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Miscellaneous ApproxFunBase tests (#104)
* Misc ApproxFunBase tests * newline * Add EOF newline to miscAFBase.jl
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‎test/miscAFBase.jl

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using ApproxFunBase
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@testset "ApproxFunOrthogonalPolynomials" begin
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@test (@inferred Fun()) == Fun(x->x, Chebyshev())
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@test (@inferred norm(Fun())) ≈ norm(Fun(), 2) ≈ √(2/3) # √∫x^2 dx over -1..1
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v = rand(4)
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v2 = transform(NormalizedChebyshev(), v)
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@test itransform(NormalizedChebyshev(), v2) ≈ v
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f = @inferred Fun(x->x^2, Chebyshev())
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v = @inferred coefficients(f, Chebyshev(), Legendre())
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@test eltype(v) == eltype(coefficients(f))
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@test v ≈ coefficients(Fun(x->x^2, Legendre()))
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# inference check for coefficients
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v = @inferred coefficients(Float64[0,0,1], Chebyshev(), Ultraspherical(1))
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@test v ≈ [-0.5, 0, 0.5]
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@testset "int coeffs" begin
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f = Fun(Chebyshev(), [0,1])
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@test f(0.4) ≈ 0.4
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f = Fun(NormalizedChebyshev(), [0,1])
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@test f(0.4) ≈ 0.4 * √(2/pi)
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f = Fun(Chebyshev(), [1])
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@test f(0.4) ≈ 1
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f = Fun(NormalizedChebyshev(), [1])
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@test f(0.4) ≈ √(1/pi)
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end
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@testset "pad" begin
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@testset "Fun" begin
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f = Fun()
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zf = zero(f)
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@test (@inferred pad([f], 3)) == [f, zf, zf]
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@test (@inferred pad([f, zf], 1)) == [f]
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v = [f, zf]
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@test @inferred pad!(v, 1) == [f]
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@test length(v) == 1
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end
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end
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@testset "inplace transform" begin
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@testset for sp_c in Any[Legendre(), Chebyshev(), Jacobi(1,2), Jacobi(0.3, 2.3),
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Ultraspherical(1), Ultraspherical(2)]
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@testset for sp in Any[sp_c, NormalizedPolynomialSpace(sp_c)]
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v = rand(10)
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v2 = copy(v)
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@test itransform!(sp, transform!(sp, v)) ≈ v
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@test transform!(sp, v) ≈ transform(sp, v2)
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@test itransform(sp, v) ≈ v2
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@test itransform!(sp, v) ≈ v2
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# different vector
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p_fwd = ApproxFunBase.plan_transform!(sp, v)
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p_inv = ApproxFunBase.plan_itransform!(sp, v)
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@test p_inv * copy(p_fwd * copy(v)) ≈ v
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end
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end
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end
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@testset "conversion" begin
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C12 = Conversion(Chebyshev(), NormalizedLegendre())
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C21 = Conversion(NormalizedLegendre(), Chebyshev())
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@test Matrix((C12 * C21)[1:10, 1:10]) ≈ I
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@test Matrix((C21 * C12)[1:10, 1:10]) ≈ I
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C12 = Conversion(Chebyshev(), NormalizedPolynomialSpace(Ultraspherical(1)))
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C1C2 = Conversion(Ultraspherical(1), NormalizedPolynomialSpace(Ultraspherical(1))) *
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Conversion(Chebyshev(), Ultraspherical(1))
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@test Matrix(C12[1:10, 1:10]) ≈ Matrix(C1C2[1:10, 1:10])
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end
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@testset "union" begin
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@test union(Chebyshev(), NormalizedLegendre()) == Jacobi(Chebyshev())
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@test union(Chebyshev(), Legendre()) == Jacobi(Chebyshev())
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end
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@testset "Fun constructor" begin
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# we make the fun go through somewhat complicated chains of functions
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# that break inference of the space
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# however, the type of coefficients should be inferred correctly.
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f = Fun(Chebyshev(0..1))
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newfc(f) = coefficients(Fun(Fun(f, Legendre(0..1)), space(f)))
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newvals(f) = values(Fun(Fun(f, Legendre(0..1)), space(f)))
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@test newfc(f) ≈ coefficients(f)
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@test newvals(f) ≈ values(f)
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newfc2(f) = coefficients(chop(pad(f, 10)))
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@test newfc2(f) == coefficients(f)
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f2 = Fun(space(f), view(Float64[1:4;], :))
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f3 = Fun(space(f), Float64[1:4;])
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@test newvals(f2) ≈ values(f3)
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@test values(f2) ≈ values(f3)
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# Ensure no trailing zeros
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f = Fun(Ultraspherical(0.5, 0..1))
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cf = coefficients(f)
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@test findlast(!iszero, cf) == length(cf)
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@testset "OneHotVector" begin
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for n in [1, 3, 10_000]
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f = Fun(Chebyshev(), [zeros(n-1); 1])
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g = ApproxFunBase.basisfunction(Chebyshev(), n)
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@test f == g
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@test f(0.5) == g(0.5)
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end
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end
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end
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@testset "multiplication of Funs" begin
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f = Fun(Chebyshev(), Float64[1:101;])
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g = Fun(Chebyshev(), Float64[1:101;]*im)
