1 #include <unsupported/Eigen/Polynomials> 2 #include <vector> 3 #include <iostream> 4 5 using namespace Eigen; 6 using namespace std; 7 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
