GLPK backend: More basis status and tableau data functions

[mkoeppe]

This is a follow-up to #18685, #18732.

It adds get_row_prim, set_row_stat, set_col_stat, warm_up.

These are the remaining functions necessary to implement #18804.

CC: @uduse @dimpase @nathanncohen @videlec @yuan-zhou

Component: numerical

Author: Aedi Wang

Branch/Commit: 37e90e8

Reviewer: Dima Pasechnik

Issue created by migration from https://trac.sagemath.org/ticket/19472

[uduse]

Branch: u/zwang/GLPK_backend_More_basis_status_and_tableau_data_functions

[mkoeppe]

New commits:

37e90e8

More basis status and tableau data functions

[mkoeppe]

Commit: 37e90e8

[dimpase]

comment:5

Is it possible to add a short explanation of (and a reference) what "warming up the basis" means?

And another question - will there be any frontend functions available to take advantage of this stuff, or it's got to be backend-specific?

[mkoeppe]

comment:6

Replying to @dimpase:

Is it possible to add a short explanation of (and a reference) what "warming up the basis" means?

The GLPK manual offers this explanation: "This operation includes computing factorization of the basis matrix (if it does not exist), com- puting primal and dual components of basic solution, and determining the solution status."
I'm not sure if it's worth adding it.

And another question - will there be any frontend functions available to take advantage of this stuff, or it's got to be backend-specific?

Our current plan is to expose these functions only through a simplified interface that we call "LPBackendDictionary" (#18804), which offers a naive "textbook-style" view on the simplex solvers.

A full-featured frontend interface would be rather tricky. OSI tried that and I'm not sure it really succeeded.

[dimpase]

comment:7

OK.

[dimpase]

Reviewer: Dima Pasechnik

[vbraun]

Changed branch from u/zwang/GLPK_backend_More_basis_status_and_tableau_data_functions to 37e90e8