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// The following code inverts the matrix input using LU-decomposition with
// backsubstitution of unit vectors. Reference: Numerical Recipies in C, 2nd
// ed., by Press, Teukolsky, Vetterling & Flannery.
// Code written by Fredrik Orderud.
// http://www.crystalclearsoftware.com/cgi-bin/boost_wiki/wiki.pl?LU_Matrix_Inversion
#ifndef INVERT_MATRIX_HPP
#define INVERT_MATRIX_HPP
// REMEMBER to update "lu.hpp" header includes from boost-CVS
#include <boost/numeric/ublas/vector.hpp>
#include <boost/numeric/ublas/vector_proxy.hpp>
#include <boost/numeric/ublas/matrix.hpp>
#include <boost/numeric/ublas/triangular.hpp>
#include <boost/numeric/ublas/lu.hpp>
#include <boost/numeric/ublas/io.hpp>
namespace ublas = boost::numeric::ublas;
/* Matrix inversion routine.
Uses lu_factorize and lu_substitute in uBLAS to invert a matrix */
template<class T>
bool invert_matrix(const ublas::matrix<T>& input, ublas::matrix<T>& inverse)
{
using namespace boost::numeric::ublas;
typedef permutation_matrix<std::size_t> pmatrix;
// create a working copy of the input
matrix<T> A(input);
// create a permutation matrix for the LU-factorization
pmatrix pm(A.size1());
// perform LU-factorization
int res = lu_factorize(A,pm);
if( res != 0 ) return false;
// create identity matrix of "inverse"
inverse.assign(ublas::identity_matrix<T>(A.size1()));
// backsubstitute to get the inverse
lu_substitute(A, pm, inverse);
return true;
}
#endif //INVERT_MATRIX_HPP
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