Try dynamic programming

dohashi — Tue, 21 Sep 2010 19:50:25 Z

Sounds like a problem with lots of repeated calculations. Can you figure out a way to structure the mulitplications so you can reuse intermediate results?

See https://secure.wikimedia.org/wikipedia/en/wiki/Dynamic_programming

Darin

-- Kernel Developer Maplesoft

product of matrices

Robert Israel — Tue, 21 Sep 2010 19:57:00 Z

You didn't attach any code. But here's a simple way to do it.

> with(LinearAlgebra):
   M:= [seq(RandomMatrix(4,4), i=1..8)];
   for p in combinat[permute](8) do
      M[p[1]] . M[p[2]] . M[p[3]] . M[p[4]] . M[p[5]] . M[p[6]] . M[p[7]] . M[p[8]]
   end do:

This took over 555 seconds of CPU time on my computer.

A slightly more sophisticated way would be to build up a tree of products. This would reduce the number of matrix
multiplications needed from 7*8! = 282240 to 8!/6! + ... + 8!/1! = 69272

> for i from 1 to 8 do P[[i]]:= M[i] end do:
for r from 2 to 8 do
  for p in combinat[permute](8, r) do
     P[p]:= P[p[1..r-1]] . M[p[r]]
  end do
end do:

This took just under 40 seconds.

MaplePrimes - answers and comments on Question, Large Computation of 4x4 Matrices

Try dynamic programming

product of matrices