| import OAI.Analysis.IrrationalRotation.Model.CharacterLaw | |
| import OAI.Analysis.IrrationalRotation.Model.ScalarSampling | |
| import Mathlib.MeasureTheory.Integral.IntervalIntegral.Periodic | |
| namespace OAI | |
| noncomputable section | |
| open scoped BigOperators | |
| namespace Invariant233.CharacterSampling | |
| def representative (x : UnitAddCircle) : ℝ := | |
| (AddCircle.equivIco (1 : ℝ) 0 x : ℝ) | |
| def kernel (endpoint : Bool) (m : ℕ) (z v : ℝ) : ℝ := | |
| if endpoint then ScalarSampling.manuscriptEndpointKernel m z v | |
| else ScalarSampling.manuscriptKernel m z v | |
| def average (m : ℕ) (powers : Finset ℕ) (endpoint : Bool) | |
| (phase : Fin m → ℝ) (spatial : UnitAddTorus (Fin m)) : ℝ := | |
| (powers.card : ℝ)⁻¹ * ∑ n ∈ powers, ∏ i : Fin m, | |
| kernel endpoint m (representative (spatial i)) ((n : ℝ) * phase i) | |
| def squaredError (m : ℕ) (powers : Finset ℕ) (endpoint : Bool) | |
| (p : (Fin m → ℝ) × UnitAddTorus (Fin m)) : ℝ := | |
| (average m powers endpoint p.1 p.2 - 1) ^ 2 | |
| end Invariant233.CharacterSampling | |
| end | |
| end OAI | |