
Ublas : 
From: Marchesi Mauro (Marchesi_at_[hidden])
Date: 20070601 09:10:12
Hello.
I tried to solve a linear system Ax=b by using the following code:
ublas::matrix<double> A = ...;
ublas::vector<double> b = ...;
ublas::permutation_matrix<size_t> pm ( A.size1() );
ublas::matrix<double> M = A;
ublas::vector<double> x = b;
ublas::lu_factorize( M, pm );
ublas::lu_substitute( M, pm, x );
This works fine, unless A is singular.
However it turns out that, because of the way the matrix is built, the
rank of the coefficient matrix A equals the rank of the augmented matrix
Ab.
So, even in this case, the linear system admits solutions, but I can't
figure out how to get them by using the uBLAS library.
I'd like to get the set of solutions in any form: for example as a
vector x0 along with a set of vectors {x1,...,xN} such that every
solution of the system can be expressed in the form x0 + k1*x1 + ... +
kN*xN (clearly the set {x1,...,xN} is empty iff A is nonsingular).
Can anyone help me?
Thanks in advance,
Mauro Marchesi