add mean value form

docs/src/lib/types.md

@@ -17,6 +17,7 @@ AbstractDirectRangeAlgorithm
 AbstractIterativeRangeAlgorithm
 BranchAndBoundEnclosure
 NaturalEnclosure
+MeanValueEnclosure
 MooreSkelboeEnclosure
 SumOfSquaresEnclosure
 TaylorModelsEnclosure

src/RangeEnclosures.jl

@@ -25,7 +25,7 @@ API
 include("enclose.jl")
 
 export enclose, relative_precision,
-  NaturalEnclosure, MooreSkelboeEnclosure, SumOfSquaresEnclosure,
+  MeanValueEnclosure, NaturalEnclosure, MooreSkelboeEnclosure, SumOfSquaresEnclosure,
   TaylorModelsEnclosure, BranchAndBoundEnclosure,
   AbstractEnclosureAlgorithm, AbstractDirectRangeAlgorithm, AbstractIterativeRangeAlgorithm
 

src/algorithms.jl

@@ -36,6 +36,15 @@ julia> enclose(x -> 1 - x^4 + x^5, 0..1, NaturalEnclosure())
 """
 struct NaturalEnclosure <: AbstractDirectRangeAlgorithm end
 
+"""
+    MeanValueEnclosure
+
+Data type to bound the range of `f` over `X` using the mean value form, that is the range
+is bounded by the expression ``f(Xc) + f'(X) * (X - Xc)``, where `Xc` is the midpoint of `X`
+and `f'` is the derivative / gradient of `f`.
+"""
+struct MeanValueEnclosure <: AbstractDirectRangeAlgorithm end
+
 """
     MooreSkelboeEnclosure{T} <: AbstractIterativeRangeAlgorithm
 

src/intervals.jl

@@ -5,3 +5,13 @@ Methods using Interval Arithmetic
 function _enclose(::NaturalEnclosure, f::Function, dom::Interval_or_IntervalBox; kwargs...)
     return f(dom...)
 end
+
+function _enclose(::MeanValueEnclosure, f::Function, dom::Interval;
+                  df=Base.Fix1(ForwardDiff.derivative, f))
+    return f(mid(dom)) + df(dom) * (dom - mid(dom))
+end
+
+function _enclose(::MeanValueEnclosure, f::Function, dom::IntervalBox;
+                  df=t->ForwardDiff.gradient(w->f(w...), t.v))
+    return f(mid.(dom)...) + dot(df(dom), dom - mid.(dom))
+end