Functions with Arrays of AbstractInterpolations cannot be handled by ForwardDiff

[keatonmill]

I've discovered an issue when passing Arrays of AbstractInterpolations to functions and then using ForwardDiff to process those functions -- even if the Interpolations are never used. Oddly, the error only occurs if you call the ForwardDiff package from within a function. A workaround is possible if you know the precise type of Interpolation you're going to have ahead of time or if you can pass an Array{Any}.

I'm not sure if this is a bug in Interpolations or ForwardDiff.

Code:

println("Start.")

using ForwardDiff
using Interpolations

function eff(p, thing)
    out = p[1] *  p[2]
    return out
end

function GradientWrapper(func, p, thing)
    f(x) = func(x, thing)
    return ForwardDiff.gradient(f,p)
end

n = 40
z = [i * j for i in 1:n, j in 1:n]
itp = interpolate(z, BSpline(Cubic(Natural())), OnGrid())


p = [5.0, 6.0]

test = [itp, itp]

println("Using type $(typeof(test))")
println("Calling the derivative directly:")
f(x) = eff(x,test)
println(ForwardDiff.gradient(f, p))
println("Calling the wrapper:")
println(GradientWrapper(eff, p, test))

test = Array{Any}(2)
test[1] = itp
test[2] = itp

println("Using type $(typeof(test))")
println("Calling the derivative directly:")
g(x) = eff(x, test)
println(ForwardDiff.gradient(g, p))
println("Calling the wrapper:")
println(GradientWrapper(eff, p, test))


test = Array{AbstractInterpolation}(2)
test[1] = itp
test[2] = itp

println("Using type $(typeof(test))")
println("Calling the derivative directly:")
h(x) = eff(x, test)
println(ForwardDiff.gradient(h, p))
println("Calling the wrapper -- this fails:")
println(GradientWrapper(eff, p, test))

println("Done.")

Output:

Start.
Using type Array{Interpolations.BSplineInterpolation{Float64,2,Array{Float64,2},Interpolations.BSpline{Interpolations.Cubic{Interpolations.Line}},Interpolations.OnGrid,1},1}
Calling the derivative directly:
[6.0, 5.0]
Calling the wrapper:
[6.0, 5.0]
Using type Array{Any,1}
Calling the derivative directly:
[6.0, 5.0]
Calling the wrapper:
[6.0, 5.0]
Using type Array{Interpolations.AbstractInterpolation,1}
Calling the derivative directly:
[6.0, 5.0]
Calling the wrapper -- this fails:
LoadError: MethodError: no method matching string(::Expr)
The applicable method may be too new: running in world age 2758, while current world is 21890.
Closest candidates are:
  string(::Any...) at strings/io.jl:120 (method too new to be called from this world context.)
  string(!Matched::BigInt) at gmp.jl:568 (method too new to be called from this world context.)
  string(!Matched::BigFloat) at mpfr.jl:885 (method too new to be called from this world context.)
  ...
while loading evensmallertest.jl, in expression starting on line 53
in GradientWrapper at evensmallertest.jl:13
in typeinf_ext at base/inference.jl:2622
in typeinf_code at base/inference.jl:2583
in typeinf_frame at base/inference.jl:2504
in typeinf at base/inference.jl:2787
in typeinf_work at base/inference.jl:2722
in abstract_eval at base/inference.jl:1950
in abstract_eval_call at base/inference.jl:1927
in abstract_call at base/inference.jl:1897
in abstract_call_gf_by_type at base/inference.jl:1420
in typeinf_edge at base/inference.jl:2535
in typeinf at base/inference.jl:2787
in typeinf_work at base/inference.jl:2722
in abstract_eval at base/inference.jl:1950
in abstract_eval_call at base/inference.jl:1927
in abstract_call at base/inference.jl:1897
in abstract_call_gf_by_type at base/inference.jl:1420
in typeinf_edge at base/inference.jl:2535
in typeinf at base/inference.jl:2787
in typeinf_work at base/inference.jl:2669
in abstract_interpret at base/inference.jl:2076
in abstract_eval at base/inference.jl:1950
in abstract_eval_call at base/inference.jl:1927
in abstract_call at base/inference.jl:1897
in abstract_call_gf_by_type at base/inference.jl:1420
in typeinf_edge at base/inference.jl:2535
in typeinf at base/inference.jl:2787
in typeinf_work at base/inference.jl:2669
in abstract_interpret at base/inference.jl:2076
in abstract_eval at base/inference.jl:1950
in abstract_eval_call at base/inference.jl:1927
in abstract_call at base/inference.jl:1701
in builtin_tfunction at base/inference.jl:1133
in builtin_tfunction at base/inference.jl:1215
in  at base/inference.jl:899
in getfield_tfunc at base/inference.jl:897
in limit_type_depth at base/inference.jl:692

[tomasaschan]

I haven't looked into this specific issue (although the stack trace indicates that it's a problem in type inference, so might be a base Julia bug?), but you do realize that Interpolations.jl has functions for gradient (and hessian) evaluation included? So there's no need to turn to ForwardDiff.jl for that specific case; you can just as well just call gradient from `Interpolations.jl.

There's more info here.