| import OAI.Combinatorics.EditApproximation.Geometry.RefinementRankCost |
|
|
| namespace OAI |
|
|
| /-! The charged request index distinguishes previous passes and coarse |
| leaves. For internal refinement its two index classes are exactly the |
| current and earlier table-read counters. -/ |
|
|
| namespace EditApproximation |
|
|
| def chargedSameWeight {M J ny passes copies T S : ℕ} |
| (parent child : ChargedPhysicalRequest M J ny passes copies T S) : ℕ := |
| if ¬ child.index < parent.index then 1 else 0 |
|
|
| def chargedEarlierWeight {M J ny passes copies T S : ℕ} |
| (parent child : ChargedPhysicalRequest M J ny passes copies T S) : ℕ := |
| if child.index < parent.index then 1 else 0 |
|
|
| theorem chargedSameWeight_table {M J ny passes copies T S : ℕ} |
| (parent : {r : PhysicalTableRequest M J ny // r.Bounded passes copies T S}) : |
| chargedSameWeight (Sum.inr parent) = chargedTableWeight 0 |
| (fun child => if ¬ child.rank T S < parent.val.rank T S then 1 else 0) := by |
| funext child |
| cases child <;> simp only [chargedSameWeight, ChargedPhysicalRequest.index, chargedTableWeight, |
| Nat.zero_lt_succ, not_true_eq_false, ite_false, Nat.add_lt_add_iff_right] |
|
|
| theorem chargedEarlierWeight_table {M J ny passes copies T S : ℕ} |
| (parent : {r : PhysicalTableRequest M J ny // r.Bounded passes copies T S}) : |
| chargedEarlierWeight (Sum.inr parent) = chargedTableWeight 1 |
| (fun child => if child.rank T S < parent.val.rank T S then 1 else 0) := by |
| funext child |
| cases child <;> simp only [chargedEarlierWeight, ChargedPhysicalRequest.index, chargedTableWeight, |
| Nat.zero_lt_succ, ite_true, Nat.add_lt_add_iff_right] |
|
|
| section Costs |
|
|
| variable {α : Type*} [DecidableEq α] {M J R : ℕ} [NeZero R] |
| (source target : List α) (N P F exponent H Q T S passes copies : ℕ) |
| (factor : ℕ → ℚ) (multiplier : ℕ → ℕ) (tau eta kappa delta : ℚ) |
| (group : ℕ → ℕ → PhysicalInternalNode M J → Fin R → CellGroupDraws M F Q) |
| (integer : ℕ → ℕ → PhysicalInternalNode M J → Fin R → ℕ → TargetInterval target.length → ℕ) |
| (initial : PhysicalEntry M J target.length → ℕ) |
| (parent : {r : PhysicalTableRequest M J target.length // r.Bounded passes copies T S}) |
| (hindex : T < parent.val.index) (hbelow : parent.val.node.1.val < J) |
| (hshort : ¬ (physicalSourceInterval source.length parent.val.node).hi - |
| (physicalSourceInterval source.length parent.val.node).lo ≤ 1) |
|
|
| include hindex hbelow hshort |
|
|
| theorem chargedGlobalQuery_current_cost : |
| (chargedGlobalQuery source target N P F exponent H Q T S passes copies factor multiplier |
| tau eta kappa delta group integer initial (Sum.inr parent)).cost |
| (fun child => chargedRequestValue source target N P F exponent H Q T S passes copies |
| factor multiplier tau eta kappa delta group integer initial child.val) |
| (fun child => chargedSameWeight (Sum.inr parent) child.val) = |
| (physicalRefinementDataRequestQuery source target N P F exponent H Q tau |
| (refinementFactor (factor parent.val.pass) F) eta kappa delta parent.val.pass parent.val.copy T S |
| (parent.val.index - T) (Nat.sub_pos_of_lt hindex) parent.val.node hbelow |
| (group parent.val.pass parent.val.copy ⟨parent.val.node, hbelow⟩ (Fin.ofNat R (parent.val.index - T - 1))) |
