Add iterate method for Root objects (#190)

* Implement iterate method for Root object

* Add tests for the iterate method for Root objects

---------

Co-authored-by: Benoît Richard <kolaru@hotmail.com>

Author: edtrelo

src/root_object.jl

@@ -54,4 +54,18 @@ IntervalArithmetic.isnai(r::Root) = isnai_region(root_region(r))
 function Base.:(==)(r1::Root, r2::Root)
     root_status(r1) != root_status(r2) && return false
     return isequal_region(root_region(r1), root_region(r2))
-end
+end
+
+big(a::Root) = Root(big(a.interval), a.status)
+
+"""
+    Base.iterate(r::Root [, state])
+
+Return successively the root region and status,
+allowing to unpack the root object as `region, status = root`.
+"""
+function Base.iterate(r::Root{T}, state::Integer=1) where {T}
+    state == 1 && return (r.region, 2)
+    state == 2 && return (r.status, 3)
+    return nothing
+end

test/roots.jl

@@ -310,4 +310,65 @@ end
         rts = roots(f, interval(0, 1) ; abstol = 1e-10, max_iteration)
         @test length(rts) <= max_iteration
     end
+end
+
+# straightforward method for unpacking the elements of a root.
+function unpacking(r::Root{T}) where T
+    return (r.region, r.status)
+end
+
+@testset "Unpacking roots" begin
+    @testset "1D" begin
+        g(x) = cos(x) * sin(1 / x)
+
+        for r in roots(g, interval(0.05, 1))
+            x, status = r
+            @test isa(x, Interval)
+            @test isa(status, Symbol)
+
+            # unpack using the straightforward method. 
+            unx, uns = unpacking(r)
+            @test isequal_interval(x, unx)
+            @test status == uns
+        end
+
+        # function with two roots
+        f(x) = x^2 - 1
+        for r in roots(f, interval(-2, 2))
+            x, status = r
+            @test status == :unique
+        end
+    end
+
+    @testset "2D" begin
+        f(x, y) = SVector(x^2 + y^2 - 1, y - 2x)
+        f(X) = f(X...)
+        X = SVector(interval(-6, 6), interval(-6, 6))
+
+        for (x, status) in roots(f, X)
+            @test isa(x, SVector{2, <:Interval})
+            @test isa(status, Symbol)
+        end
+    end
+
+    @testset "3D" begin
+        h(x, y, z) = SVector(x^2 + y^2 + z^2 - 1, y - 2x, z - 2x)
+        h(X) = h(X...)
+        X = SVector(interval(-6, 6), interval(-6, 6), interval(-6, 6)) # cube in R^3
+
+        myroots = []
+        unroots = []
+
+        for (x, status) in roots(h, X)
+            @test isa(x, SVector{3, <:Interval})
+            @test isa(status, Symbol)
+            append!(myroots, x)
+        end
+
+        for (x, status) in unpacking.(roots(h, X))
+            append!(unroots, x)
+        end
+
+        @test all(isequal_interval.(myroots, unroots))
+    end
 end