From 9af0a7ef7b224f36fd737273d9c335fdf5cfc5f4 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Tue, 4 Jun 2024 08:22:41 +0200
Subject: [PATCH 01/12] Use generic sparsity detector

---
 Project.toml      |  2 ++
 src/sparse_sym.jl | 16 +++++-----------
 test/Project.toml |  6 ++----
 3 files changed, 9 insertions(+), 15 deletions(-)

diff --git a/Project.toml b/Project.toml
index 4364b41c..8a337614 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,7 @@ uuid = "54578032-b7ea-4c30-94aa-7cbd1cce6c9a"
 version = "0.7.2"
 
 [deps]
+ADTypes = "47edcb42-4c32-4615-8424-f2b9edc5f35b"
 ColPack = "ffa27691-3a59-46ab-a8d4-551f45b8d401"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -12,6 +13,7 @@ ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 
 [compat]
+ADTypes = "1.2.1"
 ColPack = "0.4"
 ForwardDiff = "0.9.0, 0.10.0"
 NLPModels = "0.18, 0.19, 0.20, 0.21"
diff --git a/src/sparse_sym.jl b/src/sparse_sym.jl
index e90c5514..f20cb763 100644
--- a/src/sparse_sym.jl
+++ b/src/sparse_sym.jl
@@ -1,19 +1,13 @@
 function compute_hessian_sparsity(f, nvar, c!, ncon)
-  Symbolics.@variables xs[1:nvar]
-  xsi = Symbolics.scalarize(xs)
-  fun = f(xsi)
-  if ncon > 0
-    Symbolics.@variables ys[1:ncon]
-    ysi = Symbolics.scalarize(ys)
-    cx = similar(ysi)
-    fun = fun + dot(c!(cx, xsi), ysi)
-  end
-  S = Symbolics.hessian_sparsity(fun, ncon == 0 ? xsi : [xsi; ysi]) # , full = false
+  detector = Symbolics.SymbolicsSparsityDetector()  # replaceable
+  lagrangian(x) = f(x) + dot(rand(ncon), c!(zeros(ncon), x))
+  S = ADTypes.hessian_sparsity(lagrangian, rand(nvar), detector) # , full = false
   return S
 end
 
 function compute_jacobian_sparsity(c!, cx, x0)
-  S = Symbolics.jacobian_sparsity(c!, cx, x0)
+  detector = Symbolics.SymbolicsSparsityDetector()  # replaceable
+  S = ADTypes.jacobian_sparsity(c!, cx, x0, detector)
   return S
 end
 
diff --git a/test/Project.toml b/test/Project.toml
index 0f94a872..68587070 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -10,7 +10,6 @@ NLPModelsTest = "7998695d-6960-4d3a-85c4-e1bceb8cd856"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
 Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
@@ -24,7 +23,6 @@ NLPModels = "0.21"
 NLPModelsModifiers = "0.7"
 NLPModelsTest = "0.10"
 ReverseDiff = "1"
-SparseDiffTools = "2.3"
-Symbolics = "5.3"
-SymbolicUtils = "=1.5.1"
+SparseDiffTools = "2.19"
+Symbolics = "5.29"
 Zygote = "0.6"

From 873e1508da51188da12a36feb97d67906cfb5277 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Tue, 4 Jun 2024 08:37:17 +0200
Subject: [PATCH 02/12] Working

---
 src/ADNLPModels.jl | 1 +
 src/sparse_sym.jl  | 6 +++++-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/src/ADNLPModels.jl b/src/ADNLPModels.jl
index 481724bb..d3f846b4 100644
--- a/src/ADNLPModels.jl
+++ b/src/ADNLPModels.jl
@@ -3,6 +3,7 @@ module ADNLPModels
 # stdlib
 using LinearAlgebra, SparseArrays
 # external
+using ADTypes: ADTypes
 using ColPack, ForwardDiff, ReverseDiff
 # JSO
 using NLPModels
diff --git a/src/sparse_sym.jl b/src/sparse_sym.jl
index f20cb763..1c04aa00 100644
--- a/src/sparse_sym.jl
+++ b/src/sparse_sym.jl
@@ -1,6 +1,10 @@
 function compute_hessian_sparsity(f, nvar, c!, ncon)
   detector = Symbolics.SymbolicsSparsityDetector()  # replaceable
-  lagrangian(x) = f(x) + dot(rand(ncon), c!(zeros(ncon), x))
+  function lagrangian(x)
+    cx = zeros(eltype(x), ncon)
+    c!(cx, x)
+    return f(x) + dot(rand(ncon), cx)
+  end
   S = ADTypes.hessian_sparsity(lagrangian, rand(nvar), detector) # , full = false
   return S
 end

From 50e4e2c51d6243ee91a0d53ea46cdec045403a15 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Tue, 4 Jun 2024 08:38:16 +0200
Subject: [PATCH 03/12] Versions

---
 test/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Project.toml b/test/Project.toml
index 68587070..1f344a0e 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -23,6 +23,6 @@ NLPModels = "0.21"
 NLPModelsModifiers = "0.7"
 NLPModelsTest = "0.10"
 ReverseDiff = "1"
-SparseDiffTools = "2.19"
+SparseDiffTools = "2.3"
 Symbolics = "5.29"
 Zygote = "0.6"

From 1d7ead401496c66907fcb2e63c473fecdf526806 Mon Sep 17 00:00:00 2001
From: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>
Date: Tue, 4 Jun 2024 17:16:30 +0200
Subject: [PATCH 04/12] Up Symbolics in docs

---
 docs/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index c8657e93..51be8073 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -25,5 +25,5 @@ Percival = "0.7"
 Plots = "1"
 SolverBenchmark = "0.5"
 SymbolicUtils = "=1.5.1"
-Symbolics = "5.3"
+Symbolics = "5.29"
 Zygote = "0.6.62"

From 4616cddc7babaf779b998d38b31baadfb4741ba0 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Sat, 18 May 2024 03:05:18 +0200
Subject: [PATCH 05/12] Use SparseConnectivityTracer.jl

---
 Project.toml                |   2 +
 src/ADNLPModels.jl          |  49 +++-------
 src/sparse_diff_tools.jl    | 145 ------------------------------
 src/sparse_hessian.jl       |   6 +-
 src/sparse_sym.jl           | 172 ------------------------------------
 src/sparsity_pattern.jl     |  26 ++++++
 test/Project.toml           |   2 +-
 test/runtests.jl            |   8 +-
 test/script_OP.jl           |   2 -
 test/sparse_hessian.jl      |   3 -
 test/sparse_jacobian.jl     |   4 -
 test/sparse_jacobian_nls.jl |   4 -
 12 files changed, 44 insertions(+), 379 deletions(-)
 delete mode 100644 src/sparse_diff_tools.jl
 delete mode 100644 src/sparse_sym.jl
 create mode 100644 src/sparsity_pattern.jl

diff --git a/Project.toml b/Project.toml
index 8a337614..c031674f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -11,10 +11,12 @@ NLPModels = "a4795742-8479-5a88-8948-cc11e1c8c1a6"
 Requires = "ae029012-a4dd-5104-9daa-d747884805df"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
+SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 
 [compat]
 ADTypes = "1.2.1"
 ColPack = "0.4"
+SparseConnectivityTracer = "0.4"
 ForwardDiff = "0.9.0, 0.10.0"
 NLPModels = "0.18, 0.19, 0.20, 0.21"
 Requires = "1"
diff --git a/src/ADNLPModels.jl b/src/ADNLPModels.jl
index d3f846b4..391df01f 100644
--- a/src/ADNLPModels.jl
+++ b/src/ADNLPModels.jl
@@ -2,9 +2,11 @@ module ADNLPModels
 
