From b1a751f4b464ebf38d67ef044619a5f55d9e4274 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Wed, 13 Nov 2024 18:32:51 +0100
Subject: [PATCH 01/20] QuadraticSpline POC

---
 src/DataInterpolations.jl    | 24 +++++++++++++++--------
 src/interpolation_caches.jl  | 17 ++++++++++------
 src/interpolation_methods.jl | 38 +++++++++++++++++++++++++++++++++---
 src/interpolation_utils.jl   |  6 ++++++
 4 files changed, 68 insertions(+), 17 deletions(-)

diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index 393f1160..9e56531f 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -55,33 +55,39 @@ function (interp::AbstractInterpolation)(u::AbstractVector, t::AbstractVector)
     u
 end
 
-const EXTRAPOLATION_ERROR = "Cannot extrapolate as `extrapolate` keyword passed was `false`"
-struct ExtrapolationError <: Exception end
-function Base.showerror(io::IO, e::ExtrapolationError)
-    print(io, EXTRAPOLATION_ERROR)
+const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_down` keyword passed was `:none`"
+struct DownExtrapolationError <: Exception end
+function Base.showerror(io::IO, ::DownExtrapolationError)
+    print(io, DOWN_EXTRAPOLATION_ERROR)
+end
+
+const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_up` keyword passed was `:none`"
+struct UpExtrapolationError <: Exception end
+function Base.showerror(io::IO, ::UpExtrapolationError)
+    print(io, UP_EXTRAPOLATION_ERROR)
 end
 
 const INTEGRAL_NOT_FOUND_ERROR = "Cannot integrate it analytically. Please use Numerical Integration methods."
 struct IntegralNotFoundError <: Exception end
-function Base.showerror(io::IO, e::IntegralNotFoundError)
+function Base.showerror(io::IO, ::IntegralNotFoundError)
     print(io, INTEGRAL_NOT_FOUND_ERROR)
 end
 
 const DERIVATIVE_NOT_FOUND_ERROR = "Derivatives greater than second order is not supported."
 struct DerivativeNotFoundError <: Exception end
-function Base.showerror(io::IO, e::DerivativeNotFoundError)
+function Base.showerror(io::IO, ::DerivativeNotFoundError)
     print(io, DERIVATIVE_NOT_FOUND_ERROR)
 end
 
 const INTEGRAL_INVERSE_NOT_FOUND_ERROR = "Cannot invert the integral analytically. Please use Numerical methods."
 struct IntegralInverseNotFoundError <: Exception end
-function Base.showerror(io::IO, e::IntegralInverseNotFoundError)
+function Base.showerror(io::IO, ::IntegralInverseNotFoundError)
     print(io, INTEGRAL_INVERSE_NOT_FOUND_ERROR)
 end
 
 const INTEGRAL_NOT_INVERTIBLE_ERROR = "The Interpolation is not positive everywhere so its integral is not invertible."
 struct IntegralNotInvertibleError <: Exception end
-function Base.showerror(io::IO, e::IntegralNotInvertibleError)
+function Base.showerror(io::IO, ::IntegralNotInvertibleError)
     print(io, INTEGRAL_NOT_INVERTIBLE_ERROR)
 end
 
@@ -90,6 +96,8 @@ export LinearInterpolation, QuadraticInterpolation, LagrangeInterpolation,
        BSplineInterpolation, BSplineApprox, CubicHermiteSpline, PCHIPInterpolation,
        QuinticHermiteSpline, LinearInterpolationIntInv, ConstantInterpolationIntInv
 
+const extrapolation_types::Vector{Symbol} = [:none, :constant, :linear, :extension]
+
 # added for RegularizationSmooth, JJS 11/27/21
 ### Regularization data smoothing and interpolation
 struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation{T, N}} <:
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index d0bfe26e..f8f65755 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -314,14 +314,18 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
     k::kType # knot vector
     c::cType # B-spline control points
     sc::scType # Spline coefficients (preallocated memory)
-    extrapolate::Bool
+    extrapolation_down::Symbol
+    extrapolation_up::Symbol
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuadraticSpline(
-            u, t, I, p, k, c, sc, extrapolate, cache_parameters, assume_linear_t)
+            u, t, I, p, k, c, sc, extrapolation_down,
+            extrapolation_up, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
+        validate_extrapolation(extrapolation_down)
+        validate_extrapolation(extrapolation_up)
         new{typeof(u), typeof(t), typeof(I), typeof(p.α), typeof(k),
             typeof(c), typeof(sc), eltype(u), N}(u,
             t,
@@ -330,7 +334,8 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
             k,
             c,
             sc,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -339,7 +344,7 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolate = false,
+        u::uType, t; extrapolation_down::Symbol = :none, extrapolation_up::Symbol = :none,
         cache_parameters = false, assume_linear_t = 1e-2) where {uType <:
                                                                  AbstractVector{<:Number}}
     u, t = munge_data(u, t)
@@ -352,9 +357,9 @@ function QuadraticSpline(
 
     p = QuadraticSplineParameterCache(u, t, k, c, sc, cache_parameters)
     A = QuadraticSpline(
-        u, t, nothing, p, k, c, sc, extrapolate, cache_parameters, assume_linear_t)
+        u, t, nothing, p, k, c, sc, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticSpline(u, t, I, p, k, c, sc, extrapolate, cache_parameters, assume_linear_t)
+    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 function QuadraticSpline(
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index f47f9e3c..8dbf0f75 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -1,7 +1,39 @@
 function _interpolate(A, t)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) &&
-        throw(ExtrapolationError())
-    return _interpolate(A, t, A.iguesser)
+    if t < first(A.t)
+        _extrapolate_down(A, t)
+    elseif t > last(A.t)
+        _extrapolate_up(A, t)
+    else
+        _interpolate(A, t, A.iguesser)
+    end
+end
+
+function _extrapolate_down(A, t)
+    (; extrapolation_down) = A
+    if extrapolation_down == :none
+        throw(ExtrapolationError(DOWN_EXTRAPOLATION_ERROR))
+    elseif extrapolation_down == :constant
+        first(A.u)
+    elseif extrapolation_down == :linear
+        slope = derivative(A, first(A.t))
+        first(A.u) + slope * (t - first(A.t))
+    elseif extrapolation_down == :extension
+        _interpolate(A, t, A.iguesser)
+    end
+end
+
+function _extrapolate_up(A, t)
+    (; extrapolation_up) = A
+    if extrapolation_up == :none
+        throw(ExtrapolationError(DOWN_EXTRAPOLATION_ERROR))
+    elseif extrapolation_up == :constant
+        last(A.u)
+    elseif extrapolation_up == :linear
+        slope = derivative(A, last(A.t))
+        last(A.u) + slope * (t - last(A.t))
+    elseif extrapolation_up == :extension
+        _interpolate(A, t, A.iguesser)
+    end
 end
 
 # Linear Interpolation
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 2d1c6432..77470423 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -248,6 +248,12 @@ function get_parameters(A::QuinticHermiteSpline, idx)
     end
 end
 
+function validate_extrapolation(method::Symbol)
+    if method ∉ extrapolation_types
+        error("Invalid extrapolation method `$method` supplied, use one of $extrapolation_types.")
+    end
+end
+
 function du_PCHIP(u, t)
     h = diff(u)
     δ = h ./ diff(t)

From 76859cdd610997c3701bf5d7c387772a0eee08bf Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 07:04:38 +0100
Subject: [PATCH 02/20] nit

---
 src/interpolation_methods.jl | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 8dbf0f75..9dc02b95 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -25,7 +25,7 @@ end
 function _extrapolate_up(A, t)
     (; extrapolation_up) = A
     if extrapolation_up == :none
-        throw(ExtrapolationError(DOWN_EXTRAPOLATION_ERROR))
+        throw(ExtrapolationError(UP_EXTRAPOLATION_ERROR))
     elseif extrapolation_up == :constant
         last(A.u)
     elseif extrapolation_up == :linear

From 832ca31f0d71af829097fba0734dd31100fcb028 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 07:37:45 +0100
Subject: [PATCH 03/20] Use enumx for extrapolation types

---
 Project.toml                 |  2 ++
 src/DataInterpolations.jl    | 12 +++++++-----
 src/interpolation_caches.jl  | 15 ++++++++-------
 src/interpolation_methods.jl | 16 ++++++++--------
 src/interpolation_utils.jl   |  6 ------
 5 files changed, 25 insertions(+), 26 deletions(-)

diff --git a/Project.toml b/Project.toml
index 80cd1153..48e92f6f 100644
--- a/Project.toml
+++ b/Project.toml
@@ -3,6 +3,7 @@ uuid = "82cc6244-b520-54b8-b5a6-8a565e85f1d0"
 version = "6.6.0"
 
 [deps]
+EnumX = "4e289a0a-7415-4d19-859d-a7e5c4648b56"
 FindFirstFunctions = "64ca27bc-2ba2-4a57-88aa-44e436879224"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
@@ -27,6 +28,7 @@ DataInterpolationsSymbolicsExt = "Symbolics"
 Aqua = "0.8"
 BenchmarkTools = "1"
 ChainRulesCore = "1.24"
+EnumX = "1.0.4"
 FindFirstFunctions = "1.3"
 FiniteDifferences = "0.12.31"
 ForwardDiff = "0.10.36"
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index 9e56531f..eca8f783 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -7,9 +7,12 @@ abstract type AbstractInterpolation{T, N} end
 using LinearAlgebra, RecipesBase
 using PrettyTables
 using ForwardDiff
+using EnumX
 import FindFirstFunctions: searchsortedfirstcorrelated, searchsortedlastcorrelated,
                            Guesser
 
+@enumx ExtrapolationType none constant linear extension
+
 include("parameter_caches.jl")
 include("interpolation_caches.jl")
 include("interpolation_utils.jl")
@@ -55,13 +58,13 @@ function (interp::AbstractInterpolation)(u::AbstractVector, t::AbstractVector)
     u
 end
 
-const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_down` keyword passed was `:none`"
+const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_down` keyword passed was `none`"
 struct DownExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::DownExtrapolationError)
     print(io, DOWN_EXTRAPOLATION_ERROR)
 end
 
-const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_up` keyword passed was `:none`"
+const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_up` keyword passed was `none`"
 struct UpExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::UpExtrapolationError)
     print(io, UP_EXTRAPOLATION_ERROR)
@@ -94,9 +97,8 @@ end
 export LinearInterpolation, QuadraticInterpolation, LagrangeInterpolation,
        AkimaInterpolation, ConstantInterpolation, QuadraticSpline, CubicSpline,
        BSplineInterpolation, BSplineApprox, CubicHermiteSpline, PCHIPInterpolation,
-       QuinticHermiteSpline, LinearInterpolationIntInv, ConstantInterpolationIntInv
-
-const extrapolation_types::Vector{Symbol} = [:none, :constant, :linear, :extension]
+       QuinticHermiteSpline, LinearInterpolationIntInv, ConstantInterpolationIntInv,
+       ExtrapolationType
 
 # added for RegularizationSmooth, JJS 11/27/21
 ### Regularization data smoothing and interpolation
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index f8f65755..992ab265 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -314,8 +314,8 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
     k::kType # knot vector
     c::cType # B-spline control points
     sc::scType # Spline coefficients (preallocated memory)
-    extrapolation_down::Symbol
-    extrapolation_up::Symbol
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
@@ -324,8 +324,6 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
             extrapolation_up, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
-        validate_extrapolation(extrapolation_down)
-        validate_extrapolation(extrapolation_up)
         new{typeof(u), typeof(t), typeof(I), typeof(p.α), typeof(k),
             typeof(c), typeof(sc), eltype(u), N}(u,
             t,
@@ -344,7 +342,8 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolation_down::Symbol = :none, extrapolation_up::Symbol = :none,
+        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2) where {uType <:
                                                                  AbstractVector{<:Number}}
     u, t = munge_data(u, t)
@@ -357,9 +356,11 @@ function QuadraticSpline(
 
     p = QuadraticSplineParameterCache(u, t, k, c, sc, cache_parameters)
     A = QuadraticSpline(
-        u, t, nothing, p, k, c, sc, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, p, k, c, sc, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
+    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 function QuadraticSpline(
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 9dc02b95..a7692434 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -10,28 +10,28 @@ end
 
 function _extrapolate_down(A, t)
     (; extrapolation_down) = A
-    if extrapolation_down == :none
+    if extrapolation_down == ExtrapolationType.none
         throw(ExtrapolationError(DOWN_EXTRAPOLATION_ERROR))
-    elseif extrapolation_down == :constant
+    elseif extrapolation_down == ExtrapolationType.constant
         first(A.u)
-    elseif extrapolation_down == :linear
+    elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
-    elseif extrapolation_down == :extension
+    elseif extrapolation_down == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
 
 function _extrapolate_up(A, t)
     (; extrapolation_up) = A
-    if extrapolation_up == :none
+    if extrapolation_up == ExtrapolationType.none
         throw(ExtrapolationError(UP_EXTRAPOLATION_ERROR))
-    elseif extrapolation_up == :constant
+    elseif extrapolation_up == ExtrapolationType.constant
         last(A.u)
-    elseif extrapolation_up == :linear
+    elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
-    elseif extrapolation_up == :extension
+    elseif extrapolation_up == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 77470423..2d1c6432 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -248,12 +248,6 @@ function get_parameters(A::QuinticHermiteSpline, idx)
     end
 end
 
-function validate_extrapolation(method::Symbol)
-    if method ∉ extrapolation_types
-        error("Invalid extrapolation method `$method` supplied, use one of $extrapolation_types.")
-    end
-end
-
 function du_PCHIP(u, t)
     h = diff(u)
     δ = h ./ diff(t)

From ea91f76b4484eefd4777afb7a87881881dc223a2 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 10:57:36 +0100
Subject: [PATCH 04/20] Derivative extrapolation POC

---
 src/derivatives.jl           | 47 ++++++++++++++++++++++++++++++------
 src/interpolation_methods.jl |  4 +--
 2 files changed, 42 insertions(+), 9 deletions(-)

diff --git a/src/derivatives.jl b/src/derivatives.jl
index f7a2b0e1..8c9d6030 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -1,15 +1,48 @@
 function derivative(A, t, order = 1)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
-    iguess = A.iguesser
+    (order ∉ (1, 2)) && throw(DerivativeNotFoundError())
+    if t < first(A.t)
+        _extrapolate_derivative_down(A, t, order)
+    elseif t > last(A.t)
+        _extrapolate_derivative_up(A, t, order)
+    else
+        (order == 1) ? _derivative(A, t, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                _derivative(A, t, iguess)
+            end, t)
+    end
+end
 
