Move out more Fourier code

Author: dlfivefifty

src/Domains/Domains.jl

@@ -7,3 +7,31 @@ include("IntervalCurve.jl")
 
 isless(d1::IntervalOrSegment{T1},d2::Ray{false,T2}) where {T1<:Real,T2<:Real} = d1 ≤ d2.center
 isless(d2::Ray{true,T2},d1::IntervalOrSegment{T1}) where {T1<:Real,T2<:Real} = d2.center ≤ d1
+
+
+## set minus
+function Base.setdiff(d::Union{AbstractInterval,Segment,Ray,Line}, ptsin::UnionDomain{AS}) where {AS <: AbstractVector{P}} where {P <: Point}
+    pts=Number.(elements(ptsin))
+    isempty(pts) && return d
+    tol=sqrt(eps(arclength(d)))
+    da=leftendpoint(d)
+    isapprox(da,pts[1];atol=tol) && popfirst!(pts)
+    isempty(pts) && return d
+    db=rightendpoint(d)
+    isapprox(db,pts[end];atol=tol) && pop!(pts)
+
+    sort!(pts)
+    leftendpoint(d) > rightendpoint(d) && reverse!(pts)
+    filter!(p->p ∈ d,pts)
+
+    isempty(pts) && return d
+    length(pts) == 1 && return d \ pts[1]
+
+    ret = Array{Domain}(undef, length(pts)+1)
+    ret[1] = Domain(leftendpoint(d) .. pts[1])
+    for k = 2:length(pts)
+        ret[k] = Domain(pts[k-1]..pts[k])
+    end
+    ret[end] = Domain(pts[end] .. rightendpoint(d))
+    UnionDomain(ret)
+end

test/FullPDETest.jl

@@ -250,36 +250,6 @@ import ApproxFun: resizedata!, CachedOperator, RaggedMatrix, testbandedblockband
         end
     end
 
-    @testset "Periodic Poisson" begin
-        d=PeriodicSegment()^2
-        S=Space(d)
-
-        f=Fun((x,y)->exp(-10(sin(x/2)^2+sin(y/2)^2)),d)
-        A=Laplacian(d)+0.1I
-        testbandedblockbandedoperator(A)
-        @time u=A\f
-        @test u(.1,.2) ≈ u(.2,.1)
-        @test (lap(u)+.1u-f)|>coefficients|>norm < 1000000eps()
-    end
-
-
-    @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
-        @time 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
-        testbandedblockbandedoperator(A)
-
-        @time u=\([I⊗ldirichlet(dt);Dt+Dθ],[u0;0.0];tolerance=1E-6)
-        @test ≈(u(0.2,0.1),u0(0.1);atol=1E-6)
-    end
-
     @testset "Small diffusion" begin
         dx=ChebyshevInterval();dt=Interval(0,0.2)
         d=dx×dt
@@ -301,25 +271,6 @@ import ApproxFun: resizedata!, CachedOperator, RaggedMatrix, testbandedblockband
         @test u(.1,.2) ≈ 0.46810331039791464
     end
 
-    @testset "Laplace in a strip" begin
-        d=PeriodicSegment() × ChebyshevInterval()
-        g=Fun((x,y)->real(cos(x+im*y)),∂(d))  # boundary data
-
-
-        @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
-
     @testset "concatenate InterlaceOperator" begin
         a=Fun(x -> 0 ≤ x ≤ 0.5 ? 0.5 : 1, Domain(-1..1) \ [0,0.5])
         @test a(0.1) == 0.5

test/IntegralEquationsTest.jl

@@ -133,21 +133,6 @@ using ApproxFunOrthogonalPolynomials, ApproxFunBase, IntervalSets, Random, Linea
         testbandedbelowoperator(L)
     end
 
-    @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
-
-
     @testset "union domain" begin
         dom = ApproxFun.UnionDomain(0..1, 2..3)
         ⨍ = DefiniteLineIntegral(union(JacobiWeight.(-0.5,-0.5,ChebyshevDirichlet{1,1}.(components(dom)))...))

