Relax type annotations in sparse prep (#647)

* Relax type annotations in sparse prep

* f should be specified as nothing in test case

* Test complex numbers with FiniteDiff

---------

Co-authored-by: Guillaume Dalle <22795598+gdalle@users.noreply.github.com>

Author: ErikQQY

DifferentiationInterface/ext/DifferentiationInterfaceSparseMatrixColoringsExt/hessian.jl

@@ -1,7 +1,7 @@
 struct SparseHessianPrep{
     BS<:BatchSizeSettings,
     C<:AbstractColoringResult{:symmetric,:column},
-    M<:AbstractMatrix{<:Real},
+    M<:AbstractMatrix{<:Number},
     S<:AbstractVector{<:NTuple},
     R<:AbstractVector{<:NTuple},
     E2<:HVPPrep,

DifferentiationInterface/ext/DifferentiationInterfaceSparseMatrixColoringsExt/jacobian.jl

@@ -3,7 +3,7 @@
 struct PushforwardSparseJacobianPrep{
     BS<:BatchSizeSettings,
     C<:AbstractColoringResult{:nonsymmetric,:column},
-    M<:AbstractMatrix{<:Real},
+    M<:AbstractMatrix{<:Number},
     S<:AbstractVector{<:NTuple},
     R<:AbstractVector{<:NTuple},
     E<:PushforwardPrep,
@@ -19,7 +19,7 @@ end
 struct PullbackSparseJacobianPrep{
     BS<:BatchSizeSettings,
     C<:AbstractColoringResult{:nonsymmetric,:row},
-    M<:AbstractMatrix{<:Real},
+    M<:AbstractMatrix{<:Number},
     S<:AbstractVector{<:NTuple},
     R<:AbstractVector{<:NTuple},
     E<:PullbackPrep,

DifferentiationInterface/ext/DifferentiationInterfaceSparseMatrixColoringsExt/jacobian_mixed.jl

@@ -4,7 +4,7 @@ struct MixedModeSparseJacobianPrep{
     BSf<:BatchSizeSettings,
     BSr<:BatchSizeSettings,
     C<:AbstractColoringResult{:nonsymmetric,:bidirectional},
-    M<:AbstractMatrix{<:Real},
+    M<:AbstractMatrix{<:Number},
     Sf<:Vector{<:NTuple},
     Sr<:Vector{<:NTuple},
     Rf<:Vector{<:NTuple},

DifferentiationInterface/test/Back/FiniteDiff/test.jl

@@ -3,6 +3,7 @@ Pkg.add("FiniteDiff")
 
 using DifferentiationInterface, DifferentiationInterfaceTest
 using FiniteDiff: FiniteDiff
+using SparseMatrixColorings
 using Test
 
 LOGGING = get(ENV, "CI", "false") == "false"
@@ -18,3 +19,11 @@ test_differentiation(
     excluded=[:second_derivative, :hvp],
     logging=LOGGING,
 );
+
+@testset verbose = true "Complex number support" begin
+    backend = AutoSparse(AutoFiniteDiff(); coloring_algorithm=GreedyColoringAlgorithm())
+    x = float.(1:3) .+ im
+    @test_nowarn jacobian(identity, backend, x)
+    @test_nowarn jacobian(copyto!, similar(x), backend, x)
+    @test_nowarn hessian(sum, backend, x)
+end

DifferentiationInterface/test/Back/ForwardDiff/test.jl

@@ -1,6 +1,7 @@
 using Pkg
 Pkg.add("ForwardDiff")
 
+using ADTypes: ADTypes
 using ComponentArrays: ComponentArrays
 using DifferentiationInterface, DifferentiationInterfaceTest
 import DifferentiationInterfaceTest as DIT