linbox
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Gaussian elimination Rank of sparse matrix over Z or Zp.
/* -*- mode: C++; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */ // vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s /* * examples/sparseelimrank.C * * Copyright (C) 2006, 2010 J-G Dumas * * This file is part of 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 of * the License, or (at your option) any later version. * * LinBox 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 LinBox. If not, see * <http://www.gnu.org/licenses/>. */ //#include "linbox-config.h" #include <iostream> #include <vector> #include <utility> #include "linbox/field/modular-double.h" #include "linbox/field/gf2.h" #include "linbox/blackbox/sparse.h" #include "linbox/blackbox/zero-one.h" #include "linbox/solutions/rank.h" #include "linbox/util/matrix-stream.h" #include "linbox/field/givaro-rational.h" using namespace LinBox; using namespace std; int main (int argc, char **argv) { commentator.setMaxDetailLevel (-1); commentator.setMaxDepth (-1); commentator.setReportStream (std::cerr); if (argc < 2 || argc > 3) { cerr << "Usage: rank <matrix-file-in-supported-format> [<p>]" << endl; return -1; } ifstream input (argv[1]); if (!input) { cerr << "Error opening matrix file: " << argv[1] << endl; return -1; } long unsigned int r; if (argc == 2) { // rank over the integers. /* We could pick a random prime and work mod that prime, But the point here is that the rank function in solutions/ handles that issue. Our matrix here is an integer matrix and our concept is that we are getting the rank of that matrix by some blackbox magic inside linbox. */ LinBox::GivaroRational ZZ; MatrixStream<GivaroRational> ms( ZZ, input ); SparseMatrix<GivaroRational> A ( ms ); cout << "A is " << A.rowdim() << " by " << A.coldim() << endl; rank (r, A, Method::SparseElimination() ); cout << "Rank is " << r << endl; } if (argc == 3) { double q = atof(argv[2]); typedef Modular<double> Field; Field F(q); MatrixStream<Field> ms( F, input ); SparseMatrix<Field, Vector<Field>::SparseSeq > B (ms); cout << "B is " << B.rowdim() << " by " << B.coldim() << endl; if (B.rowdim() <= 20 && B.coldim() <= 20) B.write(cout) << endl; Method::SparseElimination SE; SE.strategy(Specifier::PIVOT_NONE); // using Sparse Elimination rank (r, B, SE); if (B.rowdim() <= 20 && B.coldim() <= 20) B.write(cout) << endl; cout << "Rank is " << r << endl; SE.strategy(Specifier::PIVOT_LINEAR); // using Sparse Elimination rank (r, B, SE); if (B.rowdim() <= 20 && B.coldim() <= 20) B.write(cout) << endl; cout << "Rank is " << r << endl; } return 0; }