Fixes, cleanup, and tests for broadcasting with mixtures

src/broadcasting.jl

@@ -29,6 +29,9 @@ BroadcastStyle(::Type{<:TaylorN{T}}) where {T} = TaylorNStyle{T}()
 BroadcastStyle(::TaylorNStyle{T}, ::Base.Broadcast.DefaultArrayStyle{0}) where {T} = TaylorNStyle{T}()
 BroadcastStyle(::TaylorNStyle{T}, ::Base.Broadcast.DefaultArrayStyle{1}) where {T} = Base.Broadcast.DefaultArrayStyle{1}()
 
+# Precedence rules for mixtures
+BroadcastStyle(::TaylorNStyle{Taylor1{T}}, ::Taylor1Style{T}) where {T} = TaylorNStyle{Taylor1{T}}()
+BroadcastStyle(::Taylor1Style{TaylorN{T}}, ::TaylorNStyle{T}) where {T} = Taylor1Style{TaylorN{T}}()
 
 # Extend eltypes so things like [1.0] .+ t work
 Base.Broadcast.eltypes(t::Tuple{Taylor1,AbstractArray}) =
@@ -44,17 +47,18 @@ Base.Broadcast.eltypes(t::Tuple{TaylorN,AbstractArray}) =
 Base.Broadcast.eltypes(t::Tuple{AbstractArray,TaylorN}) =
     Tuple{Base.Broadcast._broadcast_getindex_eltype(t[1]), Base.Broadcast._broadcast_getindex_eltype([t[2]])}
 
-# We follow https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-iteration-1
-"`A = find_taylor(As)` returns the first Taylor1 among the arguments."
-find_taylor(bc::Broadcasted) = find_taylor(bc.args)
-find_taylor(args::Tuple) = find_taylor(find_taylor(args[1]), Base.tail(args))
-find_taylor(x) = x
-find_taylor(a::Taylor1, rest) = a
-find_taylor(a::HomogeneousPolynomial, rest) = a
-find_taylor(a::TaylorN, rest) = a
-find_taylor(::AbstractArray, rest) = find_taylor(rest)
 
-# Extend similar
+# # We follow https://docs.julialang.org/en/v1/manual/interfaces/#man-interface-iteration-1
+# "`A = find_taylor(As)` returns the first Taylor1 among the arguments."
+# find_taylor(bc::Broadcasted) = find_taylor(bc.args)
+# find_taylor(args::Tuple) = find_taylor(find_taylor(args[1]), Base.tail(args))
+# find_taylor(x) = x
+# find_taylor(a::Taylor1, rest) = a
+# find_taylor(a::HomogeneousPolynomial, rest) = a
+# find_taylor(a::TaylorN, rest) = a
+# find_taylor(::AbstractArray, rest) = find_taylor(rest)
+#
+# # Extend similar
 # function similar(bc::Broadcasted{Taylor1Style{S}}, ::Type{T}) where {S, T}
 #     # Proper promotion
 #     R = Base.Broadcast.combine_eltypes(bc.f, bc.args)
@@ -63,7 +67,7 @@ find_taylor(::AbstractArray, rest) = find_taylor(rest)
 #     # Create the output
 #     return Taylor1(similar(A.coeffs, R), A.order)
 # end
-
+#
 # function similar(bc::Broadcasted{HomogeneousPolynomialStyle{S}}, ::Type{T}) where {S, T}
 #     # Proper promotion
 #     # combine_eltypes(f, args::Tuple) = Base._return_type(f, eltypes(args))
@@ -73,7 +77,7 @@ find_taylor(::AbstractArray, rest) = find_taylor(rest)
 #     # Create the output
 #     return HomogeneousPolynomial(similar(A.coeffs, R), A.order)
 # end
-
+#
 # function similar(bc::Broadcasted{TaylorNStyle{S}}, ::Type{T}) where {S, T}
 #     # Proper promotion
 #     R = Base.Broadcast.combine_eltypes(bc.f, bc.args)

test/broadcasting.jl

@@ -5,7 +5,7 @@ using TaylorSeries
 
 using Test
 
-@testset "Broadcasting for Taylor1 expansions" begin
+@testset "Broadcasting with Taylor1 expansions" begin
     t = Taylor1(Int, 5)
 
