1 #include <unsupported/Eigen/Polynomials>
2 #include <vector>
3 #include <iostream>
4
5 using namespace Eigen;
6 using namespace std;
7
main()8 int main()
9 {
10 typedef Matrix<double,5,1> Vector5d;
11
12 Vector5d roots = Vector5d::Random();
13 cout << "Roots: " << roots.transpose() << endl;
14 Eigen::Matrix<double,6,1> polynomial;
15 roots_to_monicPolynomial( roots, polynomial );
16
17 PolynomialSolver<double,5> psolve( polynomial );
18 cout << "Complex roots: " << psolve.roots().transpose() << endl;
19
20 std::vector<double> realRoots;
21 psolve.realRoots( realRoots );
22 Map<Vector5d> mapRR( &realRoots[0] );
23 cout << "Real roots: " << mapRR.transpose() << endl;
24
25 cout << endl;
26 cout << "Illustration of the convergence problem with the QR algorithm: " << endl;
27 cout << "---------------------------------------------------------------" << endl;
28 Eigen::Matrix<float,7,1> hardCase_polynomial;
29 hardCase_polynomial <<
30 -0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125;
31 cout << "Hard case polynomial defined by floats: " << hardCase_polynomial.transpose() << endl;
32 PolynomialSolver<float,6> psolvef( hardCase_polynomial );
33 cout << "Complex roots: " << psolvef.roots().transpose() << endl;
34 Eigen::Matrix<float,6,1> evals;
35 for( int i=0; i<6; ++i ){ evals[i] = std::abs( poly_eval( hardCase_polynomial, psolvef.roots()[i] ) ); }
36 cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl;
37
38 cout << "Using double's almost always solves the problem for small degrees: " << endl;
39 cout << "-------------------------------------------------------------------" << endl;
40 PolynomialSolver<double,6> psolve6d( hardCase_polynomial.cast<double>() );
41 cout << "Complex roots: " << psolve6d.roots().transpose() << endl;
42 for( int i=0; i<6; ++i )
43 {
44 std::complex<float> castedRoot( psolve6d.roots()[i].real(), psolve6d.roots()[i].imag() );
45 evals[i] = std::abs( poly_eval( hardCase_polynomial, castedRoot ) );
46 }
47 cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl;
48
49 cout.precision(10);
50 cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl;
51 std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() );
52 cout << "Norm of the difference: " << std::abs( psolvef.roots()[5] - castedRoot ) << endl;
53 }
54