Approxfun.jl: This MWE using nbvpsolver() puts julia compiler into infinite cpu loop.

[caMi11er]

In the REPL, typing include("<thisMWE>") puts the julia compiler into an infinite 100% cpu loop:

using ApproxFun
using LinearAlgebra

    M = 2.363   # km 

    r1 = 2.0 
    r2 = 25.0 

    r = Fun(r1..r2) 

 βP(rmβ, p) = [rmβ' - (8*π) * (r^2) * (p);
                      p' * (2*r) *(rmβ - r) - (rmβ +  (8*π) * (r^3) * p) * ( (p) + p);
		      rmβ'(r1);
		      rmβ'(r2);
		      p'(r1);
		      p'(r2);
		      rmβ(r2)-2*M]

function nbvpsolver()
    rmβ0 = one(r)
    p0 = one(r)
    newton(βP, [rmβ0, p0])
end

rmβ, p = nbvpsolver();

I'm using julia version 1.11.3
and
[28f2ccd6] ApproxFun v0.13.28
[37e2e46d] LinearAlgebra v1.11.0

On this platform (macOS 12.7.6), I have compiled dozens of other codes with no such problems.

fwiw, if I cntl-c out of this loop, here is what I get:

julia> include("src/RealMod/src/Spectralrmβp.jl")
^CERROR: LoadError: InterruptException:
Stacktrace:
  [1] GenericMemory
    @ ./boot.jl:516 [inlined]
  [2] Array
    @ ./boot.jl:578 [inlined]
  [3] Array
    @ ./boot.jl:591 [inlined]
  [4] similar
    @ ./array.jl:372 [inlined]
  [5] similar
    @ ./abstractarray.jl:822 [inlined]
  [6] getindex
    @ ./array.jl:938 [inlined]
  [7] forwardrecurrence(::Type{Float64}, S::Ultraspherical{Int64, IntervalSets.ClosedInterval{Float64}, Float64}, r::UnitRange{Int64}, x::Float64)
    @ ApproxFunOrthogonalPolynomials ~/.julia/packages/ApproxFunOrthogonalPolynomials/LkWuc/src/Spaces/PolynomialSpace.jl:366
  [8] _getindex_evaluation(::Type{Float64}, sp::Ultraspherical{Int64, IntervalSets.ClosedInterval{Float64}, Float64}, order::Int64, x::Float64, kr::UnitRange{Int64})
    @ ApproxFunOrthogonalPolynomials ~/.julia/packages/ApproxFunOrthogonalPolynomials/LkWuc/src/Spaces/PolynomialSpace.jl:382
  [9] getindex
    @ ~/.julia/packages/ApproxFunOrthogonalPolynomials/LkWuc/src/Spaces/PolynomialSpace.jl:375 [inlined]
 [10] defaultgetindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:276 [inlined]
 [11] getindex(B::ApproxFunBase.ConcreteEvaluation{Ultraspherical{…}, Float64, Int64, Float64}, k::UnitRange{Int64}, j::UnitRange{Int64})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:350
 [12] (Matrix)(V::ApproxFunBase.SubOperator{Float64, TimesOperator{…}, Tuple{…}, Tuple{…}, Tuple{…}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/general/algebra.jl:512
 [13] AbstractArray
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:958 [inlined]
 [14] defaultgetindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:397 [inlined]
 [15] defaultgetindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:378 [inlined]
 [16] getindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:350 [inlined]
 [17] getindex(P::TimesOperator{Float64, Tuple{…}, Tuple{…}, Operator{…}, Tuple{…}, Tuple{…}}, k::Int64, j::Int64)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/general/algebra.jl:434
 [18] getindex(op::ApproxFunBase.InterlaceOperator{…}, k::Int64, j::Int64)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/general/InterlaceOperator.jl:288
 [19] defaultgetindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:391 [inlined]
 [20] defaultgetindex
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/Operator.jl:378 [inlined]
 [21] getindex(L::ApproxFunBase.InterlaceOperator{…}, k::Int64, j::UnitRange{…})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/general/InterlaceOperator.jl:344
 [22] resizedata!(co::ApproxFunBase.CachedOperator{…}, n::Int64, ::Colon)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Caching/almostbanded.jl:240
 [23] resizedata!(QR::ApproxFunBase.QROperator{ApproxFunBase.CachedOperator{…}, Matrix{…}, Float64}, ::Colon, col::Int64)
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Caching/almostbanded.jl:292
 [24] mulpars(Ac::Adjoint{Float64, ApproxFunBase.QROperatorQ{…}}, B::Vector{Float64}, tolerance::Float64, maxlength::Int64, inplace::Val{false})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Caching/matrix.jl:77
 [25] mulpars
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Caching/matrix.jl:42 [inlined]
 [26] #mul_coefficients#335
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/qr.jl:155 [inlined]
 [27] mul_coefficients
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/qr.jl:153 [inlined]
 [28] ldiv_coefficients(QR::ApproxFunBase.QROperator{ApproxFunBase.CachedOperator{…}, Matrix{…}, Float64}, b::Vector{Float64})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/qr.jl:207
 [29] ldiv_coefficients(A::ApproxFunBase.InterlaceOperator{…}, b::Vector{…}; kwds::@Kwargs{})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:49
 [30] ldiv_nonambiguous(A::ApproxFunBase.InterlaceOperator{…}, b::Function; kwds::@Kwargs{})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:17
 [31] ldiv_nonambiguous
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:16 [inlined]
 [32] #\#175
    @ ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:11 [inlined]
 [33] \(A::ApproxFunBase.InterlaceOperator{…}, b::Fun{…})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:3
 [34] \(A::Matrix{Operator}, b::Fun{ApproxFunBase.ArraySpace{…}, Float64, Vector{…}}; kwds::@Kwargs{})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:61
 [35] \(A::Matrix{Operator}, b::Fun{ApproxFunBase.ArraySpace{Space{…} where D, 1, IntervalSets.ClosedInterval{…}, Float64, Vector{…}}, Float64, Vector{Float64}})
    @ ApproxFunBase ~/.julia/packages/ApproxFunBase/hBlrP/src/Operators/ldiv.jl:61
 [36] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}}; maxiterations::Int64, tolerance::Float64)
    @ ApproxFun ~/.julia/packages/ApproxFun/qxC6g/src/Extras/autodifferentiation.jl:149
 [37] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}})
    @ ApproxFun ~/.julia/packages/ApproxFun/qxC6g/src/Extras/autodifferentiation.jl:120
 [38] nbvpsolver()
    @ Main ~/Applications/Julia/RealisticSeismology-main/src/RealMod/src/Spectralrmβp.jl:30
 [39] include(fname::String)
    @ Main ./sysimg.jl:38
in expression starting at /Users/andy 1/Applications/Julia/RealisticSeismology-main/src/RealMod/src/Spectralrmβp.jl:31
Some type information was truncated. Use `show(err)` to see complete types.

