Add autoscaling for trust region

[m-bossart]

Add autoscaling option for trust region (and possibly other) methods.

[m-bossart]

@avik-pal Can you point me to where this should be implemented. I'm trying to transition from NLsolve.jl to NonlinearSolve.jl but for some larger cases NLsolve.jl converges and NonlinearSolve.jl does not (for TrustRegion and Raphson algorithms). The lack of scaling is the most obvious difference to me.

[avik-pal]

I haven't looked too much into how NLsolve does autoscaling. But it should probably go in

NonlinearSolve.jl/src/internal/jacobian.jl

Lines 115 to 152 in 45c4465

	@inline (cache::JacobianCache)(u = cache.u) = cache(cache.J, u, cache.p)
	@inline function (cache::JacobianCache)(::Nothing)
	J = cache.J
	J isa JacobianOperator && return StatefulJacobianOperator(J, cache.u, cache.p)
	return J
	end
	function (cache::JacobianCache)(J::JacobianOperator, u, p = cache.p)
	return StatefulJacobianOperator(J, u, p)
	end
	function (cache::JacobianCache)(::Number, u, p = cache.p) # Scalar
	cache.stats.njacs += 1
	J = last(__value_derivative(cache.autodiff, cache.uf, u))
	return J
	end
	# Compute the Jacobian
	function (cache::JacobianCache{iip})(
	J::Union{AbstractMatrix, Nothing}, u, p = cache.p) where {iip}
	cache.stats.njacs += 1
	if iip
	if has_jac(cache.f)
	cache.f.jac(J, u, p)
	else
	sparse_jacobian!(J, cache.autodiff, cache.jac_cache, cache.uf, cache.fu, u)
	end
	J_ = J
	else
	J_ = if has_jac(cache.f)
	cache.f.jac(u, p)
	elseif __can_setindex(typeof(J))
	sparse_jacobian!(J, cache.autodiff, cache.jac_cache, cache.uf, u)
	J
	else
	sparse_jacobian(cache.autodiff, cache.jac_cache, cache.uf, u)
	end
	end
	return J_
	end

[m-bossart]

Thanks. I will try to look into it

[avik-pal]

@m-bossart do you have a test case for this? Just so that when we implement it we can add it as a test