Merge pull request #629 from Kolaru/fowarddiff_pow

ForwardDiff extension for power

Author: Kolaru

Project.toml

@@ -1,23 +1,26 @@
 name = "IntervalArithmetic"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 repo = "https://github.com/JuliaIntervals/IntervalArithmetic.jl.git"
-version = "0.22.7"
+version = "0.22.8"
 
 [deps]
 CRlibm_jll = "4e9b3aee-d8a1-5a3d-ad8b-7d824db253f0"
 RoundingEmulator = "5eaf0fd0-dfba-4ccb-bf02-d820a40db705"
 
 [weakdeps]
 DiffRules = "b552c78f-8df3-52c6-915a-8e097449b14b"
+ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 RecipesBase = "3cdcf5f2-1ef4-517c-9805-6587b60abb01"
 
 [extensions]
 IntervalArithmeticDiffRulesExt = "DiffRules"
+IntervalArithmeticForwardDiffExt = "ForwardDiff"
 IntervalArithmeticRecipesBaseExt = "RecipesBase"
 
 [compat]
 CRlibm_jll = "1"
 DiffRules = "1"
+ForwardDiff = "0.10"
 RecipesBase = "1"
 RoundingEmulator = "0.2"
 julia = "1.9"

ext/IntervalArithmeticForwardDiffExt.jl

@@ -0,0 +1,51 @@
+module IntervalArithmeticForwardDiffExt
+
+using IntervalArithmetic, ForwardDiff
+using ForwardDiff: Dual, ≺, value, partials
+
+function isconstant_interval(x)
+    all(isthinzero.(values(partials(x))))
+end
+
+function Base.:(^)(x::Dual{Txy, <:Interval}, y::Dual{Txy, <:Interval}) where Txy
+    vx, vy = value(x), value(y)
+    expv = vx^vy
+    powval = vy * vx^(vy - interval(1))
+    if isconstant_interval(y)
+        logval = one(expv)
+    elseif isthinzero(vx) && inf(vy) > 0
+        logval = zero(vx)
+    else
+        logval = expv * log(vx)
+    end
+    new_partials = ForwardDiff._mul_partials(partials(x), partials(y), powval, logval)
+    return Dual{Txy}(expv, new_partials)
+end
+
+function Base.:(^)(x::Dual{Tx, <:Interval}, y::Dual{Ty, <:Interval}) where {Tx, Ty}
+    if Ty ≺ Tx 
+        return x^value(y)
+    else
+        return value(x)^y
+    end
+end
+
+function Base.:(^)(x::Dual{Tx, <:Interval}, y::Interval) where Tx
+    v = value(x)
+    expv = v^y
+    if isthinzero(y) || isconstant_interval(x)
+        new_partials = zero(partials(x))
+    else
+        new_partials = partials(x) * y * v^(y - interval(1))
+    end
+    return Dual{Tx}(expv, new_partials)
+end
+
+function Base.:(^)(x::Interval, y::Dual{Ty, <:Interval}) where Ty
+    v = value(y)
+    expv = x^v
+    deriv = (isthinzero(x) && inf(v) > 0) ? zero(expv) : expv*log(x)
+    return Dual{Ty}(expv, deriv * partials(y))
+end
+
+end

test/interval_tests/forwarddiff.jl

@@ -16,7 +16,7 @@ end
         @test ForwardDiff.derivative(abs, interval(-2,  2)) === interval(-1,  1, trv)
 
         f(x) = abs(x)^interval(2)
-        @test_broken ForwardDiff.derivative(f, interval(-1, 1)) === interval(-2,  2, trv)
+        @test ForwardDiff.derivative(f, interval(-1, 1)) === interval(-2,  2, trv)
 
         g(x) = abs(x)^2
         @test     ForwardDiff.derivative(g,             interval(-1, 1) )  ===  interval(convert(Interval{Float64}, -2), convert(Interval{Float64}, 2), trv)
@@ -56,12 +56,44 @@ end
     end
 
     @testset "Power" begin
-        f(x)  = interval(2)^x
-        f′(x) = log(interval(2)) * f(x)
-        df(t) = ForwardDiff.derivative(f, t)
+        fxy(xy) = xy[1]^xy[2]
 
-        # g(x) = 2^x # not guaranteed
+        for x in [0.0, 1.1, 2.2]
+            for y in [-3.3, 0.0, 4.4]
+                fx(xx) = xx^y
+                fxi(xx) = xx^interval(y)
+                fy(yy) = x^yy
+                fyi(yy) = interval(x)^yy
 
-        @test f′(0) === df(0)
+                dfdx = ForwardDiff.derivative(fxi, interval(x))
+                dfdy = ForwardDiff.derivative(fyi, interval(y))
+                grad = ForwardDiff.gradient(fxy, [interval(x), interval(y)])
+
+                @test isguaranteed(dfdx)
+                @test isguaranteed(dfdy)
+                @test isguaranteed(grad[1])
+                @test isguaranteed(grad[2])
+                
+                if iszero(x) && y < 0
+                    @test decoration(dfdx) == trv
+                else
+                    @test in_interval(ForwardDiff.derivative(fx, x), dfdx)
+                end
+
+                if iszero(x) && y <= 0 
+                    @test decoration(dfdy) == trv
+                else
+                    @test in_interval(ForwardDiff.derivative(fy, y), dfdy)
+                end
+
+                if iszero(x) && iszero(y)
+                    @test decoration(grad[1]) == trv
+                    @test decoration(dfdx) == com
+                else
+                    @test isequal_interval(dfdx, grad[1])
+                end
+                @test isequal_interval(dfdy, grad[2])
+            end
+        end
     end
-end
+end

test/runtests.jl

@@ -1,4 +1,6 @@
 using Test
+
+using ForwardDiff
 using IntervalArithmetic
 using InteractiveUtils
 
@@ -22,4 +24,4 @@ for f ∈ readdir("ITF1788_tests"; join = true)
     @testset "$f" begin
         include(f)
     end
-end
+end