refactor: extrapolate the last spline in AkimaInterpolation instead o…

…f constant

src/derivatives.jl

@@ -107,9 +107,10 @@ derivative(A::LagrangeInterpolation{<:AbstractVector}, t::Number, i) = derivativ
 derivative(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number, i) = derivative(A, t), i
 
 function derivative(A::AkimaInterpolation{<:AbstractVector}, t::Number, iguess)
-    t < A.t[1] && return zero(A.u[1]), 1
-    t > A.t[end] && return zero(A.u[end]), lastindex(t)
-    i = searchsortedlastcorrelated(A.t, t, iguess)
+    i = searchsortedfirstcorrelated(A.t, t, iguess)
+    i > length(A.t) ? i -= 1 : nothing
+    i -= 1
+    i == 0 ? i += 1 : nothing
     j = min(i, length(A.c))  # for smooth derivative at A.t[end]
     wj = t - A.t[i]
     (@evalpoly wj A.b[i] 2A.c[j] 3A.d[j]), i

src/interpolation_methods.jl

@@ -123,9 +123,7 @@ function _interpolate(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number, i)
 end
 
 function _interpolate(A::AkimaInterpolation{<:AbstractVector}, t::Number, iguess)
-    i = searchsortedlastcorrelated(A.t, t, iguess)
-    i == 0 && return A.u[1], i
-    i == length(A.t) && return A.u[end], i
+    i = max(1, min(searchsortedlastcorrelated(A.t, t, iguess), length(A.t) - 1))
     wj = t - A.t[i]
     (@evalpoly wj A.u[i] A.b[i] A.c[i] A.d[i]), i
 end

test/interpolation_tests.jl

@@ -324,8 +324,8 @@ end
 
     # Test extrapolation
     A = AkimaInterpolation(u, t; extrapolate = true)
-    @test A(-1.0) == 0.0
-    @test A(11.0) == 3.0
+    @test A(-1.0) ≈ -5.0
+    @test A(11.0) ≈ -3.924742268041234
     A = AkimaInterpolation(u, t)
     @test_throws DataInterpolations.ExtrapolationError A(-1.0)
     @test_throws DataInterpolations.ExtrapolationError A(11.0)