Close issue 326 (#327)

* Allow ChebyshevT polynomials to be evaluated outside their domain through evalpoly

Project.toml

@@ -2,7 +2,7 @@ name = "Polynomials"
 uuid = "f27b6e38-b328-58d1-80ce-0feddd5e7a45"
 license = "MIT"
 author = "JuliaMath"
-version = "2.0.2"
+version = "2.0.3"
 
 [deps]
 Intervals = "d8418881-c3e1-53bb-8760-2df7ec849ed5"

src/polynomials/ChebyshevT.jl

@@ -17,15 +17,24 @@ terms of the given variable `var`, which can be a character, symbol, or string.
 ```jldoctest ChebyshevT
 julia> using Polynomials
 
-julia> ChebyshevT([1, 0, 3, 4])
+julia> p = ChebyshevT([1, 0, 3, 4])
 ChebyshevT(1⋅T_0(x) + 3⋅T_2(x) + 4⋅T_3(x))
 
 julia> ChebyshevT([1, 2, 3, 0], :s)
 ChebyshevT(1⋅T_0(s) + 2⋅T_1(s) + 3⋅T_2(s))
 
 julia> one(ChebyshevT)
 ChebyshevT(1.0⋅T_0(x))
+
+julia> p(0.5)
+-4.5
+
+julia> Polynomials.evalpoly(5.0, p, false) # bypasses the domain check done in p(5.0)
+2088.0
 ```
+
+The latter shows how to evaluate a `ChebyshevT` polynomial outside of its domain, which is `[-1,1]`. (For newer versions of `Julia`, `evalpoly` is an exported function from Base with methods extended in this package, so the module qualification is unnecessary.
+
 """
 struct ChebyshevT{T <: Number, X} <: AbstractPolynomial{T, X}
     coeffs::Vector{T}
@@ -103,6 +112,11 @@ julia> c.(-1:0.5:1)
 """
 function evalpoly(x::S, ch::ChebyshevT{T}) where {T,S}
     x ∉ domain(ch) && throw(ArgumentError("$x outside of domain"))
+    evalpoly(x, ch, false)
+end
+
+# no checking, so can be called directly through any third argument
+function evalpoly(x::S, ch::ChebyshevT{T}, checked) where {T,S}
     R = promote_type(T, S)
     length(ch) == 0 && return zero(R)
     length(ch) == 1 && return R(ch[0])

test/ChebyshevT.jl

@@ -157,7 +157,16 @@ end
     @test d.coeffs ≈ [0, 2]
     @test r.coeffs ≈ [-2, -4]
 
-
+    # evaluation
+    c1 = ChebyshevT([0,0,1,1])
+    fn = x -> (2x^2-1) + (4x^3 - 3x)
+    for xᵢ ∈ range(-0.9, stop=0.9, length=5)
+        @test c1(xᵢ) ≈ fn(xᵢ)
+    end
+    # issue 326 evaluate outside of domain
+    @test Polynomials.evalpoly(2, c1, false) ≈ fn(2)
+    @test Polynomials.evalpoly(3, c1, false) ≈ fn(3)
+
     # GCD
     c1 = ChebyshevT([1, 2, 3])
     c2 = ChebyshevT([3, 2, 1])