# Specifying analytical Jacobian in NonlinearProblem à la Optim.only\_fg!

**URL:** https://discourse.julialang.org/t/specifying-analytical-jacobian-in-nonlinearproblem-a-la-optim-only-fg/115991
**Category:** Performance
**Tags:** nonlinearsolve
**Created:** [June 21, 2024, 8:10pm UTC](https://discourse.julialang.org/t/specifying-analytical-jacobian-in-nonlinearproblem-a-la-optim-only-fg/115991 "2024-06-21T20:10:16Z")
**Posts on this page:** 2
**Page:** 1

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### Author: ![dieg0](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/dieg0/32/210143_2.png) [@dieg0](https://discourse.julialang.org/u/dieg0)
#### Post date: [June 21, 2024, 8:10pm UTC](https://discourse.julialang.org/t/specifying-analytical-jacobian-in-nonlinearproblem-a-la-optim-only-fg/115991/1 "2024-06-21T20:10:16Z")

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When minimizing a costly function f(x) using Optim.jl and providing the gradient \nabla f(x), one can use `Optim.only_fg!` to compute the gradient and the function itself within the same function to avoid repeating computations like this:

```julia
function fg!(F, G, x)
  # do common computations here
  # ...
  if G !== nothing
    # code to compute gradient here
    # writing the result to the vector G
    # G .= ...
  end
  if F !== nothing
    # value = ... code to compute objective function
    return value
  end
end

Optim.optimize(Optim.only_fg!(fg!), [0., 0.], Optim.BFGS())

```

See [here](https://julianlsolvers.github.io/Optim.jl/stable/user/tipsandtricks/#Avoid-repeating-computations) for more info.

Now, when solving a system of nonlinear equations f(x) = 0 using NonlinearSolve.jl and we want to specify the Jacobian, we have to specify the problem as:

```julia
function f(u, p)
    # computations here
    return fval
end

function df(u, p)
    # computations here
    return du
end

fn = NonlinearFunction(f, jac = df)
prob = NonlinearProblem(fn, u0, p)
sol = solve(prob, NewtonRaphson( ;concrete_jac = true))

```

Now, there are some settings (just like in the previous case) where f and df share common costly computations so calling a function like df(u,p) with f(u) inside can be costly. Is there some equivalent `Optim.only_fg!` but that applies to NonlinearProblem.jl’s `NonlinearFunction`?

Thanks in advance!

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<div class="post-metadata">

### Author: ![mschytt](https://sea2.discourse-cdn.com/julialang/user_avatar/discourse.julialang.org/mschytt/32/209924_2.png) [@mschytt](https://discourse.julialang.org/u/mschytt)
#### Post date: [June 25, 2024, 6:55pm UTC](https://discourse.julialang.org/t/specifying-analytical-jacobian-in-nonlinearproblem-a-la-optim-only-fg/115991/2 "2024-06-25T18:55:15Z")

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I ran into a similar problem using Optimization.jl and their similar OptimizationFunction interface.

I solved the problem by memoization. In essence, i defined a cache struct which I could pass with the parameter argument to the NonlinearFunction instance. Say when df is called, both f and df are calculated and the results are stored. When f is then subsequently called (checking equality of arguments) you can immediately retrieve the answer.

I’m on phone, but I can elaborate with a code example later.