Feature request: eigenNonSymmetric() with complex eigenvalues #16298
Description
Current eigenNonSymmetric() function does not seem to support real square matrix with complex eigenvalues.
Checking that a real matrix has complex eigenvalues seems to be not trivial, see.
Example in Numpy/Scipy (from Matlab doc):
from __future__ import print_function
import numpy as np
from scipy.linalg import eig
A = np.matrix([[1, 2, 3],
[3, 1, 2],
[2, 3, 1]])
w, v = eig(A)
print('A:\n', A)
print('v:', v)
print('w:', w)
gives:
A:
[[1 2 3]
[3 1 2]
[2 3 1]]
v: [[-0.57735027+0.j 0.28867513-0.5j 0.28867513+0.5j]
[-0.57735027+0.j -0.57735027+0.j -0.57735027-0.j ]
[-0.57735027+0.j 0.28867513+0.5j 0.28867513-0.5j]]
w: [ 6.0+0.j -1.5+0.8660254j -1.5-0.8660254j]
In OpenCV:
Matx33d m(
1, 2, 3,
3, 1, 2,
2, 3, 1);
Mat eigenvalues, eigenvectors;
try
{
cv::eigenNonSymmetric(m, eigenvalues, eigenvectors);
std::cout << "m:\n" << m << std::endl;
std::cout << "eigenvalues:\n" << Mat(eigenvalues.t()) << std::endl;
std::cout << "eigenvectors:\n" << eigenvectors << std::endl;
}
catch (const cv::Exception& e)
{
std::cerr << "eigenNonSymmetric no conv: " << e.what() << std::endl;
}
catch (...)
{
std::cerr << "Unknown exception has been raised" << std::endl;
}
gives:
m:
[1, 2, 3;
3, 1, 2;
2, 3, 1]
eigenvectors:
[0.577350269189626, 0.5773502691896255, 0.577350269189626;
0.7316804540966678, -0.6796598963166424, -0.05202055778002566;
0.3623677410581142, 0.4524699901711914, -0.8148377312293055]
eigenvalues:
[6.000000000000004, -1.5, -1.5]
Possible feature implementation would be to use ?GEEV LAPACK routine to compute the eigenvalues and eigenvectors of a general square matrix. So a fallback would be needed when OpenCV is not built with LAPACK support, something like a reference LAPACK implementation?
Output would be something like CV_64FC2 to handle complex values? Or CV_64FC2 only when values are complex to keep the previous behavior?
See DGEEV doc.
See numpy.linalg.eig doc and corresponding source code.