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1 | #include <Eigen/Dense>
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2 | #include <iostream>
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3 |
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4 | using namespace Eigen;
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5 | using namespace std;
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6 |
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7 | int main(int, char**)
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8 | {
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9 | cout.precision(3);
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10 | MatrixXd X = MatrixXd::Random(5,5);
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11 | MatrixXd A = X + X.transpose();
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12 | cout << "Here is a random symmetric matrix, A:" << endl << A << endl;
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13 | X = MatrixXd::Random(5,5);
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14 | MatrixXd B = X * X.transpose();
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15 | cout << "and a random postive-definite matrix, B:" << endl << B << endl << endl;
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16 |
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17 | GeneralizedSelfAdjointEigenSolver<MatrixXd> es(A,B);
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18 | cout << "The eigenvalues of the pencil (A,B) are:" << endl << es.eigenvalues() << endl;
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19 | cout << "The matrix of eigenvectors, V, is:" << endl << es.eigenvectors() << endl << endl;
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20 |
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21 | double lambda = es.eigenvalues()[0];
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22 | cout << "Consider the first eigenvalue, lambda = " << lambda << endl;
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23 | VectorXd v = es.eigenvectors().col(0);
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24 | cout << "If v is the corresponding eigenvector, then A * v = " << endl << A * v << endl;
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25 | cout << "... and lambda * B * v = " << endl << lambda * B * v << endl << endl;
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26 |
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27 | return 0;
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28 | }
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