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9eeb9c7 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 | 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
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