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