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 X = MatrixXd::Random(5,5);
00017 MatrixXd A = X + X.transpose();
00018 cout << "Here is a random symmetric matrix, A:" << endl << A << endl;
00019 X = MatrixXd::Random(5,5);
00020 MatrixXd B = X * X.transpose();
00021 cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl;
00022
00023 GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);
00024 cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
00025 cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
00026
00027 double lambda = es.eigenvalues()[0];
00028 cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
00029 VectorXd v = es.eigenvectors().col(0);
00030 cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl;
00031 cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl;
00032
00033 return 0;
00034 }