-    return if order == 1
-        _derivative(A, t, iguess)
-    elseif order == 2
+function _extrapolate_derivative_down(A, t, order)
+    (; extrapolation_down) = A
+    typed_zero = zero(one(A.u[1]) / one(A.t[1]))
+    if extrapolation_down == ExtrapolationType.none
+        throw(UpExtrapolationError())
+    elseif extrapolation_down == ExtrapolationType.constant
+        typed_zero
+    elseif extrapolation_down == ExtrapolationType.linear
+        (order == 1) ? derivative(A, first(A.t)) : typed_zero
+    elseif extrapolation_down == ExtrapolationType.extension
+        (order == 1) ? _derivative(A, t, A.iguesser) :
+        ForwardDiff.derivative(t -> begin
+                _derivative(A, t, iguess)
+            end, t)
+    end
+end
+
+function _extrapolate_derivative_up(A, t, order)
+    (; extrapolation_up) = A
+    typed_zero = zero(one(A.u[1]) / one(A.t[1]))
+    if extrapolation_up == ExtrapolationType.none
+        throw(DownExtrapolationError())
+    elseif extrapolation_up == ExtrapolationType.constant
+        typed_zero
+    elseif extrapolation_up == ExtrapolationType.linear
+        (order == 1) ? derivative(A, last(A.t)) : typed_zero
+    elseif extrapolation_up == ExtrapolationType.extension
+        (order == 1) ? _derivative(A, t, A.iguesser) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
-    else
-        throw(DerivativeNotFoundError())
     end
 end
 
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index a7692434..836f535e 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -11,7 +11,7 @@ end
 function _extrapolate_down(A, t)
     (; extrapolation_down) = A
     if extrapolation_down == ExtrapolationType.none
-        throw(ExtrapolationError(DOWN_EXTRAPOLATION_ERROR))
+        throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
         first(A.u)
     elseif extrapolation_down == ExtrapolationType.linear
@@ -25,7 +25,7 @@ end
 function _extrapolate_up(A, t)
     (; extrapolation_up) = A
     if extrapolation_up == ExtrapolationType.none
-        throw(ExtrapolationError(UP_EXTRAPOLATION_ERROR))
+        throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
         last(A.u)
     elseif extrapolation_up == ExtrapolationType.linear

From f0efd0eb56e4f7798d8a71c5d92f40b2af32372a Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 12:50:08 +0100
Subject: [PATCH 05/20] Integral extrapolation POC

---
 src/derivatives.jl |  9 +++++---
 src/integrals.jl   | 55 ++++++++++++++++++++++++++++++++++++++--------
 2 files changed, 52 insertions(+), 12 deletions(-)

diff --git a/src/derivatives.jl b/src/derivatives.jl
index 8c9d6030..2035dec0 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -5,7 +5,8 @@ function derivative(A, t, order = 1)
     elseif t > last(A.t)
         _extrapolate_derivative_up(A, t, order)
     else
-        (order == 1) ? _derivative(A, t, A.iguesser) :
+        iguess = A.iguesser
+        (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
@@ -22,7 +23,8 @@ function _extrapolate_derivative_down(A, t, order)
     elseif extrapolation_down == ExtrapolationType.linear
         (order == 1) ? derivative(A, first(A.t)) : typed_zero
     elseif extrapolation_down == ExtrapolationType.extension
-        (order == 1) ? _derivative(A, t, A.iguesser) :
+        iguess = A.iguesser
+        (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
@@ -39,7 +41,8 @@ function _extrapolate_derivative_up(A, t, order)
     elseif extrapolation_up == ExtrapolationType.linear
         (order == 1) ? derivative(A, last(A.t)) : typed_zero
     elseif extrapolation_up == ExtrapolationType.extension
-        (order == 1) ? _derivative(A, t, A.iguesser) :
+        iguess = A.iguesser
+        (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
diff --git a/src/integrals.jl b/src/integrals.jl
index de1b4633..e1b041e9 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -1,11 +1,8 @@
 function integral(A::AbstractInterpolation, t::Number)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
-    integral(A, A.t[1], t)
+    integral(A, first(A.t), t)
 end
 
 function integral(A::AbstractInterpolation, t1::Number, t2::Number)
-    ((t1 < A.t[1] || t1 > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
-    ((t2 < A.t[1] || t2 > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     !hasfield(typeof(A), :I) && throw(IntegralNotFoundError())
     # the index less than or equal to t1
     idx1 = get_idx(A, t1, 0)
@@ -17,10 +14,10 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
         return if t1 == t2
             zero(total)
         else
-            total += _integral(A, idx1, A.t[idx1])
-            total -= _integral(A, idx1, t1)
-            total += _integral(A, idx2, t2)
-            total -= _integral(A, idx2, A.t[idx2])
+            total += __integral(A, idx1, A.t[idx1])
+            total -= __integral(A, idx1, t1)
+            total += __integral(A, idx2, t2)
+            total -= __integral(A, idx2, A.t[idx2])
             total
         end
     else
@@ -28,12 +25,52 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
         for idx in idx1:idx2
             lt1 = idx == idx1 ? t1 : A.t[idx]
             lt2 = idx == idx2 ? t2 : A.t[idx + 1]
-            total += _integral(A, idx, lt2) - _integral(A, idx, lt1)
+            total += __integral(A, idx, lt2) - __integral(A, idx, lt1)
         end
         total
     end
 end
 
+function __integral(A::AbstractInterpolation, idx::Number, t::Number)
+    if t < first(A.t)
+        _extrapolate_integral_down(A, idx, t)
+    elseif t > last(A.t)
+        _extrapolate_integral_up(A, idx, t)
+    else
+        _integral(A, idx, t)
+    end
+end
+
+function _extrapolate_integral_down(A, idx, t)
+    (; extrapolation_down) = A
+    if extrapolation_down == ExtrapolationType.none
+        throw(DownExtrapolationError())
+    elseif extrapolation_down == ExtrapolationType.constant
+        first(A.u) * (t - first(A.t))
+    elseif extrapolation_down == ExtrapolationType.linear
+        slope = derivative(A, first(A.t))
+        Δt = t - first(A.t)
+        (first(A.u) + slope * Δt/2) * Δt
+    elseif extrapolation_down == ExtrapolationType.extension
+        _integral(A, idx, t)
+    end
+end
+
+function _extrapolate_integral_up(A, idx, t)
+    (; extrapolation_up) = A
+    if extrapolation_up == ExtrapolationType.none
+        throw(UpExtrapolationError())
+    elseif extrapolation_up == ExtrapolationType.constant
+        integral(A, A.t[end-1], A.t[end]) + last(A.u) * (t - last(A.t))
+    elseif extrapolation_up == ExtrapolationType.linear
+        slope = derivative(A, last(A.t))
+        Δt = t - last(A.t)
+        integral(A, A.t[end-1], A.t[end]) + (last(A.u) + slope * Δt/2) * Δt
+    elseif extrapolation_up == ExtrapolationType.extension
+        _integral(A, idx, t)
+    end
+end
+
 function _integral(A::LinearInterpolation{<:AbstractVector{<:Number}},
         idx::Number,
         t::Number)

From 154b755c502893156cf3899bc98161ba9f164427 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 19:18:36 +0100
Subject: [PATCH 06/20] Apply extrapolation options to all interpolation types

---
 src/derivatives.jl           |   6 +-
 src/integrals.jl             |   6 +-
 src/interpolation_caches.jl  | 316 ++++++++++++++++++++++++-----------
 src/interpolation_methods.jl |  10 +-
 test/interface.jl            |   6 +-
 test/interpolation_tests.jl  | 202 ++++++++++++++--------
 6 files changed, 368 insertions(+), 178 deletions(-)

diff --git a/src/derivatives.jl b/src/derivatives.jl
index 2035dec0..6035a2eb 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -22,7 +22,8 @@ function _extrapolate_derivative_down(A, t, order)
         typed_zero
     elseif extrapolation_down == ExtrapolationType.linear
         (order == 1) ? derivative(A, first(A.t)) : typed_zero
-    elseif extrapolation_down == ExtrapolationType.extension
+    else
+        # extrapolation_down == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
@@ -40,7 +41,8 @@ function _extrapolate_derivative_up(A, t, order)
         typed_zero
     elseif extrapolation_up == ExtrapolationType.linear
         (order == 1) ? derivative(A, last(A.t)) : typed_zero
-    elseif extrapolation_up == ExtrapolationType.extension
+    else
+        # extrapolation_up == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
diff --git a/src/integrals.jl b/src/integrals.jl
index e1b041e9..a411ccd8 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -50,7 +50,7 @@ function _extrapolate_integral_down(A, idx, t)
     elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         Δt = t - first(A.t)
-        (first(A.u) + slope * Δt/2) * Δt
+        (first(A.u) + slope * Δt / 2) * Δt
     elseif extrapolation_down == ExtrapolationType.extension
         _integral(A, idx, t)
     end
@@ -61,11 +61,11 @@ function _extrapolate_integral_up(A, idx, t)
     if extrapolation_up == ExtrapolationType.none
         throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
-        integral(A, A.t[end-1], A.t[end]) + last(A.u) * (t - last(A.t))
+        integral(A, A.t[end - 1], A.t[end]) + last(A.u) * (t - last(A.t))
     elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         Δt = t - last(A.t)
-        integral(A, A.t[end-1], A.t[end]) + (last(A.u) + slope * Δt/2) * Δt
+        integral(A, A.t[end - 1], A.t[end]) + (last(A.u) + slope * Δt / 2) * Δt
     elseif extrapolation_up == ExtrapolationType.extension
         _integral(A, idx, t)
     end
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index 992ab265..bb52519c 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -1,5 +1,6 @@
 """
-    LinearInterpolation(u, t; extrapolate = false, cache_parameters = false)
+    LinearInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line.
 Extrapolation extends the last linear polynomial on each side.
@@ -11,7 +12,10 @@ Extrapolation extends the last linear polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation
     computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
@@ -24,30 +28,37 @@ struct LinearInterpolation{uType, tType, IType, pType, T, N} <: AbstractInterpol
     t::tType
     I::IType
     p::LinearParameterCache{pType}
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
-    function LinearInterpolation(u, t, I, p, extrapolate, cache_parameters, assume_linear_t)
+    function LinearInterpolation(u, t, I, p, extrapolation_down, extrapolation_up,
+            cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.slope), eltype(u), N}(
-            u, t, I, p, extrapolate, Guesser(t), cache_parameters, linear_lookup)
+            u, t, I, p, extrapolation_down, extrapolation_up,
+            Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function LinearInterpolation(
-        u, t; extrapolate = false, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     p = LinearParameterCache(u, t, cache_parameters)
     A = LinearInterpolation(
-        u, t, nothing, p, extrapolate, cache_parameters, assume_linear_t)
+        u, t, nothing, p, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    LinearInterpolation(u, t, I, p, extrapolate, cache_parameters, assume_linear_t)
+    LinearInterpolation(
+        u, t, I, p, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 """
-    QuadraticInterpolation(u, t, mode = :Forward; extrapolate = false, cache_parameters = false)
+    QuadraticInterpolation(u, t, mode = :Forward; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -60,7 +71,10 @@ Extrapolation extends the last quadratic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -74,30 +88,36 @@ struct QuadraticInterpolation{uType, tType, IType, pType, T, N} <:
     I::IType
     p::QuadraticParameterCache{pType}
     mode::Symbol
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuadraticInterpolation(
-            u, t, I, p, mode, extrapolate, cache_parameters, assume_linear_t)
+            u, t, I, p, mode, extrapolation_down,
+            extrapolation_up, cache_parameters, assume_linear_t)
         mode ∈ (:Forward, :Backward) ||
             error("mode should be :Forward or :Backward for QuadraticInterpolation")
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.l₀), eltype(u), N}(
-            u, t, I, p, mode, extrapolate, Guesser(t), cache_parameters, linear_lookup)
+            u, t, I, p, mode, extrapolation_down, extrapolation_up,
+            Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function QuadraticInterpolation(
-        u, t, mode; extrapolate = false, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t, mode; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = QuadraticParameterCache(u, t, cache_parameters)
     A = QuadraticInterpolation(
-        u, t, nothing, p, mode, extrapolate, cache_parameters, linear_lookup)
+        u, t, nothing, p, mode, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticInterpolation(u, t, I, p, mode, extrapolate, cache_parameters, linear_lookup)
+    QuadraticInterpolation(u, t, I, p, mode, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
 
 function QuadraticInterpolation(u, t; kwargs...)
@@ -105,7 +125,8 @@ function QuadraticInterpolation(u, t; kwargs...)
 end
 
 """
-    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolate = false, safetycopy = true)
+    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.
 
