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135052a | 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 | import Mathlib
import OAI.Probability.SKBarriers.Locking.NarrowTimeBlocks
import OAI.Probability.SKBarriers.Locking.NarrowBlockPenalty
import OAI.Probability.SKBarriers.Scalar.NegativePenalty
import OAI.Probability.SKBarriers.Locking.FourBlockTent
namespace OAI
section
noncomputable section
open scoped BigOperators
open Set
namespace SK.Analytic
theorem rawVariance_pos_length {l : List (ℝ × ℝ)} (h : 0<rawVariance l) : 0<l.length := by
cases l with
| nil => simp [rawVariance] at h
| cons p l => simp
namespace NarrowTimeBlocks
variable {α : ℝ → ℝ} {r h q : ℝ} (C : NarrowTimeBlocks α r h q)
theorem v_absCross (hh : 0<h) {θ : ℝ} (hθ : 0≤θ) : weightedAbsCross (C.v θ)=θ := by
simp only [v,weightedAbsCross_append,weightedAbsCross_zeroWeight,constantWeightChain_absCross,C.j_variance,add_zero]
rw [abs_of_nonneg (div_nonneg hθ hh.le)]
field_simp
theorem v_mean_bounds (hα : Monotone α) (hh : 0<h) {θ : ℝ} (hθ : 0≤θ) :
weightedMean (C.v θ)∈Icc (θ*α r) (θ*α (r+h)) := by
have HA := rawArea_bounds C.j (C.right.raw_mass_interval hα)
rw [C.j_variance] at HA
rw [C.v_mean]
have hl := mul_le_mul_of_nonneg_left HA.1 (div_nonneg hθ hh.le)
have hu := mul_le_mul_of_nonneg_left HA.2 (div_nonneg hθ hh.le)
constructor
· convert hl using 1; field_simp
· convert hu using 1; field_simp
theorem scaled_cw (β a : ℝ) :
scaleIncrementChain β (C.c a)++scaleIncrementChain β (C.w a)=
fourBlockTent (a/h) (scaleIncrementChain β C.b) (scaleIncrementChain β C.l)
(scaleIncrementChain β C.j) (scaleIncrementChain β C.k) := by
simp only [c,w,fourBlockTent,scaleIncrementChain_append,zeroWeightChain_scale,constantWeightChain_scale,neg_div]
end NarrowTimeBlocks
end SK.Analytic
end
end
end OAI
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