implemented chebyshev from roots

Author: mileslucas

src/polynomials/ChebyshevT.jl

@@ -59,16 +59,21 @@ function (ch::ChebyshevT{T})(x::S) where {T,S}
     return R(c0 + c1 * x)
 end
 
-##
-# function fromroots(P::Type{<:ChebyshevT}, r::AbstractVector{T}; var::SymbolLike = :x) where {T <: Number}
-#     n = length(r)
-#     c = zeros(T, n + 1)
-#     c[1] = one(T)
-#     @inbounds for j = 2:n, i = j:-1:1
-#         c[i + 1] = c[i + 1] - r[j] * c[i]
-#     end
-#     return ChebyshevT(reverse(c), var)
-# end
+function fromroots(P::Type{<:ChebyshevT}, roots::AbstractVector{T}; var::SymbolLike = :x) where {T <: Number}
+    p = [P([-r, 1]) for r in roots]
+    n = length(p)
+    while n > 1
+        m, r = divrem(n, 2)
+        tmp = [p[i] * p[i + m] for i in 1:m]
+        if r > 0
+            tmp[1] *= p[end]
+        end
+        p = tmp
+        n = m
+    end
+    # return truncate!(reduce(*, p))
+    return truncate!(p[1])
+end
 
 function vander(P::Type{<:ChebyshevT}, x::AbstractVector{T}, n::Integer) where {T <: Number}
     A = Matrix{T}(undef, length(x), n + 1)

test/ChebyshevT.jl

@@ -45,6 +45,17 @@ end
     @test degree(p0) == -1
 end
 
+@testset "Roots" begin
+    # from roots
+    for i in 1:5
+        roots = cos.(range(-π, 0, length = 2i + 1)[2:2:end])
+        target = ChebyshevT(append!(zeros(i), [1]))
+        res = fromroots(ChebyshevT, roots) .* 2^(i-1)
+        @test res == target
+    end
+    @test fromroots(ChebyshevT, [-1, 0, 1]) == ChebyshevT([0, -0.25, 0, 0.25])
+    @test fromroots(ChebyshevT, [-1im, 1im]) ≈ ChebyshevT([1.5 + 0im, 0 + 0im, 0.5 + 0im])
+end
 
 @testset "Values" begin
     c1 = ChebyshevT([2.5, 2.0, 1.5]) #1 + 2x + 3x^2