File size: 2,959 Bytes
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 | import OAI.Combinatorics.ContingencyTables.Dense.DenseNormalizeSemantics
import OAI.Combinatorics.ContingencyTables.Sampling.GreedyTableComplexity
namespace OAI
/-! # Dense sampling from margins with a computed grid and fallback -/
namespace ContingencyTables.DensePrograms
open MatchingFPRAS.TreeTyped ProfilePrograms
abbrev CanonicalParameters := (List ℕ×List ℕ)×(ℕ×ℕ)
abbrev CanonicalDrawData := CanonicalParameters×List Bool
def zeroGrid (z : List ℕ×List ℕ) : List ℕ :=
(cellPairs (z.1.tail,z.2.tail)).map (fun _ => 0)
def zeroGridRealizer : Realizer zeroGrid :=
composition (composition (pair (composition first tail) (composition second tail))
cellPairsRealizer) (map (constant 0))
theorem polynomial_zeroGrid : PolynomialTime zeroGridRealizer :=
polynomial_composition (polynomial_composition
(polynomial_pair (polynomial_composition polynomial_first polynomial_tail)
(polynomial_composition polynomial_second polynomial_tail)) polynomial_cellPairs)
(polynomial_map (polynomial_constant 0))
def canonicalInput (z : CanonicalDrawData) : DenseDrawData :=
(((((z.1.1,zeroGrid z.1.1),z.1.2.1),z.1.2.2),
GreedyFeasibleTable.listMatrix z.1.1.1 z.1.1.2),z.2)
def canonicalInputRealizer : Realizer canonicalInput := by
let margins : Realizer (fun z : CanonicalDrawData => z.1.1) := composition first first
let parameters : Realizer (fun z : CanonicalDrawData => z.1.2) := composition first second
let grid := composition margins zeroGridRealizer
let fallback := composition margins GreedyFeasibleTable.tableRealizer
exact pair (pair (pair (pair (pair margins grid) (composition parameters first))
(composition parameters second)) fallback) second
theorem polynomial_canonicalInput : PolynomialTime canonicalInputRealizer := by
have hm : PolynomialTime (composition
(first (A := CanonicalParameters) (B := List Bool)) first) :=
polynomial_composition polynomial_first polynomial_first
have hp : PolynomialTime (composition
(first (A := CanonicalParameters) (B := List Bool)) second) :=
polynomial_composition polynomial_first polynomial_second
unfold canonicalInputRealizer
exact polynomial_pair (polynomial_pair (polynomial_pair
(polynomial_pair (polynomial_pair hm (polynomial_composition hm polynomial_zeroGrid))
(polynomial_composition hp polynomial_first))
(polynomial_composition hp polynomial_second))
(polynomial_composition hm GreedyFeasibleTable.polynomial_table)) polynomial_second
def canonicalDenseDraw (z : CanonicalDrawData) : MatrixCode :=
normalizedDenseCode (canonicalInput z)
def canonicalDenseDrawRealizer : Realizer canonicalDenseDraw :=
composition canonicalInputRealizer normalizedDenseCodeRealizer
theorem polynomial_canonicalDenseDraw : PolynomialTime canonicalDenseDrawRealizer :=
polynomial_composition polynomial_canonicalInput polynomial_normalizedDenseCode
end ContingencyTables.DensePrograms
end OAI
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