Run tests in parallel

Project.toml

@@ -41,6 +41,7 @@ FFTW = "1"
 FastTransforms = "0.13, 0.14, 0.15, 0.16, 0.17"
 IntervalSets = "0.7.5"
 LinearAlgebra = "1"
+ParallelTestRunner = "2"
 Random = "1"
 RecipesBase = "1.0"
 Reexport = "1.0"
@@ -57,8 +58,9 @@ Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 DualNumbers = "fa6b7ba4-c1ee-5f82-b5fc-ecf0adba8f74"
 FFTW = "7a1cc6ca-52ef-59f5-83cd-3a7055c09341"
 IntervalSets = "8197267c-284f-5f27-9208-e0e47529a953"
+ParallelTestRunner = "d3525ed8-44d0-4b2c-a655-542cee43accc"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["Aqua", "BandedMatrices", "BlockBandedMatrices", "Documenter", "DualNumbers", "FFTW", "Random", "Test"]
+test = ["Aqua", "BandedMatrices", "BlockBandedMatrices", "Documenter", "DualNumbers", "FFTW", "ParallelTestRunner", "Random", "Test"]

test/AquaTest.jl

@@ -0,0 +1,5 @@
+using Aqua
+@testset "Project quality" begin
+    Aqua.test_all(ApproxFun, ambiguities=false, undefined_exports=false,
+        stale_deps=(; ignore=[:ApproxFunBaseTest]), piracies = false)
+end

test/BugInMultiplicationTest.jl

@@ -0,0 +1,19 @@
+using Test
+using ApproxFun
+using ApproxFunBase
+
+@testset "Bug in Multiplication" begin
+    dom = Interval(0.001, 1) × PeriodicSegment(-pi, pi)
+    @test blocklengths(Space(dom)) == 2:2:∞
+    r,r2 = Fun((r,t) -> [r;r^2], dom)
+    @test r(0.1,0.2) ≈ 0.1
+    @test r2(0.1,0.2) ≈ 0.1^2
+    sp = Space(dom)
+    Dr = Derivative(sp, [1,0])
+    @test blockbandwidths(Dr) == (-1,1)
+    @test subblockbandwidths(Dr)  == (1,3)
+    Dθ = Derivative(sp, [0,1])
+    Mr = Multiplication(Fun( (r, θ) -> r, sp ), sp)
+    rDr = Mr * Dr
+    testbandedblockbandedoperator(rDr)
+end

test/ChebyshevAndFourierTest.jl

@@ -0,0 +1,8 @@
+using Test
+using ApproxFun
+
+@testset "Chebyshev and Fourier" begin
+    @test norm(Fun(x->Fun(cos,Fourier(-π .. π),20)(x),20)-Fun(cos,20)) <100eps()
+    @test norm(Fun(x->Fun(cos,Fourier(-π .. π))(x))-Fun(cos)) <100eps()
+    @test norm(Fun(x->Fun(cos,Laurent)(x))-Fun(cos)) <100eps()
+end

test/ConversionTest.jl

@@ -0,0 +1,8 @@
+using Test
+using ApproxFun
+
+@testset "Conversion" begin
+    f=Fun(t->[cos(t) 0;sin(t) 1],-π..π)
+    g=Fun(f,Space(PeriodicSegment(-π,π)))
+    @test g(.1) ≈ f(.1)
+end

test/DefiniteIntegralTest.jl

@@ -0,0 +1,9 @@
+using Test
+using ApproxFun
+
+@testset "definite integral" begin
+    Σ = DefiniteIntegral()
+    f1 = Fun(t->cos(cos(t)),-π..π)
+    f = Fun(t->cos(cos(t)),Laurent(-π..π))
+    @test sum(f1) ≈ Σ*f
+end

test/DocstringsTest.jl

@@ -0,0 +1,8 @@
+using Documenter
+DocMeta.setdocmeta!(ApproxFunBase, :DocTestSetup, :(using ApproxFun); recursive=true)
+DocMeta.setdocmeta!(ApproxFun, :DocTestSetup, :(using ApproxFun); recursive=true)
+
+@testset "doctests" begin
+    doctest(ApproxFun)
+    doctest(ApproxFunBase, manual=false)
+end

test/ExtendingFunctionTest.jl

@@ -0,0 +1,9 @@
+using Test
+using ApproxFun
+
+@testset "Extending function" begin
+    Γ = Segment(-im,1.0-im) ∪ Curve(Fun(x->exp(0.8im)*(x+x^2-1+im*(x-4x^3+x^4)/6))) ∪ Circle(2.0,0.2)
+    @test isempty(component(Γ,1)\component(Γ,1))
+    @test Γ \ component(Γ,1) == component(Γ,2) ∪ component(Γ,3)
+    @test norm(Fun(ones(component(Γ,1)),Γ) - Fun(x->x ∈ component(Γ,1) ? 1.0 : 0.0,Γ)) == 0
+end

