openAI-math-dataset / lean /OAI /Analysis /IrrationalRotation /Model /ContinuousConstruction.lean
roseking's picture
Add lean source and binary files (part 19)
9eeb9c7 verified
Raw History Blame Contribute Delete
968 Bytes
import OAI.Analysis.IrrationalRotation.Model.BackgroundData
import OAI.Analysis.IrrationalRotation.Model.ParameterSmoothing
namespace OAI
noncomputable section
namespace Invariant233.CircleParameterData
def rawCost (p : CircleParameterData) (θ : ℝ) (x : Circle) : ℝ :=
∑' n : ℕ, p.rawBlock θ (n + 1) x
def continuousCost (p : CircleParameterData) (θ : ℝ) (d : BackgroundBumpData θ)
(x : Circle) : ℝ :=
backgroundCost d x + ∑' n : ℕ, p.relocatedBlock θ (n + 1) x
def continuousTransfer (p : CircleParameterData) (θ : ℝ) (d : BackgroundBumpData θ)
(x : Circle) : ℝ :=
backgroundTransferSum d x - ∑' n : ℕ,
(p.smoothBlockTransfer θ (n + 1) x + p.relocatedBlockTransfer θ (n + 1) x)
def continuousWeight (p : CircleParameterData) (θ : ℝ) (d : BackgroundBumpData θ) :
Circle → ℝ :=
Function.update (fun x => Real.exp (-p.continuousCost θ d x)) 0 0
end Invariant233.CircleParameterData
end
end OAI