verimag-polyhedra / vpl Goto Github PK

Make operators incremental: one must be able to add a constraint to the input polyhedron, and reuse the previous result to avoid recomputing everything.

Try putting normalization on all Handelman's products except the linear part of the polynomial.

Some operators (e.g. join) could benefit from the regions of their input polyhedra.

Handelman plotting has a strange shape :

open Vpl;;
open Calculator;;
open Notations;;

Flags.lin := Flags.Handelman;;
Debug.enable();;
Debug.set_colors();;
Debug.print_enable();;

PLPCore.Debug.enable DebugTypes.([Title ; MInput ; MOutput ; Normal ; Sage]);;
let p = parse "x >= 1, y >= -2, x - y >= 0, x + y <= 5, x * x + y * y <= 4";;

Assume_back requires the partition into regions to be a partition of the space of parameters.
Therefore, we need to merge subdivided regions.

Reimplement the intervalization algorithm directly in Ocaml, and remove the extracted part.

Fix the opam package for opam 2.0.
Fix VPL dependencies.

Make the user interface simpler and clearer.

The code should be reviewed to track down sources of inefficiency.
In particular, some lists may be changed into arrays when necessary.

IneqSet must maintain an optional partition into regions.
After calling a PLP operator, regions must be stored into the abstract value.

• Ocaml version?
• GLPK? Eigen?
• Coq version ?

Trace generation has been adapted for the new trace language. It needs to be checked.

Make a new operator that, given two polyhedra A and B:

1. Computes the projection A|X on a set of variables X.
2. Checks if A|X contains B

Type, module and function names should be normalized.

When assuming back a constraint which puts the normalization point outside of the result's interior, regions must be renormalized to a new normalization point.
Can it be done by simply replacing the normalization constraint with a new one in each region ?

Make more .mli with more doc, especially in the high level modules.

Make a HTML page with the VPL doc.
Upload it somewhere ?

Handelman default heuristic builds all combination up to a certain degree (the degree of the polynomial to linearize). However, it currently seems to compute too many combinations: the degree must be wrong.

Certificates may fail when computing the join of two polyhedra with strict inequalities.
Example :
First polyhedron

P1 = -1.v2 + 1.v4 <= 0
1.v2 + 1.v4 <= 5
14.v2 + 5.v4 <= 237/4
-1.v4 <= 0
-293/56.v2 + -5/2.v4 < -461/56

Second polyhedron

P2 = -1.v2 <= -1
-1.v4 <= 2
14.v2 + 5.v4 <= 237/4
1.v4 < 0
-333/56.v2 + 2.v4 < -501/56

Output

14.v2 + 5.v4 <= 237/4: 14.v2 + 5.v4 <= 237/4
-1.v2 + 1.v4 < 0: -1.v2 + 1.v4 <= 0 
1.v2 + 1.v4 < 5: 1.v2 + 1.v4 <= 5
-1.v4 < 2: -1.v4 < 2
-1.v2 < -1: -1.v2 < -1
-2221/56.v2 + 1.v4 < -2305/56: -2221/56.v2 + 1.v4 < -2305/56

Check that the oracles works as intended.