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@test f(0.5)*g(0.5) ≈ (f*g)(0.5)
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end
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@testset "Multivariate" begin
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@testset for S in Any[Chebyshev(), Legendre()]
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f = Fun(x->ones(2,2), S)
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@test (f+1) * f ≈ (1+f) * f ≈ f^2 + f
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@test (f-1) * f ≈ f^2 - f
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@test (1-f) * f ≈ f - f^2
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@test f + f ≈ 2f ≈ f*2
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end
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end
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@testset "static coeffs" begin
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f = Fun(Chebyshev(), SA[1,2,3])
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g = Fun(Chebyshev(), [1,2,3])
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@test coefficients(f^2) == coefficients(g^2)
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end
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@testset "special functions" begin
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for f in Any[Fun(), Fun(-0.5..1), Fun(Segment(1.0+im,2.0+2im))]
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for spfn in Any[sin, cos, exp]
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p = leftendpoint(domain(f))
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@test spfn(f)(p) ≈ spfn(p) atol=1e-14
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end
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end
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end
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@testset "Derivative" begin
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@test Derivative() == Derivative()
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for d in Any[(), (0..1,)]
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for ST in Any[Chebyshev, Legendre,
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(x...) -> Jacobi(2,2,x...), (x...) -> Jacobi(1.5,2.5,x...)]
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S1 = ST(d...)
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for S in [S1, NormalizedPolynomialSpace(S1)]
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@test Derivative(S) == Derivative(S,1)
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@test Derivative(S)^2 == Derivative(S,2)
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f = Fun(x->x^3, S)
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@test Derivative(S) * f ≈ Fun(x->3x^2, S)
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@test Derivative(S,2) * f ≈ Fun(x->6x, S)
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@test Derivative(S,3) * f ≈ Fun(x->6, S)
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@test Derivative(S,4) * f ≈ zeros(S)
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end
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end
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end
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@test Derivative(Chebyshev()) != Derivative(Chebyshev(), 2)
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@test Derivative(Chebyshev()) != Derivative(Legendre())
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end
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@testset "SubOperator" begin
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D = Derivative(Chebyshev())
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S = @view D[1:10, 1:10]
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@test rowrange(S, 1) == 2:2
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@test colrange(S, 2) == 1:1
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@test (@inferred BandedMatrix(S)) == (@inferred Matrix(S))
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end
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@testset "CachedOperator" begin
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C = cache(Derivative())
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C = C : Chebyshev() → Ultraspherical(2)
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D = Derivative() : Chebyshev() → Ultraspherical(2)
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@test C[1:2, 1:0] == D[1:2, 1:0]
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@test C[1:10, 1:10] == D[1:10, 1:10]
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for col in 1:5, row in 1:5
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@test C[row, col] == D[row, col]
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end
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end
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@testset "PartialInverseOperator" begin
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@testset "sanity check" begin
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A = UpperTriangular(rand(10, 10))
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B = inv(A)
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for I in CartesianIndices(B)
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@test B[I] ≈ ApproxFunBase._getindexinv(A, Tuple(I)..., UpperTriangular)
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end
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end
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C = Conversion(Chebyshev(), Ultraspherical(1))
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P = PartialInverseOperator(C, (0, 6))
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Iapprox = (P * C)[1:10, 1:10]
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@test all(isone, diag(Iapprox))
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for k in axes(Iapprox,1), j in k + 1:min(k + bandwidths(P,2), size(Iapprox, 2))
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@test Iapprox[k,j] ≈ 0 atol=eps(eltype(Iapprox))
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end
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B = AbstractMatrix(P[1:10, 1:10])
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@testset for I in CartesianIndices(B)
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@test B[I] ≈ P[Tuple(I)...] rtol=1e-8 atol=eps(eltype(B))
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end
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end
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@testset "istriu/istril" begin
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for D in Any[Derivative(Chebyshev()),
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Conversion(Chebyshev(), Legendre()),
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Multiplication(Fun(Chebyshev()), Chebyshev())]
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D2 = D[1:3, 1:3]
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for f in Any[istriu, istril]
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@test f(D) == f(D2)
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@test f(D') == f(D2')
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end
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end
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end
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@testset "inplace ldiv" begin
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@testset for T in [Float32, Float64, ComplexF32, ComplexF64]
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v = rand(T, 4)
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v2 = copy(v)
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ApproxFunBase.ldiv_coefficients!(Conversion(Chebyshev(), Ultraspherical(1)), v)
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@test ApproxFunBase.ldiv_coefficients(Conversion(Chebyshev(), Ultraspherical(1)), v2) ≈ v
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end
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end
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@testset "specialfunctionnormalizationpoint" begin
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a = @inferred ApproxFunBase.specialfunctionnormalizationpoint(exp,real,Fun())
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@test a[1] == 1
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@test a[2] ≈ exp(1)
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end
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end

