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support for clamp and min, max, clamp with ForwardDiff #642

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support for clamp and min, max, clamp with ForwardDiff #642

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60 changes: 60 additions & 0 deletions ext/IntervalArithmeticForwardDiffExt.jl
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Original file line number Diff line number Diff line change
Expand Up @@ -56,4 +56,64 @@ function Base.:(^)(x::ExactReal, y::Dual{<:Any, I}) where I<:Interval
return convert(I, x)^y
end

function Base.max(x::Dual{T,V,N}, y::AbstractFloat) where {T,V<:Interval,N}
if sup(value(x)) < y
return Dual{T,V,N}(interval(y,y), interval(0,0) * partials(x))
elseif inf(value(x)) > y
return Dual{T,V,N}(value(x), interval(1,1) * partials(x))
else
return Dual{T,V,N}(interval(y,sup(value(x))), interval(0,1) * partials(x))
end
end
function Base.max(y::AbstractFloat, x::Dual{T,V,N}) where {T,V<:Interval,N}
return max(x, y)
end

function Base.max(x::Dual{T,Dual{T2,V2,N2},N}, y::AbstractFloat) where {T,T2,V2<:Interval,N2,N}
if sup(value(value(x))) < y
return Dual{T,Dual{T2,V2,N2},N}(Dual{T2,V2,N2}(interval(y,y)), interval(0,0) * partials(x))
elseif inf(value(value(x))) > y
return Dual{T,Dual{T2,V2,N2},N}(value(x), interval(1,1) * partials(x))
else
return Dual{T,Dual{T2,V2,N2},N}(Dual{T2,V2,N2}(interval(y,sup(value(value(x)))), partials(value(x))), interval(0,1) * partials(x))
end
end
function Base.max(y::AbstractFloat, x::Dual{T,Dual{T2,V2,N2},N}) where {T,T2,V2<:Interval,N2,N}
return max(x, y)
end

function Base.min(x::Dual{T,V,N}, y::AbstractFloat) where {T,V<:Interval,N}
if inf(value(x)) > y
return Dual{T,V,N}(interval(y,y), interval(0,0) * partials(x))
elseif sup(value(x)) < y
return Dual{T,V,N}(value(x), interval(1,1) * partials(x))
else
return Dual{T,V,N}(interval(inf(value(x)),y), interval(0,1) * partials(x))
end
end
function Base.min(y::AbstractFloat, x::Dual{T,V,N}) where {T,V<:Interval,N}
return min(x, y)
end

function Base.min(x::Dual{T,Dual{T2,V2,N2},N}, y::AbstractFloat) where {T,T2,V2<:Interval,N2,N}
if inf(value(value(x))) > y
return Dual{T,Dual{T2,V2,N2},N}(Dual{T2,V2,N2}(interval(y,y)), interval(0,0) * partials(x))
elseif sup(value(value(x))) < y
return Dual{T,Dual{T2,V2,N2},N}(value(x), interval(1,1) * partials(x))
else
return Dual{T,Dual{T2,V2,N2},N}(Dual{T2,V2,N2}(interval(inf(value(value(x))),y), partials(value(x))), interval(0,1) * partials(x))
end
end
function Base.min(y::AbstractFloat, x::Dual{T,Dual{T2,V2,N2},N}) where {T,T2,V2<:Interval,N2,N}
return min(x, y)
end

function Base.clamp(i::Dual{T,V,N}, lo::AbstractFloat, hi::AbstractFloat) where {T,V<:Interval,N}
return min(max(i, lo), hi)
end

function Base.clamp(i::Dual{T,Dual{T2,V2,N2},N}, lo::AbstractFloat, hi::AbstractFloat) where {T,T2,V2<:Interval,N2,N}
return min(max(i, lo), hi)
end

end
14 changes: 14 additions & 0 deletions src/intervals/arithmetic/absmax.jl
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Expand Up @@ -50,13 +50,27 @@ for f ∈ (:min, :max)
isempty_interval(y) && return y
return _unsafe_bareinterval(T, $f(inf(x), inf(y)), $f(sup(x), sup(y)))
end
function Base.$f(x::BareInterval{T}, y::Rational) where {T<:NumTypes}
isempty_interval(x) && return x
return _unsafe_bareinterval(T, $f(inf(x), y), $f(sup(x), y))
end
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We purposely do not allow functions mixing BareInterval and Number in their computations, because BareInterval cannot keep track of guarantees ("NG" flag)or decorations.
So my first impulse here would be not to define such function.

