compute the tableau's nonbasic term in SCIP separator

Question

In traditional Simplex Algorithm notation, we have x at the current basis selection B as so:
x_B = A_B^-1b - A_B^-1A_Nx_N. How can I compute the A_B^-1A_N term inside a separator in SCIP, or at least iterate over its columns?

I see three helpful methods: getLPColsData, getLPRowsData, getLPBasisInd. I'm just not sure exactly what data those methods represent, particularly the last one, with its negative row indexes. How do I use those to get the value I want?

Do those methods return the same data no matter what LP algorithm is used? Or do I need to account for dual vs primal? How does the use of the "revised" algorithm play into my calculation?

Update: I discovered the getLPBInvARow and getLPBInvRow. That seems to be much closer to what I'm after. I don't yet understand their results; they seem to include more/less dimensions than expected. I'm still looking for understanding at how to use them to get the rays away from the corner.

Update 2: further code at https://github.com/scipopt/scip/issues/31

Answer 1

you are correct that getLPBInvRow or getLPBInvARow are the methods you want. getLPBInvARow directly returns you a of the simplex tableau, but it is not more efficient to use than getLPBInvRow and doing the multiplication yourself since the LP solver needs to also compute the actual tableau first.

I suggest you look into either sepa_gomory.c or sepa_gmi.c for examples of how to use these methods. How do they include less dimensions than expected? They both return sparse vectors.