added tests for roots

Author: stevengj

src/roots.jl

@@ -66,7 +66,7 @@ hesseneigvals!(C::UpperHessenberg{T,Matrix{T}}) where {T} = eigvals!(C.data)
 """
     roots(c::ChebPoly{1,<:Real}; tol=5eps, maxsize::Integer=50)
 
-Returns an array of the real roots of `c` on the interval `[lb,ub]` (the lower and
+Returns a sorted array of the real roots of `c` on the interval `[lb,ub]` (the lower and
 upper bounds of the interpolation domain).
 
 Uses a colleague-matrix method combined with recursive subdivision of the domain

test/runtests.jl

@@ -24,6 +24,11 @@ Random.seed!(314159) # make chainrules tests deterministic
         @test chebgradient(interp, x1) ≈′ (f(x1), f′(x1))
         test_frule(interp, x1, rtol=sqrt(eps(T)), atol=sqrt(eps(T)))
         test_rrule(interp, x1, rtol=sqrt(eps(T)), atol=sqrt(eps(T)))
+
+        @test roots(chebinterp(x -> 1.1, 10, 0,1)) ≈ Float64[]
+        @test roots(chebinterp(x -> x - 0.1, 10, 0,1)) ≈ [0.1]
+        @test roots(chebinterp(x -> (x - 0.1)*(x-0.2), 10, 0,1)) ≈ [0.1, 0.2]
+        @test roots(chebinterp(cos, 10000, 0, 1000))/pi ≈ (0:317) .+ T(0.5)
     end
 end