Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.ellipsoid

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/ellipsoid.clj1 definitions, 4 theorems

AHoF V36 Ellipsoid Propagation: over-approximate a reachable set by an ellipsoid; a point lies inside when its quadratic form (x-c)'P(x-c) is within the ellipsoid limit: in-ellipsoid? quadratic-value limit = decide (quadratic-value <= limit). Proved native and axiom-free (decision, two positive instances, at-most certificate, negative instance). Requires audit/decide-nnrat-at-most, nnrat/at-most, nnrat/decide-at-most-true-sound (all in the D63 checkpoint). Scope (measured by the kernel): this module has 4 worked instances (statements about specific values). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.ellipsoid` prints this classification.

ellipsoid/in-ellipsoid? :
  (x₁ x₂ : ℚ≥0)
  → data/Bool

ellipsoid/within-ellipsoid-inside :
  → ce-is/elite? 1/2 3/4 = data/true

ellipsoid/boundary-inside :
  → ce-is/elite? 1/2 1/2 = data/true

ellipsoid/ellipsoid-certificate :
  → 1/2 ≤ 3/4

ellipsoid/outside-ellipsoid :
  → ce-is/elite? 3/4 1/2 = data/false