 # stdlib
 using LinearAlgebra, SparseArrays
+
 # external
 using ADTypes: ADTypes
-using ColPack, ForwardDiff, ReverseDiff
+using SparseConnectivityTracer, ColPack, ForwardDiff, ReverseDiff
+
 # JSO
 using NLPModels
 using Requires
@@ -17,39 +19,13 @@ const ADModel{T, S} = Union{AbstractADNLPModel{T, S}, AbstractADNLSModel{T, S}}
 include("ad.jl")
 include("ad_api.jl")
 
-"""
-    compute_jacobian_sparsity(c!, cx, x0)
-
-Return a sparse matrix.
-"""
-function compute_jacobian_sparsity(args...)
-  throw(
-    ArgumentError(
-      "Please load Symbolics.jl to enable sparse Jacobian or implement `compute_jacobian_sparsity`.",
-    ),
-  )
-end
-
-"""
-    compute_hessian_sparsity(f, nvar, c!, ncon)
-
-Return a sparse matrix.
-"""
-function compute_hessian_sparsity(args...)
-  throw(
-    ArgumentError(
-      "Please load Symbolics.jl to enable sparse Hessian or implement `compute_hessian_sparsity`.",
-    ),
-  )
-end
-
+include("sparsity_pattern.jl")
 include("sparse_jacobian.jl")
 include("sparse_hessian.jl")
 
 include("forward.jl")
 include("reverse.jl")
 include("enzyme.jl")
-include("sparse_diff_tools.jl")
 include("zygote.jl")
 include("predefined_backend.jl")
 include("nlp.jl")
@@ -183,17 +159,12 @@ function ADNLSModel!(model::AbstractNLSModel; kwargs...)
 end
 
 @init begin
-  @require Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7" begin
-    include("sparse_sym.jl")
-
-    predefined_backend[:default][:jacobian_backend] = SparseADJacobian
-    predefined_backend[:default][:jacobian_residual_backend] = SparseADJacobian
-    predefined_backend[:optimized][:jacobian_backend] = SparseADJacobian
-    predefined_backend[:optimized][:jacobian_residual_backend] = SparseADJacobian
-
-    predefined_backend[:default][:hessian_backend] = SparseADHessian
-    predefined_backend[:optimized][:hessian_backend] = SparseReverseADHessian
-  end
+  predefined_backend[:default][:jacobian_backend] = SparseADJacobian
+  predefined_backend[:default][:jacobian_residual_backend] = SparseADJacobian
+  predefined_backend[:optimized][:jacobian_backend] = SparseADJacobian
+  predefined_backend[:optimized][:jacobian_residual_backend] = SparseADJacobian
+  predefined_backend[:default][:hessian_backend] = SparseADHessian
+  predefined_backend[:optimized][:hessian_backend] = SparseReverseADHessian
 end
 
 export get_adbackend, set_adbackend!
diff --git a/src/sparse_diff_tools.jl b/src/sparse_diff_tools.jl
deleted file mode 100644
index 8ec2917d..00000000
--- a/src/sparse_diff_tools.jl
+++ /dev/null
@@ -1,145 +0,0 @@
-@init begin
-  @require SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804" begin
-    function sparse_matrix_colors(A, alg::SparseDiffTools.SparseDiffToolsColoringAlgorithm)
-      return SparseDiffTools.matrix_colors(A, alg)
-    end
-
-    struct SDTSparseADJacobian{Tv, Ti, T, T2, T3, T4, T5} <: ADNLPModels.ADBackend
-      cfJ::SparseDiffTools.ForwardColorJacCache{T, T2, T3, T4, T5, SparseMatrixCSC{Tv, Ti}}
-    end
-
-    function SDTSparseADJacobian(
-      nvar,
-      f,
-      ncon,
-      c!;
-      x0::S = rand(nvar),
-      alg::SparseDiffTools.SparseDiffToolsColoringAlgorithm = SparseDiffTools.GreedyD1Color(),
-      kwargs...,
-    ) where {S}
-      T = eltype(S)
-      output = similar(x0, ncon)
-      J = compute_jacobian_sparsity(c!, output, x0)
-      colors = sparse_matrix_colors(J, alg)
-      jac = SparseMatrixCSC{T, Int}(J.m, J.n, J.colptr, J.rowval, T.(J.nzval))
-
-      dx = fill!(S(undef, ncon), 0)
-      cfJ = SparseDiffTools.ForwardColorJacCache(c!, x0, colorvec = colors, dx = dx, sparsity = jac)
-      SDTSparseADJacobian(cfJ)
-    end
-
-    function get_nln_nnzj(b::SDTSparseADJacobian, nvar, ncon)
-      nnz(b.cfJ.sparsity)
-    end
-
-    function NLPModels.jac_structure!(
-      b::SDTSparseADJacobian,
-      nlp::ADModel,
-      rows::AbstractVector{<:Integer},
-      cols::AbstractVector{<:Integer},
-    )
-      rows .= rowvals(b.cfJ.sparsity)
-      for i = 1:(nlp.meta.nvar)
-        for j = b.cfJ.sparsity.colptr[i]:(b.cfJ.sparsity.colptr[i + 1] - 1)
-          cols[j] = i
-        end
-      end
-      return rows, cols
-    end
-
-    function NLPModels.jac_coord!(
-      b::SDTSparseADJacobian,
-      nlp::ADModel,
-      x::AbstractVector,
-      vals::AbstractVector,
-    )
-      SparseDiffTools.forwarddiff_color_jacobian!(b.cfJ.sparsity, nlp.c!, x, b.cfJ)
-      vals .= nonzeros(b.cfJ.sparsity)
-      return vals
-    end
-
-    function NLPModels.jac_structure_residual!(
-      b::SDTSparseADJacobian,
-      nls::AbstractADNLSModel,
-      rows::AbstractVector{<:Integer},
-      cols::AbstractVector{<:Integer},
-    )
-      rows .= rowvals(b.cfJ.sparsity)
-      for i = 1:(nls.meta.nvar)
-        for j = b.cfJ.sparsity.colptr[i]:(b.cfJ.sparsity.colptr[i + 1] - 1)
-          cols[j] = i
-        end
-      end
-      return rows, cols
-    end
-
-    function NLPModels.jac_coord_residual!(
-      b::SDTSparseADJacobian,
-      nls::AbstractADNLSModel,
-      x::AbstractVector,
-      vals::AbstractVector,
-    )
-      SparseDiffTools.forwarddiff_color_jacobian!(b.cfJ.sparsity, nls.F!, x, b.cfJ)
-      vals .= nonzeros(b.cfJ.sparsity)
-      return vals
-    end
-
-    struct SDTForwardDiffADJprod{T} <: InPlaceADbackend
-      tmp_in::Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}
-      tmp_out::Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}
-    end
-
-    function SDTForwardDiffADJprod(
-      nvar::Integer,
-      f,
-      ncon::Integer = 0,
-      c!::Function = (args...) -> [];
-      x0::AbstractVector{T} = rand(nvar),
-      kwargs...,
-    ) where {T}
-      tmp_in = Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}(
-        undef,
-        nvar,
-      )
-      tmp_out = Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}(
-        undef,
-        ncon,
-      )
-      return SDTForwardDiffADJprod(tmp_in, tmp_out)
-    end
-
-    function Jprod!(b::SDTForwardDiffADJprod, Jv, c!, x, v, ::Val)
-      SparseDiffTools.auto_jacvec!(Jv, c!, x, v, b.tmp_in, b.tmp_out)
-      return Jv
-    end
-
-    struct SDTForwardDiffADHvprod{T} <: ADBackend
-      tmp_in::Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}
-      tmp_out::Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}
-    end
-    function SDTForwardDiffADHvprod(
-      nvar::Integer,
-      f,
-      ncon::Integer = 0,
-      c::Function = (args...) -> [];
-      x0::AbstractVector{T} = rand(nvar),
-      kwargs...,
-    ) where {T}
-      tmp_in = Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}(
-        undef,
-        nvar,
-      )
-      tmp_out = Vector{SparseDiffTools.Dual{ForwardDiff.Tag{SparseDiffTools.DeivVecTag, T}, T, 1}}(
-        undef,
-        nvar,
-      )
-      return SDTForwardDiffADHvprod(tmp_in, tmp_out)
-    end
-
-    function Hvprod!(b::SDTForwardDiffADHvprod, Hv, x, v, f, args...)
-      ϕ!(dy, x; f = f) = ForwardDiff.gradient!(dy, f, x)
-      SparseDiffTools.auto_hesvecgrad!(Hv, (dy, x) -> ϕ!(dy, x), x, v, b.tmp_in, b.tmp_out)
-      return Hv
-    end
-  end
-end
diff --git a/src/sparse_hessian.jl b/src/sparse_hessian.jl
index 383042fe..38d69218 100644
--- a/src/sparse_hessian.jl
+++ b/src/sparse_hessian.jl
@@ -24,8 +24,7 @@ function SparseADHessian(
   kwargs...,
 ) where {S}
   T = eltype(S)
-  Hs = compute_hessian_sparsity(f, nvar, c!, ncon)
-  H = ncon == 0 ? Hs : Hs[1:nvar, 1:nvar]
+  H = compute_hessian_sparsity(f, nvar, c!, ncon)
 
