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97c3405 | 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 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | import OAI.Combinatorics.ContingencyTables.Machines.CachedTerminalCount
import OAI.Combinatorics.ContingencyTables.Sampling.ProfileTransitionCountSemantics
import OAI.Combinatorics.ContingencyTables.Transport.IntegerPushTransport
import OAI.Combinatorics.ContingencyTables.Transport.ListedOutputSemantics
namespace OAI
/-! # Cached terminal success counts equal the actual completion law -/
namespace ContingencyTables.SmallGraphProfiles
open ProfilePrograms DensePrograms PhysicalCompletionFibres FirstPaperPhysicalMarginal
open SmallContextCoordinates CompletionCounts CompletionTranslation
open scoped BigOperators Classical
noncomputable section
variable {m n q : ℕ} (r : Fin m → ℕ) (c : Fin n → ℕ)
variable (e : Fin q ≃ Cells (paperSmall r c))
variable (hr : 0<(largeIndices ((dimensionAllowance (I := Fin m) (J := Fin n))^20,List.ofFn r)).length)
variable (hc : 0<(largeIndices ((dimensionAllowance (I := Fin m) (J := Fin n))^20,List.ofFn c)).length)
variable (b h : ℕ) (hb : Nat.clog 2 (stateBound r c+2)≤b)
local notation "d" => dimensionAllowance (I := Fin m) (J := Fin n)
local notation "R" => listedRows r c (d^20) (d^12) (stateCapacity r c) hr
local notation "P" => listedColumns r c (d^20) (d^12) (stateCapacity r c) hc
local notation "f" => 25*(d+b+h+1)^62
attribute [local irreducible] canonicalCounts listedCompletionCounts listedUnpaddedCounts
listedCompletionFactor stateCode stateCodeData completionWeights prepareTransitionCache
terminalCount listedRows listedColumns
lemma tableCode_option_eq (o : Option (Table r c)) (T : Table r c) :
o.map (fun X => matrixCode X.val)=some (matrixCode T.val) ↔ o=some T := by
cases o with
| none => simp
| some X =>
simp only [Option.map_some,Option.some.injEq]
constructor
· intro he
exact Subtype.ext (matrixCode_injective he)
· rintro rfl
rfl
def listedTerminalDecision (x : PaperStates r c) (A : Table (R x) (P x)) :
Option (Table r c) := stateTrial r c ⟨x,(paperListedEquiv r c hr hc x).symm A⟩
attribute [local irreducible] listedTerminalDecision
lemma terminal_completion_sum (x : PaperStates r c) (T : Table r c) :
((listedCompletionCounts r c hr hc b h hb x).push
(fun A => stateTrial r c ⟨x,A⟩)).count (some T)=
∑ A : Table (R x) (P x),if listedTerminalDecision r c hr hc x A=some T
then (listedUnpaddedCounts r c hr hc h x).count A*
listedCompletionFactor r c hr hc b h x else 0 := by
have he := IntegerLaw.push_equiv_count
(listedCompletionCounts r c hr hc b h hb x) (listedUnpaddedCounts r c hr hc h x)
(paperListedEquiv r c hr hc x) (listedCompletionFactor r c hr hc b h x)
(listedTerminalDecision r c hr hc x)
(listedCompletionCounts_count r c hr hc b h hb x) (some T)
simpa only [listedTerminalDecision,Equiv.symm_apply_apply] using he
lemma terminal_cache_sum (x : PaperStates r c) (T : Table r c) :
((completionWeights ((marginCode (R x),marginCode (P x)),(d,h))).map
(fun entry => entry.1.elim 0 (fun X =>
if outerTrial ((stateCodeData r c e x,d^12),X)=some (matrixCode T.val)
then entry.2 else 0))).sum=
∑ A : Table (R x) (P x),if listedTerminalDecision r c hr hc x A=some T
then (listedUnpaddedCounts r c hr hc h x).count A else 0 := by
let w : MatrixCode → ℕ := fun X =>
if outerTrial ((stateCodeData r c e x,d^12),X)=some (matrixCode T.val) then 1 else 0
have he : ((completionWeights ((marginCode (R x),marginCode (P x)),(d,h))).map
(fun entry => entry.1.elim 0 (fun X =>
if outerTrial ((stateCodeData r c e x,d^12),X)=some (matrixCode T.val)
then entry.2 else 0))).sum=
((completionWeights ((marginCode (R x),marginCode (P x)),(d,h))).map
(fun entry => entry.1.elim 0 (fun X => entry.2*w X))).sum := by
congr 1
apply List.map_congr_left
rintro ⟨o,n⟩ _
cases o with
| none => rfl
| some X => simp only [Option.elim_some,w]; split_ifs <;> simp
rw [he,sum_completionWeights (R x) (P x) (listed_dimension_fourteen r c hr hc)
(by simpa only [Fintype.card_prod,Fintype.card_fin] using (listed_dimensions r c hr hc).2.2)
(listed_row_padding r c (d^20) (d^12) (stateCapacity r c) hr hc x)
(listed_column_padding r c (d^20) (d^12) (stateCapacity r c) hr hc x)
(listed_paper_totals r c hr hc x) h w]
apply Finset.sum_congr rfl
intro A _
have ho := actualOuterTrial r c e hr hc x ((paperListedEquiv r c hr hc x).symm A)
rw [Equiv.apply_symm_apply] at ho
simp only [w,ho,tableCode_option_eq]
unfold listedTerminalDecision listedUnpaddedCounts
split_ifs <;> simp
lemma terminalCount_actual (x : PaperStates r c) (T : Table r c) :
terminalCount (prepareTransitionCache
((((stateCodeData r c e x,d^12),(d,h)),f)),matrixCode T.val)=
((listedCompletionCounts r c hr hc b h hb x).push
(fun A => stateTrial r c ⟨x,A⟩)).count (some T) := by
rw [prepareTransitionCache_encoded r c e hr hc,terminalCount_eq,
terminal_cache_sum r c e hr hc h x T,terminal_completion_sum r c hr hc b h hb x T,
Finset.mul_sum]
apply Finset.sum_congr rfl
intro A _
unfold listedCompletionFactor
split_ifs
· exact Nat.mul_comm _ _
· exact Nat.mul_zero _
end
end ContingencyTables.SmallGraphProfiles
end OAI
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