Don't hardcode zero in LeftIntegral (#860)

* don't hardcode zero in LeftIntegral

* Verbose testsets

Author: jishnub

src/Extras/fractional.jl

@@ -20,7 +20,7 @@ function LeftIntegral(S::Jacobi,k)
     if S.b==0
         ConcreteLeftIntegral(S,k)
     else
-        J=Jacobi(0.,S.a,domain(S))
+        J=Jacobi(zero(S.a),S.a,domain(S))
         LeftIntegralWrapper(LeftIntegral(J,k)*Conversion(S,J),k)
     end
 end

test/ExtrasTest.jl

@@ -7,7 +7,9 @@ using LinearAlgebra
 using SpecialFunctions
 using Test
 
-@testset "Extras" begin
+include(joinpath(@__DIR__, "testutils.jl"))
+
+@verbose @testset "Extras" begin
     @testset "Dual numbers" begin
         @test dual(1.5,1) ∈  Segment(dual(1.0,1),dual(2.0))
 

test/FractionalTest.jl

@@ -5,8 +5,9 @@ using Test
 using LinearAlgebra
 using SpecialFunctions
 using ApproxFunBaseTest: testfunctional, testbandedoperator
+include(joinpath(@__DIR__, "testutils.jl"))
 
-@testset "Fractional" begin
+@verbose @testset "Fractional" begin
     @testset "Jupyter example" begin
         S = Legendre() ⊕ JacobiWeight(0.5,0.,Ultraspherical(1))
         @time Q½ = LeftIntegral(S,0.5)
@@ -25,122 +26,116 @@ using ApproxFunBaseTest: testfunctional, testbandedoperator
 
     ## Avazzadev et al
 
-    # Example 1
-
-    x=Fun(0..1)
-    Q=gamma(0.5)*LeftIntegral(0.5)
-    @time f=(2/105*sqrt(x)*(105-56x^2+48x^3))
-    u=Q\f
-    @test norm(u-(x^3-x^2+1))<100eps()
-
-
-    # Example 2
-
-    x=Fun(0..1)
-    Q=gamma(0.5)*LeftIntegral(0.5)
-    u=Q\(exp(x)-1)
-    @time @test norm(u-exp(x)*erf(sqrt(x))/sqrt(π)) < 100eps() # 5.0036177384681187e-14
-
-
-    # Example 3
-    x=Fun(0..1)
-    Q=gamma(1/5)*LeftIntegral(1/5)
-    u=Q\(x+1)
-    @test norm(u-(1+1.25x)*sin(0.8π)/(π*x^(1/5))) < 10eps()
-
-    # Example 4
-    x=Fun(0..1)
-    Q=gamma(1-1/3)*LeftIntegral(1-1/3)
-    u=Q\x^(7/6)
-    @test norm(u-7*gamma(1/6)/(18*sqrt(π)*gamma(2/3))*sqrt(x)) < 100eps()
-
-
-    # Example 5
-
-    d=Interval(0,1)
-    x=Fun(d)
-    f=x+4/3*x^(3/2)
-    S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
-    Q=gamma(.5)*LeftIntegral(S,.5)
-
-
-    @time @test sum(f/sqrt(1-x)) ≈ last(Q*f)
-
-    L=I+Q
-    @test last(L.ops[2]*f) ≈ last(Q*f)
-    @test last(L*f) ≈ last(f)+last(Q*f)
-
-    @time u=L\f
-    @test norm(u-x)  < 10eps()
-
-
-    # Example 6
+    @testset "Example 1" begin
+        x=Fun(0..1)
+        Q=gamma(0.5)*LeftIntegral(0.5)
+        @time f=(2/105*sqrt(x)*(105-56x^2+48x^3))
+        u=Q\f
+        @test norm(u-(x^3-x^2+1))<100eps()
+    end
 
-    d=Interval(0,1)
-    x=Fun(d)
-    @time f=x^2+16/15*x^(5/2)
-    S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
-    Q=gamma(.5)*LeftIntegral(S,.5)
-    L=I+Q
-    @time u=L\f
-    @test norm(u-x^2) < 10eps()
 