‎test/runtests.jl

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include("SpeedPDETest.jl")
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include("SpeedOperatorTest.jl")
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include("showtest.jl")
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include("miscAFBase.jl")

‎test/showtest.jl

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using ApproxFunBase
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@testset "show" begin
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@test repr(Chebyshev()) == "Chebyshev()"
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@test repr(NormalizedChebyshev()) == "NormalizedChebyshev()"
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@test repr(Ultraspherical(1,0..1)) == "Ultraspherical(1,0..1)"
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@test repr(Legendre(0..1)) == "Legendre(0..1)"
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@test repr(Jacobi(1,2,0..1)) == "Jacobi(1.0,2.0,0..1)"
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io = IOBuffer()
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@testset "Derivative" begin
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D = Derivative()
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summarystr = summary(D)
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@test repr(D) == summarystr
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show(io, MIME"text/plain"(), D)
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@test contains(String(take!(io)), summarystr)
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D = Derivative(Chebyshev())
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summarystr = summary(D)
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show(io, MIME"text/plain"(), D)
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@test contains(String(take!(io)), summarystr)
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end
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@testset "SubOperator" begin
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D = Derivative(Chebyshev())
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S = @view D[1:10, 1:10]
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summarystr = summary(S)
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show(io, MIME"text/plain"(), S)
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@test contains(String(take!(io)), summarystr)
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end
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@testset "Evaluation" begin
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E = Evaluation(Chebyshev(), 0)
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summarystr = summary(E)
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show(io, MIME"text/plain"(), E)
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@test contains(String(take!(io)), summarystr)
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EA = Evaluation(Chebyshev(), 0)'
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summarystr = summary(EA)
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show(io, MIME"text/plain"(), EA)
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@test contains(String(take!(io)), summarystr)
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EA = transpose(Evaluation(Chebyshev(), 0))
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summarystr = summary(EA)
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show(io, MIME"text/plain"(), EA)
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@test contains(String(take!(io)), summarystr)
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end
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end

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