Hi Scott,
Thanks for the advice! It is a very small piece of code, so I am not extremely concerned > about performance in that area. In reference to using
----- Original Message ----- From: Jon Agiato To: Boost-Users@yahoogroups.com Sent: Thursday, November 14, 2002 3:07 PM Subject: Re: [Boost-Users] Getting a matrix to the power of n prod(A, A) in a loop, how would
one do such a thing if the power was negative, as if we are looking for a matrix to the power of -1, -2, or -3? Thanks again!
The case -1 is equivalent to solving a system of linear equations A X = Id. There are a couple of well known methods (*not* part of uBLAS) to do this.
From Scott:
Unless I've missed something, I don't think uBlas provides a way to do this (other than the _very_ inefficient prod(A, A) in a loop). If you need to do this frequently with large matrices and/or large powers (n) then you'll need to look at diagonalizing your matrix using eigenvalue/vector decomposition. This reduces your task to raising the values on the diagonal of a diagonal matrix to the power of n and doing two matrix multiplies and an inverse.
Finding the eigenvalues and corresponding eigenvectors of your matrix is a non-trivial task which imposes some restrictions on your matrix. Refer to "Numerical recipes in C" by Press et al. for some guidance as well as any good textbook on linear algebra.
Agreed. Best regards Joerg