File size: 6,584 Bytes
e63eb7f | 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 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 | 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
|