thnx

[caMi11er]

I guess I should also mention that I have no trouble compiling this analogous example from the Approxfun docs:

using ApproxFun
using LinearAlgebra

N2(u1, u2) = [u1'(0) - 0.5*u1(0)*u2(0);
                u2'(0) + 1;
                u1(1) - 1;
                u2(1) - 1;
                u1'' + u1*u2;
                u2'' - u1*u2]

function nbvpsolver2()
    x = Fun(0..1)
    u10 = one(x)
    u20 = one(x)
    newton(N2, [u10,u20])
end
u1,u2 = nbvpsolver2();

[caMi11er]

I'm sorry — the problem was not a compiler loop, but an execution loop.

But there does still seem to be a compiler issue.
This version give the error shown below…

using ApproxFun
using LinearAlgebra

    r1 = 2.0 
    r2 = 25.0 

    r = Fun(r1..r2) 

BP(rm, p) = [rm' - rm; p' -p]

function nbvpsolver()
    rm0 = one(r)
    p0 = one(r)
    newton(BP, [rm0, p0] )
end

rm, p = nbvpsolver();

results in…

ERROR: LoadError: DimensionMismatch: number of columns of each array must match (got (1, 2))
Stacktrace:
  [1] _typed_vcat(::Type{Any}, A::Tuple{Matrix{Any}, Matrix{Any}})
    @ Base ./abstractarray.jl:1726
  [2] typed_vcat(::Type{Any}, ::Matrix{Any}, ::Matrix{Any})
    @ Base ./abstractarray.jl:1740
  [3] typed_hvcat(::Type{Any}, ::Tuple{Int64, Int64}, ::ApproxFun.DualFun{Fun{…}, PlusOperator{…}}, ::Vararg{Any})
    @ Base ./abstractarray.jl:2269
  [4] hvcat(::Tuple{Int64, Int64}, ::ApproxFun.DualFun{Fun{…}, PlusOperator{…}}, ::Function, ::Function)
    @ Base ./abstractarray.jl:2246
  [5] BP(rm::ApproxFun.DualFun{Fun{Chebyshev{…}, Float64, Vector{…}}, ConstantOperator{Float64, Chebyshev{…}}}, p::Function)
    @ Main ~/Applications/Julia/RealisticSeismology-main/src/RealMod/src/test3nbvp.jl:9
  [6] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}}; maxiterations::Int64, tolerance::Float64)
    @ ApproxFun ~/.julia/packages/ApproxFun/qxC6g/src/Extras/autodifferentiation.jl:137
  [7] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}})
    @ ApproxFun ~/.julia/packages/ApproxFun/qxC6g/src/Extras/autodifferentiation.jl:120
  [8] nbvpsolver()
    @ Main ~/Applications/Julia/RealisticSeismology-main/src/RealMod/src/test3nbvp.jl:14
  [9] top-level scope
    @ ~/Applications/Julia/RealisticSeismology-main/src/RealMod/src/test3nbvp.jl:15
 [10] include(fname::String)
    @ Main ./sysimg.jl:38
 [11] top-level scope
    @ REPL[12]:1
in expression starting at /Users/andy 1/Applications/Julia/RealisticSeismology-main/src/RealMod/src/test3nbvp.jl:15
Some type information was truncated. Use `show(err)` to see complete types.

While this one with only one extra formatting space flagged by a comment compiles with no errors:

using ApproxFun
using LinearAlgebra

    r1 = 2.0 
    r2 = 25.0 

    r = Fun(r1..r2) 

BP(rm, p) = [rm' - rm; p' - p]    #  Extra space in "p' - p" eliminates error message

function nbvpsolver()
    rm0 = one(r)
    p0 = one(r)
    newton(BP, [rm0, p0] )
end

rm, p = nbvpsolver();