   colors = sparse_matrix_colors(H, alg)
   ncolors = maximum(colors)
@@ -95,8 +94,7 @@ function SparseReverseADHessian(
   alg = ColPackColoration(),
   kwargs...,
 ) where {T}
-  Hs = compute_hessian_sparsity(f, nvar, c!, ncon)
-  H = ncon == 0 ? Hs : Hs[1:nvar, 1:nvar]
+  H = compute_hessian_sparsity(f, nvar, c!, ncon)
 
   colors = sparse_matrix_colors(H, alg)
   ncolors = maximum(colors)
diff --git a/src/sparse_sym.jl b/src/sparse_sym.jl
deleted file mode 100644
index 1c04aa00..00000000
--- a/src/sparse_sym.jl
+++ /dev/null
@@ -1,172 +0,0 @@
-function compute_hessian_sparsity(f, nvar, c!, ncon)
-  detector = Symbolics.SymbolicsSparsityDetector()  # replaceable
-  function lagrangian(x)
-    cx = zeros(eltype(x), ncon)
-    c!(cx, x)
-    return f(x) + dot(rand(ncon), cx)
-  end
-  S = ADTypes.hessian_sparsity(lagrangian, rand(nvar), detector) # , full = false
-  return S
-end
-
-function compute_jacobian_sparsity(c!, cx, x0)
-  detector = Symbolics.SymbolicsSparsityDetector()  # replaceable
-  S = ADTypes.jacobian_sparsity(c!, cx, x0, detector)
-  return S
-end
-
-## ----- Symbolics Jacobian -----
-
-struct SparseSymbolicsADJacobian{T} <: ADBackend
-  nnzj::Int
-  rows::Vector{Int}
-  cols::Vector{Int}
-  cfJ::T
-end
-
-function SparseSymbolicsADJacobian(nvar, f, ncon, c!; kwargs...)
-  Symbolics.@variables xs[1:nvar] out[1:ncon]
-  wi = Symbolics.scalarize(xs)
-  wo = Symbolics.scalarize(out)
-  fun = c!(wo, wi)
-  J = Symbolics.jacobian_sparsity(c!, wo, wi)
-  rows, cols, _ = findnz(J)
-  vals = Symbolics.sparsejacobian_vals(fun, wi, rows, cols)
-  nnzj = length(vals)
-  # cfJ is a Tuple{Expr, Expr}, cfJ[2] is the in-place function
-  # that we need to update a vector `vals` with the nonzeros of Jc(x).
-  cfJ = Symbolics.build_function(vals, wi, expression = Val{false})
-  SparseSymbolicsADJacobian(nnzj, rows, cols, cfJ[2])
-end
-
-function get_nln_nnzj(b::SparseSymbolicsADJacobian, nvar, ncon)
-  b.nnzj
-end
-
-function NLPModels.jac_structure!(
-  b::SparseSymbolicsADJacobian,
-  nlp::ADModel,
-  rows::AbstractVector{<:Integer},
-  cols::AbstractVector{<:Integer},
-)
-  rows .= b.rows
-  cols .= b.cols
-  return rows, cols
-end
-
-function NLPModels.jac_coord!(
-  b::SparseSymbolicsADJacobian,
-  nlp::ADModel,
-  x::AbstractVector,
-  vals::AbstractVector,
-)
-  @eval $(b.cfJ)($vals, $x)
-  return vals
-end
-
-function NLPModels.jac_structure_residual!(
-  b::SparseSymbolicsADJacobian,
-  nls::AbstractADNLSModel,
-  rows::AbstractVector{<:Integer},
-  cols::AbstractVector{<:Integer},
-)
-  rows .= b.rows
-  cols .= b.cols
-  return rows, cols
-end
-
-function NLPModels.jac_coord_residual!(
-  b::SparseSymbolicsADJacobian,
-  nls::AbstractADNLSModel,
-  x::AbstractVector,
-  vals::AbstractVector,
-)
-  @eval $(b.cfJ)($vals, $x)
-  return vals
-end
-
-## ----- Symbolics Hessian -----
-
-struct SparseSymbolicsADHessian{T, H} <: ADBackend
-  nnzh::Int
-  rows::Vector{Int}
-  cols::Vector{Int}
-  y::AbstractVector{T}
-  cfH::H
-end
-
-function SparseSymbolicsADHessian(nvar, f, ncon, c!; x0::S = rand(nvar), kwargs...) where {S}
-  Symbolics.@variables xs[1:nvar], μs
-  xsi = Symbolics.scalarize(xs)
-  fun = μs * f(xsi)
-  Symbolics.@variables ys[1:ncon]
-  ysi = Symbolics.scalarize(ys)
-  if ncon > 0
-    cx = similar(ysi)
-    fun = fun + dot(c!(cx, xsi), ysi)
-  end
-  H = Symbolics.hessian_sparsity(fun, ncon == 0 ? xsi : [xsi; ysi], full = false)
-  H = ncon == 0 ? H : H[1:nvar, 1:nvar]
-  rows, cols, _ = findnz(H)
-  vals = Symbolics.sparsehessian_vals(fun, xsi, rows, cols)
-  nnzh = length(vals)
-  # cfH is a Tuple{Expr, Expr}, cfH[2] is the in-place function
-  # that we need to update a vector `vals` with the nonzeros of ∇²ℓ(x, y, μ).
-  cfH = Symbolics.build_function(vals, xsi, ysi, μs, expression = Val{false})
-  y = fill!(S(undef, ncon), 0)
-  return SparseSymbolicsADHessian(nnzh, rows, cols, y, cfH[2])
-end
-
-function get_nln_nnzh(b::SparseSymbolicsADHessian, nvar)
-  b.nnzh
-end
-
-function NLPModels.hess_structure!(
-  b::SparseSymbolicsADHessian,
-  nlp::ADModel,
-  rows::AbstractVector{<:Integer},
-  cols::AbstractVector{<:Integer},
-)
-  rows .= b.rows
-  cols .= b.cols
-  return rows, cols
-end
-
-function NLPModels.hess_coord!(
-  b::SparseSymbolicsADHessian,
-  nlp::ADModel,
-  x::AbstractVector,
-  y::AbstractVector,
-  obj_weight::Real,
-  vals::AbstractVector,
-)
-  @eval $(b.cfH)($vals, $x, $y, $obj_weight)
-  return vals
-end
-
-function NLPModels.hess_coord!(
-  b::SparseSymbolicsADHessian,
-  nlp::ADModel,
-  x::AbstractVector,
-  obj_weight::Real,
-  vals::AbstractVector,
-)
-  b.y .= 0
-  @eval $(b.cfH)($vals, $x, $(b.y), $obj_weight)
-  return vals
-end
-
-function NLPModels.hess_coord!(
-  b::SparseSymbolicsADHessian,
-  nlp::ADModel,
-  x::AbstractVector,
-  j::Integer,
-  vals::AbstractVector{T},
-) where {T}
-  for (w, k) in enumerate(nlp.meta.nln)
-    b.y[w] = k == j ? 1 : 0
-  end
-  obj_weight = zero(T)
-  @eval $(b.cfH)($vals, $x, $(b.y), $obj_weight)
-  return vals
-end
diff --git a/src/sparsity_pattern.jl b/src/sparsity_pattern.jl
new file mode 100644
index 00000000..aff37c32
--- /dev/null
+++ b/src/sparsity_pattern.jl
@@ -0,0 +1,26 @@
+"""
+    compute_jacobian_sparsity(c!, cx, x0)
+
+Return a sparse matrix.
+"""
+function compute_jacobian_sparsity(c!, cx, x0)
+  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+  S = ADTypes.jacobian_sparsity(c!, cx, x0, detector)
+  return S
+end
+
+"""
+    compute_hessian_sparsity(f, nvar, c!, ncon)
+
+Return a sparse matrix.
+"""
+function compute_hessian_sparsity(f, nvar, c!, ncon)
+  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+  function lagrangian(x)
+    cx = zeros(eltype(x), ncon)
+    c!(cx, x)
+    return f(x) + dot(rand(ncon), cx)
+  end
+  S = ADTypes.hessian_sparsity(lagrangian, rand(nvar), detector)
+  return S
+end
diff --git a/test/Project.toml b/test/Project.toml
index 1f344a0e..c00d9ed8 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -15,7 +15,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
-CUDA = "4, 5"
+CUDA = "5"
 Enzyme = "0.10, 0.11, 0.12"
 ForwardDiff = "0.10"
 ManualNLPModels = "0.1"
diff --git a/test/runtests.jl b/test/runtests.jl
index 3eea51f6..4bb8ec4e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -3,7 +3,7 @@ using ADNLPModels, ManualNLPModels, NLPModels, NLPModelsModifiers, NLPModelsTest
 using ADNLPModels:
   gradient, gradient!, jacobian, hessian, Jprod!, Jtprod!, directional_second_derivative, Hvprod!
 