@@ -117,7 +138,10 @@ It is the method of interpolation using Lagrange polynomials of (k-1)th order pa
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
 """
 struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
        AbstractInterpolation{T, N}
@@ -126,9 +150,10 @@ struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
     n::Int
     bcache::bcacheType
     idxs::Vector{Int}
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
-    function LagrangeInterpolation(u, t, n, extrapolate)
+    function LagrangeInterpolation(u, t, n, extrapolation_down, extrapolation_up)
         bcache = zeros(eltype(u[1]), n + 1)
         idxs = zeros(Int, n + 1)
         fill!(bcache, NaN)
@@ -138,23 +163,27 @@ struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
             n,
             bcache,
             idxs,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t)
         )
     end
 end
 
 function LagrangeInterpolation(
-        u, t, n = length(t) - 1; extrapolate = false)
+        u, t, n = length(t) - 1;
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     if n != length(t) - 1
         error("Currently only n=length(t) - 1 is supported")
     end
-    LagrangeInterpolation(u, t, n, extrapolate)
+    LagrangeInterpolation(u, t, n, extrapolation_down, extrapolation_up)
 end
 
 """
-    AkimaInterpolation(u, t; extrapolate = false, cache_parameters = false)
+    AkimaInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: [https://en.wikipedia.org/wiki/Akima_spline](https://en.wikipedia.org/wiki/Akima_spline).
 Extrapolation extends the last cubic polynomial on each side.
@@ -166,7 +195,10 @@ Extrapolation extends the last cubic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -181,12 +213,14 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
     b::bType
     c::cType
     d::dType
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function AkimaInterpolation(
-            u, t, I, b, c, d, extrapolate, cache_parameters, assume_linear_t)
+            u, t, I, b, c, d, extrapolation_down,
+            extrapolation_up, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(b), typeof(c),
@@ -196,7 +230,8 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
             b,
             c,
             d,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -205,7 +240,8 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
 end
 
 function AkimaInterpolation(
-        u, t; extrapolate = false, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     n = length(t)
@@ -229,13 +265,16 @@ function AkimaInterpolation(
     d = (b[1:(end - 1)] .+ b[2:end] .- 2.0 .* m[3:(end - 2)]) ./ dt .^ 2
 
     A = AkimaInterpolation(
-        u, t, nothing, b, c, d, extrapolate, cache_parameters, linear_lookup)
+        u, t, nothing, b, c, d, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    AkimaInterpolation(u, t, I, b, c, d, extrapolate, cache_parameters, linear_lookup)
+    AkimaInterpolation(u, t, I, b, c, d, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
 
 """
-    ConstantInterpolation(u, t; dir = :left, extrapolate = false, cache_parameters = false)
+    ConstantInterpolation(u, t; dir = :left, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on `dir`.
 If it is `:left`, then the value at the left point is chosen and if it is `:right`, the value at the right point is chosen.
@@ -249,7 +288,10 @@ Extrapolation extends the last constant polynomial at the end points on each sid
 ## Keyword Arguments
 
   - `dir`: indicates which value should be used for interpolation (`:left` or `:right`).
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -262,31 +304,38 @@ struct ConstantInterpolation{uType, tType, IType, T, N} <: AbstractInterpolation
     I::IType
     p::Nothing
     dir::Symbol # indicates if value to the $dir should be used for the interpolation
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function ConstantInterpolation(
-            u, t, I, dir, extrapolate, cache_parameters, assume_linear_t)
+            u, t, I, dir, extrapolation_down, extrapolation_up,
+            cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), eltype(u), N}(
-            u, t, I, nothing, dir, extrapolate, Guesser(t), cache_parameters, linear_lookup)
+            u, t, I, nothing, dir, extrapolation_down, extrapolation_up,
+            Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function ConstantInterpolation(
-        u, t; dir = :left, extrapolate = false,
+        u, t; dir = :left, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     A = ConstantInterpolation(
-        u, t, nothing, dir, extrapolate, cache_parameters, assume_linear_t)
+        u, t, nothing, dir, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    ConstantInterpolation(u, t, I, dir, extrapolate, cache_parameters, assume_linear_t)
+    ConstantInterpolation(u, t, I, dir, extrapolation_down, extrapolation_up,
+        cache_parameters, assume_linear_t)
 end
 
 """
-    QuadraticSpline(u, t; extrapolate = false, cache_parameters = false)
+    QuadraticSpline(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -298,7 +347,10 @@ Extrapolation extends the last quadratic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -364,7 +416,8 @@ function QuadraticSpline(
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolate = false, cache_parameters = false,
+        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
     u, t = munge_data(u, t)
@@ -387,13 +440,16 @@ function QuadraticSpline(
 
     p = QuadraticSplineParameterCache(u, t, k, c, sc, cache_parameters)
     A = QuadraticSpline(
-        u, t, nothing, p, k, c, sc, extrapolate, cache_parameters, assume_linear_t)
+        u, t, nothing, p, k, c, sc, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticSpline(u, t, I, p, k, c, sc, extrapolate, cache_parameters, assume_linear_t)
+    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 """
-    CubicSpline(u, t; extrapolate = false, cache_parameters = false)
+    CubicSpline(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous.
 Second derivative on both ends are zero, which are also called "natural" boundary conditions. Extrapolation extends the last cubic polynomial on each side.
@@ -405,7 +461,10 @@ Second derivative on both ends are zero, which are also called "natural" boundar
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -420,11 +479,13 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
     p::CubicSplineParameterCache{pType}
     h::hType
     z::zType
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
-    function CubicSpline(u, t, I, p, h, z, extrapolate, cache_parameters, assume_linear_t)
+    function CubicSpline(u, t, I, p, h, z, extrapolation_down,
+            extrapolation_up, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.c₁),
@@ -435,7 +496,8 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
             p,
             h,
             z,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -445,7 +507,8 @@ end
 
 function CubicSpline(u::uType,
         t;
-        extrapolate = false, cache_parameters = false,
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector{<:Number}}
     u, t = munge_data(u, t)
@@ -468,14 +531,17 @@ function CubicSpline(u::uType,
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolate, cache_parameters, linear_lookup)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolate, cache_parameters, linear_lookup)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
 
 function CubicSpline(u::uType,
         t;
-        extrapolate = false, cache_parameters = false,
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractArray{T, N}} where {T, N}
     u, t = munge_data(u, t)
@@ -502,13 +568,16 @@ function CubicSpline(u::uType,
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolate, cache_parameters, linear_lookup)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolate, cache_parameters, linear_lookup)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
 
 function CubicSpline(
-        u::uType, t; extrapolate = false, cache_parameters = false,
+        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
     u, t = munge_data(u, t)
@@ -528,13 +597,16 @@ function CubicSpline(
 
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolate, cache_parameters, assume_linear_t)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolate, cache_parameters, assume_linear_t)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
+        extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 """
-    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolate = false, safetycopy = true)
+    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a curve defined by the linear combination of `n` basis functions of degree `d` where `n` is the number of data points. For more information, refer [https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html](https://pages.mtu.edu/%7Eshene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html).
 Extrapolation is a constant polynomial of the end points on each side.
@@ -549,7 +621,10 @@ Extrapolation is a constant polynomial of the end points on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
@@ -566,7 +641,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
     sc::scType  # Spline coefficients (preallocated memory)
     pVecType::Symbol
     knotVecType::Symbol
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     linear_lookup::Bool
     function BSplineInterpolation(u,
@@ -578,7 +654,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
@@ -592,7 +669,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t),
             linear_lookup
         )
@@ -600,7 +678,9 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
 end
 
 function BSplineInterpolation(
-        u::AbstractVector, t, d, pVecType, knotVecType; extrapolate = false, assume_linear_t = 1e-2)
+        u::AbstractVector, t, d, pVecType, knotVecType;
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     n = length(t)
     n < d + 1 && error("BSplineInterpolation needs at least d + 1, i.e. $(d+1) points.")
@@ -665,11 +745,14 @@ function BSplineInterpolation(
     c = vec(sc \ u[:, :])
     sc = zeros(eltype(t), n)
     BSplineInterpolation(
-        u, t, d, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
+        u, t, d, p, k, c, sc, pVecType, knotVecType,
+        extrapolation_down, extrapolation_up, assume_linear_t)
 end
 
 function BSplineInterpolation(
-        u::AbstractArray{T, N}, t, d, pVecType, knotVecType; extrapolate = false,
+        u::AbstractArray{T, N}, t, d, pVecType, knotVecType;
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
         assume_linear_t = 1e-2) where {T, N}
     u, t = munge_data(u, t)
     n = length(t)
@@ -738,11 +821,13 @@ function BSplineInterpolation(
     c = reshape(c, size(u)...)
     sc = zeros(eltype(t), n)
     BSplineInterpolation(
-        u, t, d, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
+        u, t, d, p, k, c, sc, pVecType, knotVecType,
+        extrapolation_down, extrapolation_up, assume_linear_t)
 end
 
 """
-    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = false)
+    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a regression based B-spline. The argument choices are the same as the `BSplineInterpolation`, with the additional parameter `h < length(t)` which is the number of control points to use, with smaller `h` indicating more smoothing.
 For more information, refer [http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf](http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf).
@@ -759,7 +844,10 @@ Extrapolation is a constant polynomial of the end points on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
@@ -777,7 +865,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
     sc::scType  # Spline coefficients (preallocated memory)
     pVecType::Symbol
     knotVecType::Symbol
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     linear_lookup::Bool
     function BSplineApprox(u,
@@ -790,7 +879,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             assume_linear_t
     )
         linear_lookup = seems_linear(assume_linear_t, t)
@@ -806,7 +896,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolate,
+            extrapolation_down,
+            extrapolation_up,
             Guesser(t),
             linear_lookup
         )
@@ -814,7 +905,9 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
 end
 
 function BSplineApprox(
-        u::AbstractVector, t, d, h, pVecType, knotVecType; extrapolate = false, assume_linear_t = 1e-2)
+        u::AbstractVector, t, d, h, pVecType, knotVecType;
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     n = length(t)
     h < d + 1 && error("BSplineApprox needs at least d + 1, i.e. $(d+1) control points.")
@@ -900,11 +993,14 @@ function BSplineApprox(
     c[2:(end - 1)] .= vec(P)
     sc = zeros(eltype(t), h)
     BSplineApprox(
-        u, t, d, h, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
+        u, t, d, h, p, k, c, sc, pVecType, knotVecType,
+        extrapolation_down, extrapolation_up, assume_linear_t)
 end
 
 function BSplineApprox(
-        u::AbstractArray{T, N}, t, d, h, pVecType, knotVecType; extrapolate = false,
+        u::AbstractArray{T, N}, t, d, h, pVecType, knotVecType;
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
         assume_linear_t = 1e-2) where {T, N}
     u, t = munge_data(u, t)
     n = length(t)
@@ -996,10 +1092,12 @@ function BSplineApprox(
     c[ax_u..., 2:(end - 1)] = P
     sc = zeros(eltype(t), h)
     BSplineApprox(
-        u, t, d, h, p, k, c, sc, pVecType, knotVecType, extrapolate, assume_linear_t)
+        u, t, d, h, p, k, c, sc, pVecType, knotVecType,
+        extrapolation_down, extrapolation_up, assume_linear_t)
 end
 """
-    CubicHermiteSpline(du, u, t; extrapolate = false, cache_parameters = false)
+    CubicHermiteSpline(du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomial such that the value and the first derivative are equal to given values in the data points.
 
@@ -1011,7 +1109,10 @@ It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomi
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1025,33 +1126,40 @@ struct CubicHermiteSpline{uType, tType, IType, duType, pType, T, N} <:
     t::tType
     I::IType
     p::CubicHermiteParameterCache{pType}
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function CubicHermiteSpline(
-            du, u, t, I, p, extrapolate, cache_parameters, assume_linear_t)
+            du, u, t, I, p, extrapolation_down, extrapolation_up,
+            cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(du), typeof(p.c₁), eltype(u), N}(
-            du, u, t, I, p, extrapolate, Guesser(t), cache_parameters, linear_lookup)
+            du, u, t, I, p, extrapolation_down, extrapolation_up,
+            Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function CubicHermiteSpline(
-        du, u, t; extrapolate = false, cache_parameters = false, assume_linear_t = 1e-2)
+        du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du) "Length of `u` is not equal to length of `du`."
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicHermiteParameterCache(du, u, t, cache_parameters)
     A = CubicHermiteSpline(
-        du, u, t, nothing, p, extrapolate, cache_parameters, linear_lookup)
+        du, u, t, nothing, p, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicHermiteSpline(du, u, t, I, p, extrapolate, cache_parameters, linear_lookup)
+    CubicHermiteSpline(du, u, t, I, p, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
 
 """
-    PCHIPInterpolation(u, t; extrapolate = false, safetycopy = true)
+    PCHIPInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a PCHIP Interpolation, which is a type of [`CubicHermiteSpline`](@ref) where the derivative values `du` are derived from the input data
 in such a way that the interpolation never overshoots the data. See [here](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/interp.pdf),
@@ -1064,7 +1172,10 @@ section 3.4 for more details.
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1072,14 +1183,17 @@ section 3.4 for more details.
     to the straight line (see [`looks_linear`](@ref)). Defaults to 1e-2.
 """
 function PCHIPInterpolation(
-        u, t; extrapolate = false, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     u, t = munge_data(u, t)
     du = du_PCHIP(u, t)
-    CubicHermiteSpline(du, u, t; extrapolate, cache_parameters, assume_linear_t)
+    CubicHermiteSpline(
+        du, u, t; extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
 end
 
 """
-    QuinticHermiteSpline(ddu, du, u, t; extrapolate = false, safetycopy = true)
+    QuinticHermiteSpline(ddu, du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polynomial such that the value and the first and second derivative are equal to given values in the data points.
 
