Struct ParametricPolytope 

pub struct ParametricPolytope { /* private fields */ }

A family of polytopes {x : hₖ(j, x) ≥ 0} whose half-spaces are affine in x with coefficients polynomial in one parameter j.

at instantiates the family exactly at a rational j; polytope_at / vertices_at / volume_at do the same with a per-value cache, for tree builders that revisit the same samples.

use symplex::prelude::*;
use symplex::polytope::ParametricPolytope;
use symplex::linprog::{q, qi};

let ctx = Context::new();
let (j, r, t) = (ctx.symbol("j"), ctx.symbol("r"), ctx.symbol("t"));
// 0 ≤ r ≤ 1/2, 0 ≤ t ≤ 1, (2j + 1)·t ≥ j·r + 1
let hyps = [r.clone(), ctx.rational(1, 2) - &r, t.clone(), 1 - &t, (&j * 2 + 1) * &t - &j * &r - 1];
let mut cell = ParametricPolytope::new(&hyps, &[r, t], &j).unwrap();
assert_eq!(cell.volume_at(&qi(2)).unwrap(), q(7, 20));   // ∫₀^{1/2} (1 − (2r + 1)/5) dr
assert_eq!(cell.vertices_at(&qi(2)).unwrap().len(), 4);
assert!(cell.at(&qi(100)).unwrap().contains(&[q(1, 4), q(3, 4)]));

Implementations

impl ParametricPolytope

pub fn new(hyps: &[Ex], vars: &[Ex], param: &Ex) -> Result<Self, SymplexError>

Build from hypotheses hₖ(j, x) ≥ 0, each affine in vars with coefficients polynomial (rational) in param.

Errors

SymplexError::InvalidArgument if a hypothesis is not a polynomial in the variables and the parameter, is not affine in the variables, or has a symbolic coefficient; or if the lists are empty.

pub fn vars(&self) -> &[Ex]

The variables, in order.

pub fn param(&self) -> &Ex

The parameter.

pub fn hyps(&self) -> &[Poly]

The hypotheses as polynomials in (vars…, param).

pub fn at(&self, value: &Q) -> Result<Polytope, SymplexError>

The polytope at param = value, exactly (no cache). Pure rational arithmetic on the stored polynomials — no expression arena is touched, so sampling a family densely is cheap.

Errors

Only internal failures (the substitution of a rational is always affine in the variables).

pub fn polytope_at(&mut self, value: &Q) -> Result<&Polytope, SymplexError>

The polytope at param = value, cached.

Errors

As at.

pub fn vertices_at(&mut self, value: &Q) -> Result<&[Vec<Q>], SymplexError>

The vertices at param = value, cached.

Errors

As at.

pub fn volume_at(&mut self, value: &Q) -> Result<Q, SymplexError>

The volume at param = value (uses the cached polytope).

Errors

As Polytope::volume.

pub fn is_empty_at(&mut self, value: &Q) -> Result<bool, SymplexError>

Is the polytope at param = value empty?

Errors

As Polytope::is_empty.

pub fn contains_at(&mut self, value: &Q, x: &[Q]) -> Result<bool, SymplexError>

Does the polytope at param = value contain x?

Errors

As at.

pub fn clear_cache(&mut self)

Forget every cached instantiation.

Trait Implementations

impl Clone for ParametricPolytope

fn clone(&self) -> Self

Returns a duplicate of the value.

fn clone_from(&mut self, source: &Self)

Performs copy-assignment from source.

impl Debug for ParametricPolytope

fn fmt(&self, f: &mut Formatter<'_>) -> Result

Formats the value using the given formatter.