Lapack heevd seems to return wrong values on osxarm64_accelerate

[kmnhan]

• I read the conda-forge documentation and could not find the solution for my problem there.

To reproduce, i ran

conda install -c conda-forge numpy "libblas=*=*accelerate"

in a new environment. Then,

import numpy as np
a = np.array([[5+2j, 9-2j],
              [9+2j, 2-1j]])
np.linalg.eigh(a)

returns

(array([-5.84077085, 12.84077085]), 
 array([[-0.64784785-0.64784785j, -0.76176975-0.34206291j],
        [ 0.57837872+0.90888084j, -0.54137349-0.55025032j]]))

where the eigenvectors are different from those returned by other BLAS implementations. In the case of scipy, which uses evr by default instead of evd, returns the correct eigenvectors; scipy.linalg.eigh(a) returns

(array([-5.84077085, 12.84077085]),
 array([[-0.64784785+0.j        , -0.76176975+0.j        ],
        [ 0.74362978+0.16525106j, -0.63242069-0.14053793j]]))

By specifying the LAPACK driver with scipy.linalg.eigh(a, driver='evd'), I again obtain the same result as numpy.

After some testing with the LAPACK calls scipy.linalg.lapack.zheevr and scipy.linalg.lapack.zheevd, zheevd does not seem to return correct values.

Environment (conda list):

$ conda list
# Name                    Version                   Build  Channel
bzip2                     1.0.8                h3422bc3_4    conda-forge
ca-certificates           2021.10.8            h4653dfc_0    conda-forge
libblas                   3.9.0           13_osxarm64_accelerate    conda-forge
libcblas                  3.9.0           13_osxarm64_accelerate    conda-forge
libcxx                    12.0.1               h168391b_1    conda-forge
libffi                    3.4.2                h3422bc3_5    conda-forge
libgfortran               5.0.0.dev0      11_0_1_hf114ba7_23    conda-forge
libgfortran5              11.0.1.dev0         hf114ba7_23    conda-forge
liblapack                 3.9.0           13_osxarm64_accelerate    conda-forge
libzlib                   1.2.11            hee7b306_1013    conda-forge
llvm-openmp               13.0.1               hf3c4609_0    conda-forge
ncurses                   6.3                  hc470f4d_0    conda-forge
numpy                     1.22.2          py310h567df17_0    conda-forge
openssl                   3.0.0                h3422bc3_2    conda-forge
pip                       22.0.3             pyhd8ed1ab_0    conda-forge
python                    3.10.2          h38ef502_3_cpython    conda-forge
python_abi                3.10                    2_cp310    conda-forge
readline                  8.1                  hedafd6a_0    conda-forge
scipy                     1.8.0           py310h6ecf4ae_1    conda-forge
setuptools                60.9.3          py310hbe9552e_0    conda-forge
sqlite                    3.37.0               h72a2b83_0    conda-forge
tk                        8.6.12               he1e0b03_0    conda-forge
tzdata                    2021e                he74cb21_0    conda-forge
wheel                     0.37.1             pyhd8ed1ab_0    conda-forge
xz                        5.2.5                h642e427_1    conda-forge
zlib                      1.2.11            hee7b306_1013    conda-forge

Details about conda and system ( conda info ):

$ conda info
     active environment : np_test
    active env location : /Users/khan/miniforge3/envs/np_test
            shell level : 4
       user config file : /Users/khan/.condarc
 populated config files : /Users/khan/miniforge3/.condarc
                          /Users/khan/.condarc
          conda version : 4.11.0
    conda-build version : not installed
         python version : 3.9.7.final.0
       virtual packages : __osx=12.2.1=0
                          __unix=0=0
                          __archspec=1=arm64
       base environment : /Users/khan/miniforge3  (writable)
      conda av data dir : /Users/khan/miniforge3/etc/conda
  conda av metadata url : None
           channel URLs : https://conda.anaconda.org/conda-forge/osx-arm64
                          https://conda.anaconda.org/conda-forge/noarch
          package cache : /Users/khan/miniforge3/pkgs
                          /Users/khan/.conda/pkgs
       envs directories : /Users/khan/miniforge3/envs
                          /Users/khan/.conda/envs
               platform : osx-arm64
             user-agent : conda/4.11.0 requests/2.26.0 CPython/3.9.7 Darwin/21.3.0 OSX/12.2.1
                UID:GID : 501:20
             netrc file : None
           offline mode : False