linbox
examples/nullspacebasis_rank.C

NullSpace of sparse matrix over GFq.nullspace is allocated rank n.

/*
* examples/nullspacebasis_rank.C
*
* Copyright (C) 2014 J-G. Dumas
* ========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========
*/
#include <givaro/gfq.h>
#include <iostream>
using namespace LinBox;
int main (int argc, char **argv)
{
if ( argc < 2 || argc > 4) {
std::cerr << "Usage to get a random null space basis over GF(p,k): <matrix-file-in-SMS-format> p [k]" << std::endl;
return -1;
}
std::ifstream input (argv[1]);
if (!input) {
std::cerr << "Error opening matrix file " << argv[1] << std::endl;
return -1;
}
int pVal = atoi(argv[2]);
//typedef Givaro::Modular<int> Field;
typedef Givaro::GFqDom<int64_t> Field;
Field F(pVal, argc>3?atoi(argv[3]):1);
SparseMatrix<Field, SparseMatrixFormat::SparseSeq > A (F);
A.read (input);
std::cout << "A is " << A.rowdim() << " by " << A.coldim() << std::endl;
typename Field::Element Det;
unsigned long Rank;
size_t Ni(A.rowdim()),Nj(A.coldim());
Permutation<Field> P((int)Nj,F);
GD.InPlaceLinearPivoting(Rank, Det, A, P, Ni, Nj );
for(size_t i=0; i< Ni; ++i) {
if (A[i].size() == 0) {
size_t j(i);
if (nextnonzero(j,Ni,A)) {
A[i] = A[j];
A[j].resize(0);
}
else {
break;
}
}
}
size_t nullity = A.coldim()-Rank;
DenseMatrix<Field> NullSpace(F,A.coldim(),nullity);
GD.nullspacebasis(NullSpace, Rank, A, P);
NullSpace.write( std::cerr << "X:=", Tag::FileFormat::Maple ) << ';' << std::endl;
std::cerr << "NullsSpace dimensions:" << NullSpace.rowdim() << 'x' << NullSpace.coldim() << std::endl;
return 0;
}