Omar-Elrefaei/Debugging-GeneralizedSylvester

You should be able to get stated with:

$ git clone git@github.com:Omar-Elrefaei/Debugging-GeneralizedSylvester.git
$ cd Debugging-GeneralizedSylvester
$ julia --project --threads 4
julia> using Revise; includet("investigation.jl")
julia> df = scan_seeds(func=gss_test, seeds=1:10)

This will run gss_test 10 time with problem parameters as defined at the top of the gss_test function (n=m=order=4).

Caching & Performance

I found out that cond is the most expensive operation in gss_test particularly for large matrices. So I setup memorization (ghost function _cond) such that the second time you do scan_seeds(func=gss_test, seeds=1:10) with the same params, it uses the cached results.

This came to be when I was running with 1:1000, then decide that I want to add a new column to the dataframe and run again.

This workflow with n=m=4 at order 4 if pretty nice. But still fairly painful at order 5. For order 5, comment out the last dataframe columns (cond) and all the lines that mention matEq|mateq (gsylv from MatrixEquations takes about 8s at that scale)

This is why I ran a long n=m=4, order=5 scan over 5000 seeds and uploaded the resultant df as a csv. you can read it with DataFrame(CSV.File("order5.csv"))

Dataframe output

each gss_test invocation return an OrderedDict that represents a row in the df DataFrame;

If you need to add or remove columns from the dataframe, that should be done in the dict = OrderedDict(... line right away.

The rows then get merged together in the parent loop at scan_seeds. Originally that loop is supposed to simply represent the following

for seed in seeds
	res = gss_test(seed)
	append!(df, res, cols=:union)
end

but things got complicated with the introduction of threads, atomics, progress-bar. And the try-catch for better CTRL-C cancellation. Needless to say, I got a little carried away....

Analysis

I've been doing rudementary analysis like this

• Find all cases where our gss iterative solution didn't satisfy the original problem (with scaled tolerance)
  • filter(:gss_vs_orgPrb_rtol => isequal(false), df)
• Then take that and sort by the norm of the diffrences to more easily see any patterns
  • filter(:gss_vs_orgPrb_rtol => isequal(false), df) |> x -> sort(x, ["norm(GSS-OrgPrb)"])