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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 | import OAI.Combinatorics.ContingencyTables.Dense.DenseScaleMatrixProgram
namespace OAI
/-! # Computing the dense exponent directly from a binary grid matrix -/
namespace ContingencyTables.DensePrograms
open MatchingFPRAS.TreeTyped GridBoundary
def scaledData (z : ExponentData) : ExponentData := ((z.1.1,scaleMatrix z),z.2)
def scaledDataRealizer : Realizer scaledData :=
pair (pair (composition first first) scaleMatrixRealizer) second
theorem polynomial_scaledData : PolynomialTime scaledDataRealizer :=
polynomial_pair (polynomial_pair (polynomial_composition polynomial_first polynomial_first)
polynomial_scaleMatrix) polynomial_second
def gridExponent (z : ExponentData) : ℕ := fullExponent (scaledData z)
def gridExponentRealizer : Realizer gridExponent :=
composition scaledDataRealizer fullExponentRealizer
theorem polynomial_gridExponent : PolynomialTime gridExponentRealizer :=
polynomial_composition polynomial_scaledData polynomial_fullExponent
theorem gridExponent_code {m n q K : ℕ} (R : Option (Fin m) → ℕ)
(P : Option (Fin n) → ℕ) (d : ℕ) (a : Grid (I := Fin q) K)
(e : Fin m×Fin n ≃ Fin q) :
gridExponent (exponentDataCode R P d (fun i j => (corner a (e (i,j))).toNat))=
denseExponent R P d e a := by
unfold gridExponent scaledData
rw [scaleMatrix_code]
exact fullExponent_code R P d e a
end ContingencyTables.DensePrograms
end OAI
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