From d110e83a09181f929c3c45f4ee151a0eeecaeb9d Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Sat, 21 Dec 2024 21:15:25 +0100
Subject: [PATCH] Update the documentation

---
 docs/src/backend.md       | 10 +++++-----
 docs/src/predefined.md    | 14 ++++++++++++++
 src/predefined_backend.jl |  8 ++++----
 3 files changed, 23 insertions(+), 9 deletions(-)

diff --git a/docs/src/backend.md b/docs/src/backend.md
index 7e073675..c2894dcb 100644
--- a/docs/src/backend.md
+++ b/docs/src/backend.md
@@ -10,11 +10,11 @@ The functions used internally to define the NLPModel API and the possible backen
 | Functions | FowardDiff backends | ReverseDiff backends | Zygote backends | Enzyme backend | Sparse backend |
 | --------- | ------------------- | -------------------- | --------------- | -------------- | -------------- |
 | `gradient` and `gradient!` | `ForwardDiffADGradient`/`GenericForwardDiffADGradient` | `ReverseDiffADGradient`/`GenericReverseDiffADGradient` | `ZygoteADGradient` | `EnzymeADGradient` | -- |
-| `jacobian` | `ForwardDiffADJacobian` | `ReverseDiffADJacobian` | `ZygoteADJacobian` | -- | `SparseADJacobian` |
-| `hessian` | `ForwardDiffADHessian` | `ReverseDiffADHessian` | `ZygoteADHessian` | -- | `SparseADHessian`/`SparseReverseADHessian` |
-| `Jprod` | `ForwardDiffADJprod`/`GenericForwardDiffADJprod` | `ReverseDiffADJprod`/`GenericReverseDiffADJprod` | `ZygoteADJprod` | -- | -- |
-| `Jtprod` | `ForwardDiffADJtprod`/`GenericForwardDiffADJtprod` | `ReverseDiffADJtprod`/`GenericReverseDiffADJtprod` | `ZygoteADJtprod` | -- | -- |
-| `Hvprod` | `ForwardDiffADHvprod`/`GenericForwardDiffADHvprod` | `ReverseDiffADHvprod`/`GenericReverseDiffADHvprod` | -- | -- | -- |
+| `jacobian` | `ForwardDiffADJacobian` | `ReverseDiffADJacobian` | `ZygoteADJacobian` | `EnzymeADJacobian` | `SparseADJacobian` |
+| `hessian` | `ForwardDiffADHessian` | `ReverseDiffADHessian` | `ZygoteADHessian` | `EnzymeADHessian` | `SparseADHessian`/`SparseReverseADHessian` |
+| `Jprod` | `ForwardDiffADJprod`/`GenericForwardDiffADJprod` | `ReverseDiffADJprod`/`GenericReverseDiffADJprod` | `ZygoteADJprod` | `EnzymeADJprod` | -- |
+| `Jtprod` | `ForwardDiffADJtprod`/`GenericForwardDiffADJtprod` | `ReverseDiffADJtprod`/`GenericReverseDiffADJtprod` | `ZygoteADJtprod` | `EnzymeADJtprod` | -- |
+| `Hvprod` | `ForwardDiffADHvprod`/`GenericForwardDiffADHvprod` | `ReverseDiffADHvprod`/`GenericReverseDiffADHvprod` | -- | `EnzymeADHvprod` | -- |
 | `directional_second_derivative` | `ForwardDiffADGHjvprod` | -- | -- | -- | -- |
 
 The functions `hess_structure!`, `hess_coord!`, `jac_structure!` and `jac_coord!` defined in `ad.jl` are generic to all the backends for now.
diff --git a/docs/src/predefined.md b/docs/src/predefined.md
index 15793aae..6068d518 100644
--- a/docs/src/predefined.md
+++ b/docs/src/predefined.md
@@ -46,3 +46,17 @@ It is possible to use these pre-defined backends using the keyword argument `bac
 nlp = ADNLPModel!(f, x0, lvar, uvar, c!, lcon, ucon, backend = :optimized)
 get_adbackend(nlp)
 ```
+
+The backend `:enzyme` focuses on backend based on [Enzyme.jl](https://github.com/EnzymeAD/Enzyme.jl).
+
+```@example ex1
+nlp = ADNLPModel!(f, x0, lvar, uvar, c!, lcon, ucon, backend = :enzyme)
+get_adbackend(nlp)
+```
+
+The backend `:zygote` focuses on backend based on [Zygote.jl](https://github.com/FluxML/Zygote.jl).
+
+```@example ex1
+nlp = ADNLPModel!(f, x0, lvar, uvar, c!, lcon, ucon, backend = :zygote)
+get_adbackend(nlp)
+```
diff --git a/src/predefined_backend.jl b/src/predefined_backend.jl
index 1595d054..c612504b 100644
--- a/src/predefined_backend.jl
+++ b/src/predefined_backend.jl
@@ -48,14 +48,14 @@ enzyme_backend = Dict(
   :jprod_backend => EnzymeReverseADJprod,
   :jtprod_backend => EnzymeReverseADJtprod,
   :hprod_backend => EnzymeReverseADHvprod,
-  :jacobian_backend => EnzymeReverseADJacobian,
-  :hessian_backend => EnzymeReverseADHessian,
+  :jacobian_backend => SparseEnzymeADJacobian,
+  :hessian_backend => SparseEnzymeADHessian,
   :ghjvprod_backend => ForwardDiffADGHjvprod,
   :jprod_residual_backend => EnzymeReverseADJprod,
   :jtprod_residual_backend => EnzymeReverseADJtprod,
   :hprod_residual_backend => EnzymeReverseADHvprod,
-  :jacobian_residual_backend => EnzymeReverseADJacobian,
-  :hessian_residual_backend => EnzymeReverseADHessian,
+  :jacobian_residual_backend => SparseEnzymeADJacobian,
+  :hessian_residual_backend => SparseEnzymeADHessian,
 )
 
 zygote_backend = Dict(