test/MultivariateTest.jl

@@ -222,28 +222,6 @@ using ApproxFun, LinearAlgebra, SpecialFunctions, Test
         testbandedblockbandedoperator(L)
     end
 
-    @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 ApproxFun.blockbandwidths(Dr) == (-1,1)
-        @test ApproxFun.subblockbandwidths(Dr)  == (1,3)
-
-        Dθ = Derivative(sp, [0,1])
-        Mr = Multiplication(Fun( (r, θ) -> r, sp ), sp)
-        rDr = Mr * Dr
-
-        testbandedblockbandedoperator(rDr)
-    end
-
     @testset "Cheby * Interval" begin
         d = ChebyshevInterval()^2
         x,y = Fun(∂(d))
@@ -257,12 +235,6 @@ using ApproxFun, LinearAlgebra, SpecialFunctions, Test
         @test exp(x+im*y)(1.0,0.1) ≈ exp(1.0+0.1im)
     end
 
-
-    @testset "Taylor()^2, checks bug in type of plan_transform" begin
-        f = Fun((x,y)->exp((x-0.1)*cos(y-0.2)),Taylor()^2)
-        @test f(0.2,0.3) ≈ exp(0.1*cos(0.1))
-    end
-
     @testset "DefiniteIntegral" begin
         f = Fun((x,y) -> exp(-x*cos(y)))
         @test Number(DefiniteIntegral()*f) ≈ sum(f)
@@ -299,10 +271,6 @@ using ApproxFun, LinearAlgebra, SpecialFunctions, Test
         g = Fun(1, Segment(Vec(0,-1) , Vec(π,-1)))
         @test g(0.1,-1) ≈ 1
         @test g(0.1,1) ≈ 0
-
-        g = Fun(1, PeriodicSegment(Vec(0,-1) , Vec(π,-1)))
-        @test g(0.1,-1) ≈ 1
-        @test g(0.1,1) ≈ 0
     end
 
 

test/ODETest.jl

@@ -38,7 +38,6 @@ using ApproxFunOrthogonalPolynomials, ApproxFunBase, SpecialFunctions, LazyArray
         @test ≈(u(0.),airyai(0.);atol=10ncoefficients(u)*eps())
 
         B=Neumann(d);
-        @which B.op[1,2]
         A=[B;D2-X];
         b=[[airyaiprime(leftendpoint(d)),airyaiprime(rightendpoint(d))],0.];
 

test/PDETest.jl

@@ -80,26 +80,6 @@ using ApproxFun, LinearAlgebra, Test
         @test u(0.1,0.2) ≈ 1.0
     end
 
-    @testset "Periodic x Interval" begin
-        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  # tests stupid bug
-        g=Fun((x,y)->real(cos(x+im*y)),rangespace(B))  # boundary data
-
-        @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
-
     @testset "Schrodinger" begin
         dx=0..1; dt=0.0..0.001
         C=Conversion(Chebyshev(dx)*Ultraspherical(1,dt),Ultraspherical(2,dx)*Ultraspherical(1,dt))

test/SingularitiesTest.jl

@@ -117,20 +117,6 @@ using ApproxFun, IntervalSets, SpecialFunctions, LinearAlgebra, Random, Test
             @test f'(0.1) ≈ -2*0.1exp(-0.1^2)
             @test (Derivative()*f)(0.1) ≈ -2*0.1exp(-0.1^2)
         end
-
-        @testset "PeriodicLine" begin
-            d=PeriodicLine()
-            D=Derivative(d)
-
-            f = Fun(x->sech(x-0.1),d,200)
-            @test f(1.) ≈ sech(1-0.1)
-
-            f=Fun(x->sech(x-0.1),d)
-            @test f(1.) ≈ sech(1-0.1)
-
-            @test ≈((D*f)(.2),-0.0991717226583897;atol=100000eps())
-            @test ≈((D^2*f)(.2),-0.9752522555114987;atol=1000000eps())
-        end
     end
 
