Error in Newton Iteration

[MasonProtter]

I tried adapting Nonlinear Boundary Value problems example from the README to a BVP I was interested in and his this error:

using ApproxFun, Plots

@time let
  rmin = 0.01
  rmax = 5.0
  κ = 10.0

  r = Fun(identity, rmin..rmax)
  
  N = (f, h) -> [
    h'(rmin)/f(rmin)^2 + 1/(κ*rmin);
    f(rmax) - 1;
    h(rmax);
    h'(rmax);
    f'' + f'/r + κ^2 * ((h'')^2/(f^3) - f*(1 - f^2));
    h'' + h'*(1/r - 2/f) - f^2*h
  ]

  f0 = tanh(r)
  h0 = tanh(r)
  f, h = newton(N, [f0, h0])
end

#+RESULTS:
MethodError: no method matching +(::Fun{Ultraspherical{Int64, IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}})
Closest candidates are:
  +(::Fun, !Matched::UniformScaling) at /home/mason/.julia/packages/ApproxFunBase/dn7g5/src/Fun.jl:309
  +(::Fun{S, T, VT} where VT, !Matched::T) where {S, T<:Number} at /home/mason/.julia/packages/ApproxFunBase/dn7g5/src/Fun.jl:307
  +(::Fun, !Matched::Number) at /home/mason/.julia/packages/ApproxFunBase/dn7g5/src/Fun.jl:308
  ...

Stacktrace:
 [1] +(a::Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}, b::ApproxFun.DualFun{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}, Fun{Ultraspherical{Int64, IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}})
   @ ApproxFun ~/.julia/packages/ApproxFun/2jR1D/src/Extras/autodifferentiation.jl:43
 [2] +
   @ ./operators.jl:540 [inlined]
 [3] (::var"#153#154"{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}, Float64, Float64, Float64})(f::Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}, h::ApproxFun.DualFun{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}, ConstantOperator{Float64, Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}}})
   @ Main ./In[78]:11
 [4] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}}; maxiterations::Int64, tolerance::Float64)
   @ ApproxFun ~/.julia/packages/ApproxFun/2jR1D/src/Extras/autodifferentiation.jl:142
 [5] newton(N::Function, u0::Vector{Fun{Chebyshev{IntervalSets.ClosedInterval{Float64}, Float64}, Float64, Vector{Float64}}})
   @ ApproxFun ~/.julia/packages/ApproxFun/2jR1D/src/Extras/autodifferentiation.jl:121
 [6] macro expansion
   @ In[78]:22 [inlined]
 [7] top-level scope
   @ timing.jl:207
 [8] eval
   @ ./boot.jl:360 [inlined]
 [9] include_string(mapexpr::typeof(REPL.softscope), mod::Module, code::String, filename::String)
   @ Base ./loading.jl:1090

The examples in the README worked fine though.

[dlfivefifty]

N is a function of two arguments but it seems like you actually have a vector-valued case...

not sure vector-valued Jacobians work

[MasonProtter]

Isn't that also the case with the examples in the README though? E.g.

x=Fun(identity, 0..1)
N = (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]

u10 = one(x)
u20 = one(x)
u1,u2 = newton(N, [u10,u20])

[dlfivefifty]

Er it's even simpler: try adding

+(a::Fun) = copy(a)

[jishnub]

I suspect this issue is resolved now, but the original example takes far too long to run on my system. I'm closing this, but you are welcome to reopen if the issue persists.