examples/charpoly.C

Characteristic polynomial of matrix over Z or Zp.

Characteristic polynomial of matrix over Z or Zp.

/*
 * examples/charpoly.C
 *
 * Copyright (C) 2005, 2010 D. Saunders, C. Pernet, 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========
 */

#define __LB_CRA_TIMING__ 1
//#define __LINBOX_HEURISTIC_CRA
#include <linbox/linbox-config.h>
 
#include <iostream>
#include <iomanip>
 
#include <linbox/util/timer.h>
#include <linbox/ring/modular.h>
#include <givaro/zring.h>
#include <linbox/matrix/sparse-matrix.h>
using namespace std;
 
#include <linbox/solutions/charpoly.h>
#include <linbox/ring/polynomial-ring.h>
using namespace LinBox;
 
template <class Field, class Polynomial>
std::ostream& printPolynomial (std::ostream& out, const Field &F, const Polynomial &v)
{
    for (int i = (int)(v.size () - 1); i >= 0; i--) {
        F.write (out, v[(size_t)i]);
        if (i > 0)
            out << " X^" << i << " + ";
    }
    return out;
}
template <class Field, class Polynomial>
std::ostream& prettyprintIntegerPolynomial (std::ostream& out, const Field &F, const Polynomial &v)
{
    size_t n = v.size()-1;
    if (n == 0) {
        F.write(out, v[0]);
    }
    else {
        if(v[n] != 0) {
            if (v[n] != 1) F.write(out, v[n]) << '*';
            out << 'X';
            if (n > 1) out << '^' << n;
            for (int i = (int)n - 1; i > 0; i--) {
                if (v[(size_t)i] != 0) {
                    if (v[(size_t)i] >0) out << " + ";
                    if (v[(size_t)i] != 1) F.write (out, v[(size_t)i]) << '*';
                    out << 'X';
                    if (i > 1) out << '^' << i;
                }
            }
            if (v[0] != 0) {
                if (v[0] >0) out << " + ";
                F.write(out, v[0]);
            }
        }
    }
    return out;
}
template <class Field, class Factors, class Exponents>
std::ostream& printFactorization (std::ostream& out, const Field &F, const Factors &f, const Exponents& exp)
{
    typename Factors::const_iterator itf = f.begin();
    typename Exponents::const_iterator ite = exp.begin();
    for ( ; itf != f.end(); ++itf, ++ite) {
        prettyprintIntegerPolynomial(out << '(', F, *itf) << ')';
        if (*ite > 1) out << '^' << *ite;
        out << endl;
    }
    return out;
}
 
typedef Givaro::ZRing<Givaro::Integer> IntDom;
 
int main (int argc, char **argv)
{
    commentator().setMaxDetailLevel (2);
    commentator().setMaxDepth (2);
    commentator().setReportStream (std::cerr);
 
    cout<<setprecision(8);
    cerr<<setprecision(8);
    if (argc < 2 || argc > 3) {
        cerr << "Usage: charpoly <matrix-file-in-SMS-format> [<p>]" << endl;
        return -1;
    }
 
    ifstream input (argv[1]);
    if (!input) { cerr << "Error opening matrix file " << argv[1] << endl; return -1; }
 
    if (argc == 2) {
 
        IntDom ZZ;
        DenseMatrix<IntDom > A (ZZ);
        A.read (input);
        DensePolynomial<IntDom> c_A(ZZ);
 
        Timer tim; tim.clear();tim.start();
        charpoly (c_A, A);
        tim.stop();
 
        clog << "Characteristic Polynomial is ";
        printPolynomial (clog, ZZ, c_A) << endl;
        cout << tim << endl;
 
#ifdef __LINBOX_HAVE_NTL
        clog << "Do you want a factorization (y/n) ? ";
        char tmp;
        cin >> tmp;
        if (tmp == 'y' || tmp == 'Y') {
            commentator().start("Integer Polynomial factorization by NTL", "NTLfac");
            vector<DensePolynomial<IntDom> > intFactors;
            vector<uint64_t> exp;
            PolynomialRing<IntDom> IPD(ZZ);
            tim.start();
            IPD.factor (intFactors, exp, c_A);
            tim.stop();
            commentator().stop("done", NULL, "NTLfac");
            printFactorization(clog << intFactors.size() << " integer polynomial factors:" << endl, ZZ, intFactors, exp) << endl;
 
            cout << tim << endl;
 
        }
#endif
    }
    if (argc == 3) {
 
        typedef Givaro::Modular<double> Field;
        double q = atof(argv[2]);
        Field F(q);
        DenseMatrix<Field> B (F);
        B.read (input);
        clog << "B is " << B.rowdim() << " by " << B.coldim() << endl;
        DensePolynomial<Field> c_B(F);
        Timer tim; tim.clear();tim.start();
        charpoly (c_B, B);
        tim.stop();
 
        clog << "Characteristic Polynomial is ";
        printPolynomial (clog, F, c_B) << endl;
        cout << tim << endl;
    }
 
    return 0;
}
 
// Local Variables:
// mode: C++
// tab-width: 4
// indent-tabs-mode: nil
// c-basic-offset: 4
// End:
// vim:sts=4:sw=4:ts=4:et:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s