     @testset "LogWeight" begin

test/SpacesTest.jl

@@ -161,16 +161,6 @@ using ApproxFun, SpecialFunctions, LinearAlgebra, Test
         @test f(0.1) ≈ (C*f)(0.1)
     end
 
-    @testset "Piecewise + Constant" begin
-        Γ=Circle() ∪ Circle(0.0,0.4)
-        o=ones(Γ)
-        @test o(1.) ≈ 1.0
-        @test o(0.4) ≈ 1.0
-
-        @time G=Fun(z->in(z,component(Γ,2)) ? [1 0; -1/z 1] : [z 0; 0 1/z],Γ)
-        @test (G-I)(exp(0.1im)) ≈ (G(exp(0.1im))-I)
-    end
-
     @testset "Previoius segfault" begin
         x=Fun(identity,-1..1)
         @time f=x+sin(2x)*sqrt(1-x^2)
@@ -223,19 +213,7 @@ using ApproxFun, SpecialFunctions, LinearAlgebra, Test
         @test exp(z)(0.1exp(0.2im)) ≈ exp(0.1exp(0.2im))
     end
 
-    @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
-
     @testset "Line" begin
-        f=Fun(z->2exp(z^2),PeriodicLine(0.,π/2))
-        @test f(1.1im) ≈ 2exp(-1.1^2)
-
         f=Fun(z->2exp(z^2),Line(0.,π/2))
         @test f(1.1im) ≈ 2exp(-1.1^2)
     end

test/VectorTest.jl

@@ -75,55 +75,6 @@ using ApproxFunOrthogonalPolynomials, ApproxFunBase, LazyArrays, FillArrays, Lin
         @test (m+I)(0.1) ≈ m(0.1)+I
     end
 
-    @testset "CosSpace Vector" begin
-        a = [1 2; 3 4]
-        f = Fun(θ->[1,cos(θ)],CosSpace())
-        @test (a*f)(0.1) ≈ [1+2cos(0.1); 3+4cos(0.1)]
-        @test (a*f)(0.1) ≈ a*f(0.1)
-        @test Fun(a)*f ≈ a*f
-        @test Fun(a*Array(f)) ≈ a*f
-    end
-
-    @testset "CosSpace Matrix" begin
-        a = [1 2; 3 4]
-        m = Fun(θ->[1 cos(θ); cos(2θ) cos(cos(θ))],CosSpace())
-        @test (a*m)(0.1) ≈ a*m(0.1)
-        @test (m*a)(0.1) ≈ m(0.1)*a
-        @test Fun(a)*m   ≈ a*m
-        @test Fun(a*Array(m))   ≈ a*m
-
-        @test (a+m)(0.1) ≈ a+m(0.1)
-        @test (m+a)(0.1) ≈ m(0.1)+a
-
-        @test (m+I)(0.1) ≈ m(0.1)+I
-    end
-
-    @testset "SinSpace Vector" begin
-        a = [1 2; 3 4]
-        f = Fun(θ->[sin(θ),sin(2θ)],SinSpace())
-        @test (a*f)(0.1) ≈ a*f(0.1)
-        @test Fun(a)*f ≈ a*f
-        @test Fun(a*Array(f)) ≈ a*f
-
-        @test all(sp -> sp isa SinSpace, space(a*f).spaces)
-    end
-
-    @testset "CosSpace Matrix" begin
-        a = [1 2; 3 4]
-        m = Fun(θ->[sin(3θ) sin(θ); sin(2θ) sin(sin(θ))],SinSpace())
-        @test (a*m)(0.1) ≈ a*m(0.1)
-        @test (m*a)(0.1) ≈ m(0.1)*a
-        @test Fun(a)*m   ≈ a*m
-        @test Fun(a*Array(m))   ≈ a*m
-
-        @test all(sp -> sp isa SinSpace, space(a*m).spaces)
-
-        @test (a+m)(0.1) ≈ a+m(0.1)
-        @test (m+a)(0.1) ≈ m(0.1)+a
-
-        @test (m+I)(0.1) ≈ m(0.1)+I
-end
-
     @testset "Matrix{Fun}*Matrix{Fun}" begin
     # note that 2x2 and 3x3 mult are special cases
         x=Fun()
@@ -220,71 +171,7 @@ end
         @test norm((([1 2;3 4]*f)-Fun(t->[t^2+2sin(t),3t^2+4sin(t)])).coefficients)<100eps()
     end
 
