hipsolverDnDsyevdx with HIPSOLVER_EIG_RANGE_ALL does not return the correct eigenvectors

[Beanavil]

For the input matrix

     | 3.5 0.5 0.0 |
A =  | 0.5 3.5 0.0 |
     | 0.0 0.0 2.0 |

the hipSOLVER Compatibility API function hipsolverDnDsyevdx (hipsolverDnSsyevdx too) with relevant parameters:

• jobz = HIPSOLVER_EIG_MODE_VECTOR
• range = HIPSOLVER_EIG_RANGE_ALL
• uplo = HIPSOLVER_FILL_MODE_UPPER

gives the following vector of eigenvalues:

{2, 3, 4}

and the following matrix of eigenvectors (stored as columns):

| 0   -0.707107   -0.707107 |
| 0    0.707107    0.707107 |
| 1    0                 0  |

which at first sight does not make much sense because different eigenvalues (3 and 4) have the same eigenvector associated.

Also, the output from hipSOLVER's hipsolverDsyevd function with the relevant parameters:

• jobz = HIPSOLVER_EIG_MODE_VECTOR
• uplo = HIPSOLVER_FILL_MODE_UPPER

yields the same eigenvalues, but the following eigenvectors:

| 0   -0.707107    0.707107 |
| 0    0.707107    0.707107 |
| 1    0                 0  |

which I think would be the correct solution.

[jzuniga-amd]

Thanks @Beanavil for pointing this out.
The team will take a look and provide a fix if needed.

[jzuniga-amd]

@Beanavil Can you please test with the latest ROCm 6.1.2? If the issue is resolved, please close the ticket. Thanks!