@@ -1092,7 +1206,10 @@ It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polyno
 
 ## Keyword Arguments
 
-  - `extrapolate`: boolean value to allow extrapolation. Defaults to `false`.
+  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
+    Defaults to `ExtrapolationType.none`.
+  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
+    Defaults to `ExtrapolationType.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1107,29 +1224,36 @@ struct QuinticHermiteSpline{uType, tType, IType, duType, dduType, pType, T, N} <
     t::tType
     I::IType
     p::QuinticHermiteParameterCache{pType}
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuinticHermiteSpline(
-            ddu, du, u, t, I, p, extrapolate, cache_parameters, assume_linear_t)
+            ddu, du, u, t, I, p, extrapolation_down,
+            extrapolation_up, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(du),
             typeof(ddu), typeof(p.c₁), eltype(u), N}(
-            ddu, du, u, t, I, p, extrapolate, Guesser(t), cache_parameters, linear_lookup)
+            ddu, du, u, t, I, p, extrapolation_down, extrapolation_up,
+            Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
-function QuinticHermiteSpline(ddu, du, u, t; extrapolate = false,
+function QuinticHermiteSpline(
+        ddu, du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du)==length(ddu) "Length of `u` is not equal to length of `du` or `ddu`."
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = QuinticHermiteParameterCache(ddu, du, u, t, cache_parameters)
     A = QuinticHermiteSpline(
-        ddu, du, u, t, nothing, p, extrapolate, cache_parameters, linear_lookup)
+        ddu, du, u, t, nothing, p, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
     QuinticHermiteSpline(
-        ddu, du, u, t, I, p, extrapolate, cache_parameters, linear_lookup)
+        ddu, du, u, t, I, p, extrapolation_down,
+        extrapolation_up, cache_parameters, linear_lookup)
 end
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 836f535e..0c070f18 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -13,11 +13,12 @@ function _extrapolate_down(A, t)
     if extrapolation_down == ExtrapolationType.none
         throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
-        first(A.u)
+        first(A.u) * one(t)
     elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
-    elseif extrapolation_down == ExtrapolationType.extension
+    else 
+        # extrapolation_down == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
@@ -27,11 +28,12 @@ function _extrapolate_up(A, t)
     if extrapolation_up == ExtrapolationType.none
         throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
-        last(A.u)
+        last(A.u) * one(t)
     elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
-    elseif extrapolation_up == ExtrapolationType.extension
+    else 
+        # extrapolation_up == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
diff --git a/test/interface.jl b/test/interface.jl
index e7b2b81b..40fb25f6 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -18,8 +18,10 @@ end
 @testset "Symbolics" begin
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolate = true)
-    B = LinearInterpolation(u .^ 2, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
+    B = LinearInterpolation(u .^ 2, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @variables t x(t)
     substitute(A(t), Dict(t => x))
     t_val = 2.7
diff --git a/test/interpolation_tests.jl b/test/interpolation_tests.jl
index bbeb72f4..832819f3 100644
--- a/test/interpolation_tests.jl
+++ b/test/interpolation_tests.jl
@@ -8,7 +8,8 @@ function test_interpolation_type(T)
     @test T <: DataInterpolations.AbstractInterpolation
     @test hasfield(T, :u)
     @test hasfield(T, :t)
-    @test hasfield(T, :extrapolate)
+    @test hasfield(T, :extrapolation_up)
+    @test hasfield(T, :extrapolation_down)
     @test hasfield(T, :iguesser)
     @test !isempty(methods(DataInterpolations._interpolate, (T, Any, Number)))
     @test !isempty(methods(DataInterpolations._integral, (T, Any, Number)))
@@ -30,7 +31,8 @@ end
     for t in (1.0:10.0, 1.0collect(1:10))
         u = 2.0collect(1:10)
         #t = 1.0collect(1:10)
-        A = LinearInterpolation(u, t; extrapolate = true)
+        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
 
         for (_t, _u) in zip(t, u)
             @test A(_t) == _u
@@ -40,7 +42,8 @@ end
         @test A(11) == 22
 
         u = vcat(2.0collect(1:10)', 3.0collect(1:10)')
-        A = LinearInterpolation(u, t; extrapolate = true)
+        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
 
         for (_t, _u) in zip(t, eachcol(u))
             @test A(_t) == _u
@@ -53,7 +56,8 @@ end
         y = 2:4
         u_ = x' .* y
         u = [u_[:, i] for i in 1:size(u_, 2)]
-        A = LinearInterpolation(u, t; extrapolate = true)
+        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(0) == [0.0, 0.0, 0.0]
         @test A(5.5) == [11.0, 16.5, 22.0]
         @test A(11) == [22.0, 33.0, 44.0]
@@ -64,7 +68,8 @@ end
     u_ = x' .* y
     u = [u_[:, i:(i + 1)] for i in 1:2:10]
     t = 1.0collect(2:2:10)
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     @test A(0) == [-2.0 0.0; -3.0 0.0; -4.0 0.0]
     @test A(3) == [4.0 6.0; 6.0 9.0; 8.0 12.0]
@@ -74,7 +79,8 @@ end
     # with NaNs (#113)
     u = [NaN, 1.0, 2.0, 3.0]
     t = 1:4
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test isnan(A(1.0))
     @test A(2.0) == 1.0
     @test A(2.5) == 1.5
@@ -82,7 +88,8 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, NaN, 2.0, 3.0]
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test isnan(A(2.0))
     @test isnan(A(2.5))
@@ -90,7 +97,8 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, NaN, 3.0]
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test isnan(A(2.5))
@@ -98,7 +106,8 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, 2.0, NaN]
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test A(3.0) == 2.0
@@ -108,16 +117,20 @@ end
     # Test type stability
     u = Float32.(1:5)
     t = Float32.(1:5)
-    A1 = LinearInterpolation(u, t; extrapolate = true)
+    A1 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     u = 1:5
     t = 1:5
-    A2 = LinearInterpolation(u, t; extrapolate = true)
+    A2 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     u = [1 // i for i in 1:5]
     t = (1:5)
-    A3 = LinearInterpolation(u, t; extrapolate = true)
+    A3 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     u = [1 // i for i in 1:5]
     t = [1 // (6 - i) for i in 1:5]
-    A4 = LinearInterpolation(u, t; extrapolate = true)
+    A4 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     F32 = Float32(1)
     F64 = Float64(1)
@@ -126,7 +139,10 @@ end
     R32 = Int32(1) // Int32(1)
     R64 = 1 // 1
     for A in Any[A1, A2, A3, A4]
+        @show A.u
+        @show A.t
         @test @inferred(A(F32)) === A(F32)
+        println("foo")
         @test @inferred(A(F64)) === A(F64)
         @test @inferred(A(I32)) === A(I32)
         @test @inferred(A(I64)) === A(I64)
@@ -137,13 +153,15 @@ end
     # Nan time value:
     t = 0.0:3  # Floats
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
     t = 0:3  # Integers
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
@@ -156,7 +174,8 @@ end
     # Test array-valued interpolation
     u = collect.(2.0collect(1:10))
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(0) == fill(0.0)
     @test A(5.5) == fill(11.0)
     @test A(11) == fill(22)
@@ -171,13 +190,14 @@ end
     # Test extrapolation
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolate = true)
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-1.0) == -2.0
     @test A(11.0) == 22.0
     A = LinearInterpolation(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.ExtrapolationError A(11.0)
-    @test_throws DataInterpolations.ExtrapolationError A([-1.0, 11.0])
+    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
+    @test_throws DataInterpolations.DownExtrapolationError A([-1.0, 11.0])
 end
 
 @testset "Quadratic Interpolation" begin
@@ -185,7 +205,8 @@ end
 
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolate = true)
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -200,7 +221,9 @@ end
     # backward-looking interpolation
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t, :Backward; extrapolate = true)
+    A = QuadraticInterpolation(
+        u, t, :Backward; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -238,7 +261,8 @@ end
 
     # Matrix interpolation test
     u = [1.0 4.0 9.0 16.0; 1.0 4.0 9.0 16.0]
-    A = QuadraticInterpolation(u, t; extrapolate = true)
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, eachcol(u))
         @test A(_t) == _u
@@ -251,7 +275,8 @@ end
 
     u_ = [1.0, 4.0, 9.0, 16.0]' .* ones(5)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticInterpolation(u, t; extrapolate = true)
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(0) == zeros(5)
     @test A(1.5) == 2.25 * ones(5)
     @test A(2.5) == 6.25 * ones(5)
@@ -259,7 +284,8 @@ end
     @test A(5.0) == 25.0 * ones(5)
 
     u = [repeat(u[i], 1, 3) for i in 1:4]
-    A = QuadraticInterpolation(u, t; extrapolate = true)
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(0) == zeros(5, 3)
     @test A(1.5) == 2.25 * ones(5, 3)
     @test A(2.5) == 6.25 * ones(5, 3)
@@ -269,12 +295,13 @@ end
     # Test extrapolation
     u = [1.0, 4.5, 6.0, 2.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolate = true)
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(0.0) == -4.5
     @test A(5.0) == -7.5
     A = QuadraticInterpolation(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(0.0)
-    @test_throws DataInterpolations.ExtrapolationError A(5.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(0.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(5.0)
 end
 
 @testset "Lagrange Interpolation" begin
@@ -329,12 +356,13 @@ end
     # Test extrapolation
     u = [1.0, 4.0, 9.0]
     t = [1.0, 2.0, 3.0]
-    A = LagrangeInterpolation(u, t; extrapolate = true)
+    A = LagrangeInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(0.0) == 0.0
     @test A(4.0) == 16.0
     A = LagrangeInterpolation(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.ExtrapolationError A(4.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(4.0)
 end
 
 @testset "Akima Interpolation" begin
@@ -360,12 +388,13 @@ end
     test_cached_index(A)
 
     # Test extrapolation
-    A = AkimaInterpolation(u, t; extrapolate = true)
+    A = AkimaInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @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)
+    @test_throws DataInterpolations.UpExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(11.0)
 end
 
 @testset "ConstantInterpolation" begin
@@ -374,7 +403,9 @@ end
     t = [1.0, 2.0, 3.0, 4.0]
 
     @testset "Vector case" for u in [[1.0, 2.0, 0.0, 1.0], ["B", "C", "A", "B"]]
-        A = ConstantInterpolation(u, t, dir = :right; extrapolate = true)
+        A = ConstantInterpolation(
+            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -386,7 +417,8 @@ end
         @test A(4.5) == u[1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolate = true) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -403,7 +435,9 @@ end
         [1.0 2.0 0.0 1.0; 1.0 2.0 0.0 1.0],
         ["B" "C" "A" "B"; "B" "C" "A" "B"]
     ]
-        A = ConstantInterpolation(u, t, dir = :right; extrapolate = true)
+        A = ConstantInterpolation(
+            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 2]
@@ -415,7 +449,8 @@ end
         @test A(4.5) == u[:, 1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolate = true) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 1]
@@ -431,7 +466,9 @@ end
     @testset "Vector of Vectors case" for u in [
         [[1.0, 2.0], [0.0, 1.0], [1.0, 2.0], [0.0, 1.0]],
         [["B", "C"], ["A", "B"], ["B", "C"], ["A", "B"]]]
-        A = ConstantInterpolation(u, t, dir = :right; extrapolate = true)
+        A = ConstantInterpolation(
+            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -443,7 +480,8 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolate = true) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -459,7 +497,9 @@ end
     @testset "Vector of Matrices case" for u in [
         [[1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0], [1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0]],
         [["B" "C"; "B" "C"], ["A" "B"; "A" "B"], ["B" "C"; "B" "C"], ["A" "B"; "A" "B"]]]
-        A = ConstantInterpolation(u, t, dir = :right; extrapolate = true)
+        A = ConstantInterpolation(
+            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -471,7 +511,8 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolate = true) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -486,17 +527,19 @@ end
 
     # Test extrapolation
     u = [1.0, 2.0, 0.0, 1.0]
-    A = ConstantInterpolation(u, t; extrapolate = true)
+    A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-1.0) == 1.0
     @test A(11.0) == 1.0
     A = ConstantInterpolation(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.ExtrapolationError A(11.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
 
     # Test extrapolation with infs with regularly spaced t
     u = [1.67e7, 1.6867e7, 1.7034e7, 1.7201e7, 1.7368e7]
     t = [0.0, 0.1, 0.2, 0.3, 0.4]
-    A = ConstantInterpolation(u, t; extrapolate = true)
+    A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(Inf) == last(u)
     @test A(-Inf) == first(u)
 end
@@ -507,7 +550,8 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = QuadraticSpline(u, t; extrapolate = true)
+    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
 
     # Solution
     P₁ = x -> 0.5 * (x + 1) * (x + 2)
@@ -523,14 +567,16 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticSpline(u, t; extrapolate = true)
+    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-2.0) == P₁(-2.0) * ones(4)
     @test A(-0.5) == P₁(-0.5) * ones(4)
     @test A(0.7) == P₁(0.7) * ones(4)
     @test A(2.0) == P₁(2.0) * ones(4)
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = QuadraticSpline(u, t; extrapolate = true)
+    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-2.0) == P₁(-2.0) * ones(4, 3)
     @test A(-0.5) == P₁(-0.5) * ones(4, 3)
     @test A(0.7) == P₁(0.7) * ones(4, 3)
@@ -539,12 +585,13 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = QuadraticSpline(u, t; extrapolate = true)
+    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-2.0) == 0.0
     @test A(2.0) == 6.0
     A = QuadraticSpline(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(-2.0)
-    @test_throws DataInterpolations.ExtrapolationError A(2.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(-2.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(2.0)
 end
 
 @testset "CubicSpline Interpolation" begin
@@ -553,7 +600,8 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = CubicSpline(u, t; extrapolate = true)
+    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     test_cached_index(A)
 
     # Solution
@@ -572,7 +620,8 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = CubicSpline(u, t; extrapolate = true)
+    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4)
     end
@@ -581,7 +630,8 @@ end
     end
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = CubicSpline(u, t; extrapolate = true)
+    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4, 3)
     end
@@ -592,12 +642,13 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = CubicSpline(u, t; extrapolate = true)
+    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(-2.0) ≈ -1.0
     @test A(2.0) ≈ 5.0
     A = CubicSpline(u, t)
-    @test_throws DataInterpolations.ExtrapolationError A(-2.0)
-    @test_throws DataInterpolations.ExtrapolationError A(2.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(-2.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(2.0)
 
     @testset "AbstractMatrix" begin
         t = 0.1:0.1:1.0
@@ -636,12 +687,14 @@ end
         test_cached_index(A)
 
         # Test extrapolation
-        A = BSplineInterpolation(u, t, 2, :Uniform, :Uniform; extrapolate = true)
+        A = BSplineInterpolation(
+            u, t, 2, :Uniform, :Uniform; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :Uniform, :Uniform)
-        @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.ExtrapolationError A(300.0)
+        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
 
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
 
@@ -656,12 +709,14 @@ end
         @test_nowarn BSplineInterpolation(u[1:3], t[1:3], 2, :Uniform, :Uniform)
 
         # Test extrapolation
-        A = BSplineInterpolation(u, t, 2, :ArcLen, :Average; extrapolate = true)
+        A = BSplineInterpolation(
+            u, t, 2, :ArcLen, :Average; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
-        @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.ExtrapolationError A(300.0)
+        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
 
         @testset "AbstractMatrix" begin
             t = 0.1:0.1:1.0
@@ -713,12 +768,14 @@ end
         @test_nowarn BSplineApprox(u, t, 2, 3, :Uniform, :Uniform)
 
         # Test extrapolation
-        A = BSplineApprox(u, t, 2, 4, :Uniform, :Uniform; extrapolate = true)
+        A = BSplineApprox(
+            u, t, 2, 4, :Uniform, :Uniform; extrapolation_up = ExtrapolationType.extension,
+            extrapolation_down = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineApprox(u, t, 2, 4, :Uniform, :Uniform)
-        @test_throws DataInterpolations.ExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.ExtrapolationError A(300.0)
+        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
 