-    # Example 7
+    @testset "Example 2" begin
+        x=Fun(0..1)
+        Q=gamma(0.5)*LeftIntegral(0.5)
+        u=Q\(exp(x)-1)
+        @time @test norm(u-exp(x)*erf(sqrt(x))/sqrt(π)) < 100eps() # 5.0036177384681187e-14
+    end
 
-    d=Interval(0.,1.)
-    x=Fun(d)
-    f=2sqrt(x)
-    S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
-    Q=gamma(.5)*LeftIntegral(S,.5)
-    @time L=I+Q
-    u=L\f
 
-    @time @test norm(1-exp(π*x)*erfc(sqrt(π*x))-u) < 100eps()
+    @testset "Example 3" begin
+        x=Fun(0..1)
+        Q=gamma(1/5)*LeftIntegral(1/5)
+        u=Q\(x+1)
+        @test norm(u-(1+1.25x)*sin(0.8π)/(π*x^(1/5))) < 10eps()
+    end
 
+    @testset "Example 4" begin
+        x=Fun(0..1)
+        Q=gamma(1-1/3)*LeftIntegral(1-1/3)
+        u=Q\x^(7/6)
+        @test norm(u-7*gamma(1/6)/(18*sqrt(π)*gamma(2/3))*sqrt(x)) < 100eps()
+    end
 
-    # Example 8
+    @testset "Example 5" begin
+        d=Interval(0,1)
+        x=Fun(d)
+        f=x+4/3*x^(3/2)
+        S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
+        Q=gamma(.5)*LeftIntegral(S,.5)
+        @time @test sum(f/sqrt(1-x)) ≈ last(Q*f)
 
-    d=Interval(0.,1.)
-    x=Fun(d)
-    @time f=1/(x+1)+2*Fun(x->asinh(sqrt(x))/sqrt(1+x),JacobiWeight(.5,0.,d))
-    S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
-    Q=gamma(.5)*LeftIntegral(S,.5)
-    L=I+Q
-    u=L\f
-    @test norm((u-1/(x+1)).coefficients) < 1000eps()   # 1.2011889731154679e-14
+        L=I+Q
+        @test last(L.ops[2]*f) ≈ last(Q*f)
+        @test last(L*f) ≈ last(f)+last(Q*f)
 
+        @time u=L\f
+        @test norm(u-x)  < 10eps()
+    end
 
+    @testset "Example 6" begin
+        d=Interval(0,1)
+        x=Fun(d)
+        @time f=x^2+16/15*x^(5/2)
+        S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
+        Q=gamma(.5)*LeftIntegral(S,.5)
+        L=I+Q
+        @time u=L\f
+        @test norm(u-x^2) < 10eps()
+    end
 
+    @testset "Example 7" begin
+        d=Interval(0.,1.)
+        x=Fun(d)
+        f=2sqrt(x)
+        S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
+        Q=gamma(.5)*LeftIntegral(S,.5)
+        @time L=I+Q
+        u=L\f
 
-    ## Test for bug
+        @time @test norm(1-exp(π*x)*erfc(sqrt(π*x))-u) < 100eps()
+    end
 
-    QL = LeftIntegral(0.5)	: Legendre() →	JacobiWeight(0.5,0.,Ultraspherical(1))
-    QU = LeftIntegral(0.5)	: JacobiWeight(0.5,0.,Ultraspherical(1)) → Legendre()
 
+    @testset "Example 8" begin
+        d=Interval(0.,1.)
+        x=Fun(d)
+        @time f=1/(x+1)+2*Fun(x->asinh(sqrt(x))/sqrt(1+x),JacobiWeight(.5,0.,d))
+        S=Legendre(d)⊕JacobiWeight(.5,0.,Jacobi(.5,.5,d))
+        Q=gamma(.5)*LeftIntegral(S,.5)
+        L=I+Q
+        u=L\f
+        @test norm((u-1/(x+1)).coefficients) < 1000eps()   # 1.2011889731154679e-14
+    end
 
-    λ=0.25
-    @time L=[λ*I QU; QL λ*I]
-    @test L[2,5] ≈ 0.
 
