Multivariate Rootfinding: problem with NLsolve (dual numbers not applicable for a function I am using)

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1

Hi there,

I have a multivariate rootfinding problem, where one of the functions utilizes QuantEcon.jl’s qnwnorm which generates the nodes for the Gauss-Hermite quadrature. However, using NLsolve on one of the parameters that is an input to qnwnorm throws an error, as qnwnorm tries to transform the dual number to a Float64, which fails.

A admittedly contrived MWE would be something like this:

using QuantEcon, NLsolve

function f!(res, x)
    nodes, weights = qnwnorm(10,x[1],1)
    res[1]         = x[1] + x[2] - 3.5
    res[2]         = mean(nodes) - 1
    return res
end

nlsolve(f!, [1., 1.], autodiff = :forward)

which throws

MethodError: no method matching Float64(::ForwardDiff.Dual{ForwardDiff.Tag{typeof(f!),Float64},Float64,2})
Closest candidates are:
  Float64(::Real, !Matched::RoundingMode) where T<:AbstractFloat at rounding.jl:194
  Float64(::T<:Number) where T<:Number at boot.jl:718
  Float64(!Matched::Int8) at float.jl:60
  ...

Is there a different solver/package in Julia that can handle these kinds of problems?

Thanks a lot!

2

You chopped off the important parts of the error message, so it’s hard to know what’s going on here. But it looks like it’s your function which isn’t AD-compatible, so turn off AD. No change of a rootfinding library would fix that because it’s based on the functions you’re using in f!.

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3

Also consider using one of my all-time favourite packages GitHub - JuliaApproximation/FastGaussQuadrature.jl: Julia package for Gaussian quadrature

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