#include <unsupported/Eigen/Polynomials> #include <vector> #include <iostream> using namespace Eigen; using namespace std; int main() { typedef Matrix<double, 5, 1> Vector5d; Vector5d roots = Vector5d::Random(); cout << "Roots: " << roots.transpose() << endl; Eigen::Matrix<double, 6, 1> polynomial; roots_to_monicPolynomial(roots, polynomial); PolynomialSolver<double, 5> psolve(polynomial); cout << "Complex roots: " << psolve.roots().transpose() << endl; std::vector<double> realRoots; psolve.realRoots(realRoots); Map<Vector5d> mapRR(&realRoots[0]); cout << "Real roots: " << mapRR.transpose() << endl; cout << endl; cout << "Illustration of the convergence problem with the QR algorithm: " << endl; cout << "---------------------------------------------------------------" << endl; Eigen::Matrix<float, 7, 1> hardCase_polynomial; hardCase_polynomial << -0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125; cout << "Hard case polynomial defined by floats: " << hardCase_polynomial.transpose() << endl; PolynomialSolver<float, 6> psolvef(hardCase_polynomial); cout << "Complex roots: " << psolvef.roots().transpose() << endl; Eigen::Matrix<float, 6, 1> evals; for (int i = 0; i < 6; ++i) { evals[i] = std::abs(poly_eval(hardCase_polynomial, psolvef.roots()[i])); } cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl; cout << "Using double's almost always solves the problem for small degrees: " << endl; cout << "-------------------------------------------------------------------" << endl; PolynomialSolver<double, 6> psolve6d(hardCase_polynomial.cast<double>()); cout << "Complex roots: " << psolve6d.roots().transpose() << endl; for (int i = 0; i < 6; ++i) { std::complex<float> castedRoot(psolve6d.roots()[i].real(), psolve6d.roots()[i].imag()); evals[i] = std::abs(poly_eval(hardCase_polynomial, castedRoot)); } cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl; cout.precision(10); cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl; std::complex<float> castedRoot(psolve6d.roots()[5].real(), psolve6d.roots()[5].imag()); cout << "Norm of the difference: " << std::abs(psolvef.roots()[5] - castedRoot) << endl; }