         @testset "AbstractMatrix" begin
             t = 0.1:0.1:1.0
@@ -759,7 +816,8 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = CubicHermiteSpline(du, u, t; extrapolate = true)
+    A = CubicHermiteSpline(du, u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.106770 rtol=1e-5
     @test A(300.0)≈9.901542 rtol=1e-5
@@ -787,7 +845,8 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolate = true)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.107996 rtol=1e-5
     @test A(300.0)≈11.364162 rtol=1e-5
@@ -818,10 +877,11 @@ end
     @test vs ≈ us
 
     # Test extrapolation
-    A = Curvefit(u, t, model, p0, LBFGS(); extrapolate = true)
+    A = Curvefit(u, t, model, p0, LBFGS(); extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test A(15.0) == model(15.0, A.pmin)
     A = Curvefit(u, t, model, p0, LBFGS())
-    @test_throws DataInterpolations.ExtrapolationError A(15.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(15.0)
 end
 
 @testset "Type of vector returned" begin

From b1e4bb7cebf5fcb4f0737569ca8acbf2ea6aa693 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Thu, 14 Nov 2024 21:41:32 +0100
Subject: [PATCH 07/20] Fix tests

---
 ...ataInterpolationsRegularizationToolsExt.jl | 70 +++++++++++++------
 src/DataInterpolations.jl                     | 15 +++-
 src/derivatives.jl                            | 12 ++--
 src/integral_inverses.jl                      | 10 +--
 src/interpolation_methods.jl                  |  8 +--
 test/derivative_tests.jl                      | 24 +++++--
 test/integral_inverse_tests.jl                |  3 +-
 test/integral_tests.jl                        | 11 +--
 test/interpolation_tests.jl                   | 12 ++--
 test/regularization.jl                        |  5 +-
 test/zygote_tests.jl                          |  8 ++-
 11 files changed, 112 insertions(+), 66 deletions(-)

diff --git a/ext/DataInterpolationsRegularizationToolsExt.jl b/ext/DataInterpolationsRegularizationToolsExt.jl
index 732ea1bb..6856996d 100644
--- a/ext/DataInterpolationsRegularizationToolsExt.jl
+++ b/ext/DataInterpolationsRegularizationToolsExt.jl
@@ -69,13 +69,17 @@ A = RegularizationSmooth(u, t, t̂, wls, wr, d; λ = 1.0, alg = :gcv_svd)
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
-        λ::Real = 1.0, alg::Symbol = :gcv_svd, extrapolate::Bool = false)
+        λ::Real = 1.0, alg::Symbol = :gcv_svd,
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     M = _mapping_matrix(t̂, t)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
-    RegularizationSmooth(u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+    RegularizationSmooth(
+        u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolation_down, extrapolation_up)
 end
 """
 Direct smoothing, no `t̂` or weights
@@ -86,14 +90,16 @@ A = RegularizationSmooth(u, t, d; λ = 1.0, alg = :gcv_svd, extrapolate = false)
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
         λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolate::Bool = false)
+        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
     M = Array{Float64}(LA.I, N, N)
     Wls½ = Array{Float64}(LA.I, N, N)
     Wr½ = Array{Float64}(LA.I, N - d, N - d)
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -104,7 +110,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 """
 `t̂` provided, no weights
@@ -115,13 +122,15 @@ A = RegularizationSmooth(u, t, t̂, d; λ = 1.0, alg = :gcv_svd, extrapolate = f
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolate::Bool = false)
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
     Wls½ = Array{Float64}(LA.I, N, N)
     Wr½ = Array{Float64}(LA.I, N̂ - d, N̂ - d)
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -132,7 +141,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 """
 `t̂` and `wls` provided
@@ -143,13 +153,15 @@ A = RegularizationSmooth(u, t, t̂, wls, d; λ = 1.0, alg = :gcv_svd, extrapolat
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolate::Bool = false)
+        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = Array{Float64}(LA.I, N̂ - d, N̂ - d)
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -160,7 +172,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 """
 `wls` provided, no `t̂`
@@ -172,14 +185,16 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolate::Bool = false)
+        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
     M = Array{Float64}(LA.I, N, N)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = Array{Float64}(LA.I, N - d, N - d)
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -190,7 +205,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 """
 `wls` and `wr` provided, no `t̂`
@@ -202,14 +218,17 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
-        λ::Real = 1.0, alg::Symbol = :gcv_svd, extrapolate::Bool = false)
+        λ::Real = 1.0, alg::Symbol = :gcv_svd,
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
     M = Array{Float64}(LA.I, N, N)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -220,7 +239,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 """
 Keyword provided for `wls`, no `t̂`
@@ -232,7 +252,8 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::Symbol, d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolate::Bool = false)
+        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -240,7 +261,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
     wls, wr = _weighting_by_kw(t, d, wls)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
-    û, λ, Aitp = _reg_smooth_solve(u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolate)
+    û, λ, Aitp = _reg_smooth_solve(
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
     RegularizationSmooth(u,
         û,
         t,
@@ -251,7 +273,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolate)
+        extrapolation_down,
+        extrapolation_up)
 end
 # """ t̂ provided and keyword for wls  _TBD_ """
 # function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
@@ -262,7 +285,8 @@ Solve for the smoothed dependent variables and create spline interpolator
 """
 function _reg_smooth_solve(
         u::AbstractVector, t̂::AbstractVector, d::Int, M::AbstractMatrix,
-        Wls½::AbstractMatrix, Wr½::AbstractMatrix, λ::Real, alg::Symbol, extrapolate::Bool)
+        Wls½::AbstractMatrix, Wr½::AbstractMatrix, λ::Real, alg::Symbol,
+        extrapolation_down::ExtrapolationType.T, extrapolation_up::ExtrapolationType.T)
     λ = float(λ) # `float` expected by RT
     D = _derivative_matrix(t̂, d)
     Ψ = RT.setupRegularizationProblem(Wls½ * M, Wr½ * D)
@@ -279,7 +303,7 @@ function _reg_smooth_solve(
         û = result.x
         λ = result.λ
     end
-    Aitp = CubicSpline(û, t̂; extrapolate)
+    Aitp = CubicSpline(û, t̂; extrapolation_down, extrapolation_up)
     # It seems logical to use B-Spline of order d+1, but I am unsure if theory supports the
     # extra computational cost, JJS 12/25/21
     #Aitp = BSplineInterpolation(û,t̂,d+1,:ArcLen,:Average)
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index eca8f783..700ffb98 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -58,6 +58,12 @@ function (interp::AbstractInterpolation)(u::AbstractVector, t::AbstractVector)
     u
 end
 
+const EXTRAPOLATION_ERROR = "Cannot extrapolate as `extrapolate` keyword passed was `false`"
+struct ExtrapolationError <: Exception end
+function Base.showerror(io::IO, ::ExtrapolationError)
+    print(io, EXTRAPOLATION_ERROR)
+end
+
 const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_down` keyword passed was `none`"
 struct DownExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::DownExtrapolationError)
@@ -114,7 +120,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
     λ::T2        # regularization parameter
     alg::Symbol  # how to determine λ: `:fixed`, `:gcv_svd`, `:gcv_tr`, `L_curve`
     Aitp::ITP
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     function RegularizationSmooth(u,
             û,
             t,
@@ -125,7 +132,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
             λ,
             alg,
             Aitp,
-            extrapolate)
+            extrapolation_down,
+            extrapolation_up)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), eltype(u), typeof(λ), N, typeof(Aitp)}(
             u,
@@ -138,7 +146,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
             λ,
             alg,
             Aitp,
-            extrapolate)
+            extrapolation_down,
+            extrapolation_up)
     end
 end
 
diff --git a/src/derivatives.jl b/src/derivatives.jl
index 6035a2eb..6632c13f 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -15,9 +15,9 @@ end
 
 function _extrapolate_derivative_down(A, t, order)
     (; extrapolation_down) = A
-    typed_zero = zero(one(A.u[1]) / one(A.t[1]))
+    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_down == ExtrapolationType.none
-        throw(UpExtrapolationError())
+        throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
         typed_zero
     elseif extrapolation_down == ExtrapolationType.linear
@@ -34,9 +34,9 @@ end
 
 function _extrapolate_derivative_up(A, t, order)
     (; extrapolation_up) = A
-    typed_zero = zero(one(A.u[1]) / one(A.t[1]))
+    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_up == ExtrapolationType.none
-        throw(DownExtrapolationError())
+        throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
         typed_zero
     elseif extrapolation_up == ExtrapolationType.linear
@@ -67,7 +67,6 @@ function _derivative(A::QuadraticInterpolation, t::Number, iguess)
 end
 
 function _derivative(A::LagrangeInterpolation{<:AbstractVector}, t::Number)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     der = zero(A.u[1])
     for j in eachindex(A.t)
         tmp = zero(A.t[1])
@@ -101,7 +100,6 @@ function _derivative(A::LagrangeInterpolation{<:AbstractVector}, t::Number)
 end
 
 function _derivative(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     der = zero(A.u[:, 1])
     for j in eachindex(A.t)
         tmp = zero(A.t[1])
@@ -153,12 +151,10 @@ function _derivative(A::ConstantInterpolation, t::Number, iguess)
 end
 
 function _derivative(A::ConstantInterpolation{<:AbstractVector}, t::Number, iguess)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     return isempty(searchsorted(A.t, t)) ? zero(A.u[1]) : eltype(A.u)(NaN)
 end
 
 function _derivative(A::ConstantInterpolation{<:AbstractMatrix}, t::Number, iguess)
-    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     return isempty(searchsorted(A.t, t)) ? zero(A.u[:, 1]) : eltype(A.u)(NaN) .* A.u[:, 1]
 end
 
diff --git a/src/integral_inverses.jl b/src/integral_inverses.jl
index 33621f1a..71313adb 100644
--- a/src/integral_inverses.jl
+++ b/src/integral_inverses.jl
@@ -37,13 +37,14 @@ struct LinearInterpolationIntInv{uType, tType, itpType, T, N} <:
        AbstractIntegralInverseInterpolation{T, N}
     u::uType
     t::tType
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     itp::itpType
     function LinearInterpolationIntInv(u, t, A)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(A), eltype(u), N}(
-            u, t, A.extrapolate, Guesser(t), A)
+            u, t, A.extrapolation_down, A.extrapolation_up, Guesser(t), A)
     end
 end
 
@@ -84,13 +85,14 @@ struct ConstantInterpolationIntInv{uType, tType, itpType, T, N} <:
        AbstractIntegralInverseInterpolation{T, N}
     u::uType
     t::tType
-    extrapolate::Bool
+    extrapolation_down::ExtrapolationType.T
+    extrapolation_up::ExtrapolationType.T
     iguesser::Guesser{tType}
     itp::itpType
     function ConstantInterpolationIntInv(u, t, A)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(A), eltype(u), N}(
-            u, t, A.extrapolate, Guesser(t), A
+            u, t, A.extrapolation_down, A.extrapolation_up, Guesser(t), A
         )
     end
 end
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 0c070f18..209e2541 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -13,11 +13,11 @@ function _extrapolate_down(A, t)
     if extrapolation_down == ExtrapolationType.none
         throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
-        first(A.u) * one(t)
+        first(A.u) + zero(eltype(A.p.slope)) * t
     elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
-    else 
+    else
         # extrapolation_down == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
@@ -28,11 +28,11 @@ function _extrapolate_up(A, t)
     if extrapolation_up == ExtrapolationType.none
         throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
-        last(A.u) * one(t)
+        last(A.u) + zero(eltype(A.p.slope)) * t
     elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
-    else 
+    else
         # extrapolation_up == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
diff --git a/test/derivative_tests.jl b/test/derivative_tests.jl
index 37595a4f..d81f346b 100644
--- a/test/derivative_tests.jl
+++ b/test/derivative_tests.jl
@@ -9,7 +9,11 @@ using Optim
 using ForwardDiff
 
 function test_derivatives(method; args = [], kwargs = [], name::String)
-    func = method(args...; kwargs..., extrapolate = true)
+    kwargs_extrapolation = (method == Curvefit) ?
+                           [:extrapolate => true] :
+                           [:extrapolation_up => ExtrapolationType.extension,
+        :extrapolation_down => ExtrapolationType.extension]
+    func = method(args...; kwargs..., kwargs_extrapolation...)
     (; t) = func
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
     trange_exclude = filter(x -> !in(x, t), trange)
@@ -68,8 +72,13 @@ function test_derivatives(method; args = [], kwargs = [], name::String)
     @test_throws DataInterpolations.DerivativeNotFoundError derivative(
         func, t[1], 3)
     func = method(args...)
-    @test_throws DataInterpolations.ExtrapolationError derivative(func, t[1] - 1.0)
-    @test_throws DataInterpolations.ExtrapolationError derivative(func, t[end] + 1.0)
+    if method == Curvefit
+        @test_throws DataInterpolations.ExtrapolationError derivative(func, t[1] - 1.0)
+        @test_throws DataInterpolations.ExtrapolationError derivative(func, t[end] + 1.0)
+    else
+        @test_throws DataInterpolations.DownExtrapolationError derivative(func, t[1] - 1.0)
+        @test_throws DataInterpolations.UpExtrapolationError derivative(func, t[end] + 1.0)
+    end
     @test_throws DataInterpolations.DerivativeNotFoundError derivative(
         func, t[1], 3)
 end
@@ -232,7 +241,8 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(CubicHermiteSpline; args = [du, u, t],
         name = "Cubic Hermite Spline")
-    A = CubicHermiteSpline(du, u, t; extrapolate = true)
+    A = CubicHermiteSpline(du, u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative(A, 100.0)≈0.0105409 rtol=1e-5
     @test derivative(A, 300.0)≈-0.0806717 rtol=1e-5
@@ -245,7 +255,8 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(QuinticHermiteSpline; args = [ddu, du, u, t],
         name = "Quintic Hermite Spline")
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolate = true)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative.(Ref(A), t, 2) ≈ ddu
     @test derivative(A, 100.0)≈0.0103916 rtol=1e-5
@@ -324,7 +335,8 @@ end
 @testset "Jacobian tests" begin
     u = rand(5)
     t = 0:4
-    interp = LinearInterpolation(u, t, extrapolate = true)
+    interp = LinearInterpolation(u, t, extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     grad1 = ForwardDiff.derivative(interp, 2.4)
 
