I am trying to familiarize myself with the NonlinearSolve ecosystem for curve fitting and am having difficulty getting a simple fit to an exponential function. I have seen other discussions on doing this here, but I’m not sure where I’m going wrong.

```
using NonlinearSolve
using GLMakie
model(x, p) = @. p[1] * exp(-x / p[2]) + p[3]
xdata = range(0, 10, length=100)
ydata = model(xdata, [1.0, 2.0, 0.0]) .+ 0.1 * randn(length(xdata))
function loss(p, data)
x = data[1]
y = data[2]
Y_pred = @. p[1] * exp(-x / p[2]) + p[3]
return sum(abs2, Y_pred .- y)
end
p0 = [0.8, 0.4, 0.2]
data = [xdata, ydata]
prob = NonlinearLeastSquaresProblem(loss, p0, data)
res = solve(prob, LevenbergMarquardt())
fig = Figure()
ax = Axis(fig[1, 1])
lines!(xdata, ydata)
# lines!(xdata, model(xdata, params))
fig
```

Error message hits at `solve()`

:

```
ERROR: MethodError: no method matching similar(::Float64, ::Type{Float64}, ::Int64, ::Int64)
Closest candidates are:
similar(::RecursiveArrayTools.AbstractVectorOfArray, ::Any...)
@ RecursiveArrayTools ~/.julia/packages/RecursiveArrayTools/xGKIm/src/vector_of_array.jl:711
similar(::AbstractArray, ::Type{T}, ::Union{Integer, AbstractUnitRange}...) where T
@ Base abstractarray.jl:833
similar(::Type{T}, ::Union{Integer, AbstractUnitRange}...) where T<:AbstractArray
@ Base abstractarray.jl:875
...
Stacktrace:
[1] init_jacobian(::Nothing, ::Type{Float64}, fx::Float64, x::Vector{Float64}; kwargs::@Kwargs{preserve_immutable::Val{…}})
@ SparseDiffTools ~/.julia/packages/SparseDiffTools/jpC2n/src/highlevel/common.jl:329
[2] init_jacobian(c::SparseDiffTools.ForwardDiffJacobianCache{…}; preserve_immutable::Val{…})
@ SparseDiffTools ~/.julia/packages/SparseDiffTools/jpC2n/src/highlevel/common.jl:325
[3] NonlinearSolve.JacobianCache(prob::NonlinearLeastSquaresProblem{…}, alg::GeneralizedFirstOrderAlgorithm{…}, f::NonlinearFunction{…}, fu_::Float64, u::Vector{…}, p::Vector{…}; stats::SciMLBase.NLStats, autodiff::Nothing, vjp_autodiff::Nothing, jvp_autodiff::Nothing, linsolve::Nothing)
@ NonlinearSolve ~/.julia/packages/NonlinearSolve/sETeN/src/internal/jacobian.jl:88
[4] __init(::NonlinearLeastSquaresProblem{…}, ::GeneralizedFirstOrderAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, maxiters::Int64, abstol::Nothing, reltol::Nothing, maxtime::Nothing, termination_condition::Nothing, internalnorm::Function, linsolve_kwargs::@NamedTuple{}, kwargs::@Kwargs{})
@ NonlinearSolve ~/.julia/packages/NonlinearSolve/sETeN/src/core/generalized_first_order.jl:173
[5] __init
@ ~/.julia/packages/NonlinearSolve/sETeN/src/core/generalized_first_order.jl:154 [inlined]
[6] __solve(::NonlinearLeastSquaresProblem{…}, ::GeneralizedFirstOrderAlgorithm{…}; stats::SciMLBase.NLStats, kwargs::@Kwargs{})
@ NonlinearSolve ~/.julia/packages/NonlinearSolve/sETeN/src/core/generic.jl:3
[7] __solve
@ ~/.julia/packages/NonlinearSolve/sETeN/src/core/generic.jl:1 [inlined]
[8] #solve_call#44
@ ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:612 [inlined]
[9] solve_call
@ ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:569 [inlined]
[10] #solve_up#53
@ ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:1072 [inlined]
[11] solve_up
@ ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:1066 [inlined]
[12] #solve#51
@ ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:1003 [inlined]
[13] solve(prob::NonlinearLeastSquaresProblem{…}, args::GeneralizedFirstOrderAlgorithm{…})
@ DiffEqBase ~/.julia/packages/DiffEqBase/slKc5/src/solve.jl:993
[14] top-level scope
@ ~/Documents/projects/scratch/test_optimization_pkg.jl:19
Some type information was truncated. Use `show(err)` to see complete types.
```

### Additional info

I have abandoned LsqFit.jl because I have difficulty getting it to resolve many problems (and because of recommendations by others against using it).I often use Optim.jl for this kind of thing, but I wanted to try out NonlinearSolve.jl since there are discussions of a simple CurveFit package coming out of this ecosystem.