54 lines
2.3 KiB
C++
54 lines
2.3 KiB
C++
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#include <unsupported/Eigen/Polynomials>
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#include <vector>
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#include <iostream>
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using namespace Eigen;
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using namespace std;
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int main()
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{
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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: " << endl;
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cout << "---------------------------------------------------------------" << endl;
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Eigen::Matrix<float,7,1> hardCase_polynomial;
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hardCase_polynomial <<
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-0.957, 0.9219, 0.3516, 0.9453, -0.4023, -0.5508, -0.03125;
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cout << "Hard case polynomial defined by floats: " << 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 ){ evals[i] = std::abs( poly_eval( hardCase_polynomial, psolvef.roots()[i] ) ); }
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cout << "Norms of the evaluations of the polynomial at the roots: " << evals.transpose() << endl << endl;
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cout << "Using double's almost always solves the problem for small degrees: " << endl;
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cout << "-------------------------------------------------------------------" << 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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{
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std::complex<float> castedRoot( psolve6d.roots()[i].real(), 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: " << evals.transpose() << endl << endl;
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cout.precision(10);
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cout << "The last root in float then in double: " << psolvef.roots()[5] << "\t" << psolve6d.roots()[5] << endl;
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std::complex<float> castedRoot( psolve6d.roots()[5].real(), psolve6d.roots()[5].imag() );
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cout << "Norm of the difference: " << std::abs( psolvef.roots()[5] - castedRoot ) << endl;
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}
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