Crash if the Jacobian is singular

[mbaz]

I am running curve_fit on a large number of sinusoidal signals with random parameters. Sometimes this causes curve_fit to crash:

ERROR: LinearAlgebra.SingularException(4)
Stacktrace:
  [1] checknonsingular
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/factorization.jl:19 [inlined]
  [2] checknonsingular
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/factorization.jl:22 [inlined]
  [3] #lu!#170
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/lu.jl:82 [inlined]
  [4] lu!
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/lu.jl:80 [inlined]
  [5] #lu#176
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/lu.jl:299 [inlined]
  [6] lu (repeats 2 times)
    @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/lu.jl:298 [inlined]
  [7] \(A::Matrix{Float64}, B::Vector{Float64})
    @ LinearAlgebra ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/generic.jl:1115
  [8] levenberg_marquardt(df::NLSolversBase.OnceDifferentiable{Vector{Float64}, Matrix{Float64}, Vector{Float64}}, initial_x::Vector{Float64}; x_tol::Float64, g_tol::Float64, maxIter::Int64, lambda::Float64, tau::Float64, lambda_increase::Float64, lambda_decrease::Float64, min_step_quality::Float64, good_step_quality::Float64, show_trace::Bool, lower::Vector{Float64}, upper::Vector{Float64}, avv!::Nothing)
    @ LsqFit ~/.julia/packages/LsqFit/BBrNp/src/levenberg_marquardt.jl:126

Line 126 of levenberg_marquardt.jl is

v .= JJ \ n_buffer

The crash comes from Julia's LinearAlgebra library:

julia> [1 1; 2 2] \ [1,2]
ERROR: SingularException(2)
Stacktrace:
 [1] checknonsingular
   @ ~/bin/julia-1.9.0/share/julia/stdlib/v1.9/LinearAlgebra/src/factorization.jl:19 [inlined]

My question is if it would be a good idea for curve_fit to identify the problem and report a convergence failure instead of crashing.

Here's a (contrived) MWE:

@. model(t, p) = p[2] + p[3]*sin(2π*p[1]*t) + p[4]*cos(2π*p[1]*t)
x = 0.0:0.01:0.99
y = [-1.292216825464793, -1.2952938565190915, -1.2551966338159637, -1.2594439105244135, -1.3076054335159406, -1.3149351825115647, -1.312209749725464, -1.3269535160643398, -1.2984183842790722, -1.303705622851796, -1.3240442209719487, -1.3185467134476756, -1.2920091086995027, -1.3508679319812065, -1.3138831361533125, -1.3288156603748804, -1.3374467671365593, -1.3214155571007546, -1.3345566676824927, -1.3099685384899566, -1.3383345778026294, -1.3424184979594376, -1.3659379865515553, -1.3666092119332536, -1.3546244224167894, -1.3461938039663555, -1.3744705639413841, -1.3558035734301572, -1.366282907440218, -1.384523372856264, -1.3547780867475971, -1.3534927204414966, -1.3784457260898326, -1.3849878335512766, -1.3705499109266617, -1.4039611248225348, -1.3638808575182875, -1.3996096373182176, -1.3695277942522208, -1.3956773456560045, -1.3944176582906345, -1.3888745957965418, -1.4019836833612387, -1.3807867183801328, -1.3670239495026903, -1.368947317022084, -1.4031411232441346, -1.395581690288087, -1.4120342024349177, -1.4041289343717054,-1.3839689705528686, -1.4002894263556378, -1.4184162622846428, -1.405149489054179, -1.4114871418858892, -1.4222275035322312, -1.4256980150295218, -1.4075697904186666, -1.3991503262399105, -1.3897641047882807, -1.4114617303708386, -1.392394110993734, -1.4110963331027842, -1.4015406700955888, -1.4385967619129176, -1.424500270734283, -1.3883848675018182, -1.4163251768143987, -1.412981869672577, -1.3994066129962857, -1.3902008709251659, -1.4099019279995255, -1.3989053027341685, -1.389705906745122, -1.3989551114198944, -1.4303485320691924, -1.4043753587199719, -1.4379813803381887, -1.39796758362759, -1.4140632282920367, -1.4173650734536793, -1.396226753254768, -1.4314186046971933, -1.4160899972739944, -1.4299401762694293, -1.4033402272213507, -1.406893342242255, -1.4029985469222355, -1.4063905371082013, -1.4066009638861554, -1.4246921390814296, -1.3931986016522087, -1.387359465544153, -1.4287405658403294, -1.4137967618095058, -1.3894842928027942, -1.4131847625397986, -1.4126843863647254, -1.4152401545011943, -1.3952122566090701]
curve_fit(model, x, y, [0.5, 1798.4487118441707, -21.805084064105603, -1799.7304824749904])