-    @testset "Two circles" begin
-        Γ = Circle() ∪ Circle(0.5)
-
-        f = Fun(z -> in(z,component(Γ,2)) ? 1 : z,Γ)
-        @test f(exp(0.1im)) ≈ exp(0.1im)
-        @test f(0.5exp(0.1im)) ≈ 1
-
-        G = Fun(z -> in(z,component(Γ,2)) ? [1 -z^(-1); 0 1] :
-                                            [z 0; 0 z^(-1)], Γ);
-
-        @test G(exp(0.1im)) ≈ [exp(0.1im) 0 ; 0 exp(-0.1im)]
-        @test G(0.5exp(0.1im)) ≈ [1 -2exp(-0.1im) ; 0 1]
-
-        G1=Fun(Array(G)[:,1])
-
-        @test G1(exp(0.1im)) ≈ [exp(0.1im),0.]
-        @test G1(0.5exp(0.1im)) ≈ [1,0.]
-
-        M = Multiplication(G, space(G1))
-        testblockbandedoperator(M)
-
-        for z in (0.5exp(0.1im),exp(0.2im))
-            @test G[1,1](z) ≈ G[1](z)
-            @test (M.op.ops[1,1]*G1[1])(z) ≈ M.f[1,1](z)*G1[1](z)
-            @test (M.op.ops[2,1]*G1[1])(z) ≈ M.f[2,1](z)*G1[1](z)
-            @test (M.op.ops[1,2]*G1[2])(z) ≈ M.f[1,2](z)*G1[2](z)
-            @test (M.op.ops[2,2]*G1[2])(z) ≈ M.f[2,2](z)*G1[2](z)
-        end
-
-        u = M*G1
-        @test norm(u(exp(.1im))-[exp(.2im),0])<100eps()
-        @test norm(u(.5exp(.1im))-[1,0])<100eps()
-    end
-
-    @testset "Circle" begin
-        G = Fun(z->[-1 -3; -3 -1]/z +
-                   [ 2  2;  1 -3] +
-                   [ 2 -1;  1  2]*z, Circle())
-
-        @test G[1,1](exp(0.1im)) == G(exp(0.1im))[1,1]
-
-        F̃ = Array((G-I)[:,1])
-        F = (G-I)[:,1]
-
-        @test Fun(F) ≡ F
-
-        @test F(exp(0.1im)) ≈ [-exp(-0.1im)+1+2exp(0.1im);-3exp(-0.1im)+1+1exp(0.1im)]
-        @test Fun(F̃,space(F))(exp(0.1im)) ≈ [-exp(-0.1im)+1+2exp(0.1im);-3exp(-0.1im)+1+1exp(0.1im)]
-
-        @test coefficients(F̃,space(F)) == F.coefficients
-        @test Fun(F̃,space(F)) == F
-
-        @test F == Fun(vec(F),space(F))
-
-        @test inv(G(exp(0.1im))) ≈ inv(G)(exp(0.1im))
-
-        @test Fun(Matrix(I,2,2),space(G))(exp(0.1im)) ≈ Matrix(I,2,2)
-        @test Fun(I,space(G))(exp(0.1im)) ≈ Matrix(I,2,2)
-    end
-
     @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)
-
         a = ArraySpace(JacobiWeight(1/2,1/2, Chebyshev()), 2)
         b = ArraySpace(JacobiWeight(1/2,1/2, Ultraspherical(1)), 2)
         C = Conversion(a, b)