| (integer parent.val.pass parent.val.copy ⟨parent.val.node, hbelow⟩ (Fin.ofNat R (parent.val.index - T - 1))) |
| parent.val.state).cost |
| (fun child => localRequestValue source target N P F exponent H Q T S copies factor multiplier |
| tau eta kappa delta group integer initial child.val) |
| (fun child => physicalCurrentReadWeight (T + (parent.val.index - T)) child.val) := by |
| simp only [chargedSameWeight_table] |
| rw [chargedGlobalQuery_refinement_cost source target N P F exponent H Q T S passes copies |
| factor multiplier tau eta kappa delta group integer initial parent hindex hbelow hshort] |
| have hrank : (PhysicalTableRequest.refinement parent.val.pass parent.val.copy parent.val.node |
| T (parent.val.index - T) parent.val.state).rank T S = parent.val.rank T S := by |
| unfold PhysicalTableRequest.refinement PhysicalTableRequest.rank |
| dsimp only |
| congr 1 |
| omega |
| rw [← hrank] |
| exact physicalRefinementDataRequest_same_rank_cost source target N P F exponent H Q tau |
| (refinementFactor (factor parent.val.pass) F) eta kappa delta parent.val.pass parent.val.copy T S |
| (parent.val.index - T) (Nat.sub_pos_of_lt hindex) parent.val.node hbelow _ _ parent.val.state _ |
|
|
| theorem chargedGlobalQuery_earlier_cost : |
| (chargedGlobalQuery source target N P F exponent H Q T S passes copies factor multiplier |
| tau eta kappa delta group integer initial (Sum.inr parent)).cost |
| (fun child => chargedRequestValue source target N P F exponent H Q T S passes copies |
| factor multiplier tau eta kappa delta group integer initial child.val) |
| (fun child => chargedEarlierWeight (Sum.inr parent) child.val) = |
| (physicalRefinementDataRequestQuery source target N P F exponent H Q tau |
| (refinementFactor (factor parent.val.pass) F) eta kappa delta parent.val.pass parent.val.copy T S |
| (parent.val.index - T) (Nat.sub_pos_of_lt hindex) parent.val.node hbelow |
| (group parent.val.pass parent.val.copy ⟨parent.val.node, hbelow⟩ (Fin.ofNat R (parent.val.index - T - 1))) |
| (integer parent.val.pass parent.val.copy ⟨parent.val.node, hbelow⟩ (Fin.ofNat R (parent.val.index - T - 1))) |
| parent.val.state).cost |
| (fun child => localRequestValue source target N P F exponent H Q T S copies factor multiplier |
| tau eta kappa delta group integer initial child.val) |
| (fun child => physicalEarlierReadWeight (T + (parent.val.index - T)) child.val) := by |
| simp only [chargedEarlierWeight_table] |
| rw [chargedGlobalQuery_refinement_cost source target N P F exponent H Q T S passes copies |
| factor multiplier tau eta kappa delta group integer initial parent hindex hbelow hshort] |
| have hrank : (PhysicalTableRequest.refinement parent.val.pass parent.val.copy parent.val.node |
| T (parent.val.index - T) parent.val.state).rank T S = parent.val.rank T S := by |
| unfold PhysicalTableRequest.refinement PhysicalTableRequest.rank |
| dsimp only |
| congr 1 |
| omega |
| rw [← hrank] |
| exact physicalRefinementDataRequest_earlier_rank_cost source target N P F exponent H Q tau |
| (refinementFactor (factor parent.val.pass) F) eta kappa delta parent.val.pass parent.val.copy T S |
| (parent.val.index - T) (Nat.sub_pos_of_lt hindex) parent.val.node hbelow _ _ parent.val.state _ |
|
|
| end Costs |
|
|
| end EditApproximation |
|
|
| end OAI |
|
|
