add tests for hankel

Author: heltonmc

src/Bessels.jl

@@ -22,18 +22,23 @@ export besselk0x
 export besselk1
 export besselk1x
 
+export besselh
+export hankelh1
+export hankelh2
+
 include("besseli.jl")
 include("besselj.jl")
 include("besselk.jl")
 include("bessely.jl")
-include("constants.jl")
+include("hankel.jl")
 
 include("Float128/besseli.jl")
 include("Float128/besselj.jl")
 include("Float128/besselk.jl")
 include("Float128/bessely.jl")
 include("Float128/constants.jl")
 
+include("constants.jl")
 include("math_constants.jl")
 include("U_polynomials.jl")
 include("recurrence.jl")
@@ -42,6 +47,4 @@ include("Polynomials/besselj_polys.jl")
 include("asymptotics.jl")
 include("gamma.jl")
 
-include("hankel.jl")
-
 end

src/hankel.jl

@@ -97,7 +97,7 @@ function besseljy_positive_args(nu::Real, x::T) where T
 
     Hnu = hankel_debye(v2, x)
     Hnum1 = hankel_debye(v2 - 1, x)
-    
+
     # forward recurrence is stable for Hankel when x >= nu
     if x >= nu
         H = besselj_up_recurrence(x, Hnu, Hnum1, v2, nu)[1]
@@ -133,7 +133,7 @@ function besselj_ratio_jnu_jnum1(n, x::T) where T
     return h
 end
 
-function besselh(nu::Float64, k::Integer, x::AbstractFloat)
+function besselh(nu::Real, k::Integer, x)
     Jn, Yn = besseljy(nu, x)
     if k == 1
         return complex(Jn, Yn)
@@ -144,5 +144,5 @@ function besselh(nu::Float64, k::Integer, x::AbstractFloat)
     end
 end
 
-hankelh1(nu, z) = besselh(nu, 1, z)
-hankelh2(nu, z) = besselh(nu, 2, z)
+hankelh1(nu, x) = besselh(nu, 1, x)
+hankelh2(nu, x) = besselh(nu, 2, x)

test/hankel_test.jl

@@ -0,0 +1,28 @@
+# most of the tests are contained in bessely_test and besselj_test which test the besseljy function
+# which is called by hankelh1 and besselh
+# here we will test just a few cases of the overal hankel function
+# focusing on negative arguments and reflection
+
+v, x = 1.5, 1.3
+@test isapprox(hankelh1(v, x), SpecialFunctions.hankelh1(v, x), rtol=2e-13)
+@test isapprox(hankelh2(v, x), SpecialFunctions.hankelh2(v, x), rtol=2e-13)
+@test isapprox(besselh(v, 1, x), SpecialFunctions.besselh(v, 1, x), rtol=2e-13)
+@test isapprox(besselh(v, 2, x), SpecialFunctions.besselh(v, 2, x), rtol=2e-13)
+
+v, x = -2.6, 9.2
+@test isapprox(hankelh1(v, x), SpecialFunctions.hankelh1(v, x), rtol=2e-13)
+@test isapprox(hankelh2(v, x), SpecialFunctions.hankelh2(v, x), rtol=2e-13)
+@test isapprox(besselh(v, 1, x), SpecialFunctions.besselh(v, 1, x), rtol=2e-13)
+@test isapprox(besselh(v, 2, x), SpecialFunctions.besselh(v, 2, x), rtol=2e-13)
+
+v, x = -4.0, 11.4
+@test isapprox(hankelh1(v, x), SpecialFunctions.hankelh1(v, x), rtol=2e-13)
+@test isapprox(hankelh2(v, x), SpecialFunctions.hankelh2(v, x), rtol=2e-13)
+@test isapprox(besselh(v, 1, x), SpecialFunctions.besselh(v, 1, x), rtol=2e-13)
+@test isapprox(besselh(v, 2, x), SpecialFunctions.besselh(v, 2, x), rtol=2e-13)
+
+v, x = 14.3, 29.4
+@test isapprox(hankelh1(v, x), SpecialFunctions.hankelh1(v, x), rtol=2e-13)
+@test isapprox(hankelh2(v, x), SpecialFunctions.hankelh2(v, x), rtol=2e-13)
+@test isapprox(besselh(v, 1, x), SpecialFunctions.besselh(v, 1, x), rtol=2e-13)
+@test isapprox(besselh(v, 2, x), SpecialFunctions.besselh(v, 2, x), rtol=2e-13)

test/runtests.jl

@@ -6,4 +6,5 @@ import SpecialFunctions
 @time @testset "besselk" begin include("besselk_test.jl") end
 @time @testset "besselj" begin include("besselj_test.jl") end
 @time @testset "bessely" begin include("bessely_test.jl") end
+@time @testset "hankel" begin include("hankel_test.jl") end
 @time @testset "gamma" begin include("gamma_test.jl") end