Re: [boost] C++ library with matrix inversion?

From: Howard Hinnant (hinnant_at_[hidden])
Date: 2004-10-27 15:47:22

On Oct 27, 2004, at 2:39 PM, Bronek Kozicki wrote:

> I know that question is little off-topic here, but I hope there is 
> someone who can answer it. Could you recommend some C++ library for 
> matrix calculation that supports matrix inversion? Blizt++ does not 
> have it, neither boost.ublas. Or I missed it. Ideas?

It's been a few years since I was doing linear algebra (omg, nearly a 
decade!), and I'm not familiar with the interface of Blitz++ or 
boost.ublas, but if the library supports direct factorization of a 
matrix, I believe you can compute the inverse very efficiently with 
something like:

factor(matrix);
vector f = {0};
for (unsigned i = 0; i < ncols; ++i)
     f[i] = 1;
     solve(matrix, inverse.col(i), f);
     f[i] = 0;

I.e. you can generate a column of the inverse at a time by solving 
against a vector with all zero's except for a 1 in the column/row of 
interest.  Indeed, it is because of this relationship that it may not 
be necessary at all to ever store the entire inverse.  The factored 
original is just as good.

-Howard