linbox
examples/charpoly.C

Characteristic polynomial of 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/charpoly.C
 *
 * Copyright (C) 2005, 2010 D. Saunders, C. Pernet, 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 <iostream>
#include <iomanip>

#include "linbox/util/timer.h"
#include "linbox/field/modular-double.h"
#include "linbox/field/unparametric.h"
#include "linbox/blackbox/sparse.h"
#include "linbox/blackbox/blas-blackbox.h"
using namespace std;

#include "linbox/solutions/charpoly.h"
#include "linbox/ring/givaro-polynomial.h"
using namespace LinBox;

template <class Field, class Polynomial>
std::ostream& printPolynomial (std::ostream& out, const Field &F, const Polynomial &v)
{
    for (int i = v.size () - 1; i >= 0; i--) {
        F.write (out, v[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[i] != 0) {
                    if (v[i] >0) out << " + ";
                    if (v[i] != 1) F.write (out, v[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;
}

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) {

        PID_integer ZZ;
        DenseMatrix<PID_integer > A (ZZ);
        A.read (input);
        typedef GivPolynomialRing<PID_integer,::Givaro::Dense> IntPolRing;
        IntPolRing::Element c_A;

        Timer tim; tim.clear();tim.start();
        charpoly (c_A, A, Method::Blackbox());
        tim.stop();

        cout << "Characteristic Polynomial is ";
        //printPolynomial (cout, ZZ, c_A) << endl;
        cout << tim << endl;

#ifdef __LINBOX_HAVE_NTL
        cout << "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<IntPolRing::Element*> intFactors;
            vector<unsigned long> exp;
            IntPolRing IPD(ZZ);
            tim.start();
            IPD.factor (intFactors, exp, c_A);
            tim.stop();
            commentator.stop("done", NULL, "NTLfac");
            printFactorization(cout << intFactors.size() << " integer polynomial factors:" << endl, ZZ, intFactors, exp) << endl;
            vector<IntPolRing::Element*>::const_iterator itf = intFactors.begin();
            for ( ; itf != intFactors.end(); ++itf)
                delete *itf;

            cout << tim << endl;

        }
#endif
    }
    if (argc == 3) {

        typedef Modular<double> Field;
        double q = atof(argv[2]);
        Field F(q);
        DenseMatrix<Field> B (F);
        B.read (input);
        cout << "B is " << B.rowdim() << " by " << B.coldim() << endl;
        GivPolynomialRing<Field,::Givaro::Dense>::Element c_B;
        Timer tim; tim.clear();tim.start();
        charpoly (c_B, B);
        tim.stop();

        cout << "Characteristic Polynomial is ";
        //printPolynomial (cout, F, c_B) << endl;
        cout << tim << endl;
    }

    return 0;
}