-@testset "Error without loading package for sparsity pattern" begin
+@testset "Test sparsity pattern of Jacobian and Hessian" begin
   f(x) = sum(x)
   c!(cx, x) = begin
     cx .= 1
@@ -12,12 +12,10 @@ using ADNLPModels:
   nvar, ncon = 2, 1
   x0 = ones(nvar)
   cx = rand(ncon)
-  @test_throws ArgumentError ADNLPModels.compute_jacobian_sparsity(c!, cx, x0)
-  @test_throws ArgumentError ADNLPModels.compute_hessian_sparsity(f, nvar, c!, ncon)
+  S = ADNLPModels.compute_jacobian_sparsity(c!, cx, x0)
+  S = ADNLPModels.compute_hessian_sparsity(f, nvar, c!, ncon)
 end
 
-using SparseDiffTools, Symbolics
-
 @testset "Test using a NLPModel instead of AD-backend" begin
   include("manual.jl")
 end
diff --git a/test/script_OP.jl b/test/script_OP.jl
index 2ecad87c..3b8cd908 100644
--- a/test/script_OP.jl
+++ b/test/script_OP.jl
@@ -2,8 +2,6 @@
 
 # optional deps
 # using Enzyme
-# using SparseDiffTools
-using Symbolics
 
 # AD deps
 using ForwardDiff, ReverseDiff
diff --git a/test/sparse_hessian.jl b/test/sparse_hessian.jl
index ce35c886..a7f277aa 100644
--- a/test/sparse_hessian.jl
+++ b/test/sparse_hessian.jl
@@ -1,9 +1,6 @@
 list_sparse_hess_backend = (
   (ADNLPModels.SparseADHessian, Dict()),
-  (ADNLPModels.SparseADHessian, Dict(:alg => SparseDiffTools.GreedyD1Color())),
-  (ADNLPModels.SparseADHessian, Dict(:alg => SparseDiffTools.AcyclicColoring())),
   (ADNLPModels.ForwardDiffADHessian, Dict()),
-  (ADNLPModels.SparseSymbolicsADHessian, Dict()),
 )
 
 dt = (Float32, Float64)
diff --git a/test/sparse_jacobian.jl b/test/sparse_jacobian.jl
index 1d3da99d..20b4d05e 100644
--- a/test/sparse_jacobian.jl
+++ b/test/sparse_jacobian.jl
@@ -1,10 +1,6 @@
 list_sparse_jac_backend = (
   (ADNLPModels.SparseADJacobian, Dict()), # default
-  (ADNLPModels.SparseADJacobian, Dict(:alg => SparseDiffTools.GreedyD1Color())),
-  (ADNLPModels.SparseADJacobian, Dict(:alg => SparseDiffTools.AcyclicColoring())),
   (ADNLPModels.ForwardDiffADJacobian, Dict()),
-  (ADNLPModels.SparseSymbolicsADJacobian, Dict()),
-  (ADNLPModels.SDTSparseADJacobian, Dict()),
 )
 dt = (Float32, Float64)
 @testset "Basic Jacobian derivative with backend=$(backend) and T=$(T)" for T in dt,
diff --git a/test/sparse_jacobian_nls.jl b/test/sparse_jacobian_nls.jl
index f0b94607..23df0dc3 100644
--- a/test/sparse_jacobian_nls.jl
+++ b/test/sparse_jacobian_nls.jl
@@ -1,10 +1,6 @@
 list_sparse_jac_backend = (
   (ADNLPModels.SparseADJacobian, Dict()), # default
-  (ADNLPModels.SparseADJacobian, Dict(:alg => SparseDiffTools.GreedyD1Color())),
-  (ADNLPModels.SparseADJacobian, Dict(:alg => SparseDiffTools.AcyclicColoring())),
   (ADNLPModels.ForwardDiffADJacobian, Dict()),
-  (ADNLPModels.SparseSymbolicsADJacobian, Dict()),
-  (ADNLPModels.SDTSparseADJacobian, Dict()),
 )
 dt = (Float32, Float64)
 @testset "Basic Jacobian of residual derivative with backend=$(backend) and T=$(T)" for T in dt,

