Fix bugs hit by th_cheb2jac(x, 1,1) (#230)

* Fix bugs hit by th_cheb2jac(x, 1,1)

* Update toeplitzhankel.jl

Author: dlfivefifty

Project.toml

@@ -1,6 +1,6 @@
 name = "FastTransforms"
 uuid = "057dd010-8810-581a-b7be-e3fc3b93f78c"
-version = "0.15.9"
+version = "0.15.10"
 
 [deps]
 AbstractFFTs = "621f4979-c628-5d54-868e-fcf4e3e8185c"

src/toeplitzhankel.jl

@@ -283,8 +283,17 @@ end
 isapproxinteger(::Integer) = true
 isapproxinteger(x) = isinteger(x) || x ≈ round(Int,x)  || x+1 ≈ round(Int,x+1)
 
+"""
+  _nearest_jacobi_par(α, γ)
 
-_nearest_jacobi_par(α, γ) = isapproxinteger(α-γ) ? α : round(Int,α,RoundDown) + mod(γ,1)
+returns a number that is an integer different than γ but less than 1 away from α.
+"""
+function _nearest_jacobi_par(α::T, γ::T) where T
+    ret = isapproxinteger(α-γ) ? α : round(Int,α,RoundDown) + mod(γ,1)
+    ret ≤ -1 ? ret + 1 : ret
+end
+_nearest_jacobi_par(α::T, ::T) where T<:Integer = α
+_nearest_jacobi_par(α, γ) = _nearest_jacobi_par(promote(α,γ)...)
 
 
 struct Ultra2UltraPlanTH{T, Plans, Dims} <: Plan{T}
@@ -296,12 +305,16 @@ end
 
 function *(P::Ultra2UltraPlanTH, A::AbstractArray)
     ret = A
-    for p in P.plans
-        ret = p*ret
-    end
-    c = _nearest_jacobi_par(P.λ₁, P.λ₂)
+    if isapproxinteger(P.λ₂ - P.λ₁)
+        _ultra2ultra_integerinc!(ret, P.λ₁, P.λ₂, P.dims)
+    else
+        for p in P.plans
+            ret = p*ret
+        end
+        c = _nearest_jacobi_par(P.λ₁, P.λ₂)
 
-    _ultra2ultra_integerinc!(ret, c, P.λ₂, P.dims)
+        _ultra2ultra_integerinc!(ret, c, P.λ₂, P.dims)
+    end
 end
 
 function _ultra2ultraTH_TLC(::Type{S}, mn, λ₁, λ₂, d) where {S}

test/toeplitzhankeltests.jl

@@ -36,6 +36,8 @@ Random.seed!(0)
 
         @test th_cheb2jac(x, 0.2, 0.3) ≈ cheb2jac(x, 0.2, 0.3)
         @test th_jac2cheb(x, 0.2, 0.3) ≈ jac2cheb(x, 0.2, 0.3)
+        @test th_cheb2jac(x, 1, 1) ≈ cheb2jac(x, 1, 1)
+        @test th_jac2cheb(x, 1, 1) ≈ jac2cheb(x, 1, 1)
 
         @test th_cheb2leg(th_leg2cheb(x)) ≈ x
         @test th_leg2cheb(th_cheb2leg(x)) ≈ x