Crate flag_algebra

An implementation of flag algebras.

Example

extern crate flag_algebra;

use flag_algebra::*;
use crate::sdp::Problem;
use crate::flags::Graph;
use crate::operator::Basis;

pub fn main() {
    // Work on the graphs of size 3.
    let basis = Basis::new(3);

    // Define useful flags.
    let k3 = flag(&Graph::new(3, &[(0,1),(1,2),(2,0)])); // Triangle
    let e3 = flag(&Graph::new(3, &[])); // Independent set of size 3

    // Definition of the optimization problem.
    let pb = Problem::<i64, _> {
        // Constraints
        ineqs: vec!(total_sum_is_one(basis),
                    flags_are_nonnegative(basis)),
        // Use all relevant Cauchy-Schwarz inequalities.
        cs: basis.all_cs(),
        // Minimize density of triangle plus density of independent of size 3.
        obj: k3 + e3,
    };

    // Write the correspondind SDP program in "goodman.sdpa".
    // This program can then be solved by CSDP.
    pb.write_sdpa("goodman").unwrap();
}

Re-exports

pub use crate::operator::Basis;

Modules

combinatorics	Basic combinatorial functions.
common	Flat data structures for binary relations.
density	Computing coefficients of a flag algebra operator.
flags	Example of flags.
iterators	Streaming iterators on combinatorial objects (subsets, functions, ...).
operator	Computing and stocking operators of the flag algebra.
prettyprint	Print expression of computations in the flag algebra.
sdp	Create and manipulate semi-definite problems.

Structs

Ineq	A set of bounds on elements of a flag algebra.
IneqData	Contains the vector and the bound of one inequality in a flag algebra. This inequality has the form self.flag ≥ self.bound. Expression recording how the left sides where constructed.
IneqMeta	Contains informations about a set of inequalities of a flag algebra.
QFlag	An element of a flag algebra.
SubClass	A wrapper type for flags from a sub-class of flags.

Traits

Flag	Interface for object that can be used as flags.
SubFlag	Mechanism for defining a subclass of a flag class.

Functions

flag	Return the vector corresponding to the unlabeled flag f
flags_are_nonnegative	Return the inequalities expressing that the flags of basis are larger than zero.
total_sum_is_one	Return the inequalities expressing that the sum of the flags of basis is equal to one.