Re: [Boost-Users] Getting a matrix to the power of n

From: jhr.walter_at_[hidden]
Date: 2002-11-17 03:20:54

----- Original Message -----
From: Jon Agiato
To: Boost-Users_at_[hidden]
Sent: Thursday, November 14, 2002 3:07 PM
Subject: Re: [Boost-Users] Getting a matrix to the power of n

> 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
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