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birmbirm
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split tests into components (#211)
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‎test/bessel.jl

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@testset "airy" begin
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@test_throws AmosException airyai(200im)
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@test_throws AmosException airybi(200)
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for T in [Float16, Float32, Float64,Complex{Float16}, Complex{Float32},Complex{Float64}]
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@test airyai(T(1.8)) ≈ 0.0470362168668458052247
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@test airyaiprime(T(1.8)) ≈ -0.0685247801186109345638
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@test airybi(T(1.8)) ≈ 2.595869356743906290060
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@test airybiprime(T(1.8)) ≈ 2.98554005084659907283
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end
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for T in [Complex{Float16}, Complex{Float32}, Complex{Float64}]
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z = convert(T,1.8 + 1.0im)
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@test airyaix(z) ≈ airyai(z) * exp(2/3 * z * sqrt(z))
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@test airyaiprimex(z) ≈ airyaiprime(z) * exp(2/3 * z * sqrt(z))
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@test airybix(z) ≈ airybi(z) * exp(-abs(real(2/3 * z * sqrt(z))))
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@test airybiprimex(z) ≈ airybiprime(z) * exp(-abs(real(2/3 * z * sqrt(z))))
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end
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@test_throws MethodError airyai(complex(big(1.0)))
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for x = -3:3
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@test airyai(x) ≈ airyai(complex(x))
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@test airyaiprime(x) ≈ airyaiprime(complex(x))
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@test airybi(x) ≈ airybi(complex(x))
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@test airybiprime(x) ≈ airybiprime(complex(x))
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if x >= 0
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@test airyaix(x) ≈ airyaix(complex(x))
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@test airyaiprimex(x) ≈ airyaiprimex(complex(x))
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else
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@test_throws DomainError airyaix(x)
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@test_throws DomainError airyaiprimex(x)
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end
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@test airybix(x) ≈ airybix(complex(x))
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@test airybiprimex(x) ≈ airybiprimex(complex(x))
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end
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end
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@testset "bessel functions" begin
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bessel_funcs = [(bessely0, bessely1, bessely), (besselj0, besselj1, besselj)]
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@testset "$z, $o" for (z, o, f) in bessel_funcs
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@test z(Float32(2.0)) ≈ z(Float64(2.0))
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@test o(Float32(2.0)) ≈ o(Float64(2.0))
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@test z(Float16(2.0)) ≈ z(Float64(2.0))
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@test o(Float16(2.0)) ≈ o(Float64(2.0))
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@test z(2) ≈ z(2.0)
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@test o(2) ≈ o(2.0)
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@test z(2.0 + im) ≈ f(0, 2.0 + im)
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@test o(2.0 + im) ≈ f(1, 2.0 + im)
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end
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@testset "besselj error throwing" begin
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@test_throws MethodError besselj(1.2,big(1.0))
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@test_throws MethodError besselj(1,complex(big(1.0)))
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@test_throws MethodError besseljx(1,big(1.0))
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@test_throws MethodError besseljx(1,complex(big(1.0)))
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end
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@testset "besselh" begin
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true_h133 = 0.30906272225525164362 - 0.53854161610503161800im
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@test besselh(3,1,3) ≈ true_h133
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@test besselh(-3,1,3) ≈ -true_h133
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@test besselh(Float32(3),1,Float32(3)) ≈ true_h133
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@test besselh(Float16(3),1,Float16(3)) ≈ true_h133
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@test besselh(3,2,3) ≈ conj(true_h133)
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@test besselh(-3,2,3) ≈ -conj(true_h133)
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@test besselh(1,1,0) ≈ complex(0,-Inf)
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@test besselh(1,2,0) ≈ complex(0,Inf)
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@testset "Error throwing" begin
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@test_throws AmosException besselh(1,5,0)
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@test_throws MethodError besselh(1,big(1.0))
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@test_throws MethodError besselh(1,complex(big(1.0)))
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@test_throws MethodError besselhx(1,big(1.0))
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@test_throws MethodError besselhx(1,complex(big(1.0)))
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end
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end
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@testset "besseli" begin
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true_i33 = 0.95975362949600785698
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@test besseli(3,3) ≈ true_i33
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@test besseli(-3,3) ≈ true_i33
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@test besseli(3,-3) ≈ -true_i33
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@test besseli(-3,-3) ≈ -true_i33
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@test besseli(Float32(-3),Complex{Float32}(-3,0)) ≈ -true_i33
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@test besseli(Float16(-3),Complex{Float16}(-3,0)) ≈ -true_i33
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true_im3p1_3 = 0.84371226532586351965
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@test besseli(-3.1,3) ≈ true_im3p1_3
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for i in [-5 -3 -1 1 3 5]
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@test besseli(i,0) == 0.0
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@test besseli(i,Float32(0)) == 0
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@test besseli(i,Complex{Float32}(0)) == 0
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@test besseli(i,Float16(0)) == 0
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@test besseli(i,Complex{Float16}(0)) == 0
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end
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@testset "Error throwing" begin
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@test_throws AmosException besseli(1,1000)
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@test_throws DomainError besseli(0.4,-1.0)
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@test_throws MethodError besseli(1,big(1.0))
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@test_throws MethodError besseli(1,complex(big(1.0)))
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@test_throws MethodError besselix(1,big(1.0))
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@test_throws MethodError besselix(1,complex(big(1.0)))
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end
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end
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@testset "besselj" begin
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@test besselj(0,0) == 1
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for i in [-5 -3 -1 1 3 5]
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@test besselj(i,0) == 0
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@test besselj(i,Float32(0)) == 0
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@test besselj(i,Complex{Float32}(0)) == 0.0
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end
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j33 = besselj(3,3.)
