File size: 3,142 Bytes
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 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 | import OAI.Combinatorics.ContingencyTables.Sampling.ExactBranchChoice
import OAI.Combinatorics.ContingencyTables.Sampling.AllSamplingAccuracy
namespace OAI
/-! # The finite ordinary branch of the exact sampler -/
namespace ContingencyTables.ProfilePrograms
open MatchingFPRAS MatchingFPRAS.TreeTyped MatchingFPRAS.PhysicalStream DensePrograms Polynomial
def exactOrdinaryWord (z : CompletionMargins×List Bool) : MatrixCode :=
samplingMatrixAll (exactSamplingParameters z.1,z.2)
def exactOrdinaryWordRealizer : Realizer exactOrdinaryWord :=
composition (f := fun z : CompletionMargins×List Bool => (exactSamplingParameters z.1,z.2))
(g := samplingMatrixAll)
(pair (composition (f := Prod.fst) (g := exactSamplingParameters)
first exactSamplingParametersRealizer) second) samplingMatrixAllRealizer
lemma polynomial_exactOrdinaryWord : PolynomialTime exactOrdinaryWordRealizer :=
polynomial_composition (polynomial_pair
(polynomial_composition polynomial_first polynomial_exactSamplingParameters) polynomial_second)
polynomial_samplingMatrixAll
def exactOrdinary (z : CompletionMargins) : Experiment MatrixCode :=
FiniteWordExecution.experiment exactOrdinaryBits exactOrdinaryWord z
noncomputable def exactOrdinaryRealizer : OnlineTree.Realizer exactOrdinary :=
FiniteWordExecution.realizer exactOrdinaryBitsRealizer exactOrdinaryWordRealizer
lemma work_exactOrdinary : OnlineTree.WorkBound exactOrdinaryRealizer
(FiniteWordExecution.wordMeasure exactOrdinaryBits) :=
FiniteWordExecution.work_realizer polynomial_exactOrdinaryBits polynomial_exactOrdinaryWord
/-- The gate retains the margins for either branch. -/
def exactGate (z : CompletionMargins) : Experiment (Bool×CompletionMargins) :=
(rareBranch z).map (fun rare => (rare,z))
noncomputable def exactGateRealizer : OnlineTree.Realizer exactGate :=
(OnlineTree.pair rareBranchRealizer (OnlineTree.deterministic identity)).congr
(by intro z g; simp only [Experiment.mean_bind,Experiment.mean,Experiment.mean_map,exactGate,id_eq])
lemma work_exactGate : OnlineTree.WorkBound exactGateRealizer exactParameterMeasure := by
unfold exactGateRealizer
apply OnlineTree.work_congr
apply OnlineTree.work_pair work_rareBranch
(OnlineTree.work_of_polynomial (OnlineTree.polynomial_deterministic polynomial_identity) X
(by intro z; simp only [eval_X,exactParameterMeasure]; omega)) X
intro z
simp only [eval_X,exactParameterMeasure]
omega
end ContingencyTables.ProfilePrograms
namespace ContingencyTables.SmallGraphProfiles
open ProfilePrograms DensePrograms MatchingFPRAS.PhysicalStream
open scoped BigOperators
variable {m n : ℕ} (r : Fin m → ℕ) (c : Fin n → ℕ)
lemma exactOrdinaryWord_code (htotal : (∑ i,r i)=∑ j,c j)
(bits : Fin (finiteSamplerBits r c (2*correctionPrecision r c)) → Bool) :
exactOrdinaryWord ((List.ofFn r,List.ofFn c),List.ofFn bits)=
matrixCode (scheduledTableDraw r c htotal (2*correctionPrecision r c) bits).val := by
rw [exactOrdinaryWord,exactSamplingParameters_ofFn,samplingMatrixAll_code r c htotal]
end ContingencyTables.SmallGraphProfiles
end OAI
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