`solve` fails when passed vectorial tolerances.

[lte678]

Description

solve fails when called on nonlinear systems of equations with vectorial tolerances.
This is for both reltol and abstol.

Since NonlinearSolve is used internally to solve inconsistent DAE initializations in DifferentialEquations.jl, this causes crashes when solving DAEs with a vector supplied for reltol (in fact, this happens for vector-valued abstol as well, if SciML/OrdinaryDiffEq.jl#1214 has been patched out). I think this is a good motivation to consider this a bug either in NonlinearSolve or OrdinaryDiffEqNonlinearSolve.

Reproducable Test

using NonlinearSolve, StaticArrays

f(u, p) = u .* u .- 2
u0 = @SVector[1.0, 1.0]
solver = solve(NonlinearProblem(f, u0), reltol=[1e-3, 1e-4])

Stacktrace

ERROR: MethodError: no method matching Float64(::Vector{Float64})
The type `Float64` exists, but no method is defined for this combination of argument types when trying to construct it.

Closest candidates are:
  Float64(::IrrationalConstants.Halfπ)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/vp5v4/src/macro.jl:112
  Float64(::IrrationalConstants.Twoinvπ)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/vp5v4/src/macro.jl:112
  Float64(::IrrationalConstants.Inv2π)
   @ IrrationalConstants ~/.julia/packages/IrrationalConstants/vp5v4/src/macro.jl:112
  ...

Stacktrace:
  [1] convert_real(::Type{Float64}, x::Vector{Float64})
    @ NonlinearSolveBase.Utils ~/.julia/packages/NonlinearSolveBase/Kek5u/src/utils.jl:91
  [2] get_tolerance(η::Vector{Float64}, ::Type{Float64})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/common_defaults.jl:37
  [3] get_tolerance(::SVector{2, Float64}, η::Vector{Float64}, ::Type{Float64})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/common_defaults.jl:43
  [4] init_termination_cache(prob::NonlinearProblem{…}, abstol::Nothing, reltol::Vector{…}, du::SVector{…}, u::SVector{…}, tc::AbsNormSafeBestTerminationMode{…}, ::Val{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/termination_conditions.jl:295
  [5] init_termination_cache(prob::NonlinearProblem{…}, abstol::Nothing, reltol::Vector{…}, du::SVector{…}, u::SVector{…}, ::Nothing, callee::Val{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/termination_conditions.jl:286
  [6] __init(::NonlinearProblem{…}, ::GeneralizedFirstOrderAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, maxiters::Int64, abstol::Nothing, reltol::Vector{…}, maxtime::Nothing, termination_condition::Nothing, internalnorm::Function, linsolve_kwargs::@NamedTuple{}, initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveFirstOrder ~/.julia/packages/NonlinearSolveFirstOrder/3kzAL/src/solve.jl:156
  [7] __solve(::NonlinearProblem{…}, ::GeneralizedFirstOrderAlgorithm{…}; kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:5
  [8] macro expansion
    @ ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:173 [inlined]
  [9] __generated_polysolve(::NonlinearProblem{…}, ::NonlinearSolvePolyAlgorithm{…}; stats::SciMLBase.NLStats, alias_u0::Bool, verbose::Bool, initializealg::NonlinearSolveBase.NonlinearSolveDefaultInit, kwargs::@Kwargs{…})
    @ NonlinearSolveBase ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:130
 [10] __generated_polysolve
    @ ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:130 [inlined]
 [11] #__solve#154
    @ ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:127 [inlined]
 [12] __solve
    @ ~/.julia/packages/NonlinearSolveBase/Kek5u/src/solve.jl:124 [inlined]
 [13] #__solve#18
    @ ~/.julia/packages/NonlinearSolve/IChU2/src/default.jl:27 [inlined]
 [14] __solve
    @ ~/.julia/packages/NonlinearSolve/IChU2/src/default.jl:24 [inlined]
 [15] #__solve#72
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:1438 [inlined]
 [16] __solve
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:1429 [inlined]
 [17] #solve_call#44
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:634 [inlined]
 [18] solve_call
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:591 [inlined]
 [19] #solve_up#53
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:1107 [inlined]
 [20] solve_up
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:1101 [inlined]
 [21] #solve#52
    @ ~/.julia/packages/DiffEqBase/R2Vjs/src/solve.jl:1095 [inlined]
 [22] top-level scope
    @ ~/Projects/scratchpad/dae_vector_init_bug/nonlinear_solve.jl:5
Some type information was truncated. Use `show(err)` to see complete type

Environment

• Julia Version 1.11.2
• NonlinearSolve v4.3.0

[avik-pal]

This is currently not supported. But should be easy to do with a patch in NonlinearSolveBase