     myvec = rand(20) .* 4.0
diff --git a/test/integral_inverse_tests.jl b/test/integral_inverse_tests.jl
index fd83be67..0e9e4cf2 100644
--- a/test/integral_inverse_tests.jl
+++ b/test/integral_inverse_tests.jl
@@ -3,7 +3,8 @@ using DataInterpolations: integral, derivative, invert_integral
 using FiniteDifferences
 
 function test_integral_inverses(method; args = [], kwargs = [])
-    A = method(args...; kwargs..., extrapolate = true)
+    A = method(args...; kwargs..., extrapolation_down = ExtrapolationType.extension,
+        extrapolation_up = ExtrapolationType.extension)
     @test hasfield(typeof(A), :I)
     A_intinv = invert_integral(A)
     @test A_intinv isa DataInterpolations.AbstractIntegralInverseInterpolation
diff --git a/test/integral_tests.jl b/test/integral_tests.jl
index 3d59a6c0..142e0d1f 100644
--- a/test/integral_tests.jl
+++ b/test/integral_tests.jl
@@ -6,7 +6,8 @@ using RegularizationTools
 using StableRNGs
 
 function test_integral(method; args = [], kwargs = [], name::String)
-    func = method(args...; kwargs..., extrapolate = true)
+    func = method(args...; kwargs..., extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     (; t) = func
     t1 = minimum(t)
     t2 = maximum(t)
@@ -48,10 +49,10 @@ function test_integral(method; args = [], kwargs = [], name::String)
         @test isapprox(qint, aint, atol = 1e-6, rtol = 1e-8)
     end
     func = method(args...; kwargs...)
-    @test_throws DataInterpolations.ExtrapolationError integral(func, t[1] - 1.0)
-    @test_throws DataInterpolations.ExtrapolationError integral(func, t[end] + 1.0)
-    @test_throws DataInterpolations.ExtrapolationError integral(func, t[1] - 1.0, t[2])
-    @test_throws DataInterpolations.ExtrapolationError integral(func, t[1], t[end] + 1.0)
+    @test_throws DataInterpolations.DownExtrapolationError integral(func, t[1] - 1.0)
+    @test_throws DataInterpolations.UpExtrapolationError integral(func, t[end] + 1.0)
+    @test_throws DataInterpolations.DownExtrapolationError integral(func, t[1] - 1.0, t[2])
+    @test_throws DataInterpolations.UpExtrapolationError integral(func, t[1], t[end] + 1.0)
 end
 
 @testset "LinearInterpolation" begin
diff --git a/test/interpolation_tests.jl b/test/interpolation_tests.jl
index 832819f3..041507f7 100644
--- a/test/interpolation_tests.jl
+++ b/test/interpolation_tests.jl
@@ -139,10 +139,7 @@ end
     R32 = Int32(1) // Int32(1)
     R64 = 1 // 1
     for A in Any[A1, A2, A3, A4]
-        @show A.u
-        @show A.t
         @test @inferred(A(F32)) === A(F32)
-        println("foo")
         @test @inferred(A(F64)) === A(F64)
         @test @inferred(A(I32)) === A(I32)
         @test @inferred(A(I64)) === A(I64)
@@ -393,8 +390,8 @@ end
     @test A(-1.0) ≈ -5.0
     @test A(11.0) ≈ -3.924742268041234
     A = AkimaInterpolation(u, t)
-    @test_throws DataInterpolations.UpExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.DownExtrapolationError A(11.0)
+    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
 end
 
 @testset "ConstantInterpolation" begin
@@ -877,11 +874,10 @@ end
     @test vs ≈ us
 
     # Test extrapolation
-    A = Curvefit(u, t, model, p0, LBFGS(); extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = Curvefit(u, t, model, p0, LBFGS(); extrapolate = true)
     @test A(15.0) == model(15.0, A.pmin)
     A = Curvefit(u, t, model, p0, LBFGS())
-    @test_throws DataInterpolations.UpExtrapolationError A(15.0)
+    @test_throws DataInterpolations.ExtrapolationError A(15.0)
 end
 
 @testset "Type of vector returned" begin
diff --git a/test/regularization.jl b/test/regularization.jl
index fcf7580d..3e6579cf 100644
--- a/test/regularization.jl
+++ b/test/regularization.jl
@@ -180,10 +180,11 @@ end
 end
 
 @testset "Extrapolation" begin
-    A = RegularizationSmooth(uₒ, tₒ; alg = :fixed, extrapolate = true)
+    A = RegularizationSmooth(
+        uₒ, tₒ; alg = :fixed, extrapolation_up = ExtrapolationType.extension)
     @test A(10.0) == A.Aitp(10.0)
     A = RegularizationSmooth(uₒ, tₒ; alg = :fixed)
-    @test_throws DataInterpolations.ExtrapolationError A(10.0)
+    @test_throws DataInterpolations.UpExtrapolationError A(10.0)
 end
 
 @testset "Type inference" begin
diff --git a/test/zygote_tests.jl b/test/zygote_tests.jl
index 7af735af..6476ee0f 100644
--- a/test/zygote_tests.jl
+++ b/test/zygote_tests.jl
@@ -3,7 +3,9 @@ using ForwardDiff
 using Zygote
 
 function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name::String)
-    func = method(args..., u, t, args_after...; kwargs..., extrapolate = true)
+    func = method(args..., u, t, args_after...; kwargs...,
+        extrapolation_up = ExtrapolationType.extension,
+        extrapolation_down = ExtrapolationType.extension)
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
     trange_exclude = filter(x -> !in(x, t), trange)
     @testset "$name, derivatives w.r.t. input" begin
@@ -19,7 +21,9 @@ function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name
        [LagrangeInterpolation, BSplineInterpolation, BSplineApprox, QuadraticSpline]
         @testset "$name, derivatives w.r.t. u" begin
             function f(u)
-                A = method(args..., u, t, args_after...; kwargs..., extrapolate = true)
+                A = method(args..., u, t, args_after...; kwargs...,
+                    extrapolation_up = ExtrapolationType.extension,
+                    extrapolation_down = ExtrapolationType.extension)
                 out = if u isa AbstractVector{<:Real}
                     zero(eltype(u))
                 elseif u isa AbstractMatrix

From 3b3b6267a7afb55b608b054daea84ef313f38866 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Fri, 15 Nov 2024 09:51:13 +0100
Subject: [PATCH 08/20] Add docs page

---
 docs/make.jl                      |  3 +-
 docs/src/extrapolation_methods.md | 56 +++++++++++++++++++++++++++++++
 docs/src/interface.md             |  4 +--
 src/interpolation_methods.jl      |  6 ++--
 4 files changed, 64 insertions(+), 5 deletions(-)
 create mode 100644 docs/src/extrapolation_methods.md

diff --git a/docs/make.jl b/docs/make.jl
index 6438f482..a6b062b5 100644
--- a/docs/make.jl
+++ b/docs/make.jl
@@ -12,7 +12,8 @@ makedocs(modules = [DataInterpolations],
     linkcheck = true,
     format = Documenter.HTML(assets = ["assets/favicon.ico"],
         canonical = "https://docs.sciml.ai/DataInterpolations/stable/"),
-    pages = ["index.md", "Methods" => "methods.md",
+    pages = ["index.md", "Interpolation methods" => "methods.md",
+        "Extrapolation methods" => "extrapolation_methods.md",
         "Interface" => "interface.md", "Using with Symbolics/ModelingToolkit" => "symbolics.md",
         "Manual" => "manual.md", "Inverting Integrals" => "inverting_integrals.md"])
 
diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
new file mode 100644
index 00000000..ad431027
--- /dev/null
+++ b/docs/src/extrapolation_methods.md
@@ -0,0 +1,56 @@
+# Extrapolation methods
+
+We will use the following interpolation to demonstrate the various extrapolation methods.
+
+```@example tutorial
+using DataInterpolations, Plots
+
+u = [0.86, 0.65, 0.44, 0.76, 0.73]
+t = [0.0022, 0.68, 1.41, 2.22, 2.46]
+t_eval_down = range(-1, first(t), length = 25)
+t_eval_up = range(last(t), 3.5, length = 25)
+A = QuadraticSpline(u, t)
+plot(A)
+```
+
+Extrapolation behavior can be set for `t` beyond the data in the negative and positive direction separately with the `extrapolation_down` and `extrapolation_up` keywords of the interpolation constructors respectively.
+
+## `ExtrapolationType.none`
+
+This extrapolation type will throw an error when the input `t` is beyond the data in the specified direction.
+
+## `ExtrapolationType.constant`
+
+This extrapolation type extends the interpolation with the boundary values of the data `u`.
+
+```@example tutorial
+A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.constant,
+    extrapolation_up = ExtrapolationType.constant)
+plot(A)
+plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
+plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+```
+
+## `ExtrapolationType.linear`
+
+This extrapolation type extends the interpolation with a linear continuation of the interpolation, making it $C^1$ smooth at the data boundaries.
+
+```@example tutorial
+A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.linear,
+    extrapolation_up = ExtrapolationType.linear)
+plot(A)
+plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
+plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+```
+
+## `ExtrapolationType.extension`
+
+This extrapolation type extends the interpolation with a continuation of the expression for the interpolation at the boundary intervals for maximum smoothness.
+
+```@example tutorial
+A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.extension,
+    extrapolation_up = ExtrapolationType.extension)
+plot(A)
+plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
+plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+```
diff --git a/docs/src/interface.md b/docs/src/interface.md
index cfc9ed0b..05dd0760 100644
--- a/docs/src/interface.md
+++ b/docs/src/interface.md
@@ -17,7 +17,7 @@ t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
 
 All interpolation methods return an object from which we can compute the value of the dependent variable at any time point.
 
