Michael F. Herbst

See #939

Superseeded by #942.

**Note:** The original [scipy implementation](https://github.com/scipy/scipy/blob/v1.1.0/scipy/sparse/linalg/eigen/lobpcg/lobpcg.py#L109-L568) does not suffer from this problem. For example ```py from scipy.sparse.linalg import lobpcg import numpy as np lobpcg(np.diag(A), orth(np.random.randn(len(A), 5)), largest=False) ``` returns the correct...

Thanks for looking into this. Indeed, this shows some similarity with #223. E.g. block size `5` is a magic number. `4` or `6` work much better with the `A` defined...

I came up with a larger example, that still illustrates the `PosDefException` problem, see [this gist](https://gist.github.com/mfherbst/0732c386039457e7eb424e3572ebb129). On my machine this has a success rate of about 97%. This is not...

@mohamed82008 (related to scipy/scipy#10258) I added a julia version to the example repository [mfherbst/issue_scipy_lobpcg_guess](https://github.com/mfherbst/issue_scipy_lobpcg_guess) for convenience and out of curiosity. As it turns out and as suspected by @lobpcg, the...

The naive julia implementation referenced in scipy/scipy#10258 actually does pretty good in the example of [mfherbst/issue_scipy_lobpcg_guess](https://github.com/mfherbst/issue_scipy_lobpcg_guess). Even converging down to 1e-14 tolerance in a reasonable number of iterations (some 250...

As I said on the [discourse thread](https://discourse.julialang.org/t/iterativesolvers-and-positive-definite-matrices/50292/7) our implementation at its current stage is not complete drop-in replacement for the lobpcg of this package (e.g. generalised eigensolves are not tested...

Thanks for looking into this! This time I am travelling for the week :smile:. I'll try to get to it asap.

@mohamed82008 I've done a little testing in our application (DFTK.jl). The solver now runs a lot more stable, but I still seem to get some spurious (zero) eigenvalues. I'll take...