From c8321436dfdeaa7667723af0433a6c3fd82913b0 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Sun, 19 May 2024 14:56:08 +0200
Subject: [PATCH 06/12] Modifications done during the flight

---
 src/sparsity_pattern.jl | 25 ++++++++++++++++++++-----
 test/runtests.jl        | 11 ++++-------
 2 files changed, 24 insertions(+), 12 deletions(-)

diff --git a/src/sparsity_pattern.jl b/src/sparsity_pattern.jl
index aff37c32..293be764 100644
--- a/src/sparsity_pattern.jl
+++ b/src/sparsity_pattern.jl
@@ -1,8 +1,17 @@
 """
+    compute_jacobian_sparsity(c, x0)
     compute_jacobian_sparsity(c!, cx, x0)
 
 Return a sparse matrix.
 """
+function compute_jacobian_sparsity end
+
+function compute_jacobian_sparsity(c, x0)
+  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+  S = SparseConnectivityTracer.jacobian_pattern(c, x0, detector)
+  return S
+end
+
 function compute_jacobian_sparsity(c!, cx, x0)
   detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
   S = ADTypes.jacobian_sparsity(c!, cx, x0, detector)
@@ -15,12 +24,18 @@ end
 Return a sparse matrix.
 """
 function compute_hessian_sparsity(f, nvar, c!, ncon)
-  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
   function lagrangian(x)
-    cx = zeros(eltype(x), ncon)
-    c!(cx, x)
-    return f(x) + dot(rand(ncon), cx)
+    if ncon == 0
+      return f(x)
+    else
+      cx = zeros(eltype(x), ncon)
+      y0 = rand(ncon)
+      return f(x) + dot(c!(cx, x), y0)
+    end
   end
-  S = ADTypes.hessian_sparsity(lagrangian, rand(nvar), detector)
+
+  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+  x0 = rand(nvar)
+  S = ADTypes.hessian_sparsity(lagrangian, x0, detector)
   return S
 end
diff --git a/test/runtests.jl b/test/runtests.jl
index 4bb8ec4e..abf66f40 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -5,13 +5,12 @@ using ADNLPModels:
 
 @testset "Test sparsity pattern of Jacobian and Hessian" begin
   f(x) = sum(x)
-  c!(cx, x) = begin
-    cx .= 1
-    return x
-  end
-  nvar, ncon = 2, 1
+  c(x) = x
+  c!(cx, x) = copyto!(cx, x)
+  nvar, ncon = 2, 2
   x0 = ones(nvar)
   cx = rand(ncon)
+  S = ADNLPModels.compute_jacobian_sparsity(c, x0)
   S = ADNLPModels.compute_jacobian_sparsity(c!, cx, x0)
   S = ADNLPModels.compute_hessian_sparsity(f, nvar, c!, ncon)
 end
@@ -41,13 +40,11 @@ push!(
   ADNLPModels.predefined_backend,
   :zygote_backend => Dict(
     :gradient_backend => ADNLPModels.ZygoteADGradient,
-    :hprod_backend => ADNLPModels.SDTForwardDiffADHvprod,
     :jprod_backend => ADNLPModels.ZygoteADJprod,
     :jtprod_backend => ADNLPModels.ZygoteADJtprod,
     :jacobian_backend => ADNLPModels.ZygoteADJacobian,
     :hessian_backend => ADNLPModels.ZygoteADHessian,
     :ghjvprod_backend => ADNLPModels.ForwardDiffADGHjvprod,
-    :hprod_residual_backend => ADNLPModels.SDTForwardDiffADHvprod,
     :jprod_residual_backend => ADNLPModels.ZygoteADJprod,
     :jtprod_residual_backend => ADNLPModels.ZygoteADJtprod,
     :jacobian_residual_backend => ADNLPModels.ZygoteADJacobian,

From 2425a6595fe27df5512aa41c567fd7410cac5891 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 28 May 2024 11:24:00 -0400
Subject: [PATCH 07/12] Update SCT.jl

---
 Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/Project.toml b/Project.toml
index c031674f..dec03ff0 100644
--- a/Project.toml
+++ b/Project.toml
@@ -16,7 +16,7 @@ SparseConnectivityTracer = "9f842d2f-2579-4b1d-911e-f412cf18a3f5"
 [compat]
 ADTypes = "1.2.1"
 ColPack = "0.4"
-SparseConnectivityTracer = "0.4"
+SparseConnectivityTracer = "0.5"
 ForwardDiff = "0.9.0, 0.10.0"
 NLPModels = "0.18, 0.19, 0.20, 0.21"
 Requires = "1"

From 5d99aaa6cc10e33ca8bc8b7ed3904f62a593c654 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 4 Jun 2024 12:01:50 -0400
Subject: [PATCH 08/12] Remove Symbolics.jl

---
 docs/Project.toml | 4 ----
 test/Project.toml | 2 --
 2 files changed, 6 deletions(-)

diff --git a/docs/Project.toml b/docs/Project.toml
index 51be8073..0d1e6c95 100644
--- a/docs/Project.toml
+++ b/docs/Project.toml
@@ -10,8 +10,6 @@ OptimizationProblems = "5049e819-d29b-5fba-b941-0eee7e64c1c6"
 Percival = "01435c0c-c90d-11e9-3788-63660f8fbccc"
 Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
 SolverBenchmark = "581a75fa-a23a-52d0-a590-d6201de2218a"
-SymbolicUtils = "d1185830-fcd6-423d-90d6-eec64667417b"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
@@ -24,6 +22,4 @@ OptimizationProblems = "0.7"
 Percival = "0.7"
 Plots = "1"
 SolverBenchmark = "0.5"
-SymbolicUtils = "=1.5.1"
-Symbolics = "5.29"
 Zygote = "0.6.62"
diff --git a/test/Project.toml b/test/Project.toml
index c00d9ed8..75c06577 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -10,7 +10,6 @@ NLPModelsTest = "7998695d-6960-4d3a-85c4-e1bceb8cd856"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
 SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
-Symbolics = "0c5d862f-8b57-4792-8d23-62f2024744c7"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
@@ -24,5 +23,4 @@ NLPModelsModifiers = "0.7"
 NLPModelsTest = "0.10"
 ReverseDiff = "1"
 SparseDiffTools = "2.3"
-Symbolics = "5.29"
 Zygote = "0.6"

From 370717a031df792edfddcf75c21959ef748e2990 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 4 Jun 2024 12:05:27 -0400
Subject: [PATCH 09/12] Keep CUDA.jl v4 for the tests...

---
 test/Project.toml | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/Project.toml b/test/Project.toml
index 75c06577..7350cde7 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -14,7 +14,7 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [compat]
-CUDA = "5"
+CUDA = "4, 5"
 Enzyme = "0.10, 0.11, 0.12"
 ForwardDiff = "0.10"
 ManualNLPModels = "0.1"

From 9c4b9ef6f29084e84d57652e8231d73ca9301f39 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 4 Jun 2024 19:26:37 -0400
Subject: [PATCH 10/12] Update the documentation and fix a few typos

---
 README.md                 |  2 --
 docs/src/backend.md       | 20 ++++++++++----------
 docs/src/performance.md   |  2 +-
 docs/src/predefined.md    | 26 +++++---------------------
 docs/src/reference.md     | 12 ++++++------
 src/ADNLPModels.jl        |  9 ---------
 src/predefined_backend.jl | 12 ++++++------
 src/sparsity_pattern.jl   |  2 +-
 test/Project.toml         |  2 --
 9 files changed, 29 insertions(+), 58 deletions(-)

diff --git a/README.md b/README.md
index 40459ac6..67b58f2d 100644
--- a/README.md
+++ b/README.md
@@ -96,8 +96,6 @@ The following AD packages are supported:
 and as optional dependencies (you must load the package before):
 
 - `Enzyme.jl`;
-- `SparseDiffTools.jl`;
-- `Symbolics.jl`;
 - `Zygote.jl`.
 
