Tests and fixes

Author: Kolaru

ext/IntervalArithmeticForwardDiffExt.jl

@@ -3,13 +3,23 @@ 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)
-    primal = vx^vy
+    expv = vx^vy
     powval = vy * vx^(vy - interval(1))
-    logval = primal * log(vx)
-    new_partials = _mul_partials(partials(x), partials(y), powval, logval)
-    return Dual{Txy}(primal, new_partials)
+    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}
@@ -22,15 +32,20 @@ end
 
 function Base.:(^)(x::Dual{Tx, <:Interval}, y::Interval) where Tx
     v = value(x)
-    new_partials = partials(x) * y * v^(y - interval(1))
-    return Dual{Tx}(v^y, new_partials)
+    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)
-    primal = x^v
-    deriv = primal*log(x)
-    return Dual{Ty}(primal, deriv * partials(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