fix: add basis handling for empty arrays

DifferentiationInterface/src/first_order/jacobian.jl

@@ -215,7 +215,7 @@ function _prepare_jacobian_aux(
         ntuple(b -> seeds[1 + ((a - 1) * B + (b - 1)) % N], Val(B)) for a in 1:A
     ]
     batched_results = [ntuple(b -> similar(y), Val(B)) for _ in batched_seeds]
-    seed_example = ntuple(b -> zero(x), Val(B))
+    seed_example = ntuple(b -> basis(x), Val(B))
     pushforward_prep = prepare_pushforward_nokwarg(
         strict, f_or_f!y..., backend, x, seed_example, contexts...
     )
@@ -246,7 +246,7 @@ function _prepare_jacobian_aux(
         ntuple(b -> seeds[1 + ((a - 1) * B + (b - 1)) % N], Val(B)) for a in 1:A
     ]
     batched_results = [ntuple(b -> similar(x), Val(B)) for _ in batched_seeds]
-    seed_example = ntuple(b -> zero(y), Val(B))
+    seed_example = ntuple(b -> basis(y), Val(B))
     pullback_prep = prepare_pullback_nokwarg(
         strict, f_or_f!y..., backend, x, seed_example, contexts...
     )

DifferentiationInterface/src/first_order/pullback.jl

@@ -285,7 +285,11 @@ function _prepare_pullback_aux(
     contexts::Vararg{Context,C};
 ) where {F,C}
     _sig = signature(f, backend, x, ty, contexts...; strict)
-    dx = zero(x)
+    dx = if x isa Number
+        oneunit(x)
+    else
+        basis(x)
+    end
     pushforward_prep = prepare_pushforward_nokwarg(
         strict, f, backend, x, (dx,), contexts...
     )
@@ -303,7 +307,11 @@ function _prepare_pullback_aux(
     contexts::Vararg{Context,C};
 ) where {F,C}
     _sig = signature(f!, y, backend, x, ty, contexts...; strict)
-    dx = zero(x)
+    dx = if x isa Number
+        oneunit(x)
+    else
+        basis(x)
+    end
     pushforward_prep = prepare_pushforward_nokwarg(
         strict, f!, y, backend, x, (dx,), contexts...
     )

DifferentiationInterface/src/first_order/pushforward.jl

@@ -290,7 +290,11 @@ function _prepare_pushforward_aux(
 ) where {F,C}
     _sig = signature(f, backend, x, tx, contexts...; strict)
     y = f(x, map(unwrap, contexts)...)
-    dy = zero(y)
+    dy = if y isa Number
+        oneunit(y)
+    else
+        basis(y)
+    end
     pullback_prep = prepare_pullback_nokwarg(strict, f, backend, x, (dy,), contexts...)
     return PullbackPushforwardPrep(_sig, pullback_prep)
 end
@@ -306,7 +310,7 @@ function _prepare_pushforward_aux(
     contexts::Vararg{Context,C};
 ) where {F,C}
     _sig = signature(f!, y, backend, x, tx, contexts...; strict)
-    dy = zero(y)
+    dy = basis(y)
     pullback_prep = prepare_pullback_nokwarg(strict, f!, y, backend, x, (dy,), contexts...)
     return PullbackPushforwardPrep(_sig, pullback_prep)
 end

DifferentiationInterface/src/second_order/hessian.jl

@@ -84,13 +84,15 @@ struct HVPGradientHessianPrep{
     BS<:BatchSizeSettings,
     S<:AbstractVector{<:NTuple},
     R<:AbstractVector{<:NTuple},
+    SE<:NTuple,
     E2<:HVPPrep,
     E1<:GradientPrep,
 } <: HessianPrep{SIG}
     _sig::Val{SIG}
     batch_size_settings::BS
     batched_seeds::S
     batched_results::R
+    seed_example::SE
     hvp_prep::E2
     gradient_prep::E1
 end
@@ -119,10 +121,17 @@ function _prepare_hessian_aux(
         ntuple(b -> seeds[1 + ((a - 1) * B + (b - 1)) % N], Val(B)) for a in 1:A
     ]
     batched_results = [ntuple(b -> similar(x), Val(B)) for _ in batched_seeds]
-    hvp_prep = prepare_hvp_nokwarg(strict, f, backend, x, batched_seeds[1], contexts...)
+    seed_example = ntuple(b -> basis(x), Val(B))
+    hvp_prep = prepare_hvp_nokwarg(strict, f, backend, x, seed_example, contexts...)
     gradient_prep = prepare_gradient_nokwarg(strict, f, inner(backend), x, contexts...)
     return HVPGradientHessianPrep(
-        _sig, batch_size_settings, batched_seeds, batched_results, hvp_prep, gradient_prep
+        _sig,
+        batch_size_settings,
+        batched_seeds,
+        batched_results,
+        seed_example,
+        hvp_prep,
+        gradient_prep,
     )
 end
 
