Attempt to fix ql

[MasonProtter]

This change seems to fix the example #153, but it'd be good if there were also tests we could put in to check.

[dlfivefifty]

Great, thanks for that! I probably changed the interface at some point. It would be great if you could a test.

Btw I forgot that I implemented ∞-QL for such matrices. It probably only works for operators that are asymptotically block Toeplitz, which may not include your original example (it does include bi-infinite discrete Schrödinger operators).

It was very experimental code that hasn't really been used so I'm not sure I'd recommend using it, but if it's something you'd like to explore collaboratively I'd be happy to help. Doing inverse iteration via \ might be better as it uses QR instead of QL.

[codecov]

Codecov Report

All modified and coverable lines are covered by tests ✅

Comparison is base (2a85133) 79.76% compared to head (a96af3e) 81.50%.

Additional details and impacted files

@@            Coverage Diff             @@
##           master     #154      +/-   ##
==========================================
+ Coverage   79.76%   81.50%   +1.74%     
==========================================
  Files          10       10              
  Lines        1379     1379              
==========================================
+ Hits         1100     1124      +24     
+ Misses        279      255      -24     

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[MasonProtter]

It would be great if you could a test.

Yeah, I just wasn't sure what or how to properly test it.

Btw I forgot that I implemented ∞-QL for such matrices. It probably only works for operators that are asymptotically block Toeplitz, which may not include your original example (it does include bi-infinite discrete Schrödinger operators).

It was very experimental code that hasn't really been used so I'm not sure I'd recommend using it, but if it's something you'd like to explore collaboratively I'd be happy to help. Doing inverse iteration via \ might be better as it uses QR instead of QL.

Yep, fair enough!

[dlfivefifty]

In the first instance you can just do a test that makes sure It doesn't error. Eg something like ql(A-x*I).L[1,1] isa Float64

[dlfivefifty]

Looks fine, thanks for that!

Let me know if you want to use this more seriously. The philosophy is very much similar to the discussion on Discourse, that is you do the ∞-dimensional tail exactly, but here we construct matrix factorisations rather than inverses. I'd expect it to be more numerically stable; its essentially the difference between QL algorithm and inverse iteration.

[MasonProtter]

Thanks! I think for now, for my puposes, the brute force approach with a truncated matrix is working fine, but I may revisit this soon.

[MasonProtter]

@dlfivefifty do you mind merging this? I have merge rights (through JuliaLinearAlgebra) but it feels a little rude for me to do it since I'm not normally active in this repo.

[dlfivefifty]

Apologies! I think tests were still running last time I looked

[MasonProtter]

Not a problem :)