Reference · The Applied Higher-Order Functions catalogue

rainbow.algorithms.proofs.ahof.dfp

The Applied Higher-Order Functions cataloguesrc/rainbow/algorithms/proofs/ahof/dfp.clj3 definitions, 3 theorems

AHoF O28 DFP (Davidon-Fletcher-Powell): a quasi-Newton method whose curvature update uses the step vector s = x_{k+1} - x_k: step-vector x-new x-old = x-new - x-old. Worked: 3-1=2. Values proved by signed cross-product equivalence. Proved native and axiom-free. Requires signed/subtract, signed/from-nnrat, signed/equivalent (all in the D63 checkpoint). Scope (measured by the kernel): this module has 2 worked instances (statements about specific values) and 1 definitional unfoldings (true by unfolding a definition). None of its theorems is a guarantee about the algorithm for all inputs; `lein verify rainbow.algorithms.proofs.ahof.dfp` prints this classification.

dfp/step-vector :
  (x₁ x₂ : ℚ)
  → ℚ

dfp/step-example :
  → ℚ

dfp/no-step :
  → ℚ

dfp/step-vector-unfold :
  (a b : ℚ)
  → dfp/step-vector a b = a - b

dfp/step-example-is-2 :
  → dfp/step-example = signed/from-nnrat 2

dfp/no-step-is-0 :
  → dfp/no-step = signed/from-nnrat 0