How to optimize matrix multiplication operation [duplicate]

Answer 1

Boost uBLAS I think is definitely the way to go with this sort of thing. Boost is well designed, well tested and used in a lot of applications.

Answer 2

There are plenty of algorithms for efficient matrix multiplication.

Algorithms for efficient matrix multiplication

Look at the algorithms, find an implementations.

You can also make a multi-threaded implementation for it.

Answer 3

Eigen is by far one of the fastest, if not the fastest, linear algebra libraries out there. It is well written and it is of high quality. Also, it uses expression template which makes writing code that is more readable. Version 3 just released uses OpenMP for data parallelism.

#include <iostream>
#include <Eigen/Dense>

using Eigen::MatrixXd;

int main()
{
  MatrixXd m(2,2);
  m(0,0) = 3;
  m(1,0) = 2.5;
  m(0,1) = -1;
  m(1,1) = m(1,0) + m(0,1);
  std::cout << m << std::endl;
}

Answer 4

Consider GNU Scientific Library, or MV++

If you're okay with C, BLAS is a low-level library that incorporates both C and C-wrapped FORTRAN instructions and is used a huge number of higher-level math libraries.

I don't know anything about this, but another option might be Meschach which seems to have decent performance.

Edit: With respect to your comment about not wanting to use libraries that use your graphics card, I'll point out that in many cases, the libraries that use your graphics card are specialized implementations of standard (non-GPU) libraries. For example, various implementations of BLAS are listed on it's Wikipedia page, only some are designed to leverage your GPU.

Answer 5

There is a book called Introduction to Algorithms. You may like to check the chapter of Dynamic Programming. It has an excellent matrix multiplication algo using dynamic programming. Its worth a read. Well, this info was in case you want to write your own logic instead of using a library.