Go to the documentation of this file.00001 #include <Eigen/Core>
00002 #include <Eigen/LU>
00003 #include <Eigen/QR>
00004 #include <Eigen/Cholesky>
00005 #include <Eigen/Geometry>
00006 #include <Eigen/Jacobi>
00007 #include <Eigen/Eigenvalues>
00008 #include <iostream>
00009
00010 using namespace Eigen;
00011 using namespace std;
00012
00013 int main(int, char**)
00014 {
00015 cout.precision(3);
00016 MatrixXd A = MatrixXd::Random(6,6);
00017 cout << "Here is a random 6x6 matrix, A:" << endl << A << endl << endl;
00018
00019 EigenSolver<MatrixXd> es(A);
00020 cout << "The eigenvalues of A are:" << endl << es.eigenvalues() << endl;
00021 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
00022
00023 complex<double> lambda = es.eigenvalues()[0];
00024 cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
00025 VectorXcd v = es.eigenvectors().col(0);
00026 cout << "If v is the corresponding eigenvector, then lambda * v = " << endl << lambda * v << endl;
00027 cout << "... and A * v = " << endl << A.cast<complex<double> >() * v << endl << endl;
00028
00029 MatrixXcd D = es.eigenvalues().asDiagonal();
00030 MatrixXcd V = es.eigenvectors();
00031 cout << "Finally, V * D * V^(-1) = " << endl << V * D * V.inverse() << endl;
00032
00033 return 0;
00034 }