added issubset, mig, mag, mid for complex intervals (#483)

* added issubset, mig, mag, mid for complex intervals

* bump patch version

Author: lucaferranti

Project.toml

@@ -1,7 +1,7 @@
 name = "IntervalArithmetic"
 uuid = "d1acc4aa-44c8-5952-acd4-ba5d80a2a253"
 repo = "https://github.com/JuliaIntervals/IntervalArithmetic.jl.git"
-version = "0.19.0"
+version = "0.19.1"
 
 [deps]
 CRlibm = "96374032-68de-5a5b-8d9e-752f78720389"

src/intervals/complex.jl

@@ -1,5 +1,9 @@
 
-⊆(x::Complex{Interval{T}}, y::Complex{Interval{T}}) where T = real(x) ⊆ real(y) && imag(x) ⊆ imag(y)
+for op in (:⊆, :⊂)
+    @eval function $(op)(x::Complex{Interval{T}}, y::Complex{Interval{S}}) where {T, S}
+        return $(op)(real(x), real(y)) && $(op)(imag(x), imag(y))
+    end
+end
 
 function ^(x::Complex{Interval{T}}, n::Integer) where {T}
     if n < 0
@@ -116,4 +120,9 @@ end
 # # \left( |x|^p \right)^{1/p}.
 # function norm(z::Complex{T}, p=2) where T<:Interval
 #     return (abs(z)^(p))^(1 / p)
-# end 
+# end
+
+# real functions
+mid(z::Complex{T}) where {T <: Interval} = mid(real(z)) + mid(imag(z)) * im
+mag(z::Complex{T}) where {T <: Interval} = sup(abs(z))
+mig(z::Complex{T}) where {T <: Interval} = inf(abs(z))

test/interval_tests/complex.jl

@@ -8,6 +8,11 @@ using LinearAlgebra
     b = @interval 4im + 3
     c = (@interval -1 4) + (@interval 0 2)*im
 
+    @test a ⊂ c
+    @test a ⊆ c
+    @test (b ⊂ c) == false
+    @test (b ⊆ c) == false
+
     @test typeof(a) == Complex{IntervalArithmetic.Interval{Float64}}
     @test a ==  Interval(0) + Interval(1)*im
     @test a * a == Interval(-1)
@@ -58,3 +63,10 @@ end
     @test abs(y).lo == 0.0
     @test abs2(y).lo == 0.0
 end
+
+@testset "real functions" begin
+    x = (0..3) + (0..4)*im
+    @test mag(x) == 5
+    @test mig(x) == 0
+    @test mid(x) == 1.5 + 2im
+end