchange 中查找有关 Linear Algebra 的更多信息

标签

Community Treasure Hunt

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!

Translated by