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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 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 | import OAI.Analysis.IrrationalRotation.Model.CircleDigitCoupling
import OAI.Analysis.IrrationalRotation.Model.CircleParameters
import OAI.Analysis.IrrationalRotation.Model.MixedRadixCircle
import Mathlib.Probability.ProductMeasure
namespace OAI
noncomputable section
open MeasureTheory ProbabilityTheory
namespace Invariant233.CircleCoupling
open CircleDigitCoupling CircleParameterData OneCoordinateCoupling
abbrev Sample := ℕ → CoordinateSample
def initialLaw : Measure CoordinateSample :=
baseLaw.map (fun x => (none, (x, x)))
def tag (j s : ℕ) : ℝ := if s = j then 1 else 0
def coordinateLaw (p : CircleParameterData) (j i : ℕ) : Measure CoordinateSample :=
if i = 0 then initialLaw else
rawLaw (kappa (p.blockIndex i)) (p.m (p.blockIndex i))
(p.a (p.blockIndex i)) (p.b (p.blockIndex i)) (tag j (p.blockIndex i))
def law (p : CircleParameterData) (j : ℕ) : Measure Sample :=
Measure.infinitePi (coordinateLaw p j)
def observedDigit (p : CircleParameterData) (hr : ∀ i, 0 < MixedRadix.radices p.q i)
(side : Bool) (i : ℕ) (z : CoordinateSample) : Fin (MixedRadix.radices p.q i) := by
letI : NeZero (MixedRadix.radices p.q i) := ⟨Nat.ne_of_gt (hr i)⟩
exact UniformQuantization.quantize (MixedRadix.radices p.q i) (endpoint side z)
def digits (p : CircleParameterData) (hr : ∀ i, 0 < MixedRadix.radices p.q i)
(side : Bool) (ω : Sample) : MixedRadix.Digits (MixedRadix.radices p.q) :=
fun i => observedDigit p hr side i (ω i)
def point (p : CircleParameterData) (hr : ∀ i, 0 < MixedRadix.radices p.q i)
(side : Bool) (ω : Sample) : Circle := MixedRadix.circleValue (digits p hr side ω)
def label (i : ℕ) (ω : Sample) : Label := (ω i).1
def posterior (p : CircleParameterData) (j : ℕ) (side : Bool) (i : ℕ) :
Kernel (Fin (MixedRadix.radices p.q i)) Label :=
if i = 0 then Kernel.const _ (Measure.dirac none) else
labelsGivenDigit side (MixedRadix.radices p.q i) (kappa (p.blockIndex i))
(p.m (p.blockIndex i)) (p.a (p.blockIndex i)) (p.b (p.blockIndex i))
(tag j (p.blockIndex i))
end Invariant233.CircleCoupling
end
end OAI
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