-We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolate = true` keyword if we want to allow the interpolation to go beyond the range of the timepoints. The default value is `extrapolate = false`.
+We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolation_up = ExtrapolationType.extension` keyword if we want to allow the interpolation to go beyond the range of the timepoints in the positive `t` direction. The default value is `extrapolation_up = ExtrapolationType.none`. For more information on extrapolation see [Extrapolation methods](extrapolation_methods.md).
 
 ```@example interface
 A1 = CubicSpline(u, t)
@@ -25,7 +25,7 @@ A1 = CubicSpline(u, t)
 # For interpolation do, A(t)
 A1(100.0)
 
-A2 = CubicSpline(u, t; extrapolate = true)
+A2 = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension)
 
 # Extrapolation
 A2(300.0)
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 209e2541..d7d4dce0 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -13,7 +13,8 @@ function _extrapolate_down(A, t)
     if extrapolation_down == ExtrapolationType.none
         throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
-        first(A.u) + zero(eltype(A.p.slope)) * t
+        slope = derivative(A, first(A.t))
+        first(A.u) + slope * zero(t)
     elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
@@ -28,7 +29,8 @@ function _extrapolate_up(A, t)
     if extrapolation_up == ExtrapolationType.none
         throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
-        last(A.u) + zero(eltype(A.p.slope)) * t
+        slope = derivative(A, last(A.t))
+        last(A.u) + slope * zero(t)
     elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))

From c6ab856aaa9b9855381ecd7ec73e86ddadbe8f07 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Sat, 16 Nov 2024 10:00:51 +0100
Subject: [PATCH 09/20] Add some tests, refactor most of integration

---
 src/integrals.jl            | 143 ++++++++++++++++++++----------------
 src/interpolation_utils.jl  |  14 +++-
 test/extrapolation_tests.jl |  84 +++++++++++++++++++++
 test/runtests.jl            |   1 +
 4 files changed, 176 insertions(+), 66 deletions(-)
 create mode 100644 test/extrapolation_tests.jl

diff --git a/src/integrals.jl b/src/integrals.jl
index a411ccd8..6c0f97d6 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -4,89 +4,112 @@ end
 
 function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     !hasfield(typeof(A), :I) && throw(IntegralNotFoundError())
+
+    if t1 == t2 
+        # If the integration interval is trivial then the result is 0
+        return zero(eltype(A.I))
+    elseif t1 > t2
+        # Make sure that t1 < t2
+        return -integral(A, t2, t1)
+    end
+
     # the index less than or equal to t1
     idx1 = get_idx(A, t1, 0)
     # the index less than t2
     idx2 = get_idx(A, t2, 0; idx_shift = -1, side = :first)
 
-    if A.cache_parameters
-        total = A.I[idx2] - A.I[idx1]
-        return if t1 == t2
-            zero(total)
-        else
-            total += __integral(A, idx1, A.t[idx1])
-            total -= __integral(A, idx1, t1)
-            total += __integral(A, idx2, t2)
-            total -= __integral(A, idx2, A.t[idx2])
-            total
+    total = zero(eltype(A.I))
+
+    # Lower potentially incomplete interval
+    if t1 < first(A.t)
+
+        if t2 < first(A.t)
+            # If interval is entirely below data
+            return _extrapolate_integral_down(A, t2) - extrapolate_integral_down(A.t1)
         end
+
+        idx1 -= 1 # Make sure lowest complete interval is included
+        total += _extrapolate_integral_down(A, t1)
     else
-        total = zero(eltype(A.u))
-        for idx in idx1:idx2
-            lt1 = idx == idx1 ? t1 : A.t[idx]
-            lt2 = idx == idx2 ? t2 : A.t[idx + 1]
-            total += __integral(A, idx, lt2) - __integral(A, idx, lt1)
+        total += _integral(A, idx1, t1, A.t[idx1 + 1])
+    end
+
+    # Upper potentially incomplete interval
+    if t2 > last(A.t)
+
+        if t1 > last(A.t)
+            # If interval is entirely above data
+            return _extrapolate_integral_up(A, t2) - extrapolate_integral_up(A.t, t1)
         end
-        total
+
+        idx2 += 1 # Make sure highest complete interval is included
+        total += _extrapolate_integral_up(A, t2)
+    else
+        total += _integral(A, idx2, A.t[idx2], t2)
     end
-end
 
-function __integral(A::AbstractInterpolation, idx::Number, t::Number)
-    if t < first(A.t)
-        _extrapolate_integral_down(A, idx, t)
-    elseif t > last(A.t)
-        _extrapolate_integral_up(A, idx, t)
+    if idx1 == idx2
+        return _integral(A, idx1, t1, t2)
+    end
+
+    # Complete intervals
+    if A.cache_parameters
+        total += A.I[idx2] - A.I[idx1 + 1]
     else
-        _integral(A, idx, t)
+        for idx in (idx1 + 1):(idx2 - 1)
+            total += _integral(A, idx, A.t[idx], A.t[idx + 1])
+        end
     end
+
+    return total
 end
 
-function _extrapolate_integral_down(A, idx, t)
+function _extrapolate_integral_down(A, t)
     (; extrapolation_down) = A
     if extrapolation_down == ExtrapolationType.none
         throw(DownExtrapolationError())
     elseif extrapolation_down == ExtrapolationType.constant
-        first(A.u) * (t - first(A.t))
+        first(A.u) * (first(A.t) - t)
     elseif extrapolation_down == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
-        Δt = t - first(A.t)
-        (first(A.u) + slope * Δt / 2) * Δt
+        Δt = first(A.t) - t
+        (first(A.u) - slope * Δt / 2) * Δt
     elseif extrapolation_down == ExtrapolationType.extension
-        _integral(A, idx, t)
+        _integral(A, 1, t, first(A.t))
     end
 end
 
-function _extrapolate_integral_up(A, idx, t)
+function _extrapolate_integral_up(A, t)
     (; extrapolation_up) = A
     if extrapolation_up == ExtrapolationType.none
         throw(UpExtrapolationError())
     elseif extrapolation_up == ExtrapolationType.constant
-        integral(A, A.t[end - 1], A.t[end]) + last(A.u) * (t - last(A.t))
+        last(A.u) * (t - last(A.t))
     elseif extrapolation_up == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         Δt = t - last(A.t)
-        integral(A, A.t[end - 1], A.t[end]) + (last(A.u) + slope * Δt / 2) * Δt
+        (last(A.u) + slope * Δt / 2) * Δt
     elseif extrapolation_up == ExtrapolationType.extension
-        _integral(A, idx, t)
+        _integral(A, length(A.t) - 1, last(A.t), t)
     end
 end
 
 function _integral(A::LinearInterpolation{<:AbstractVector{<:Number}},
-        idx::Number,
-        t::Number)
-    Δt = t - A.t[idx]
+        idx::Number, t1::Number, t2::Number)
     slope = get_parameters(A, idx)
-    Δt * (A.u[idx] + slope * Δt / 2)
+    u_mean = A.u[idx] + slope * ((t1 + t2)/2 - A.t[idx])
+    u_mean * (t2 - t1)
 end
 
 function _integral(
-        A::ConstantInterpolation{<:AbstractVector{<:Number}}, idx::Number, t::Number)
+        A::ConstantInterpolation{<:AbstractVector{<:Number}}, idx::Number, t1::Number, t2::Number)
+    Δt = t2 - t1
     if A.dir === :left
         # :left means that value to the left is used for interpolation
-        return A.u[idx] * t
+        return A.u[idx] * Δt
     else
         # :right means that value to the right is used for interpolation
-        return A.u[idx + 1] * t
+        return A.u[idx + 1] * Δt
     end
 end
 
@@ -107,30 +130,27 @@ function _integral(A::QuadraticInterpolation{<:AbstractVector{<:Number}},
     return Iu₀ + Iu₁ + Iu₂
 end
 
-function _integral(A::QuadraticSpline{<:AbstractVector{<:Number}}, idx::Number, t::Number)
+function _integral(A::QuadraticSpline{<:AbstractVector{<:Number}}, idx::Number, t1::Number, t2::Number)
     α, β = get_parameters(A, idx)
     uᵢ = A.u[idx]
-    Δt = t - A.t[idx]
-    Δt_full = A.t[idx + 1] - A.t[idx]
-    Δt * (α * Δt^2 / (3Δt_full^2) + β * Δt / (2Δt_full) + uᵢ)
+    tᵢ = A.t[idx]
+    t1_rel = t1 - tᵢ
+    t2_rel = t2 - tᵢ
+    Δt = t2 - t1
+    Δt * (α * (t2_rel^2 + t1_rel * t2_rel + t1_rel^2) / 3 + β * (t2_rel + t1_rel) / 2 + uᵢ)
 end
 
-function _integral(A::CubicSpline{<:AbstractVector{<:Number}}, idx::Number, t::Number)
-    Δt₁sq = (t - A.t[idx])^2 / 2
-    Δt₂sq = (A.t[idx + 1] - t)^2 / 2
-    II = (-A.z[idx] * Δt₂sq^2 + A.z[idx + 1] * Δt₁sq^2) / (6A.h[idx + 1])
+function _integral(A::CubicSpline{<:AbstractVector{<:Number}}, idx::Number, t1::Number, t2::Number)
+    tᵢ = A.t[idx]
+    tᵢ₊₁ = A.t[idx + 1]
     c₁, c₂ = get_parameters(A, idx)
-    IC = c₁ * Δt₁sq
-    ID = -c₂ * Δt₂sq
-    II + IC + ID
+    integrate_cubic_polynomial(t1, t2, tᵢ, 0, c₁, 0, A.z[idx + 1] / (6A.h[idx + 1])) +
+    integrate_cubic_polynomial(t1, t2, tᵢ₊₁, 0, -c₂, 0, -A.z[idx] / (6A.h[idx + 1]))
 end
 
 function _integral(A::AkimaInterpolation{<:AbstractVector{<:Number}},
-        idx::Number,
-        t::Number)
-    t1 = A.t[idx]
-    A.u[idx] * (t - t1) + A.b[idx] * ((t - t1)^2 / 2) + A.c[idx] * ((t - t1)^3 / 3) +
-    A.d[idx] * ((t - t1)^4 / 4)
+        idx::Number, t1::Number, t2::Number)
+    integrate_cubic_polynomial(t1, t2, A.t[idx], A.u[idx], A.b[idx], A.c[idx], A.d[idx])
 end
 
 _integral(A::LagrangeInterpolation, idx::Number, t::Number) = throw(IntegralNotFoundError())
@@ -139,15 +159,12 @@ _integral(A::BSplineApprox, idx::Number, t::Number) = throw(IntegralNotFoundErro
 
 # Cubic Hermite Spline
 function _integral(
-        A::CubicHermiteSpline{<:AbstractVector{<:Number}}, idx::Number, t::Number)
-    Δt₀ = t - A.t[idx]
-    Δt₁ = t - A.t[idx + 1]
-    out = Δt₀ * (A.u[idx] + Δt₀ * A.du[idx] / 2)
+        A::CubicHermiteSpline{<:AbstractVector{<:Number}}, idx::Number, t1::Number, t2::Number)
     c₁, c₂ = get_parameters(A, idx)
-    p = c₁ + Δt₁ * c₂
-    dp = c₂
-    out += Δt₀^3 / 3 * (p - dp * Δt₀ / 4)
-    out
+    tᵢ = A.t[idx]
+    tᵢ₊₁ = A.t[idx + 1]
+    c = c₁ - c₂ * (tᵢ₊₁ - tᵢ)
+    integrate_cubic_polynomial(t1, t2, tᵢ, A.u[idx], A.du[idx], c, c₂)
 end
 
 # Quintic Hermite Spline
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 2d1c6432..eac4862e 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -190,9 +190,8 @@ function get_idx(A::AbstractInterpolation, t, iguess::Union{<:Integer, Guesser};
 end
 
 function cumulative_integral(A, cache_parameters)
-    if cache_parameters && hasmethod(_integral, Tuple{typeof(A), Number, Number})
-        integral_values = [_integral(A, idx, A.t[idx + 1]) - _integral(A, idx, A.t[idx])
-                           for idx in 1:(length(A.t) - 1)]
+    if cache_parameters && hasmethod(_integral, Tuple{typeof(A), Number, Number, Number})
+        integral_values = _integral.(Ref(A), 1:(length(A.t) - 1), A.t[1:end-1], A.t[2:end])
         pushfirst!(integral_values, zero(first(integral_values)))
         cumsum(integral_values)
     else
@@ -282,3 +281,12 @@ function du_PCHIP(u, t)
 
     return _du.(eachindex(t))
 end
+
+function integrate_cubic_polynomial(t1, t2, offset, a, b, c, d)
+    t1_rel = t1 - offset
+    t2_rel = t2 - offset
+    t_sum = t1_rel + t2_rel
+    t_sq_sum = t1_rel^2 + t2_rel^2
+    Δt = t2 - t1
+    Δt * (a + t_sum * (b / 2 + d * t_sq_sum / 4) + c * (t_sq_sum + t1_rel * t2_rel) / 3)
+end
\ No newline at end of file
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
new file mode 100644
index 00000000..a93ef127
--- /dev/null
+++ b/test/extrapolation_tests.jl
@@ -0,0 +1,84 @@
+using DataInterpolations
+
+@testset "Linear Interpolation" begin
+    u = [1.0, 2.0]
+    t = [1.0, 2.0]
+
+    A = LinearInterpolation(u, t; extrapolation_down = ExtrapolationType.constant)
+    t_eval = 0.0
+    @test A(t_eval) == 1.0
+    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+    @test DataInterpolations.integral(A, t_eval) == -1.0
+    t_eval = 3.0
+    @test_throws DataInterpolations.UpExtrapolationError A(t_eval)
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval)
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(A, t_eval)
+
+    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.constant)
+    t_eval = 3.0
+    @test A(t_eval) == 2.0
+    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+    @test DataInterpolations.integral(A, t_eval) == 3.5
+    t_eval = 0.0
+    @test_throws DataInterpolations.DownExtrapolationError A(t_eval)
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval)
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(A, t_eval)
+
+    for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
+        A = LinearInterpolation(u, t; extrapolation_down = extrapolation_type)
+        t_eval = 0.0
+        @test A(t_eval) == 0.0
+        @test DataInterpolations.derivative(A, t_eval) == 1.0
+        @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+        @test DataInterpolations.integral(A, t_eval) == -0.5
+        t_eval = 3.0
+        @test_throws DataInterpolations.UpExtrapolationError A(t_eval)
+        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval)
+        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(A, t_eval)
+
+        A = LinearInterpolation(u, t; extrapolation_up = extrapolation_type)
+        t_eval = 3.0
+        @test A(t_eval) == 3.0
+        @test DataInterpolations.derivative(A, t_eval) == 1.0
+        @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+        @test DataInterpolations.integral(A, t_eval) == 4.0
+        t_eval = 0.0
+        @test_throws DataInterpolations.DownExtrapolationError A(t_eval)
+        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval)
+        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(A, t_eval)
+    end
+end
+
+@testset "Quadratic Interpolation" begin
+    u = [1.0, 3.0, 2.0]
+    t = 1:3
+    f = t -> (-3t^2 + 13t - 8)/2
+
+    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.constant)
+    t_eval = 0.0
+    @test A(t_eval) ≈ 1.0 
+    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+    @test DataInterpolations.integral(A, t_eval) ≈ -1.0
+    t_eval = 4.0
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval)
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(A, t_eval)
+
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.constant)
+    t_eval = 4.0
+    @test A(t_eval) ≈ 2.0
+    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
+    @test DataInterpolations.integral(A, t[end], t_eval) ≈ 2.0
+    t_eval = 0.0
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval)
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(A, t_eval, 2)
+    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(A, t_eval)
+end
\ No newline at end of file
diff --git a/test/runtests.jl b/test/runtests.jl
index 80080a75..774ad497 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -7,6 +7,7 @@ using SafeTestsets
 @safetestset "Derivative Tests" include("derivative_tests.jl")
 @safetestset "Integral Tests" include("integral_tests.jl")
 @safetestset "Integral Inverse Tests" include("integral_inverse_tests.jl")
+@safetestset "Extrapolation" include("extrapolation_tests.jl")
 @safetestset "Online Tests" include("online_tests.jl")
 @safetestset "Regularization Smoothing" include("regularization.jl")
 @safetestset "Show methods" include("show.jl")

From a562bf7105a3287b99785e3f0cb9a193a40c85aa Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Sun, 17 Nov 2024 17:00:38 +0100
Subject: [PATCH 10/20] Complete tests

---
 test/extrapolation_tests.jl | 130 ++++++++++++++++++------------------
 1 file changed, 65 insertions(+), 65 deletions(-)

diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index f282fa10..5c934d83 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -1,40 +1,45 @@
 using DataInterpolations
 
+function test_extrapolation_errors(method, u, t)
+    A = method(u, t)
+    @test A.extrapolation_up == ExtrapolationType.none
+    @test A.extrapolation_down == ExtrapolationType.none
+    for (error_type, t_eval) in zip(
+        (DataInterpolations.DownExtrapolationError,
+            DataInterpolations.UpExtrapolationError),
+        (first(t) - 1, last(t) + 1))
+        @test_throws error_type A(t_eval)
+        @test_throws error_type DataInterpolations.derivative(
+            A, t_eval)
+        @test_throws error_type DataInterpolations.derivative(
+            A, t_eval, 2)
+        @test_throws error_type DataInterpolations.integral(
+            A, t_eval)
+    end
+end
+
+function test_constant_extrapolation(method, u, t)
+    A = method(u, t; extrapolation_down = ExtrapolationType.constant,
+        extrapolation_up = ExtrapolationType.constant)
+    t_lower = first(t) - 1
+    t_upper = last(t) + 1 
+    @test A(t_lower) == first(u)
+    @test A(t_upper) == last(u)
+    @test DataInterpolations.derivative(A, t_lower) == 0
+    @test DataInterpolations.derivative(A, t_upper) == 0
+    @test DataInterpolations.integral(A, t_lower, first(t)) ≈ first(u) * (first(t) - t_lower)
+    @test DataInterpolations.integral(A, last(t), t_upper) ≈ last(u) * (t_upper - last(t))
+end
+
 @testset "Linear Interpolation" begin
     u = [1.0, 2.0]
     t = [1.0, 2.0]
 
-    A = LinearInterpolation(u, t; extrapolation_down = ExtrapolationType.constant)
-    t_eval = 0.0
-    @test A(t_eval) == 1.0
-    @test DataInterpolations.derivative(A, t_eval) == 0.0
-    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
-    @test DataInterpolations.integral(A, t_eval) == -1.0
-    t_eval = 3.0
-    @test_throws DataInterpolations.UpExtrapolationError A(t_eval)
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-        A, t_eval)
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-        A, t_eval, 2)
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(
-        A, t_eval)
-
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.constant)
-    t_eval = 3.0
-    @test A(t_eval) == 2.0
-    @test DataInterpolations.derivative(A, t_eval) == 0.0
-    @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
-    @test DataInterpolations.integral(A, t_eval) == 3.5
-    t_eval = 0.0
-    @test_throws DataInterpolations.DownExtrapolationError A(t_eval)
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-        A, t_eval)
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-        A, t_eval, 2)
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(
-        A, t_eval)
+    test_extrapolation_errors(LinearInterpolation, u, t)
+    test_constant_extrapolation(LinearInterpolation, u, t)
 
     for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
+        # Down extrapolation
         A = LinearInterpolation(u, t; extrapolation_down = extrapolation_type)
         t_eval = 0.0
         @test A(t_eval) == 0.0
@@ -42,14 +47,8 @@ using DataInterpolations
         @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
         @test DataInterpolations.integral(A, t_eval) == -0.5
         t_eval = 3.0
-        @test_throws DataInterpolations.UpExtrapolationError A(t_eval)
-        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-            A, t_eval)
-        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-            A, t_eval, 2)
-        @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(
-            A, t_eval)
 
+        # Up extrapolation
         A = LinearInterpolation(u, t; extrapolation_up = extrapolation_type)
         t_eval = 3.0
         @test A(t_eval) == 3.0
@@ -57,46 +56,47 @@ using DataInterpolations
         @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
         @test DataInterpolations.integral(A, t_eval) == 4.0
         t_eval = 0.0
-        @test_throws DataInterpolations.DownExtrapolationError A(t_eval)
-        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-            A, t_eval)
-        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-            A, t_eval, 2)
-        @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(
-            A, t_eval)
     end
 end
 
 @testset "Quadratic Interpolation" begin
     u = [1.0, 3.0, 2.0]
     t = 1:3
-    f = t -> (-3t^2 + 13t - 8) / 2
 
-    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.constant)
+    test_extrapolation_errors(QuadraticInterpolation, u, t)
+    test_constant_extrapolation(LinearInterpolation, u, t)
+
+    # Linear down extrapolation
+    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.linear)
     t_eval = 0.0
-    @test A(t_eval) ≈ 1.0
-    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test A(t_eval) ≈ -2.5
+    @test DataInterpolations.derivative(A, t_eval) == 3.5
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
-    @test DataInterpolations.integral(A, t_eval) ≈ -1.0
-    t_eval = 4.0
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-        A, t_eval)
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.derivative(
-        A, t_eval, 2)
-    @test_throws DataInterpolations.UpExtrapolationError DataInterpolations.integral(
-        A, t_eval)
+    @test DataInterpolations.integral(A, t_eval) ≈ 0.75
 
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.constant)
+    # Linear up extrapolation
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.linear)
     t_eval = 4.0
-    @test A(t_eval) ≈ 2.0
-    @test DataInterpolations.derivative(A, t_eval) == 0.0
+    @test A(t_eval) ≈ -0.5
+    @test DataInterpolations.derivative(A, t_eval) == -2.5
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
-    @test DataInterpolations.integral(A, t[end], t_eval) ≈ 2.0
+    @test DataInterpolations.integral(A, t[end], t_eval) ≈ 0.75
+
+    # Extension down extrapolation
+    f = t -> (-3t^2 + 13t - 8) / 2
+    df = t -> (-6t + 13) / 2
+    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.extension)
     t_eval = 0.0
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-        A, t_eval)
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.derivative(
-        A, t_eval, 2)
-    @test_throws DataInterpolations.DownExtrapolationError DataInterpolations.integral(
-        A, t_eval)
+    @test A(t_eval) ≈ -4.0
+    @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
+    @test DataInterpolations.derivative(A, t_eval, 2) == -3
+    @test DataInterpolations.integral(A, t_eval) ≈ 1.25
+
+    # Extension up extrapolation
+    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension)
+    t_eval = 4.0
+    @test A(t_eval) ≈ -2.0
+    @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
+    @test DataInterpolations.derivative(A, t_eval, 2) == -3
+    @test DataInterpolations.integral(A, t_eval) ≈ 5.25
 end

From d145c4b4a7e6c2faafc54c19740f53592a99a5ee Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart.dekoning@deltares.nl>
Date: Sun, 17 Nov 2024 17:02:31 +0100
Subject: [PATCH 11/20] Formatting

---
 test/extrapolation_tests.jl | 5 +++--
 1 file changed, 3 insertions(+), 2 deletions(-)

diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index 5c934d83..e87fd340 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -22,12 +22,13 @@ function test_constant_extrapolation(method, u, t)
     A = method(u, t; extrapolation_down = ExtrapolationType.constant,
         extrapolation_up = ExtrapolationType.constant)
     t_lower = first(t) - 1
-    t_upper = last(t) + 1 
+    t_upper = last(t) + 1
     @test A(t_lower) == first(u)
     @test A(t_upper) == last(u)
     @test DataInterpolations.derivative(A, t_lower) == 0
     @test DataInterpolations.derivative(A, t_upper) == 0
-    @test DataInterpolations.integral(A, t_lower, first(t)) ≈ first(u) * (first(t) - t_lower)
+    @test DataInterpolations.integral(A, t_lower, first(t)) ≈
+          first(u) * (first(t) - t_lower)
     @test DataInterpolations.integral(A, last(t), t_upper) ≈ last(u) * (t_upper - last(t))
 end
 

From 3c54932735dbae3d9c99de8163ab89cc0c72cad2 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Tue, 19 Nov 2024 19:09:18 +0100
Subject: [PATCH 12/20] Comments adressed

---
 docs/src/extrapolation_methods.md             |  11 +-
 docs/src/interface.md                         |   4 +-
 ...ataInterpolationsRegularizationToolsExt.jl |  72 +--
 src/DataInterpolations.jl                     |  16 +-
 src/derivatives.jl                            |  20 +-
 src/integral_inverses.jl                      |  12 +-
 src/integrals.jl                              |  20 +-
 src/interpolation_caches.jl                   | 510 ++++++++++--------
 src/interpolation_methods.jl                  |  20 +-
 src/interpolation_utils.jl                    |   8 +
 test/derivative_tests.jl                      |  13 +-
 test/extrapolation_tests.jl                   |  20 +-
 test/integral_inverse_tests.jl                |   3 +-
 test/integral_tests.jl                        |   4 +-
 test/interface.jl                             |   6 +-
 test/interpolation_tests.jl                   | 145 ++---
 test/regularization.jl                        |   2 +-
 test/zygote_tests.jl                          |   6 +-
 18 files changed, 461 insertions(+), 431 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index ad431027..5b6286ba 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -13,7 +13,7 @@ A = QuadraticSpline(u, t)
 plot(A)
 ```
 
