Reproducing code example:

See this gist for reproducing codes and system version information.

Basically, I used intelpython3, whose python and numpy are shipped with intel parallel studio xe 2019.3. Numpy version is 1.16.1.

For symmetric matrix with dimension larger or equal than 32767, np.linalg.eigh() returns wrong results with all zeros immediately (no error message). Other eigen functions like eigvalsh works as expected. 32767 reminds me of possible issues with data type int16.

This may also be an issue from intel mkl or intel version of numpy or python (very unlikely, since the issue exists for various distributions of numpy, including the default one linked to openblas). Anyway, I will open the issue here until I have further analysis on this problem and find better place to report the issue.