diff --git a/src/sparsity_pattern.jl b/src/sparsity_pattern.jl
index ac83be98..ba16683c 100644
--- a/src/sparsity_pattern.jl
+++ b/src/sparsity_pattern.jl
@@ -1,8 +1,16 @@
 """
+    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)
+  S = SparseConnectivityTracer.jacobian_pattern(c, x0)
+  return S
+end
+
 function compute_jacobian_sparsity(c!, cx, x0)
   S = SparseConnectivityTracer.jacobian_pattern(c!, cx, x0)
   return S
@@ -21,8 +29,10 @@ function compute_hessian_sparsity(f, nvar, c!, ncon)
   else
     x0 = rand(nvar)
     y0 = rand(ncon)
-    cx = similar(y0)
-    ℓ(x) = f(x) + sum(c!(cx, x)[i] * y0[i] for i = 1:ncon)
+    function ℓ(x)
+      cx = similar(x, ncon)
+      return f(x) + sum(c!(cx, x)[i] * y0[i] for i = 1:ncon)
+    end
     S = SparseConnectivityTracer.hessian_pattern(ℓ, x0)
     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,