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@test besselj(3,3) == j33
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@test besselj(-3,-3) == j33
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@test besselj(-3,3) == -j33
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@test besselj(3,-3) == -j33
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@test besselj(3,3f0) ≈ j33
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@test besselj(3,complex(3.)) ≈ j33
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@test besselj(3,complex(3f0)) ≈ j33
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@test besselj(3,complex(3)) ≈ j33
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j43 = besselj(4,3.)
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@test besselj(4,3) == j43
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@test besselj(-4,-3) == j43
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@test besselj(-4,3) == j43
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@test besselj(4,-3) == j43
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@test besselj(4,3f0) ≈ j43
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@test besselj(4,complex(3.)) ≈ j43
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@test besselj(4,complex(3f0)) ≈ j43
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@test besselj(4,complex(3)) ≈ j43
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@test j33 ≈ 0.30906272225525164362
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@test j43 ≈ 0.13203418392461221033
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@test besselj(0.1, complex(-0.4)) ≈ 0.820421842809028916 + 0.266571215948350899im
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@test besselj(3.2, 1.3+0.6im) ≈ 0.01135309305831220201 + 0.03927719044393515275im
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@test besselj(1, 3im) ≈ 3.953370217402609396im
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@test besselj(1.0,3im) ≈ besselj(1,3im)
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true_jm3p1_3 = -0.45024252862270713882
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@test besselj(-3.1,3) ≈ true_jm3p1_3
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@test besselj(Float16(-3.1),Float16(3)) ≈ true_jm3p1_3
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@testset "Error throwing" begin
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@test_throws DomainError besselj(0.1, -0.4)
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@test_throws AmosException besselj(20,1000im)
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@test_throws MethodError besselj(big(1.0),3im)
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end
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end
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@testset "besselk" begin
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true_k33 = 0.12217037575718356792
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@test besselk(3,3) ≈ true_k33
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@test besselk(Float32(3),Float32(3)) ≈ true_k33
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@test besselk(Float16(3),Float16(3)) ≈ true_k33
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@test besselk(-3,3) ≈ true_k33
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true_k3m3 = -0.1221703757571835679 - 3.0151549516807985776im
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@test besselk(3,complex(-3)) ≈ true_k3m3
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@test besselk(-3,complex(-3)) ≈ true_k3m3
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# issue #6564
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@test besselk(1.0,0.0) == Inf
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@testset "Error throwing" begin
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@test_throws AmosException besselk(200,0.01)
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@test_throws DomainError besselk(3,-3)
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@test_throws MethodError besselk(1,big(1.0))
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@test_throws MethodError besselk(1,complex(big(1.0)))
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@test_throws MethodError besselkx(1,big(1.0))
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@test_throws MethodError besselkx(1,complex(big(1.0)))
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end
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end
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@testset "bessely" begin
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y33 = bessely(3,3.)
