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<div class="title">examples/charpoly.C</div> </div>
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<p>Characteristic polynomial of matrix over Z or Zp.</p>
<div class="fragment"><pre class="fragment"><span class="comment">/* -*- mode: C++; tab-width: 8; indent-tabs-mode: t; c-basic-offset: 8 -*- */</span>
<span class="comment">// vim:sts=8:sw=8:ts=8:noet:sr:cino=>s,f0,{0,g0,(0,\:0,t0,+0,=s</span>
<span class="comment">/*</span>
<span class="comment"> * examples/charpoly.C</span>
<span class="comment"> *</span>
<span class="comment"> * Copyright (C) 2005, 2010 D. Saunders, C. Pernet, J-G. Dumas</span>
<span class="comment"> *</span>
<span class="comment"> * This file is part of LinBox.</span>
<span class="comment"> *</span>
<span class="comment"> * LinBox is free software: you can redistribute it and/or modify</span>
<span class="comment"> * it under the terms of the GNU Lesser General Public License as</span>
<span class="comment"> * published by the Free Software Foundation, either version 2 of</span>
<span class="comment"> * the License, or (at your option) any later version.</span>
<span class="comment"> *</span>
<span class="comment"> * LinBox is distributed in the hope that it will be useful,</span>
<span class="comment"> * but WITHOUT ANY WARRANTY; without even the implied warranty of</span>
<span class="comment"> * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the</span>
<span class="comment"> * GNU Lesser General Public License for more details.</span>
<span class="comment"> *</span>
<span class="comment"> * You should have received a copy of the GNU Lesser General Public</span>
<span class="comment"> * License along with LinBox. If not, see</span>
<span class="comment"> * <http://www.gnu.org/licenses/>.</span>
<span class="comment"> */</span>
<span class="preprocessor">#include <iostream></span>
<span class="preprocessor">#include <iomanip></span>
<span class="preprocessor">#include "<a class="code" href="timer_8h.html" title="LinBox timer is Givaro's.">linbox/util/timer.h</a>"</span>
<span class="preprocessor">#include "<a class="code" href="modular-double_8h.html" title="Standard representation of Z/mZ over double .">linbox/field/modular-double.h</a>"</span>
<span class="preprocessor">#include "linbox/field/unparametric.h"</span>
<span class="preprocessor">#include "linbox/blackbox/sparse.h"</span>
<span class="preprocessor">#include "linbox/blackbox/blas-blackbox.h"</span>
<span class="keyword">using namespace </span>std;
<span class="preprocessor">#include "linbox/solutions/charpoly.h"</span>
<span class="preprocessor">#include "<a class="code" href="givaro-polynomial_8h.html" title="NO DOC.">linbox/ring/givaro-polynomial.h</a>"</span>
<span class="keyword">using namespace </span>LinBox;
<span class="keyword">template</span> <<span class="keyword">class</span> Field, <span class="keyword">class</span> Polynomial>
std::ostream& printPolynomial (std::ostream& out, <span class="keyword">const</span> <a name="_a0"></a><a class="code" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html" title="Specialization of class Modular for uint32_t element type.">Field</a> &F, <span class="keyword">const</span> Polynomial &v)
{
<span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = v.size () - 1; i >= 0; i--) {
F.write (out, v[i]);
<span class="keywordflow">if</span> (i > 0)
out << <span class="stringliteral">" X^"</span> << i << <span class="stringliteral">" + "</span>;
}
<span class="keywordflow">return</span> out;
}
<span class="keyword">template</span> <<span class="keyword">class</span> Field, <span class="keyword">class</span> Polynomial>
std::ostream& prettyprintIntegerPolynomial (std::ostream& out, <span class="keyword">const</span> <a class="code" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html" title="Specialization of class Modular for uint32_t element type.">Field</a> &F, <span class="keyword">const</span> Polynomial &v)
{
<span class="keywordtype">size_t</span> n = v.size()-1;
<span class="keywordflow">if</span> (n == 0) {
F.write(out, v[0]);
}
<span class="keywordflow">else</span> {
<span class="keywordflow">if</span>(v[n] != 0) {
<span class="keywordflow">if</span> (v[n] != 1) F.write(out, v[n]) << <span class="charliteral">'*'</span>;
out << <span class="charliteral">'X'</span>;
<span class="keywordflow">if</span> (n > 1) out << <span class="charliteral">'^'</span> << n;
<span class="keywordflow">for</span> (<span class="keywordtype">int</span> i = (<span class="keywordtype">int</span>)n - 1; i > 0; i--) {
<span class="keywordflow">if</span> (v[i] != 0) {
<span class="keywordflow">if</span> (v[i] >0) out << <span class="stringliteral">" + "</span>;
<span class="keywordflow">if</span> (v[i] != 1) F.write (out, v[i]) << <span class="charliteral">'*'</span>;
out << <span class="charliteral">'X'</span>;
<span class="keywordflow">if</span> (i > 1) out << <span class="charliteral">'^'</span> << i;
}
}
<span class="keywordflow">if</span> (v[0] != 0) {
<span class="keywordflow">if</span> (v[0] >0) out << <span class="stringliteral">" + "</span>;
F.write(out, v[0]);
}
}
}
<span class="keywordflow">return</span> out;
}
<span class="keyword">template</span> <<span class="keyword">class</span> Field, <span class="keyword">class</span> Factors, <span class="keyword">class</span> Exponents>