 ## Bug reports and discussions
diff --git a/docs/src/backend.md b/docs/src/backend.md
index 22b0d6a8..30e0ebc6 100644
--- a/docs/src/backend.md
+++ b/docs/src/backend.md
@@ -7,14 +7,14 @@ The backend information is in a structure [`ADNLPModels.ADModelBackend`](@ref) i
 
 The functions used internally to define the NLPModel API and the possible backends are defined in the following table:
 
-| Functions | FowardDiff backends | ReverseDiff backends | Zygote backends | Enzyme backend | SparseDiffTools backend | Symbolics backend |
+| Functions | FowardDiff backends | ReverseDiff backends | Zygote backends | Enzyme backend | Sparse backend |
 | ----------- | ----------- | ----------- | ----------- |  ----------- |  ----------- |  ----------- |
-| `gradient` and `gradient!` | `ForwardDiffADGradient`/`GenericForwardDiffADGradient` | `ReverseDiffADGradient`/`GenericReverseDiffADGradient` | `ZygoteADGradient` | `EnzymeADGradient` | -- | -- |
-| `jacobian` | `ForwardDiffADJacobian` | `ReverseDiffADJacobian` | `ZygoteADJacobian` | -- | `SDTSparseADJacobian` | `SparseADJacobian`/`SparseSymbolicsADJacobian` |
-| `hessian` | `ForwardDiffADHessian` | `ReverseDiffADHessian` | `ZygoteADHessian` | -- | -- | `SparseADHessian`/`SparseSymbolicsADHessian` |
-| `Jprod` | `ForwardDiffADJprod`/`GenericForwardDiffADJprod` | `ReverseDiffADJprod`/`GenericReverseDiffADJprod` | `ZygoteADJprod` | -- | `SDTForwardDiffADJprod` | -- | 
-| `Jtprod` | `ForwardDiffADJtprod`/`GenericForwardDiffADJtprod` | `ReverseDiffADJtprod`/`GenericReverseDiffADJtprod` | `ZygoteADJtprod` | -- | -- | -- | 
-| `Hvprod` | `ForwardDiffADHvprod`/`GenericForwardDiffADHvprod` | `ReverseDiffADHvprod`/`GenericReverseDiffADHvprod` | -- | -- | `SDTForwardDiffADHvprod` | -- | 
+| `gradient` and `gradient!` | `ForwardDiffADGradient`/`GenericForwardDiffADGradient` | `ReverseDiffADGradient`/`GenericReverseDiffADGradient` | `ZygoteADGradient` | `EnzymeADGradient` | -- |
+| `jacobian` | `ForwardDiffADJacobian` | `ReverseDiffADJacobian` | `ZygoteADJacobian` | -- | `SparseADJacobian` |
+| `hessian` | `ForwardDiffADHessian` | `ReverseDiffADHessian` | `ZygoteADHessian` | -- | `SparseADHessian` |
+| `Jprod` | `ForwardDiffADJprod`/`GenericForwardDiffADJprod` | `ReverseDiffADJprod`/`GenericReverseDiffADJprod` | `ZygoteADJprod` | -- |
+| `Jtprod` | `ForwardDiffADJtprod`/`GenericForwardDiffADJtprod` | `ReverseDiffADJtprod`/`GenericReverseDiffADJtprod` | `ZygoteADJtprod` | -- |
+| `Hvprod` | `ForwardDiffADHvprod`/`GenericForwardDiffADHvprod` | `ReverseDiffADHvprod`/`GenericReverseDiffADHvprod` | -- |
 | `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.
@@ -49,7 +49,7 @@ Thanks to the backends inside `ADNLPModels.jl`, it is easy to change the backend
 
 ```@example adnlp
 nlp = ADNLPModel(f, x0, gradient_backend = ADNLPModels.ReverseDiffADGradient)
-grad(nlp, nlp.meta.x0) # returns the gradient at x0 using `ReverseDiff`
+grad(nlp, nlp.meta.x0)  # returns the gradient at x0 using `ReverseDiff`
 ```
 
 It is also possible to try some new implementation for each function. First, we define a new `ADBackend` structure.
@@ -81,7 +81,7 @@ Finally, we use the homemade backend to compute the gradient.
 
 ```@example adnlp
 nlp = ADNLPModel(sum, ones(3), gradient_backend = NewADGradient)
-grad(nlp, nlp.meta.x0) # returns the gradient at x0 using `NewADGradient`
+grad(nlp, nlp.meta.x0)  # returns the gradient at x0 using `NewADGradient`
 ```
 
 ### Change backend
@@ -104,7 +104,7 @@ set_adbackend!(nlp, adback)
 get_adbackend(nlp)
 ```
 
-The alternative is to use ``set_adbackend!` and pass the new backends via `kwargs`. In the second approach, it is possible to pass either the type of the desired backend or an instance as shown below.
+The alternative is to use `set_adbackend!` and pass the new backends via `kwargs`. In the second approach, it is possible to pass either the type of the desired backend or an instance as shown below.
 
 ```@example adnlp2
 set_adbackend!(
diff --git a/docs/src/performance.md b/docs/src/performance.md
index f2625538..0110a03d 100644
--- a/docs/src/performance.md
+++ b/docs/src/performance.md
@@ -84,7 +84,7 @@ v = ones(2)
 It is tempting to define the most generic and efficient `ADNLPModel` from the start.
 
 ```@example ex2
-using ADNLPModels, NLPModels, Symbolics
+using ADNLPModels, NLPModels
 f(x) = (x[1] - x[2])^2
 x0 = ones(2)
 lcon = ucon = ones(1)
diff --git a/docs/src/predefined.md b/docs/src/predefined.md
index 5dce2e6b..214c6350 100644
--- a/docs/src/predefined.md
+++ b/docs/src/predefined.md
@@ -49,30 +49,12 @@ get_adbackend(nlp)
 
 ## Hessian and Jacobian computations
 
-It is to be noted that by default the Jacobian and Hessian matrices are dense.
+It is to be noted that by default the Jacobian and Hessian matrices are sparse.
 
