Fix evaluate for mixtures over Intervals (#352)

Author: lbenet

Project.toml

@@ -1,7 +1,7 @@
 name = "TaylorSeries"
 uuid = "6aa5eb33-94cf-58f4-a9d0-e4b2c4fc25ea"
 repo = "https://github.com/JuliaDiff/TaylorSeries.jl.git"
-version = "0.17.1"
+version = "0.17.2"
 
 [deps]
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"

ext/TaylorSeriesIAExt.jl

@@ -190,6 +190,27 @@ function evaluate(a::TaylorN, dx::IntervalBox{N,T}) where {T<:Real,N}
     return suma
 end
 
+function evaluate(a::Taylor1{TaylorN{T}}, dx::Interval{S}) where {T<:Real, S<:Real}
+    order = a.order
+    uno = one(dx)
+    dx2 = dx^2
+    if iseven(order)
+        kend = order-2
+        @inbounds sum_even = a[end]*uno
+        @inbounds sum_odd = a[end-1]*zero(dx)
+    else
+        kend = order-3
+        @inbounds sum_odd = a[end]*uno
+        @inbounds sum_even = a[end-1]*uno
+    end
+    @inbounds for k in kend:-2:0
+        sum_odd = sum_odd*dx2 + a[k+1]
+        sum_even = sum_even*dx2 + a[k]
+    end
+    return sum_even + sum_odd*dx
+end
+
+
 function evaluate(a::HomogeneousPolynomial, dx::IntervalBox{N,T}) where {T<:Real,N}
     @assert N == get_numvars()
     dx == IntervalBox(-1..1, Val(N)) && return _evaluate(a, dx, Val(true))

test/intervals.jl

@@ -4,7 +4,7 @@
 using TaylorSeries, IntervalArithmetic
 
 using Test
-eeuler = Base.MathConstants.e
+# eeuler = Base.MathConstants.e
 
 @testset "Tests Taylor1 and TaylorN expansions over Intervals" begin
     a = 1..2
@@ -100,6 +100,12 @@ eeuler = Base.MathConstants.e
     @test string(Taylor1(vc, 5)) ==
         " ( [1.5, 2] + [0, 0]im ) - ( [1, 2] + [-1, 1]im ) t + ( [-1, 1.5] + [-1, 1.5]im ) t² + ( [0, 0] + [-1, 1.5]im ) t³ + 𝒪(t⁶)"
 
+    # Iss 351 (inspired by a test in ReachabilityAnalysis)
+    p1 = Taylor1([0 .. 0, (0 .. 0.1) + (0 .. 0.01) * y], 4)
+    p2 = Taylor1([0 .. 0, (0 .. 0.5) + (0 .. 0.02) * x + (0 .. 0.03) * y], 4)
+    @test evaluate([p1, p2], 0 .. 1) == [p1[1], p2[1]]
+    @test typeof(p1(0 .. 1)) == TaylorN{Interval{Float64}}
+
     # Tests related to Iss #311
     # `sqrt` and `pow` defined on Interval(0,Inf)
     @test_throws DomainError sqrt(ti)