| import OAI.Analysis.IrrationalRotation.Model.CircleParameters |
| import Mathlib.MeasureTheory.Measure.WithDensity |
|
|
| namespace OAI |
|
|
| noncomputable section |
| open MeasureTheory |
| open scoped BigOperators ENNReal |
|
|
| namespace Invariant233.CircleParameterData |
|
|
| def samplingDensity (p : CircleParameterData) (θ : ℝ) (j n : ℕ) |
| (endpoint : Bool) (x : Circle) : ℝ := |
| ∏ i ∈ p.block j, orientedKernel endpoint (p.m j) (p.coordinate i x) |
| (Int.fract ((n : ℝ) * p.alpha θ i)) |
|
|
| def samplingTranslation (θ : ℝ) (n : ℕ) (x : Circle) : Circle := |
| x + (((n : ℝ) * θ : ℝ) : Circle) |
|
|
| def samplingGraph (p : CircleParameterData) (θ : ℝ) (j n : ℕ) : |
| Measure (Circle × Circle) := |
| (circleMeasure.withDensity |
| (fun x => ENNReal.ofReal (p.samplingDensity θ j n false x))).map |
| (fun x => (x, samplingTranslation θ n x)) |
|
|
| def samplingGraphAverage (p : CircleParameterData) (θ : ℝ) (j r : ℕ) : |
| Measure (Circle × Circle) := |
| ENNReal.ofReal (1 / ((p.samples j r).card : ℝ)) • |
| ∑ n ∈ p.samples j r, p.samplingGraph θ j n |
|
|
| end Invariant233.CircleParameterData |
|
|
| end |
|
|
| end OAI |
|
|
