# Does NonlinearSolve use the analytical jacobian?
**URL:** https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508
**Category:** General Usage
**Tags:** question
**Created:** [July 2, 2024, 8:50am UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508 "2024-07-02T08:50:44Z")
**Posts on this page:** 7
**Page:** 1
### Author:  [@RayleighLord](https://discourse.julialang.org/u/RayleighLord)
#### Post date: [July 2, 2024, 8:50am UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/1 "2024-07-02T08:50:44Z")
This question came up when I did some tests related to this [post](https://discourse.julialang.org/t/finding-roots-of-an-integral-equation/116503).
Imagine I have the code
```julia
using NonlinearSolve
function f(u, p)
return u^2 - 2
end
function df(u, p)
println("Hey")
return 2u
end
fn = NonlinearFunction(f, jac=df)
prob = NonlinearProblem(fn, 1.0)
sol = solve(prob, NewtonRaphson(; concrete_jac=true))
```
Running this code does not print `"Hey"` to the terminal, so I guess that automatic differentiation is being used to compute the jacobian instead of the given function. I noticed this behavior because in the post that I mentioned, there was an incompatible interaction between AD and `QuadGK` that was present even if you provide the analytical jacobian.
Is this intended behavior? How could I provide the analytical jacobian to a problem? Also, does it need to be given to `NonlinearFunction` always and cannot be an optional parameter to `NonlinearProblem`?
At least in a quick review of the documentation I did not see a clear explanation on how to provide analytical jacobians.
PD: I am using the version
```julia
[8913a72c] NonlinearSolve v3.13.1
```
---
### Author:  [@afossa](https://discourse.julialang.org/u/afossa)
#### Post date: [July 4, 2024, 5:14pm UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/2 "2024-07-04T17:14:09Z")
Hello,
I am experiencing the same issue. In my case, `NonlinearSolve` is used to find the root of a scalar equation `f(u,p)=0`. This equation appears in the evaluation of a constraint of an optimization problem that I am trying to solve with `Optimization.jl`.
A workaround seems to be rewriting the scalar function as a vector function, with `u` vector of length one. For example:
```julia
using NonlinearSolve
f_scl(u,p) = cos(u) - p*u
f_vec(u,p) = [cos(u[1]) - p*u[1]]
function J_scl(u,p)
println("hop!")
return -sin(u) - p
end
function J_vec(u,p)
println("hop!")
return [-sin(u[1]) - p;;]
end
u0 = 0.0
p = 3.0
alg = SimpleNewtonRaphson()
nf_scl = NonlinearFunction(f_scl,jac=J_scl)
pb_scl = NonlinearProblem(nf_scl,u0,p)
sl_scl = solve(pb_scl,alg)
println("scalar solution: ", sl_scl.u)
nf_vec = NonlinearFunction(f_vec,jac=J_vec)
pb_vec = NonlinearProblem(nf_vec,[u0],p)
sl_vec = solve(pb_vec,alg)
println("vector solution: ", sl_vec.u[1])
```
output of the above:
```julia
scalar solution: 0.3167508287712211
hop!
hop!
hop!
hop!
hop!
vector solution: 0.3167508287712211
```
so indeed the analytical Jacobian is evaluated only in the second case.
I tried to swap `SimpleNewtonRaphson()` with `NewtonRaphson()` but without luck.
Is there any way to force the solver to use the analytical Jacobian also in the scalar case?
Thanks!
---
### Author:  [@RayleighLord](https://discourse.julialang.org/u/RayleighLord)
#### Post date: [July 4, 2024, 6:37pm UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/3 "2024-07-04T18:37:14Z")
Oh, so it is only in the scalar case, thank you for detecting that. I opened an issue on GitHub since this seems mostly a bug, because this behavior is most surely unintended.
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [July 5, 2024, 1:41am UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/4 "2024-07-05T01:41:39Z")
for scalar functions if it is using a bisection type method (i.e. ITP), that would make a lot of sense. You don’t need jacobians for scalar equations.
---
### Author:  [@RayleighLord](https://discourse.julialang.org/u/RayleighLord)
#### Post date: [July 5, 2024, 7:55am UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/5 "2024-07-05T07:55:42Z")
Yeah, but what if you use NewtonRaphson? I would expect that if you provide the analytical derivative, then it uses it. Otherwise the interface is a little bit misleading.
---
### Author:  [@ChrisRackauckas](https://discourse.julialang.org/u/ChrisRackauckas)
#### Post date: [July 6, 2024, 6:33pm UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/6 "2024-07-06T18:33:41Z")
Can you open an issue?
---
### Author:  [@Oscar\_Smith](https://discourse.julialang.org/u/Oscar_Smith)
#### Post date: [July 6, 2024, 7:05pm UTC](https://discourse.julialang.org/t/does-nonlinearsolve-use-the-analytical-jacobian/116508/7 "2024-07-06T19:05:26Z")
already exists: [Analytical Jacobian is not being used in the 3.13 version of NonlinearSolve · Issue #451 · SciML/NonlinearSolve.jl · GitHub](https://github.com/SciML/NonlinearSolve.jl/issues/451)