 ```@example ex1
-(get_nnzj(nlp), get_nnzh(nlp)) # number of nonzeros elements in the Jacobian and Hessian
+(get_nnzj(nlp), get_nnzh(nlp))  # number of nonzeros elements in the Jacobian and Hessian
 ```
 
-To enable sparse computations of these entries, one needs to first load the package [`Symbolics.jl`](https://github.com/JuliaSymbolics/Symbolics.jl)
-
-```@example ex1
-using Symbolics
-```
-
-and now
-
-```@example ex1
-ADNLPModels.predefined_backend[:optimized][:jacobian_backend]
-```
-
-```@example ex1
-ADNLPModels.predefined_backend[:optimized][:hessian_backend]
-```
-
-Choosing another optimization problem with the optimized backend will compute sparse Jacobian and Hessian matrices.
-
 ```@example ex1
 f(x) = (x[1] - 1)^2
 T = Float64
@@ -92,4 +74,6 @@ x = rand(T, 2)
 jac(nlp, x)
 ```
 
-The package [`Symbolics.jl`](https://github.com/JuliaSymbolics/Symbolics.jl) is used to compute the sparsity pattern of the sparse matrix. The evaluation of the number of directional derivatives needed to evaluate the matrix is done by [`ColPack.jl`](https://github.com/michel2323/ColPack.jl).
+The package [`SparseConnectivityTracer.jl`](https://github.com/adrhill/SparseConnectivityTracer.jl) is used to compute the sparsity pattern of Jacobians and Hessians.
+The evaluation of the number of directional derivatives needed to evaluate the matrix is done by [`ColPack.jl`](https://github.com/exanauts/ColPack.jl).
+We acknowledge Guillaume Dalle (@gdalle), Adrian Hill (@adrhill), and Michel Schanen (@michel2323) for the development of these packages.
diff --git a/docs/src/reference.md b/docs/src/reference.md
index bfe346a7..d0ac148a 100644
--- a/docs/src/reference.md
+++ b/docs/src/reference.md
@@ -1,17 +1,17 @@
 # Reference
-​
+
 ## Contents
-​
+
 ```@contents
 Pages = ["reference.md"]
 ```
-​
+
 ## Index
-​
+
 ```@index
 Pages = ["reference.md"]
 ```
-​
+
 ```@autodocs
 Modules = [ADNLPModels]
-```
\ No newline at end of file
+```
diff --git a/src/ADNLPModels.jl b/src/ADNLPModels.jl
index 391df01f..b86d5947 100644
--- a/src/ADNLPModels.jl
+++ b/src/ADNLPModels.jl
@@ -158,15 +158,6 @@ function ADNLSModel!(model::AbstractNLSModel; kwargs...)
   end
 end
 
-@init begin
-  predefined_backend[:default][:jacobian_backend] = SparseADJacobian
-  predefined_backend[:default][:jacobian_residual_backend] = SparseADJacobian
-  predefined_backend[:optimized][:jacobian_backend] = SparseADJacobian
-  predefined_backend[:optimized][:jacobian_residual_backend] = SparseADJacobian
-  predefined_backend[:default][:hessian_backend] = SparseADHessian
-  predefined_backend[:optimized][:hessian_backend] = SparseReverseADHessian
-end
-
 export get_adbackend, set_adbackend!
 
 """
diff --git a/src/predefined_backend.jl b/src/predefined_backend.jl
index 2b207ccf..6e2d0ffd 100644
--- a/src/predefined_backend.jl
+++ b/src/predefined_backend.jl
@@ -3,13 +3,13 @@ default_backend = Dict(
   :hprod_backend => ForwardDiffADHvprod,
   :jprod_backend => ForwardDiffADJprod,
   :jtprod_backend => ForwardDiffADJtprod,
-  :jacobian_backend => ForwardDiffADJacobian,
-  :hessian_backend => ForwardDiffADHessian,
+  :jacobian_backend => SparseADJacobian, # ForwardDiffADJacobian
+  :hessian_backend => SparseADHessian, # ForwardDiffADHessian
   :ghjvprod_backend => ForwardDiffADGHjvprod,
   :hprod_residual_backend => ForwardDiffADHvprod,
   :jprod_residual_backend => ForwardDiffADJprod,
   :jtprod_residual_backend => ForwardDiffADJtprod,
-  :jacobian_residual_backend => ForwardDiffADJacobian,
+  :jacobian_residual_backend => SparseADJacobian, # ForwardDiffADJacobian,
   :hessian_residual_backend => ForwardDiffADHessian,
 )
 
@@ -18,13 +18,13 @@ optimized = Dict(
   :hprod_backend => ReverseDiffADHvprod,
   :jprod_backend => ForwardDiffADJprod,
   :jtprod_backend => ReverseDiffADJtprod,
-  :jacobian_backend => ForwardDiffADJacobian,
-  :hessian_backend => ForwardDiffADHessian,
+  :jacobian_backend => SparseADJacobian, # ForwardDiffADJacobian
+  :hessian_backend => SparseReverseADHessian, # ForwardDiffADHessian,
   :ghjvprod_backend => ForwardDiffADGHjvprod,
   :hprod_residual_backend => ReverseDiffADHvprod,
   :jprod_residual_backend => ForwardDiffADJprod,
   :jtprod_residual_backend => ReverseDiffADJtprod,
-  :jacobian_residual_backend => ForwardDiffADJacobian,
+  :jacobian_residual_backend => SparseADJacobian, # ForwardDiffADJacobian
   :hessian_residual_backend => ForwardDiffADHessian,
 )
 
diff --git a/src/sparsity_pattern.jl b/src/sparsity_pattern.jl
index 293be764..27a4a67d 100644
--- a/src/sparsity_pattern.jl
+++ b/src/sparsity_pattern.jl
@@ -8,7 +8,7 @@ function compute_jacobian_sparsity end
 
 function compute_jacobian_sparsity(c, x0)
   detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
-  S = SparseConnectivityTracer.jacobian_pattern(c, x0, detector)
+  S = ADTypes.jacobian_sparsity(c, x0, detector)
   return S
 end
 
diff --git a/test/Project.toml b/test/Project.toml
index 7350cde7..2843f676 100644
--- a/test/Project.toml
+++ b/test/Project.toml
@@ -9,7 +9,6 @@ NLPModelsModifiers = "e01155f1-5c6f-4375-a9d8-616dd036575f"
 NLPModelsTest = "7998695d-6960-4d3a-85c4-e1bceb8cd856"
 ReverseDiff = "37e2e3b7-166d-5795-8a7a-e32c996b4267"
 SparseArrays = "2f01184e-e22b-5df5-ae63-d93ebab69eaf"
-SparseDiffTools = "47a9eef4-7e08-11e9-0b38-333d64bd3804"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
@@ -22,5 +21,4 @@ NLPModels = "0.21"
 NLPModelsModifiers = "0.7"
 NLPModelsTest = "0.10"
 ReverseDiff = "1"
-SparseDiffTools = "2.3"
 Zygote = "0.6"

From d1cde67e6862042c971d3a645d1366ac4bfd50fe Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Tue, 4 Jun 2024 19:29:41 -0400
Subject: [PATCH 11/12] Update runtests.jl

---
 test/runtests.jl | 2 ++
 1 file changed, 2 insertions(+)

diff --git a/test/runtests.jl b/test/runtests.jl
index abf66f40..fb31e839 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -42,11 +42,13 @@ push!(
     :gradient_backend => ADNLPModels.ZygoteADGradient,
     :jprod_backend => ADNLPModels.ZygoteADJprod,
     :jtprod_backend => ADNLPModels.ZygoteADJtprod,
+    :hprod_backend => ADNLPModels.ForwardDiffADHvprod,
     :jacobian_backend => ADNLPModels.ZygoteADJacobian,
     :hessian_backend => ADNLPModels.ZygoteADHessian,
     :ghjvprod_backend => ADNLPModels.ForwardDiffADGHjvprod,
     :jprod_residual_backend => ADNLPModels.ZygoteADJprod,
     :jtprod_residual_backend => ADNLPModels.ZygoteADJtprod,
+    :hprod_residual_backend => ADNLPModels.ForwardDiffADHvprod,
     :jacobian_residual_backend => ADNLPModels.ZygoteADJacobian,
     :hessian_residual_backend => ADNLPModels.ZygoteADHessian,
   ),