Base.$f(x::BareInterval, y::BareInterval) = $f(promote(x, y)...)
Base.$f(x::BareInterval, y::Rational) = $f(promote(x), y)
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Same comment as above.


function Base.$f(x::Interval, y::Interval)
r = $f(bareinterval(x), bareinterval(y))
d = min(decoration(x), decoration(y))
t = isguaranteed(x) & isguaranteed(y)
return _unsafe_interval(r, d, t)
end

function Base.$f(x::Interval, y::Rational)
r = $f(bareinterval(x), y)
d = decoration(x)
return _unsafe_interval(r, d, false)
end
Base.$f(x::Rational, y::Interval) = $f(y, x)
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On the latest version of IntervalArithmetic.jl, min and max already do this ; so defining these functions is maybe superfluous here ? Or am I missing something ?

end
end

Base.clamp(i::Interval, lo, hi) = min(max(i, lo), hi)
19 changes: 18 additions & 1 deletion test/interval_tests/consistency.jl
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Expand Up @@ -268,7 +268,7 @@
@test radius(2.125) == 0
end

@testset "abs, min, max, sign" begin
@testset "abs, min, max, sign, clamp" begin
@test isequal_interval(abs(entireinterval()), interval(0.0, Inf))
@test isequal_interval(abs(emptyinterval()), emptyinterval())
@test isequal_interval(abs(interval(-3.0,1.0)), interval(0.0, 3.0))
Expand All @@ -279,14 +279,31 @@
@test isequal_interval(min(emptyinterval(), interval(3.0,4.0)), emptyinterval())
@test isequal_interval(min(interval(-3.0,1.0), interval(3.0,4.0)), interval(-3.0, 1.0))
@test isequal_interval(min(interval(-3.0,-1.0), interval(3.0,4.0)), interval(-3.0, -1.0))
@test isequal_interval(min(interval(1, 2), 1.5), interval(1, 1.5))
@test isequal_interval(min(interval(1, 2), 0.5), interval(0.5, 0.5))
@test isequal_interval(min(interval(1, 2), 2.5), interval(1, 2))
@test !isguaranteed(min(interval(1, 2), 1.5))
@test isequal_interval(min(1.5, interval(1,2)), interval(1, 1.5))
@test !isguaranteed(min(1.5, interval(1,2)))
@test isequal_interval(max(entireinterval(), interval(3.0,4.0)), interval(3.0, Inf))
@test isequal_interval(max(emptyinterval(), interval(3.0,4.0)), emptyinterval())
@test isequal_interval(max(interval(-3.0,1.0), interval(3.0,4.0)), interval(3.0, 4.0))
@test isequal_interval(max(interval(-3.0,-1.0), interval(3.0,4.0)), interval(3.0, 4.0))
@test isequal_interval(max(interval(1, 2), 1.5), interval(1.5, 2))
@test isequal_interval(max(interval(1, 2), 0.5), interval(1, 2))
@test isequal_interval(max(interval(1, 2), 2.5), interval(2.5, 2.5))
@test !isguaranteed(max(interval(1, 2), 1.5))
@test isequal_interval(max(1.5, interval(1,2)), interval(1.5, 2))
@test !isguaranteed(max(1.5, interval(1,2)))
@test isequal_interval(sign(entireinterval()), interval(-1.0, 1.0))
@test isequal_interval(sign(emptyinterval()), emptyinterval())
@test isequal_interval(sign(interval(-3.0,1.0)), interval(-1.0, 1.0))
@test isequal_interval(sign(interval(-3.0,-1.0)), interval(-1.0, -1.0))
@test isequal_interval(clamp(interval(1, 2), 1.5, 2.5), interval(1.5, 2))
@test isequal_interval(clamp(interval(1, 2), 0.5, 1.5), interval(1, 1.5))
@test isequal_interval(clamp(interval(1, 2), 2.5, 3.5), interval(2.5, 2.5))
@test isequal_interval(clamp(interval(1, 2), 0.5, 2.5), interval(1, 2))
@test !isguaranteed(clamp(interval(1, 2), 1.5, 2.5))