@@ -150,11 +159,11 @@ function hessian(
     contexts::Vararg{Context,C},
 ) where {F,SIG,B,aligned,C}
     check_prep(f, prep, backend, x, contexts...)
-    (; batch_size_settings, batched_seeds, hvp_prep) = prep
+    (; batch_size_settings, batched_seeds, seed_example, hvp_prep) = prep
     (; A, B_last) = batch_size_settings
 
     hvp_prep_same = prepare_hvp_same_point(
-        f, hvp_prep, backend, x, batched_seeds[1], contexts...
+        f, hvp_prep, backend, x, seed_example, contexts...
     )
 
     hess = mapreduce(hcat, eachindex(batched_seeds)) do a
@@ -178,11 +187,11 @@ function hessian!(
     contexts::Vararg{Context,C},
 ) where {F,SIG,B,C}
     check_prep(f, prep, backend, x, contexts...)
-    (; batch_size_settings, batched_seeds, batched_results, hvp_prep) = prep
+    (; batch_size_settings, batched_seeds, batched_results, seed_example, hvp_prep) = prep
     (; N) = batch_size_settings
 
     hvp_prep_same = prepare_hvp_same_point(
-        f, hvp_prep, backend, x, batched_seeds[1], contexts...
+        f, hvp_prep, backend, x, seed_example, contexts...
     )
 
     for a in eachindex(batched_seeds, batched_results)

DifferentiationInterface/src/utils/basis.jl

@@ -1,29 +1,39 @@
-"""
-    basis(a::AbstractArray, i)
+pre_basis(a::AbstractArray{T}) where {T} = fill!(similar(a), zero(T))
 
-Construct the `i`-th standard basis array in the vector space of `a`.
-"""
-function basis(a::AbstractArray{T}, i) where {T}
-    b = similar(a)
-    fill!(b, zero(T))
-    b[i] = oneunit(T)
+function post_basis(b::AbstractArray, a::AbstractArray)
     if ismutable_array(a)
         return b
     else
         return map(+, zero(a), b)
     end
 end
 
+"""
+    basis(a::AbstractArray, i)
+
+Construct the `i`-th standard basis array in the vector space of `a`.
+"""
+function basis(a::AbstractArray, i)
+    b = pre_basis(a)
+    b[i] = oneunit(eltype(b))
+    return post_basis(b, a)
+end
+
+# compatible with zero-length vectors
+function basis(a::AbstractArray)
+    b = pre_basis(a)
+    return post_basis(b, a)
+end
+
 """
     multibasis(a::AbstractArray, inds)
 
 Construct the sum of the `i`-th standard basis arrays in the vector space of `a` for all `i ∈ inds`.
 """
-function multibasis(a::AbstractArray{T}, inds) where {T}
-    b = similar(a)
-    fill!(b, zero(T))
+function multibasis(a::AbstractArray, inds)
+    b = pre_basis(a)
     for i in inds
-        b[i] = oneunit(T)
+        b[i] = oneunit(eltype(b))
     end
-    return ismutable_array(a) ? b : map(+, zero(a), b)
+    return post_basis(b, a)
 end

DifferentiationInterface/test/Core/Internals/basis.jl

@@ -26,4 +26,7 @@ using Dates
 
     t = [Time(1) - Time(0)]
     @test basis(t, 1) isa Vector{Nanosecond}
+
+    @test basis([1, 2]) == [0, 0]
+    @test basis(Int[]) == Int[]
 end