std::ostream& printFactorization (std::ostream& out, <span class="keyword">const</span> <a class="code" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html" title="Specialization of class Modular for uint32_t element type.">Field</a> &F, <span class="keyword">const</span> Factors &f, <span class="keyword">const</span> Exponents& exp)
{
<span class="keyword">typename</span> Factors::const_iterator itf = f.begin();
<span class="keyword">typename</span> Exponents::const_iterator ite = exp.begin();
<span class="keywordflow">for</span> ( ; itf != f.end(); ++itf, ++ite) {
prettyprintIntegerPolynomial(out << <span class="charliteral">'('</span>, F, *(*itf)) << <span class="charliteral">')'</span>;
<span class="keywordflow">if</span> (*ite > 1) out << <span class="charliteral">'^'</span> << *ite;
out << endl;
}
<span class="keywordflow">return</span> out;
}
<span class="keywordtype">int</span> main (<span class="keywordtype">int</span> argc, <span class="keywordtype">char</span> **argv)
{
commentator.<a name="a1"></a>setMaxDetailLevel (2);
commentator.<a name="a2"></a>setMaxDepth (2);
commentator.<a name="a3"></a>setReportStream (std::cerr);
cout<<setprecision(8);
cerr<<setprecision(8);
<span class="keywordflow">if</span> (argc < 2 || argc > 3) {
cerr << <span class="stringliteral">"Usage: charpoly <matrix-file-in-SMS-format> [<p>]"</span> << endl;
<span class="keywordflow">return</span> -1;
}
ifstream input (argv[1]);
<span class="keywordflow">if</span> (!input) { cerr << <span class="stringliteral">"Error opening matrix file "</span> << argv[1] << endl; <span class="keywordflow">return</span> -1; }
<span class="keywordflow">if</span> (argc == 2) {
<a name="_a4"></a><a class="code" href="class_lin_box_1_1_p_i_d__integer.html" title="Domain for integer operations.">PID_integer</a> ZZ;
<a name="_a5"></a><a class="code" href="class_lin_box_1_1_dense_matrix.html" title="Blackbox interface to dense matrix representation.">DenseMatrix<PID_integer ></a> A (ZZ);
A.read (input);
<span class="keyword">typedef</span> <a name="_a6"></a><a class="code" href="class_lin_box_1_1_giv_polynomial_ring.html" title="Polynomials.">GivPolynomialRing<PID_integer,::Givaro::Dense></a> <a class="code" href="class_lin_box_1_1_giv_polynomial_ring.html" title="Polynomials.">IntPolRing</a>;
IntPolRing::Element c_A;
Timer tim; tim.clear();tim.start();
charpoly (c_A, A, <a name="_a7"></a><a class="code" href="struct_lin_box_1_1_blackbox_specifier.html" title="BlackboxSpecifier.">Method::Blackbox</a>());
tim.stop();
cout << <span class="stringliteral">"Characteristic Polynomial is "</span>;
<span class="comment">//printPolynomial (cout, ZZ, c_A) << endl;</span>
cout << tim << endl;
<span class="preprocessor">#ifdef __LINBOX_HAVE_NTL</span>
<span class="preprocessor"></span> cout << <span class="stringliteral">"Do you want a factorization (y/n) ? "</span>;
<span class="keywordtype">char</span> tmp;
cin >> tmp;
<span class="keywordflow">if</span> (tmp == <span class="charliteral">'y'</span> || tmp == <span class="charliteral">'Y'</span>) {
commentator.<a name="a8"></a><a class="code" href="class_lin_box_1_1_commentator.html#a9b3772c898bc20f270af8d75ddc62090" title="Start an activity.">start</a>(<span class="stringliteral">"Integer Polynomial factorization by NTL"</span>, <span class="stringliteral">"NTLfac"</span>);
vector<IntPolRing::Element*> intFactors;
vector<unsigned long> exp;
IntPolRing IPD(ZZ);
tim.start();
IPD.factor (intFactors, exp, c_A);
tim.stop();
commentator.<a name="a9"></a><a class="code" href="class_lin_box_1_1_commentator.html#a3a418a21b882e15baa44fe8bef7aca84" title="Stop an activity.">stop</a>(<span class="stringliteral">"done"</span>, NULL, <span class="stringliteral">"NTLfac"</span>);
printFactorization(cout << intFactors.size() << <span class="stringliteral">" integer polynomial factors:"</span> << endl, ZZ, intFactors, exp) << endl;
vector<IntPolRing::Element*>::const_iterator itf = intFactors.begin();
<span class="keywordflow">for</span> ( ; itf != intFactors.end(); ++itf)
<span class="keyword">delete</span> *itf;
cout << tim << endl;
}
<span class="preprocessor">#endif</span>
<span class="preprocessor"></span> }
<span class="keywordflow">if</span> (argc == 3) {
<span class="keyword">typedef</span> <a name="_a10"></a><a class="code" href="class_lin_box_1_1_modular_3_01double_01_4.html" title="Standard representation of .">Modular<double></a> <a class="code" href="class_lin_box_1_1_modular_3_01uint32__t_01_4.html" title="Specialization of class Modular for uint32_t element type.">Field</a>;
<span class="keywordtype">double</span> q = atof(argv[2]);
Field F(q);
<a name="_a11"></a><a class="code" href="class_lin_box_1_1_dense_matrix.html">DenseMatrix<Field></a> B (F);
B.read (input);
cout << <span class="stringliteral">"B is "</span> << B.rowdim() << <span class="stringliteral">" by "</span> << B.coldim() << endl;
GivPolynomialRing<Field,::Givaro::Dense>::Element c_B;
Timer tim; tim.clear();tim.start();
charpoly (c_B, B);
tim.stop();
cout << <span class="stringliteral">"Characteristic Polynomial is "</span>;
<span class="comment">//printPolynomial (cout, F, c_B) << endl;</span>
cout << tim << endl;
}
<span class="keywordflow">return</span> 0;
}
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