Indexing a residual of an InitializationProblem

[1-Bart-1]

As described here: https://discourse.julialang.org/t/indexing-a-residual-of-an-initializationproblem/123356?u=bart_van_de_lint
Symbolic indexing on the residual of a solution is not possible yet. This would be a good debugging tool. I would suggest this feature to work similarly to normal symbolic indexing. So instead of sol[symbol] it would work like sol.resid[symbol].

Example:

using ModelingToolkit, OrdinaryDiffEq
using ModelingToolkit: t_nounits as t, D_nounits as D

@parameters g
@variables x(t) y(t) [state_priority = 10] λ(t)
eqs = [D(D(x)) ~ λ * x
       D(D(y)) ~ λ * y - g
       x^2 + y^2 ~ 1]
@mtkbuild pend = ODESystem(eqs, t)

iprob = ModelingToolkit.InitializationProblem(pend, 0.0,
    [x => 1, y => 0.0, D(y) => 2.0, λ => 1], [g => 1], guesses = [λ => 1])
using NonlinearSolve
sol = solve(iprob)
sol.resid[x] # indexing the residual