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Generalized eigenvalues
http://forum.alglib.net/viewtopic.php?f=2&t=4326		 Page 1 of 1
Author:  denkir77 [ Thu May 21, 2020 12:03 pm ]
Post subject:  Generalized eigenvalues
I have 2 matrices.

Code:
F =
   -0.1000    0.0200    0.0200    0.0104
    1.0000         0         0         0
         0    1.0000         0         0
         0         0    1.0000         0
             
F1 =
     1     0     0     0
     0     1     0     0
     0     0     1     0
     0     0     0     1


I need to calculate the generalized eigenvalues of these 2 matrices in ALGLIB.
I found alglib::smatrixgevd() function. But as far as I can see, it doesn't return complex values.

I've already done that in MATLAB and Visual Studio (Eigen library).
1) Matlab code:
Code:
F=[-0.1,0.02,0.02,0.0104;1,0,0,0;0,1,0,0;0,0,1,0];
F1=[1,0,0,0;0,1,0,0;0,0,1,0;0,0,0,1];
eigenvalues = eig(F,F1);
|---------------------------------------------------------------------------|
The results is:
eigenvalues =
   0.3531 + 0.0000i
  -0.0723 + 0.3003i
  -0.0723 - 0.3003i
  -0.3086 + 0.0000i


2) C++ code (Eigen library):
Code:
#include <iostream>
#include <Eigen/Eigenvalues>

using namespace std;
using Eigen::MatrixXd;
using Eigen::VectorXcd;
using Eigen::GeneralizedEigenSolver;

int main()
{
    //--- 1) Matrices
    MatrixXd F_MX(4,4);
    F_MX.row(0) << -0.1, 0.02, 0.02, 0.0104;
    F_MX.row(1) << 1, 0, 0, 0;
    F_MX.row(2) << 0, 1, 0, 0;
    F_MX.row(3) << 0, 0, 1, 0;
    MatrixXd F1_MX = MatrixXd::Identity(4, 4);
       
    //--- 2) the generalized eigenvalues of square matrices F_MX and F1_MX
    GeneralizedEigenSolver<MatrixXd> ges;
    ges.compute(F_MX, F1_MX,true);
    cout << "The (complex) generalized eigenvalues are (alphas./beta): \n" << ges.eigenvalues() << endl;
}
|---------------------------------------------------------------------------|
The results is:
eigenvalues =
  (0.353145,-0)
  (-0.0722619,-0.300335)
  (-0.0722619,0.300335)
  (-0.308622,0)

Please give a hint to solving the problem.
Thanks.
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