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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 | import OAI.Combinatorics.ContingencyTables.Dense.DenseMatrixLayoutProgram
namespace OAI
/-! # Evaluating the dense exponent on the flat coordinate encoding -/
namespace ContingencyTables.DensePrograms
open MatchingFPRAS.TreeTyped GridBoundary
abbrev FlatExponentData := GridFlatData×ℕ
def flatToGridData (z : FlatExponentData) : ExponentData :=
((z.1.1,unflattenGrid z.1),z.2)
def flatToGridDataRealizer : Realizer flatToGridData :=
pair (pair (composition first first) (composition first unflattenGridRealizer)) second
theorem polynomial_flatToGridData : PolynomialTime flatToGridDataRealizer :=
polynomial_pair (polynomial_pair (polynomial_composition polynomial_first polynomial_first)
(polynomial_composition polynomial_first polynomial_unflattenGrid)) polynomial_second
def flatExponent (z : FlatExponentData) : ℕ := gridExponent (flatToGridData z)
def flatExponentRealizer : Realizer flatExponent := composition flatToGridDataRealizer gridExponentRealizer
theorem polynomial_flatExponent : PolynomialTime flatExponentRealizer :=
polynomial_composition polynomial_flatToGridData polynomial_gridExponent
theorem flatExponent_code {m n K : ℕ} (R : Option (Fin m) → ℕ)
(P : Option (Fin n) → ℕ) (d : ℕ) (a : Grid (I := Fin (m*n)) K) :
flatExponent (((marginCode R,marginCode P),gridNatCode a),d)=
denseExponent R P d finProdFinEquiv a := by
unfold flatExponent flatToGridData gridNatCode
rw [unflattenGrid_code]
exact gridExponent_code R P d a finProdFinEquiv
end ContingencyTables.DensePrograms
end OAI
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