Squashed 'third_party/eigen/' content from commit 61d72f6
Change-Id: Iccc90fa0b55ab44037f018046d2fcffd90d9d025
git-subtree-dir: third_party/eigen
git-subtree-split: 61d72f6383cfa842868c53e30e087b0258177257
diff --git a/unsupported/doc/examples/PolynomialSolver1.cpp b/unsupported/doc/examples/PolynomialSolver1.cpp
new file mode 100644
index 0000000..cd777a4
--- /dev/null
+++ b/unsupported/doc/examples/PolynomialSolver1.cpp
@@ -0,0 +1,53 @@
+#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;
+}