| import OAI.LinearAlgebra.MatrixMultiplication.FieldHistory.Regrouping |
|
|
| namespace OAI |
|
|
| /-! Finite extraction histories, inherited masks and recovery bounds. -/ |
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|
| noncomputable section |
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|
| namespace MatrixMultiplication.AllFieldHistoryTickCarry |
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|
| open MatrixMultiplication.Foundation AllFieldHistory AllFieldFiniteFamily |
| open AllFieldHistoryRegrouping |
| open scoped Classical |
| attribute [local instance] Classical.propDecidable Classical.decEq |
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|
| section Distribution |
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|
| 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 |
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|
| end MatrixMultiplication.AllFieldHistoryTickCarry |
|
|
| end |
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| end OAI |
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|
