File size: 3,092 Bytes
cdec422 | 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 | import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.Regrouping
namespace OAI
/-! Finite extraction histories, inherited masks and recovery bounds. -/
noncomputable section
namespace MatrixMultiplication.AllFieldHistoryTickCarry
open MatrixMultiplication.Foundation AllFieldHistory AllFieldFiniteFamily
open AllFieldHistoryRegrouping
open scoped Classical
attribute [local instance] Classical.propDecidable Classical.decEq
section Distribution
variable {F : Type*} [Field F]
def distributeProduct
{X Y Z U V W : Type}
[Fintype X] [Fintype Y] [Fintype Z]
[Fintype U] [Fintype V] [Fintype W]
(active : Tensor F X Y Z) (carried : Tensor F U V W)
(J : Type) [Fintype J] :
LocalMap (Tensor.product (Tensor.directSum (fun _ : J => active)) carried)
(Tensor.directSum (fun _ : J => Tensor.product active carried)) where
x := fun x s => if s = ((x.1, x.2.1), x.2.2) then 1 else 0
y := fun y s => if s = ((y.1, y.2.1), y.2.2) then 1 else 0
z := fun z s => if s = ((z.1, z.2.1), z.2.2) then 1 else 0
coefficient := by
rw [← Tensor.pullback_eq_restrict]
funext x y z
simp [Tensor.pullback, Tensor.directSum, Tensor.product, ite_mul]
end Distribution
variable {K tick : ℕ} (allocation : Allocation) (m : ℕ)
(F : Type*) [Field F] (ε : ℝ) {J : Type} [Fintype J]
def liftExecution
(E : Execution
(activeTensor (K := K) (tick := tick) allocation m F ε)
(Tensor.directSum (fun _ : J =>
producedTensor (K := K) (tick := tick) allocation m F ε))) :
Execution (stateTensor F (K := K) allocation m ε tick)
(Tensor.directSum (fun _ : J =>
stateTensor F (K := K) allocation m ε (tick + 1))) where
Copies := E.Copies
copies_positive := E.copies_positive
map :=
((activeCarriedMap (K := K) (tick := tick) allocation m F ε).parallelCopies E.Copies).comp
((LocalMap.replicationProduct
(activeTensor (K := K) (tick := tick) allocation m F ε)
(carriedTensor (K := K) (tick := tick) allocation m F ε) E.Copies).comp
((E.map.product
(LocalMap.identity (carriedTensor (K := K) (tick := tick) allocation m F ε))).comp
((distributeProduct
(producedTensor (K := K) (tick := tick) allocation m F ε)
(carriedTensor (K := K) (tick := tick) allocation m F ε) J).comp
((nextMap (K := K) (tick := tick) allocation m F ε).parallelCopies J))))
@[simp] theorem liftExecution_copies
(E : Execution
(activeTensor (K := K) (tick := tick) allocation m F ε)
(Tensor.directSum (fun _ : J =>
producedTensor (K := K) (tick := tick) allocation m F ε))) :
(liftExecution allocation m F ε E).Copies = E.Copies := rfl
@[simp] theorem liftExecution_card_copies
(E : Execution
(activeTensor (K := K) (tick := tick) allocation m F ε)
(Tensor.directSum (fun _ : J =>
producedTensor (K := K) (tick := tick) allocation m F ε))) :
Fintype.card (liftExecution allocation m F ε E).Copies = Fintype.card E.Copies := rfl
end MatrixMultiplication.AllFieldHistoryTickCarry
end
end OAI
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