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d5b7741 | 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 55 | import OAI.Combinatorics.ContingencyTables.Sampling.AllSmallFibres
namespace OAI
/-! # Reading the unique all-small completion directly from its profile -/
namespace ContingencyTables.SmallGraphProfiles
open scoped BigOperators Classical
open CompletionCounts PhysicalCompletionFibres PaddedCompletions
universe u
variable {I J : Type u} [Fintype I] [Fintype J] [LinearOrder I] [LinearOrder J]
variable (r : I → ℕ) (c : J → ℕ)
/-- The output data consists only of the two stored small views. Existence
of a completion supplies the erased proof that these are valid margins. -/
noncomputable def allSmallFibre
(hsmall : ∀ i j,FirstPaperPhysicalMarginal.paperSmall r c i j=true)
(z : PaperStates r c) : PaperFibre r c z := by
let p := SmallContextFibres.naturalProfile z.val.val
let views := (fun i j => p (⟨(i,j),hsmall i j⟩,false),
fun i j => stateCapacity r c i j-p (⟨(i,j),hsmall i j⟩,true))
have hv : ∃ h, (⟨views,h⟩ : RowColumnPair
(fun i => r i+PaddedCompletions.rowLargeCount (FirstPaperPhysicalMarginal.paperSmall r c) i*
((dimensionAllowance (I := I) (J := J))^12))
(fun j => c j+PaddedCompletions.columnLargeCount (FirstPaperPhysicalMarginal.paperSmall r c) j*
((dimensionAllowance (I := I) (J := J))^12))).val=views := by
obtain ⟨Z⟩ := (inferInstance : Nonempty (PaperFibre r c z))
have he : views=Z.val.val := by
apply Prod.ext
· funext i j
exact (Z.property.2.2.1 i j (hsmall i j)).1.symm
· funext i j
exact (Z.property.2.2.1 i j (hsmall i j)).2.symm
exact ⟨by rw [he]; exact Z.val.property,rfl⟩
let pair := (⟨views,hv.choose⟩ : RowColumnPair
(fun i => r i+PaddedCompletions.rowLargeCount (FirstPaperPhysicalMarginal.paperSmall r c) i*
((dimensionAllowance (I := I) (J := J))^12))
(fun j => c j+PaddedCompletions.columnLargeCount (FirstPaperPhysicalMarginal.paperSmall r c) j*
((dimensionAllowance (I := I) (J := J))^12)))
refine ⟨pair,?_⟩
obtain ⟨Z⟩ := (inferInstance : Nonempty (PaperFibre r c z))
have he : pair=Z.val := by
apply Subtype.ext
apply Prod.ext
· funext i j
exact (Z.property.2.2.1 i j (hsmall i j)).1.symm
· funext i j
exact (Z.property.2.2.1 i j (hsmall i j)).2.symm
exact he.symm ▸ Z.property
end ContingencyTables.SmallGraphProfiles
end OAI
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