# Test putting functions in interval:
@test issubset_interval(log(interval(-2, 5)), interval(-Inf, log(interval(5))))
Expand Down
44 changes: 44 additions & 0 deletions test/interval_tests/forwarddiff.jl
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Expand Up @@ -96,4 +96,48 @@ end
end
end
end

@testset "min" begin
@test isequal_interval(ForwardDiff.derivative(x->min(x, 1.5), interval(1, 2)), interval(0, 1))
@test isequal_interval(ForwardDiff.derivative(x->min(x, 1.5), interval(1.75, 2)), interval(0))
@test isequal_interval(ForwardDiff.derivative(x->min(x, 1.5), interval(0.5, 0.75)), interval(1))
@test isequal_interval(ForwardDiff.derivative(x->min(x, 1.5), interval(1, 2)), ForwardDiff.derivative(x->min(1.5, x), interval(1, 2)))

@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 1.5), y), interval(1, 2)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 1.5)^2, y), interval(1, 2)), interval(0, 2))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 1.5)^3, y), interval(1, 2)), interval(0, 9))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 3.0)^3, y), interval(1, 2)), interval(6, 12))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 3.0)^3, y), interval(4, 5)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(x, 1.5)^3, y), interval(1, 2)), ForwardDiff.derivative(y->ForwardDiff.derivative(x->min(1.5, x)^3, y), interval(1, 2)))
end

@testset "max" begin
@test isequal_interval(ForwardDiff.derivative(x->max(x, 1.5), interval(1, 2)), interval(0, 1))
@test isequal_interval(ForwardDiff.derivative(x->max(x, 1.5), interval(1.75, 2)), interval(1))
@test isequal_interval(ForwardDiff.derivative(x->max(x, 1.5), interval(0.5, 0.75)), interval(0))
@test isequal_interval(ForwardDiff.derivative(x->max(x, 1.5), interval(1, 2)), ForwardDiff.derivative(x->max(1.5, x), interval(1, 2)))

@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 1.5), y), interval(1, 2)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 1.5)^2, y), interval(1, 2)), interval(0, 2))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 1.5)^3, y), interval(1, 2)), interval(0, 12))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 3.0)^3, y), interval(1, 2)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 3.0)^3, y), interval(4, 5)), interval(24, 30))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(x, 1.5)^3, y), interval(1, 2)), ForwardDiff.derivative(y->ForwardDiff.derivative(x->max(1.5, x)^3, y), interval(1, 2)))
end

@testset "clamp" begin
@test isequal_interval(ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), interval(1, 2)), interval(0, 1))
@test isequal_interval(ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), interval(2, 3)), interval(0, 1))
@test isequal_interval(ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), interval(1.75, 2)), interval(1))
@test isequal_interval(ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), interval(2.75, 3)), interval(0))
@test isequal_interval(ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), interval(0.75, 1)), interval(0))

@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5), y), interval(1, 2)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^2, y), interval(1, 2)), interval(0, 2))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^3, y), interval(1, 2)), interval(0, 12))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^3, y), interval(2, 3)), interval(0, 15))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^3, y), interval(3, 4)), interval(0))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^3, y), interval(1.75, 2)), interval(6*1.75, 12))
@test isequal_interval(ForwardDiff.derivative(y->ForwardDiff.derivative(x->clamp(x, 1.5, 2.5)^3, y), interval(0, 1)), interval(0))
end
end