 
+    @testset "Test for bug" begin
+        QL = LeftIntegral(0.5)	: Legendre() →	JacobiWeight(0.5,0.,Ultraspherical(1))
+        QU = LeftIntegral(0.5)	: JacobiWeight(0.5,0.,Ultraspherical(1)) → Legendre()
 
-    ## Paper examples
+        λ=0.25
+        @time L=[λ*I QU; QL λ*I]
+        @test L[2,5] ≈ 0.
+    end
 
-    S=Legendre()⊕JacobiWeight(0.5,0.,Ultraspherical(1))
-    Q½=LeftIntegral(S,0.5)
+    @testset "paper examples" begin
+        S=Legendre()⊕JacobiWeight(0.5,0.,Ultraspherical(1))
+        Q½=LeftIntegral(S,0.5)
 
-    y=(I+Q½)\1
+        y=(I+Q½)\1
 
-    x=Fun()
-    @time @test norm(exp(1+x)*erfc(sqrt(1+x))-y) < 100eps()
+        x=Fun()
+        @time @test norm(exp(1+x)*erfc(sqrt(1+x))-y) < 100eps()
 
-    S=Legendre()⊕JacobiWeight(0.5,0.,Ultraspherical(1))
-    x=Fun()
-    Q½=LeftIntegral(S,0.5)
+        S=Legendre()⊕JacobiWeight(0.5,0.,Ultraspherical(1))
+        x=Fun()
+        Q½=LeftIntegral(S,0.5)
 
-    @time y=(I+exp(-(1+x)/2)*Q½[exp((1+x)/2)])\exp(-(1+x)/2)
+        @time y=(I+exp(-(1+x)/2)*Q½[exp((1+x)/2)])\exp(-(1+x)/2)
 
-    @test norm(y-exp((1+x)/2)*erfc(sqrt(1+x))) < 100eps()
+        @test norm(y-exp((1+x)/2)*erfc(sqrt(1+x))) < 100eps()
+    end
 end
 
 end # module

test/NumberTypeTest.jl

@@ -6,7 +6,9 @@ using Test
 using FFTW
 using LinearAlgebra
 
-@testset "BigFloat" begin
+include(joinpath(@__DIR__, "testutils.jl"))
+
+@verbose @testset "BigFloat" begin
     @testset "BigFloat constructor" begin
         single_sin = Fun(sin,Interval(0.f0,1.f0))
         double_sin = Fun(sin,Interval(0.,1.))

test/ReadmeTest.jl

@@ -7,7 +7,9 @@ using Test
 
 const EXAMPLES_DIR = joinpath(dirname(dirname(pathof(ApproxFun))), "examples")
 
-@testset "Readme" begin
+include(joinpath(@__DIR__, "testutils.jl"))
+
+@verbose @testset "Readme" begin
     @testset "Calculus and algebra" begin
         x = Fun(identity,0..10)
         f = sin(x^2)

test/runtests.jl

@@ -24,6 +24,8 @@ DocMeta.setdocmeta!(ApproxFun, :DocTestSetup, :(using ApproxFun); recursive=true
     doctest(ApproxFunBase, manual=false)
 end
 
+include(joinpath(@__DIR__, "testutils.jl"))
+
 include("ReadmeTest.jl")
 include("ExtrasTest.jl")
 include("NumberTypeTest.jl")

test/testutils.jl

@@ -0,0 +1,10 @@
+macro verbose(ex)
+    head = ex.head
+    args = ex.args
+    @assert args[1] == Symbol("@testset")
+    name = args[3] isa String ? args[3] : nothing
+    if VERSION >= v"1.8"
+        insert!(args, 3, Expr(:(=), :verbose, true))
+    end
+    Expr(head, args...)
+end