/usr/include/linbox/algorithms/gauss/gauss-solve.inl is in liblinbox-dev 1.3.2-1.1build2.
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* Copyright (C) LinBox 2008
*
* Written by Jean-Guillaume Dumas <Jean-Guillaume.Dumas@imag.fr>
* Time-stamp: <23 Mar 12 17:33:46 Jean-Guillaume.Dumas@imag.fr>
*
*
* ========LICENCE========
* This file is part of the library LinBox.
*
* LinBox is free software: you can redistribute it and/or modify
* it under the terms of the GNU Lesser General Public
* License as published by the Free Software Foundation; either
* version 2.1 of the License, or (at your option) any later version.
*
* This library is distributed in the hope that it will be useful,
* but WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* Lesser General Public License for more details.
*
* You should have received a copy of the GNU Lesser General Public
* License along with this library; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
* ========LICENCE========
*.
*/
#ifndef __LINBOX_gauss_solve_INL
#define __LINBOX_gauss_solve_INL
// #include "linbox/algorithms/gauss.h"
#include "linbox/algorithms/triangular-solve.h"
#include "linbox/blackbox/permutation.h"
namespace LinBox
{
template <class _Field>
template <class Matrix, class Perm, class Vector1, class Vector2> inline Vector1&
GaussDomain<_Field>::solve(Vector1& x, Vector1& w, unsigned long Rank, const Perm& Q, const Matrix& L, const Matrix& U, const Perm& P, const Vector2& b) const
{
Vector2 y(U.rowdim()), v(U.rowdim());
Q.applyTranspose(y, b);
lowerTriangularUnitarySolve(v, L, y);
upperTriangularSolve(w, U, v);
return P.applyTranspose(x, w);
}
template <class _Field>
template <class Matrix, class Vector1, class Vector2> inline Vector1&
GaussDomain<_Field>::solvein(Vector1& x, Matrix& A, const Vector2& b) const
{
typename Field::Element Det;
unsigned long Rank;
Matrix L(_field, A.rowdim(), A.rowdim());
Permutation<Field> Q((int)A.rowdim(),_field);
Permutation<Field> P((int)A.coldim(),_field);
this->QLUPin(Rank, Det, Q, L, A, P, A.rowdim(), A.coldim() );
// Sets solution values to 0 for coldim()-Rank columns
// Therefore, prune unnecessary elements
// in those last columns of U
for(typename Matrix::RowIterator row=A.rowBegin();
row != A.rowEnd(); ++row) {
if (row->size()) {
size_t ns=0;
for(typename Matrix::Row::iterator it = row->begin();
it != row->end(); ++it, ++ns) {
if (it->first >= Rank) {
row->resize(ns);
break;
}
}
}
}
Vector1 w(A.coldim());
for(typename Vector1::iterator it=w.begin()+Rank;it!=w.end();++it)
_field.init(*it,0);
return this->solve(x, w, Rank, Q, L, A, P, b);
}
template <class _Field>
template <class Matrix, class Vector1, class Vector2, class Random> inline Vector1&
GaussDomain<_Field>::solvein(Vector1& x, Matrix& A, const Vector2& b, Random& generator) const
{
THIS_CODE_MAY_NOT_COMPILE_AND_IS_NOT_TESTED;
typename Field::Element Det;
unsigned long Rank;
Matrix L(_field, A.rowdim(), A.rowdim());
Permutation<Field> Q((int)A.rowdim(),_field);
Permutation<Field> P((int)A.coldim(),_field);
this->QLUPin(Rank, Det, Q, L, A, P, A.rowdim(), A.coldim() );
Vector1 w(A.coldim());
for(typename Vector1::iterator it=w.begin()+Rank;it!=w.end();++it)
generator.random( *it );
return this->solve(x, w, Rank, Q, L, A, P, b);
}
} // namespace LinBox
#endif // __LINBOX_gauss_solve_INL
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