test/LaplaceInAStripTest.jl

@@ -0,0 +1,17 @@
+using Test
+using ApproxFun
+
+@testset "Laplace in a strip" begin
+    d = PeriodicSegment() × ChebyshevInterval()
+    g=Fun((x,y)->real(cos(x+im*y)),∂(d))
+    @test g(0.1,1.0) ≈ real(cos(0.1+im))
+    @test g(0.1,-1.0) ≈ real(cos(0.1-im))
+    v=[g;0]
+    @test v(0.1,-1) ≈ [real(cos(0.1-im));0]
+    A=[Dirichlet(d);Laplacian(d)]
+    a = space(v)
+    b = rangespace(A)
+    @test Fun(component(v[1],1), component(b[1],1))(0.1,-1.0) ≈ v(0.1,-1.0)[1]
+    @test Fun(component(v[1],2), component(b[1],2))(0.1,1.0) ≈ v(0.1,1.0)[1]
+    @test ApproxFun.default_Fun(v[1] , b[1])(0.1,1.0) ≈ v(0.1,1.0)[1]
+end

test/MixFourierChebyshevTest.jl

@@ -0,0 +1,17 @@
+using Test
+using ApproxFun
+
+@testset "Mix Fourier-Chebyshev (#602)" begin
+    s = Chebyshev(-π..π)
+    a = Fun(t-> 1+sin(cos(2t)), s)
+    L = Derivative() + a
+    f = Fun(t->exp(sin(10t)), s)
+    B = periodic(s,0)
+    @time uChebyshev = [B;L] \ [0.;f]
+    s = Fourier(-π..π)
+    a = Fun(t-> 1+sin(cos(2t)), s)
+    L = Derivative() + a
+    f = Fun(t->exp(sin(10t)), s)
+    @time uFourier = L\f
+    @test norm(uFourier-uChebyshev) ≤ 100eps()
+end

test/NonlinearPowTest.jl

@@ -0,0 +1,16 @@
+using Test
+using ApproxFun
+
+@testset "nonlinear pow" begin
+    x  = Fun(identity, 0..10)
+    n = 2
+    u₀ = 0.0x # initial guess
+    N = u -> [u'(0), u(0)-1, x*u'' + 2*u' + x*u^n]
+    u = newton(N, u₀) # perform Newton iteration in function space
+    @test u(0.1) ≈ 0.9983349985461484
+    n = 4.5
+    u₀ = 0.0x+1 # initial guess
+    N = u -> [u'(0), u(0)-1, x*u'' + 2*u' + x*u^n]
+    u = newton(N, u₀) # perform Newton iteration in function space
+    @test u(0.1) ≈ 0.9983370741307388
+end

test/NullSpaceTest.jl

@@ -0,0 +1,19 @@
+using Test
+using ApproxFun
+
+@testset "Null space" begin
+    d=ChebyshevInterval()
+    D=Derivative(d)
+    A=D^2-I
+    @time κ=nullspace(A)
+    @test length(κ) == 2
+    c=[κ(0.);κ'(0.)]\[exp(0.),exp(0.)]
+    u=(κ*c)[1]
+    @test u(1.0) ≈ ℯ
+    d=(-50..5.)
+    x=Fun(identity,d)
+    D=Derivative(d)
+    @time u=nullspace(D^2-x)
+    c=[u(leftendpoint(d)); u(rightendpoint(d))]\[airyai.(endpoints(d))...]
+    @test norm((u*c)[1]-Fun(airyai,d))<10000eps()
+end

