From 55ad935e9578fdeb5992c48da1ba41fa2386a2b4 Mon Sep 17 00:00:00 2001
From: Adam Wheeler <adamwhlr@gmail.com>
Date: Fri, 16 May 2025 11:17:34 -0400
Subject: [PATCH 1/3] make hessians of scaled interpolants work, and add a test
 that would have caught the bug

---
 ext/InterpolationsForwardDiffExt.jl |  9 +++++----
 test/hessian.jl                     | 17 +++++++++++++++++
 2 files changed, 22 insertions(+), 4 deletions(-)

diff --git a/ext/InterpolationsForwardDiffExt.jl b/ext/InterpolationsForwardDiffExt.jl
index 39a09a21..19d89b40 100644
--- a/ext/InterpolationsForwardDiffExt.jl
+++ b/ext/InterpolationsForwardDiffExt.jl
@@ -14,10 +14,11 @@ end
 
 # apply partials from arbitrarily nested ForwardDiff.Dual to a value
 # used in maybe_clamp, above
-function apply_partials(x_dual::D, val::Number) where D <: ForwardDiff.Dual
-    ∂s = ForwardDiff.partials(x_dual)
-    apply_partials(ForwardDiff.value(x_dual), D(val, ∂s))
+function apply_partials(dual_number::D, x::Number) where D <: ForwardDiff.Dual
+    ∂s = ForwardDiff.partials(dual_number)
+    val = ForwardDiff.value(dual_number)
+    D(apply_partials(val, x) , ∂s)
 end
-apply_partials(_::Number, val::Number) = val
+apply_partials(_::Number, x::Number) = x
 
 end
diff --git a/test/hessian.jl b/test/hessian.jl
index 614936c8..6de27282 100644
--- a/test/hessian.jl
+++ b/test/hessian.jl
@@ -72,4 +72,21 @@ using Test, Interpolations, LinearAlgebra, ForwardDiff
             end
         end
     end
+
+    @testset "scaled interpolators / convienience constructors (issue 627)" begin
+        N = 11
+        x = range(1.0, 3.0, N)
+        y = range(-3.0, 3.0, N)
+        u = rand(N, N)
+
+        for uitp in [
+            Interpolations.linear_interpolation((x, y), u),
+            Interpolations.cubic_spline_interpolation((x, y), u),
+        ]
+            f = x -> uitp(x[1], x[2])
+            x = [π/3, -π/2]
+
+            @test ForwardDiff.hessian(f, x) ≈ Interpolations.hessian(uitp, x[1], x[2])
+        end
+    end
 end

From 364b90d275882a8a3601d12866832645ffbb9f2c Mon Sep 17 00:00:00 2001
From: Adam Wheeler <adamwhlr@gmail.com>
Date: Fri, 16 May 2025 15:40:35 -0400
Subject: [PATCH 2/3] make the test deterministic

---
 test/hessian.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/test/hessian.jl b/test/hessian.jl
index 6de27282..39ad0903 100644
--- a/test/hessian.jl
+++ b/test/hessian.jl
@@ -77,7 +77,7 @@ using Test, Interpolations, LinearAlgebra, ForwardDiff
         N = 11
         x = range(1.0, 3.0, N)
         y = range(-3.0, 3.0, N)
-        u = rand(N, N)
+        u = reshape(sin.(1 : (N^2)), N, N)
 
         for uitp in [
             Interpolations.linear_interpolation((x, y), u),

From a625a349606a96fda30209052b2db8b1b9c4e3d2 Mon Sep 17 00:00:00 2001
From: Mark Kittisopikul <markkitt@gmail.com>
Date: Mon, 19 May 2025 03:15:18 -0400
Subject: [PATCH 3/3] Bump version and news

---
 NEWS.md      | 5 +++++
 Project.toml | 2 +-
 2 files changed, 6 insertions(+), 1 deletion(-)

diff --git a/NEWS.md b/NEWS.md
index 088234da..c3c45957 100644
--- a/NEWS.md
+++ b/NEWS.md
@@ -1,5 +1,10 @@
 For a comprehensive list of changes, see [Releases](https://github.com/JuliaMath/Interpolations.jl/releases).
 
+# v0.16.1
+
+Fixes:
+- Fix `hessian` with ForwardDiff.jl for scaled interpolants ([#628](https://github.com/JuliaMath/Interpolations.jl/pull/628))
+
 # v0.16
 
 Breaking changes:
diff --git a/Project.toml b/Project.toml
index b464c710..ede2f88b 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "Interpolations"
 uuid = "a98d9a8b-a2ab-59e6-89dd-64a1c18fca59"
-version = "0.16.0"
+version = "0.16.1"
 
 [deps]
 Adapt = "79e6a3ab-5dfb-504d-930d-738a2a938a0e"