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distinguish between direct and iterative methods #81

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Jun 8, 2022
Merged

distinguish between direct and iterative methods #81

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15db596
updated types
lucaferranti Jun 7, 2022
5ec4e04
added abstract types to docs
lucaferranti Jun 7, 2022
69bccad
Update src/algorithms.jl
lucaferranti Jun 7, 2022
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2 changes: 2 additions & 0 deletions docs/src/lib/types.md
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Expand Up @@ -13,6 +13,8 @@ CurrentModule = RangeEnclosures

```@docs
AbstractEnclosureAlgorithm
AbstractDirectRangeAlgorithm
AbstractIterativeRangeAlgorithm
BranchAndBoundEnclosure
NaturalEnclosure
MooreSkelboeEnclosure
Expand Down
2 changes: 1 addition & 1 deletion src/RangeEnclosures.jl
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Expand Up @@ -27,6 +27,6 @@ include("enclose.jl")
export enclose, relative_precision,
NaturalEnclosure, MooreSkelboeEnclosure, SumOfSquaresEnclosure,
TaylorModelsEnclosure, BranchAndBoundEnclosure,
AbstractEnclosureAlgorithm
AbstractEnclosureAlgorithm, AbstractDirectRangeAlgorithm, AbstractIterativeRangeAlgorithm

end # module
36 changes: 26 additions & 10 deletions src/algorithms.jl
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Expand Up @@ -6,7 +6,23 @@ Abstract type for range enclosure algorithms.
abstract type AbstractEnclosureAlgorithm end

"""
NaturalEnclosure <: AbstractEnclosureAlgorithm
AbstractDirectRangeAlgorithm <: AbstractEnclosureAlgorithm

Abstract type for range enclosures algorithms that directly evaluate the functions over a
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given domain.
"""
abstract type AbstractDirectRangeAlgorithm <: AbstractEnclosureAlgorithm end

"""
AbstractIterativeRangeAlgorithm <: AbstractEnclosureAlgorithm

Abstract type for algorithms that iteratively bound the range of a function over a given
domain.
"""
abstract type AbstractIterativeRangeAlgorithm <: AbstractEnclosureAlgorithm end

"""
NaturalEnclosure <: AbstractDirectRangeAlgorithm

Data type to bound the range of `f` over `X` using natural enclosure, i.e., to
evaluate `f(X)` with interval arithmetic.
Expand All @@ -18,10 +34,10 @@ julia> enclose(x -> 1 - x^4 + x^5, 0..1, NaturalEnclosure())
[0, 2]
```
"""
struct NaturalEnclosure <: AbstractEnclosureAlgorithm end
struct NaturalEnclosure <: AbstractDirectRangeAlgorithm end

"""
MooreSkelboeEnclosure{T} <: AbstractEnclosureAlgorithm
MooreSkelboeEnclosure{T} <: AbstractIterativeRangeAlgorithm

Data type to bound the range of `f` over `X` using the Moore-Skelboe algorithm, which
rigorously computes the global minimum and maximum of the function.
Expand All @@ -48,13 +64,13 @@ julia> enclose(x -> 1 - x^4 + x^5, 0..1, MooreSkelboeEnclosure()) # default para
julia> enclose(x -> 1 - x^4 + x^5, 0..1, MooreSkelboeEnclosure(; tol=1e-2))
[0.900812, 1.0326]
"""
Base.@kwdef struct MooreSkelboeEnclosure{T} <: AbstractEnclosureAlgorithm
Base.@kwdef struct MooreSkelboeEnclosure{T} <: AbstractIterativeRangeAlgorithm
structure::T = HeapedVector
tol::Float64 = 1e-3
end

"""
TaylorModelsEnclosure <: AbstractEnclosureAlgorithm
TaylorModelsEnclosure <: AbstractDirectRangeAlgorithm

Data type to bound the range of `f` over `X` using Taylor models.
See [`TaylorModels.jl`](https://github.com/JuliaIntervals/TaylorModels.jl) for more details.
Expand All @@ -77,14 +93,14 @@ julia> enclose(x -> 1 - x^4 + x^5, 0..1, TaylorModelsEnclosure(; order=4))

```
"""
Base.@kwdef struct TaylorModelsEnclosure <: AbstractEnclosureAlgorithm
Base.@kwdef struct TaylorModelsEnclosure <: AbstractDirectRangeAlgorithm
order::Int = 10
normalize::Bool = true
end


"""
SumOfSquaresEnclosure{T} <: AbstractEnclosureAlgorithm
SumOfSquaresEnclosure{T} <: AbstractIterativeRangeAlgorithm

Data type to bound the range of `f` over `X` using sum-of-squares optimization.
See [`SumOfSquares.jl`](https://github.com/jump-dev/SumOfSquares.jl) for more details
Expand All @@ -110,13 +126,13 @@ julia> enclose(x -> -x^3/6 + 5x, 1..4, SumOfSquaresEnclosure(; backend=backend))
[4.8333, 10.541]
```
"""
Base.@kwdef struct SumOfSquaresEnclosure{T} <: AbstractEnclosureAlgorithm
Base.@kwdef struct SumOfSquaresEnclosure{T} <: AbstractIterativeRangeAlgorithm
backend::T
order::Int = 5
end

"""
BranchAndBoundEnclosure
BranchAndBoundEnclosure <: AbstractIterativeRangeAlgorithm

Data type to bound the range of `f` over `X` using the branch and bound algorithm.

Expand Down Expand Up @@ -144,7 +160,7 @@ julia> enclose(x -> -x^3/6 + 5x, 1..4, BranchAndBoundEnclosure())
julia> enclose(x -> -x^3/6 + 5x, 1..4, BranchAndBoundEnclosure(tol=1e-2); df=x->-x^2/2+5)
[4.83333, 10.5709]
"""
Base.@kwdef struct BranchAndBoundEnclosure <: AbstractEnclosureAlgorithm
Base.@kwdef struct BranchAndBoundEnclosure <: AbstractIterativeRangeAlgorithm
maxdepth = 10
tol = 1e-3
end