I want to do the EVD wth this 4x4 covariance matrix:

cuDoubleComplex m_cov_[16] = {
        make_cuDoubleComplex(2.0301223848037391, 3.4235008150792548e-17),
        make_cuDoubleComplex(1.0365842528472908, -2.1028119220635375),
        make_cuDoubleComplex(2.7516978261134084, 0.95059712173944222),
        make_cuDoubleComplex(-1.350157109070875, -1.1815219722269694),
        make_cuDoubleComplex(1.0365842528472908, 2.1028119220635375),
        make_cuDoubleComplex(2.7073859851827988, 8.7392491301242207e-17),
        make_cuDoubleComplex(0.42038828834095354, 3.3356003818061963),
        make_cuDoubleComplex(0.53443422887585779, -2.0017874620940646),
        make_cuDoubleComplex(2.7516978261134084, -0.95059712173944222),
        make_cuDoubleComplex(0.42038828834095354, -3.3356003818061963),
        make_cuDoubleComplex(4.1748595442022722, 2.0100622219496206e-17),
        make_cuDoubleComplex(-2.3832926547827333, -0.9692696339061293),
        make_cuDoubleComplex(-1.350157109070875, 1.1815219722269694),
        make_cuDoubleComplex(0.53443422887585779, 2.0017874620940646),
        make_cuDoubleComplex(-2.3832926547827333, 0.9692696339061293),
        make_cuDoubleComplex(1.5855784922744534, -1.5877902777669332e-17)
    };

// EVD
Eigen::SelfAdjointEigenSolver<Eigen::MatrixXcd> eigensolver(m_cov_);
eigenValues_ = eigensolver.eigenvalues();
eigenVectors_ = eigensolver.eigenvectors();

By C++ Eigen lib, the eigen values are below:

{{x = -2.2573766836348074e-15, y = 0},
 {x = -9.709294041296323e-16, y = 0}, 
 {x = 8.9445808618868127e-17, y = 0},
 {x = 10.280850897111305, y = 0}}

And the 4x4 eigen vectors are below:

{{x = -0.3470929425161523, y = 0}, {x = -0.77713832029830621, y = -0}, {x = -0.15994536685820598, y = 0}, {x = 0.5, y = 0}}, 
{{x = -0.4597724303808105, y = 0.48181665117044714}, {x = 0.12469176895072034, y = -0.019363390950754053}, {x = -0.28597710463196591, y = 0.45689839613393701}, {x = -0.21684345356939669, y = 0.45053181535169839}},
{{x = -0.42256553981019185, y = -0.42733105533794741}, {x = 0.41437862159459787, y = 0.29068296724286291}, {x = 0.33214873805084277, y = 0.14932354148008731}, {x = 0.45697128218787925, y = 0.2029217761985285}}, 
{{x = -0.21707002501160269, y = 0.16642011333440535}, {x = -0.27240794554375036, y = 0.22298146715732753}, {x = 0.60350719516570406, y = -0.43247796708208042}, {x = -0.38102789443353835, y = 0.32375568514474662}}}

But with the same input, cuBLAS return the different results.

I use the cuBLAS EVD function below:

CHECK_CUSOLVER(cusolverDnZheevd(cusolverH, CUSOLVER_EIG_MODE_VECTOR, CUBLAS_FILL_MODE_UPPER, N, m_eigen_vec.data(), N, m_eigen_value.data(), d_work, lwork, devInfo));

And the eigen values and eigen vectors are below:

// Eigen Values
{-5.2180864461495171e-16,
-3.0110342183593702e-16,
2.8548936444323134e-16, 
10.497946406463264}

// Eigen Vectors
{{x = -0.38208898741712083, y = 0.41581487741664563}, {x = 0.32043709404849968, 
    y = -0.4517568232420171}, {x = 0.21717632600175682, y = -0.36577789346231687}, {x = -0.33093161501032731, 
    y = 0.28959813033042575}, {x = -0.17547383350755327, y = -0.69642001620440552}, {x = -0.10241833368805221, 
    y = -0.43952076894648784}, {x = 0.047402059701005216, y = 0.14281594546174881}, {x = 0.13099303872894871, 
    y = 0.49065012752041015}, {x = -0.32475905997549959, y = 0.077154117638887132}, {x = -0.32253254381877083, 
    y = 0.2157036870035538}, {x = -0.50261510442239055, y = 0.29617238148252628}, {x = -0.58415934115419899, 
    y = 0.23757380765099248}, {x = -0.23214840790484073, y = 0}, {x = 0.58224779741288002, y = 0}, {x = -0.67532037122395228, 
    y = 0}, {x = 0.38863480971863701, y = 0}}

You can notice that the sorted eigen values calc from Eigen Lib and from cuBLAS are the same (three ~0 values and one larger value) but the eigen vectors are totally different.

I’ve wrote a lot of unit tests for each step, and I’m sure that the eigen values and vectors from Eigen lib are correct, can someone tell me how to get the same answer with cuBLAS EVD?