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WIP: Improve the upper bound of TMs with range bounders #88

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WIP: Improve the upper bound of TMs with range bounders #88

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c339604
add aux function to select the bound to improve in the linear dominat…
Sep 5, 2020
3ead2b9
fix typos and add full signature to ldb
Sep 6, 2020
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20 changes: 19 additions & 1 deletion src/bounds.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -156,7 +156,7 @@ the bound of `fT` gets tighter than `ϵ` or the number of steps reachs `max_iter
The returned bound corresponds to the improved polynomial bound with the remainder
of the `TaylorModel1` included.
"""
function linear_dominated_bounder(fT::TaylorModel1{T, S}; ϵ=1e-3, max_iter=5) where {T, S}
function linear_dominated_bounder(fT::TaylorModel1{T, S}; ϵ::Float64=1e-3, max_iter::Int=5) where {T, S}
d = 1.
Dn = fT.dom
Dm = fT.x0
Expand Down Expand Up @@ -195,6 +195,24 @@ function linear_dominated_bounder(fT::TaylorModel1{T, S}; ϵ=1e-3, max_iter=5) w
return interval(bound.lo, hi) + fT.rem
end

function linear_dominated_bounder(fT::TaylorModel1{T, S}, bound::Symbol=:lower, max_iter::Int=5, tol::Float64=1e-5) where {T, S}
if bound == :upper
bound = -linear_dominated_bounder(-fT, ϵ=tol, max_iter=max_iter)
elseif bound == :lower
bound = linear_dominated_bounder(fT, ϵ=tol, max_iter=max_iter)
elseif bound == :both
ldb_bounds = Array{Interval{T}}(undef, 2)
aux = [-1, 1]
Threads.@threads for i in eachindex(aux)
@inbounds ldb_bounds[i] = aux[i] * linear_dominated_bounder(aux[i] * fT, ϵ=tol, max_iter=max_iter)
end
bound = ldb_bounds[1] ∩ ldb_bounds[2]
end

return bound
end


"""
linear_dominated_bounder(fT::TaylorModelN, ϵ=1e-3::Float64, max_iter=5::Int)

Expand Down