From 9529aa21bd85b66eb1d62f2d221628fee63dd843 Mon Sep 17 00:00:00 2001
From: Alexis Montoison <alexis.montoison@polymtl.ca>
Date: Wed, 5 Jun 2024 09:46:08 -0400
Subject: [PATCH 12/12] Add an option to provide a detector

---
 docs/src/predefined.md  |  2 +-
 src/ADNLPModels.jl      |  2 +-
 src/sparse_hessian.jl   |  6 ++++--
 src/sparse_jacobian.jl  |  3 ++-
 src/sparsity_pattern.jl | 19 ++++++++-----------
 test/runtests.jl        |  5 ++++-
 6 files changed, 20 insertions(+), 17 deletions(-)

diff --git a/docs/src/predefined.md b/docs/src/predefined.md
index 214c6350..8a64c2a7 100644
--- a/docs/src/predefined.md
+++ b/docs/src/predefined.md
@@ -75,5 +75,5 @@ jac(nlp, x)
 ```
 
 The package [`SparseConnectivityTracer.jl`](https://github.com/adrhill/SparseConnectivityTracer.jl) is used to compute the sparsity pattern of Jacobians and Hessians.
-The evaluation of the number of directional derivatives needed to evaluate the matrix is done by [`ColPack.jl`](https://github.com/exanauts/ColPack.jl).
+The evaluation of the number of directional derivatives and the seeds needed to evaluate the compressed Jacobians and Hessians is done by [`ColPack.jl`](https://github.com/exanauts/ColPack.jl).
 We acknowledge Guillaume Dalle (@gdalle), Adrian Hill (@adrhill), and Michel Schanen (@michel2323) for the development of these packages.
diff --git a/src/ADNLPModels.jl b/src/ADNLPModels.jl
index b86d5947..18650372 100644
--- a/src/ADNLPModels.jl
+++ b/src/ADNLPModels.jl
@@ -4,7 +4,7 @@ module ADNLPModels
 using LinearAlgebra, SparseArrays
 
 # external
-using ADTypes: ADTypes
+using ADTypes: ADTypes, AbstractSparsityDetector
 using SparseConnectivityTracer, ColPack, ForwardDiff, ReverseDiff
 
 # JSO
diff --git a/src/sparse_hessian.jl b/src/sparse_hessian.jl
index 38d69218..d72d5dcd 100644
--- a/src/sparse_hessian.jl
+++ b/src/sparse_hessian.jl
@@ -21,10 +21,11 @@ function SparseADHessian(
   c!;
   x0::S = rand(nvar),
   alg = ColPackColoration(),
+  detector::AbstractSparsityDetector = TracerSparsityDetector(),
   kwargs...,
 ) where {S}
   T = eltype(S)
-  H = compute_hessian_sparsity(f, nvar, c!, ncon)
+  H = compute_hessian_sparsity(f, nvar, c!, ncon, detector=detector)
 
   colors = sparse_matrix_colors(H, alg)
   ncolors = maximum(colors)
@@ -92,9 +93,10 @@ function SparseReverseADHessian(
   c!;
   x0::AbstractVector{T} = rand(nvar),
   alg = ColPackColoration(),
+  detector::AbstractSparsityDetector = TracerSparsityDetector(),
   kwargs...,
 ) where {T}
-  H = compute_hessian_sparsity(f, nvar, c!, ncon)
+  H = compute_hessian_sparsity(f, nvar, c!, ncon, detector=detector)
 
   colors = sparse_matrix_colors(H, alg)
   ncolors = maximum(colors)
diff --git a/src/sparse_jacobian.jl b/src/sparse_jacobian.jl
index 1b12fd2c..fccfad2d 100644
--- a/src/sparse_jacobian.jl
+++ b/src/sparse_jacobian.jl
@@ -16,10 +16,11 @@ function SparseADJacobian(
   c!;
   x0::AbstractVector{T} = rand(nvar),
   alg = ColPackColoration(),
+  detector::AbstractSparsityDetector = TracerSparsityDetector(),
   kwargs...,
 ) where {T}
   output = similar(x0, ncon)
-  J = compute_jacobian_sparsity(c!, output, x0)
+  J = compute_jacobian_sparsity(c!, output, x0, detector=detector)
 
   colors = sparse_matrix_colors(J, alg)
   ncolors = maximum(colors)
diff --git a/src/sparsity_pattern.jl b/src/sparsity_pattern.jl
index 27a4a67d..74051fe0 100644
--- a/src/sparsity_pattern.jl
+++ b/src/sparsity_pattern.jl
@@ -1,29 +1,27 @@
 """
-    compute_jacobian_sparsity(c, x0)
-    compute_jacobian_sparsity(c!, cx, x0)
+    compute_jacobian_sparsity(c, x0; detector)
+    compute_jacobian_sparsity(c!, cx, x0; detector)
 
-Return a sparse matrix.
+Return a sparse boolean matrix that represents the adjacency matrix of the Jacobian of c(x).
 """
 function compute_jacobian_sparsity end
 
-function compute_jacobian_sparsity(c, x0)
-  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+function compute_jacobian_sparsity(c, x0; detector::AbstractSparsityDetector=TracerSparsityDetector())
   S = ADTypes.jacobian_sparsity(c, x0, detector)
   return S
 end
 
-function compute_jacobian_sparsity(c!, cx, x0)
-  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
+function compute_jacobian_sparsity(c!, cx, x0; detector::AbstractSparsityDetector=TracerSparsityDetector())
   S = ADTypes.jacobian_sparsity(c!, cx, x0, detector)
   return S
 end
 
 """
-    compute_hessian_sparsity(f, nvar, c!, ncon)
+    compute_hessian_sparsity(f, nvar, c!, ncon; detector)
 
-Return a sparse matrix.
+Return a sparse boolean matrix that represents the adjacency matrix of the Hessian of f(x) + λᵀc(x).
 """
-function compute_hessian_sparsity(f, nvar, c!, ncon)
+function compute_hessian_sparsity(f, nvar, c!, ncon; detector::AbstractSparsityDetector=TracerSparsityDetector())
   function lagrangian(x)
     if ncon == 0
       return f(x)
@@ -34,7 +32,6 @@ function compute_hessian_sparsity(f, nvar, c!, ncon)
     end
   end
 
-  detector = SparseConnectivityTracer.TracerSparsityDetector()  # replaceable
   x0 = rand(nvar)
   S = ADTypes.hessian_sparsity(lagrangian, x0, detector)
   return S
diff --git a/test/runtests.jl b/test/runtests.jl
index fb31e839..565d85cb 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -4,15 +4,18 @@ using ADNLPModels:
   gradient, gradient!, jacobian, hessian, Jprod!, Jtprod!, directional_second_derivative, Hvprod!
 
 @testset "Test sparsity pattern of Jacobian and Hessian" begin
-  f(x) = sum(x)
+  f(x) = sum(x.^2)
   c(x) = x
   c!(cx, x) = copyto!(cx, x)
   nvar, ncon = 2, 2
   x0 = ones(nvar)
   cx = rand(ncon)
   S = ADNLPModels.compute_jacobian_sparsity(c, x0)
+  @test S == I
   S = ADNLPModels.compute_jacobian_sparsity(c!, cx, x0)
+  @test S == I
   S = ADNLPModels.compute_hessian_sparsity(f, nvar, c!, ncon)
+  @test S == I
 end
 
 @testset "Test using a NLPModel instead of AD-backend" begin