     # @test t .= t
@@ -19,7 +19,7 @@ using Test
     @test typeof(1.0 .+ [t]) == Vector{Taylor1{Float64}}
     @test 1.0 .+ [t, 2t] == [1.0 + t, 1.0 + 2t]
     @test [1.0,2.0] .+ [t 2t] == [1.0+t 1.0+2t; 2.0+t 2.0+2t]
-    @test [1.0] .+ t == [1.0 + t]
+    @test [1.0] .+ t == t .+ [1.0] == [1.0 + t]
     @test 1.0 .* t == t
     @test typeof(1.0 .* t) == Taylor1{Float64}
 
@@ -58,7 +58,7 @@ using Test
     @test ttts == -1
 end
 
-@testset "Broadcasting for HomogeneousPolynomial and TaylorN" begin
+@testset "Broadcasting with HomogeneousPolynomial and TaylorN" begin
     x, y = set_variables("x y", order=3)
     xH = x[1]
     yH = y[1]
@@ -78,7 +78,7 @@ end
 
     @test 1 .* xH == xH
     @test 1 .* [xH] == [xH]
-    @test [1] .* xH == [xH]
+    @test [1] .* xH == xH .* [1] == [xH]
 
     @test x .== x
     @test y .≈ y
@@ -103,3 +103,62 @@ end
     @test 1.0 .* y == y
     @test typeof(1.0 .* x .* y) == TaylorN{Float64}
 end
+
+@testset "Broadcasting with mixtures Taylor1{TalorN{T}}" begin
+    x, y = set_variables("x", numvars=2, order=6)
+    tN = Taylor1(TaylorN{Float64}, 3)
+
+    @test tN .== tN
+    @test tN .≈ tN
+    @test tN .!= (1 + tN)
+
+    @test 1.0 .+ tN == 1.0 + tN
+    @test typeof(1.0 .+ tN) == Taylor1{TaylorN{Float64}}
+    @test 1.0 .+ [tN] == [1.0 + tN]
+    @test typeof(1.0 .+ [tN]) == Vector{Taylor1{TaylorN{Float64}}}
+    @test 1.0 .+ [tN, 2tN] == [1.0 + tN, 1.0 + 2tN]
+    @test [1.0,2.0] .+ [tN 2tN] == [1.0+tN 1.0+2tN; 2.0+tN 2.0+2tN]
+    @test [1.0] .+ tN == tN .+ [1.0] == [1.0 + tN]
+    @test 1.0 .* tN == 1.0 * tN
+    @test typeof(1.0 .* tN) == Taylor1{TaylorN{Float64}}
+
+    tNs = similar(tN);
+    @test get_order(tN) == get_order(tNs) == 3
+    @test typeof(tNs) == Taylor1{TaylorN{Float64}}
+    tNs .= tN
+    @test tNs == tN
+    @. tNs = y[1] * tN^2 - 1
+    @test tNs == y[1] * tN^2 - 1
+    @. tNs = y * tN^2 - 1
+    @test tNs == y * tN^2 - 1
+end
+
+@testset "Broadcasting with mixtures TaylorN{Talor1{T}}" begin
+    set_variables("x", numvars=2, order=6)
+    t = Taylor1(3)
+    xHt = HomogeneousPolynomial([one(t), zero(t)])
+    yHt = HomogeneousPolynomial([zero(t), t])
+    tN1 = TaylorN([HomogeneousPolynomial([t]),xHt,yHt^2])
+
+    @test tN1 .== tN1
+    @test tN1 .≈ tN1
+    @test tN1 .!= (1 + tN1)
+
+    @test 1.0 .+ tN1 == 1.0 + tN1
+    @test typeof(1.0 .+ tN1) == TaylorN{Taylor1{Float64}}
+    @test 1.0 .+ [tN1] == [1.0 + tN1]
+    @test typeof(1.0 .+ [tN1]) == Vector{TaylorN{Taylor1{Float64}}}
+    @test 1.0 .+ [tN1, 2tN1] == [1.0 + tN1, 1.0 + 2tN1]
+    @test [1.0, 2.0] .+ [tN1 2tN1] == [1.0+tN1 1.0+2tN1; 2.0+tN1 2.0+2tN1]
+    @test [1.0] .+ tN1 == tN1 .+ [1.0] == [1.0 + tN1]
+    @test 1.0 .* tN1 == tN1
+    @test typeof(1.0 .* tN1) == TaylorN{Taylor1{Float64}}
+
+    tN1s = similar(tN1);
+    @test get_order(tN1) == get_order(tN1s) == 2
+    @test typeof(tN1s) == TaylorN{Taylor1{Float64}}
+    tN1s .= tN1
+    @test tN1s == tN1
+    @. tN1s = t * tN1^2 - 1
+    @test tN1s == t * tN1^2 - 1
+end