test/PeriodicXIntervalTest.jl

@@ -0,0 +1,32 @@
+using Test
+using ApproxFun
+using Random
+using LinearAlgebra
+using ApproxFunBase
+
+@testset "periodic x interval" begin
+    dθ=PeriodicSegment(-2.,2.)
+    dt=Interval(0,1.)
+    d=dθ×dt
+    Dθ=Derivative(d,[1,0])
+    Dt=Derivative(d,[0,1])
+    u0=Fun(θ->exp(-20θ^2), dθ)
+    ε = 0.1
+    u=\([I⊗ldirichlet(dt); Dt-ε*Dθ^2-Dθ], [u0; 0.]; tolerance=1E-4)
+    @test ≈(u(0.1,0.2),0.3103472600253807;atol=1E-2)
+    A=Dt+Dθ
+    ApproxFunBase.TestUtils.testbandedblockbandedoperator(A)
+    u=\([I⊗ldirichlet(dt); Dt+Dθ], [u0; 0.0]; tolerance=1E-6)
+    @test ≈(u(0.2,0.1),u0(0.1);atol=1E-6)
+
+    d=PeriodicSegment() × ChebyshevInterval()
+    u_ex=Fun((x,y)->real(cos(x+im*y)),d)
+    @test u_ex(1.0,0.1) ≈ real(cos(1.0+im*0.1)) atol=10eps()
+    B=Dirichlet(Space(d))
+    @test B.order == 0
+    g=Fun((x,y)->real(cos(x+im*y)),rangespace(B))
+    @test norm((B*u_ex-g).coefficients) < 100eps()
+    testbandedblockbandedoperator(Laplacian(d))
+    @time u=[B;Laplacian(d)]\[g;0.]
+    @test u(.1,.2) ≈ real(cos(.1+.2im))
+end

test/PiecewiseSampleTest.jl

@@ -0,0 +1,11 @@
+using Test
+using ApproxFun
+
+@testset "piecewise sample (#635)" begin
+    f = abs(Fun(sin, -5..5))
+    @test integrate(f)(-4.0) ≈ -(cos(-4.0) - cos(-5.0))
+    @test -(cos(-π) - cos(-5.0)) + cos(-3.0) - cos(-π) ≈ integrate(f)(-3.0)
+    r = ApproxFun.sample(f,10)
+    @test maximum(r) ≤ 5
+    @test minimum(r) ≥ -5
+end

test/PiecewiseSpaceDefiniteIntegralTest.jl

@@ -0,0 +1,13 @@
+using Test
+using ApproxFun
+using Random
+
+@testset "Piecewise space definite integral" begin
+    Γ=Segment(-im,1.0-im) ∪ Curve(Fun(x->exp(0.8im)*(x+x^2-1+im*(x-4x^3+x^4)/6))) ∪ Circle(2.0,0.2)
+    z=Fun(Γ)
+    S=PiecewiseSpace(map(d->isa(d,Circle) ? Fourier(d) : JacobiWeight(0.5,0.5,Ultraspherical(1,d)),components(Γ)))
+    B=DefiniteLineIntegral(S)
+    Random.seed!(0)
+    f=Fun(S,rand(20))
+    @test B*f ≈ linesum(component(f,1)) + linesum(component(f,2)) + linesum(component(f,3))
+end

test/SampleTest.jl

@@ -0,0 +1,8 @@
+using Test
+using ApproxFun
+
+@testset "sample" begin
+    f=Fun(exp)
+    sample(f,100000)
+    @time sample(f,100000)
+end

test/SamplingTest.jl

@@ -0,0 +1,13 @@
+using Test
+using ApproxFun
+
+@testset "Sampling" begin
+    ff=(x,y)->(x-y)^2*exp(-x^2/2-y^2/2)
+    f=Fun(ff,Domain(-4..4)^2)
+    r=ApproxFun.sample(f,5000)
+    g=sum(f,1)/sum(f)
+    @test  g(0.1) ≈ 0.2004758624973169
+    f = Fun(x -> exp(-x^2/2),-5..5)
+    g = cumsum(f)
+    @test g(ApproxFun.bisectioninv(g,0.5)) ≈ 0.5
+end

test/ShowTest.jl

@@ -0,0 +1,21 @@
+using Test
+using ApproxFun
+
+@testset "show" begin
+    op = Derivative(Chebyshev())
+    io = IOBuffer()
+    @test summary(io, op) isa Nothing
+    @test contains(String(take!(io)), " : $(domainspace(op)) → $(rangespace(op))")
+    show(io, op)
+    @test contains(String(take!(io)), " : $(domainspace(op)) → $(rangespace(op))")
+    @test summary(io, ApproxFun.ArraySpace(Chebyshev(), 2)) isa Nothing
+    @test contains(String(take!(io)), "ArraySpace")
+    Q = QuotientSpace(Dirichlet(Chebyshev()))
+    @test startswith(repr(Q), "Chebyshev() /")
+    show(io, MIME"text/plain"(), Q)
+    s = String(take!(io))
+    @test startswith(s, "Chebyshev() /")
+    f = Fun(Chebyshev()^2, [1,3,4])
+    @test contains(repr(f), repr(space(f)))
+    @test contains(repr(f), repr(coefficients(f)))
+end