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@test bessely(3,3) == y33
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@test bessely(3.,3.) == y33
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@test bessely(3,Float32(3.)) ≈ y33
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@test bessely(-3,3) ≈ -y33
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@test y33 ≈ -0.53854161610503161800
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@test bessely(3,complex(-3)) ≈ 0.53854161610503161800 - 0.61812544451050328724im
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@testset "Error throwing" begin
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@test_throws AmosException bessely(200.5,0.1)
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@test_throws DomainError bessely(3,-3)
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@test_throws DomainError bessely(0.4,-1.0)
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@test_throws DomainError bessely(0.4,Float32(-1.0))
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@test_throws DomainError bessely(1,Float32(-1.0))
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@test_throws DomainError bessely(0.4,BigFloat(-1.0))
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@test_throws DomainError bessely(1,BigFloat(-1.0))
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@test_throws DomainError bessely(Cint(3),Float32(-3.))
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@test_throws DomainError bessely(Cint(3),Float64(-3.))
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@test_throws MethodError bessely(1.2,big(1.0))
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@test_throws MethodError bessely(1,complex(big(1.0)))
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@test_throws MethodError besselyx(1,big(1.0))
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@test_throws MethodError besselyx(1,complex(big(1.0)))
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end
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end
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@testset "besselhx" begin
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for elty in [Complex{Float16},Complex{Float32},Complex{Float64}]
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z = convert(elty, 1.0 + 1.9im)
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@test besselhx(1.0, 1, z) ≈ convert(elty,-0.5949634147786144 - 0.18451272807835967im)
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@test besselhx(Float32(1.0), 1, z) ≈ convert(elty,-0.5949634147786144 - 0.18451272807835967im)
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end
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@testset "Error throwing" begin
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@test_throws MethodError besselh(1,1,big(1.0))
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@test_throws MethodError besselh(1,1,complex(big(1.0)))
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@test_throws MethodError besselhx(1,1,big(1.0))
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@test_throws MethodError besselhx(1,1,complex(big(1.0)))
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end
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end
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@testset "scaled bessel[ijky] and hankelh[12]" begin
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for x in (1.0, 0.0, -1.0), y in (1.0, 0.0, -1.0), nu in (1.0, 0.0, -1.0)
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z = Complex{Float64}(x + y * im)
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z == zero(z) || @test hankelh1x(nu, z) ≈ hankelh1(nu, z) * exp(-z * im)
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z == zero(z) || @test hankelh2x(nu, z) ≈ hankelh2(nu, z) * exp(z * im)
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(nu < 0 && z == zero(z)) || @test besselix(nu, z) ≈ besseli(nu, z) * exp(-abs(real(z)))
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(nu < 0 && z == zero(z)) || @test besseljx(nu, z) ≈ besselj(nu, z) * exp(-abs(imag(z)))
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z == zero(z) || @test besselkx(nu, z) ≈ besselk(nu, z) * exp(z)
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z == zero(z) || @test besselyx(nu, z) ≈ bessely(nu, z) * exp(-abs(imag(z)))
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end
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@test besselkx(1, 0) == Inf
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for i = [-5 -3 -1 1 3 5]
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@test besseljx(i,0) == 0
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@test besselix(i,0) == 0
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@test besseljx(i,Float32(0)) == 0
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@test besselix(i,Float32(0)) == 0
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@test besseljx(i,Complex{Float32}(0)) == 0
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@test besselix(i,Complex{Float32}(0)) == 0
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@test besseljx(i,Float16(0)) == 0
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@test besselix(i,Float16(0)) == 0
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@test besseljx(i,Complex{Float16}(0)) == 0
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@test besselix(i,Complex{Float16}(0)) == 0
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end
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@testset "Error throwing" begin
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@test_throws AmosException hankelh1x(1, 0)
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@test_throws AmosException hankelh2x(1, 0)
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@test_throws AmosException besselix(-1.01, 0)
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@test_throws AmosException besseljx(-1.01, 0)
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@test_throws AmosException besselyx(1, 0)
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@test_throws DomainError besselix(0.4,-1.0)
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@test_throws DomainError besseljx(0.4, -1.0)
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@test_throws DomainError besselkx(0.4,-1.0)
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@test_throws DomainError besselyx(0.4,-1.0)
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end
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end
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@testset "issue #6653" begin
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@testset "$f" for f in (besselj,bessely,besseli,besselk,hankelh1,hankelh2)
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@test f(0,1) ≈ f(0,Complex{Float64}(1))
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@test f(0,1) ≈ f(0,Complex{Float32}(1))
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@test f(0,1) ≈ f(0,Complex{Float16}(1))
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end
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end
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end

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