MATLAB: Multiply then sum elements of two matrices

additionmatricesmultiplication

What's the best way to 1) multiply all the elements between two similar sized matrices then 2) sum them into one single number/outcome?

It is not clear from your question whether corresponding elements are to be multiplied or if you are wanting to do a matrix multiplication.

If corresponding elements are to be multiplied, then you could calculate the sum-of-products using

dot(A(:),B(:))

   a=1:10000000;
  b=repmat(3,size(a));
  tic
  c1=a.^b;
  toc
  tic
  c2=a.^3;
  toc
  tic
  c3=a.*a.*a;
  toc

And then the results are,

 Elapsed time is 0.118509 seconds.
 Elapsed time is 0.129281 seconds.
 Elapsed time is 0.006726 seconds.

SUM is memory bound. The issue directly relates to throughput on the CPU(s). The following results illustrate this:

1. Two cores share one BUS

>> x = rand(1000);
>> tic; mean(mean(x)); toc
Elapsed time is 0.002357 seconds.

2. Two cores with two BUSES

>> x = rand(1000);
>> tic; mean(mean(x)); toc
Elapsed time is 0.001802 seconds.

3. Using ‘-singleCompThread’:

>> x = rand(1000);
>> tic; mean(mean(x)); toc
Elapsed time is 0.002660 seconds.