advice on matrix libraries

[DMonniaux]

Hi all,

I doing computations on generators of linear affine subspaces of Q^n.
More specifically:
* I maintain a subspace description as F0 + X*Fi where X ranges over
Q^m and Fi is a m×n matrix.
* I sometimes add more constraints C: I compute F'0 and F'i such that
{ F'0 + X*F'i | X in Q^m } = { F0 + X*Fi | X in Q^m } \cap \ker C
* I convert F0 and Fi to floating-point.
* I do some matrix-matrix and vector-matrix multiplications, and also
build some matrices out of pieces of other matrices.
* I echelonize matrices (I don't care so much about echelon form; I
just want a full-rank matrix whose rows span the same space as my
original matrix).
* I test for positive semidefiniteness.

Currently I'm working with Boost uBlas and rational numbers (a wrapper
over GMP that avoids going to GMP for computations over small integers
and rationals with small numerator and denominator).

My code is spending most of its time in uBlas, and maybe this is not
so efficient.

My test cases are about dimension n=400, very sparse. I'm also
interested in larger cases.