-Extrapolation behavior can be set for `t` beyond the data in the negative and positive direction separately with the `extrapolation_down` and `extrapolation_up` keywords of the interpolation constructors respectively.
+Extrapolation behavior can be set left and right of the data simultaneously with the `extension` keyword, or left and right separately with the `extension_left` and `extension_right` keywords respectively.
 
 ## `ExtrapolationType.none`
 
@@ -24,8 +24,7 @@ This extrapolation type will throw an error when the input `t` is beyond the dat
 This extrapolation type extends the interpolation with the boundary values of the data `u`.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.constant,
-    extrapolation_up = ExtrapolationType.constant)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.constant)
 plot(A)
 plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
 plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
@@ -36,8 +35,7 @@ plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
 This extrapolation type extends the interpolation with a linear continuation of the interpolation, making it $C^1$ smooth at the data boundaries.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.linear,
-    extrapolation_up = ExtrapolationType.linear)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.linear)
 plot(A)
 plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
 plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
@@ -48,8 +46,7 @@ plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
 This extrapolation type extends the interpolation with a continuation of the expression for the interpolation at the boundary intervals for maximum smoothness.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation_down = ExtrapolationType.extension,
-    extrapolation_up = ExtrapolationType.extension)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
 plot(A)
 plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
 plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
diff --git a/docs/src/interface.md b/docs/src/interface.md
index 05dd0760..21bfd27a 100644
--- a/docs/src/interface.md
+++ b/docs/src/interface.md
@@ -17,7 +17,7 @@ t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
 
 All interpolation methods return an object from which we can compute the value of the dependent variable at any time point.
 
-We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolation_up = ExtrapolationType.extension` keyword if we want to allow the interpolation to go beyond the range of the timepoints in the positive `t` direction. The default value is `extrapolation_up = ExtrapolationType.none`. For more information on extrapolation see [Extrapolation methods](extrapolation_methods.md).
+We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolation = ExtrapolationType.extension` keyword if we want to allow the interpolation to go beyond the range of the timepoints in the positive `t` direction. The default value is `extrapolation = ExtrapolationType.none`. For more information on extrapolation see [Extrapolation methods](extrapolation_methods.md).
 
 ```@example interface
 A1 = CubicSpline(u, t)
@@ -25,7 +25,7 @@ A1 = CubicSpline(u, t)
 # For interpolation do, A(t)
 A1(100.0)
 
-A2 = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension)
+A2 = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
 
 # Extrapolation
 A2(300.0)
diff --git a/ext/DataInterpolationsRegularizationToolsExt.jl b/ext/DataInterpolationsRegularizationToolsExt.jl
index 6856996d..84693c49 100644
--- a/ext/DataInterpolationsRegularizationToolsExt.jl
+++ b/ext/DataInterpolationsRegularizationToolsExt.jl
@@ -70,16 +70,16 @@ A = RegularizationSmooth(u, t, t̂, wls, wr, d; λ = 1.0, alg = :gcv_svd)
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
         λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     M = _mapping_matrix(t̂, t)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(
-        u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolation_down, extrapolation_up)
+        u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolation_left, extrapolation_right)
 end
 """
 Direct smoothing, no `t̂` or weights
@@ -90,8 +90,8 @@ A = RegularizationSmooth(u, t, d; λ = 1.0, alg = :gcv_svd, extrapolate = false)
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
         λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -99,7 +99,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
     Wls½ = Array{Float64}(LA.I, N, N)
     Wr½ = Array{Float64}(LA.I, N - d, N - d)
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -110,8 +110,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 """
 `t̂` provided, no weights
@@ -122,15 +122,15 @@ A = RegularizationSmooth(u, t, t̂, d; λ = 1.0, alg = :gcv_svd, extrapolate = f
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
     Wls½ = Array{Float64}(LA.I, N, N)
     Wr½ = Array{Float64}(LA.I, N̂ - d, N̂ - d)
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -141,8 +141,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 """
 `t̂` and `wls` provided
@@ -153,15 +153,15 @@ A = RegularizationSmooth(u, t, t̂, wls, d; λ = 1.0, alg = :gcv_svd, extrapolat
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = Array{Float64}(LA.I, N̂ - d, N̂ - d)
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -172,8 +172,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 """
 `wls` provided, no `t̂`
@@ -185,8 +185,8 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -194,7 +194,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = Array{Float64}(LA.I, N - d, N - d)
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -205,8 +205,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 """
 `wls` and `wr` provided, no `t̂`
@@ -219,8 +219,8 @@ A = RegularizationSmooth(
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
         λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -228,7 +228,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -239,8 +239,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 """
 Keyword provided for `wls`, no `t̂`
@@ -252,8 +252,8 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::Symbol, d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -262,7 +262,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
     Wls½ = LA.diagm(sqrt.(wls))
     Wr½ = LA.diagm(sqrt.(wr))
     û, λ, Aitp = _reg_smooth_solve(
-        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_down, extrapolation_up)
+        u, t̂, d, M, Wls½, Wr½, λ, alg, extrapolation_left, extrapolation_right)
     RegularizationSmooth(u,
         û,
         t,
@@ -273,8 +273,8 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing
         λ,
         alg,
         Aitp,
-        extrapolation_down,
-        extrapolation_up)
+        extrapolation_left,
+        extrapolation_right)
 end
 # """ t̂ provided and keyword for wls  _TBD_ """
 # function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
@@ -286,7 +286,7 @@ Solve for the smoothed dependent variables and create spline interpolator
 function _reg_smooth_solve(
         u::AbstractVector, t̂::AbstractVector, d::Int, M::AbstractMatrix,
         Wls½::AbstractMatrix, Wr½::AbstractMatrix, λ::Real, alg::Symbol,
-        extrapolation_down::ExtrapolationType.T, extrapolation_up::ExtrapolationType.T)
+        extrapolation_left::ExtrapolationType.T, extrapolation_right::ExtrapolationType.T)
     λ = float(λ) # `float` expected by RT
     D = _derivative_matrix(t̂, d)
     Ψ = RT.setupRegularizationProblem(Wls½ * M, Wr½ * D)
@@ -303,7 +303,7 @@ function _reg_smooth_solve(
         û = result.x
         λ = result.λ
     end
-    Aitp = CubicSpline(û, t̂; extrapolation_down, extrapolation_up)
+    Aitp = CubicSpline(û, t̂; extrapolation_left, extrapolation_right)
     # It seems logical to use B-Spline of order d+1, but I am unsure if theory supports the
     # extra computational cost, JJS 12/25/21
     #Aitp = BSplineInterpolation(û,t̂,d+1,:ArcLen,:Average)
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index 700ffb98..ee15a452 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -64,13 +64,13 @@ function Base.showerror(io::IO, ::ExtrapolationError)
     print(io, EXTRAPOLATION_ERROR)
 end
 
-const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_down` keyword passed was `none`"
+const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_left` keyword passed was `none`"
 struct DownExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::DownExtrapolationError)
     print(io, DOWN_EXTRAPOLATION_ERROR)
 end
 
-const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_up` keyword passed was `none`"
+const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_right` keyword passed was `none`"
 struct UpExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::UpExtrapolationError)
     print(io, UP_EXTRAPOLATION_ERROR)
@@ -120,8 +120,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
     λ::T2        # regularization parameter
     alg::Symbol  # how to determine λ: `:fixed`, `:gcv_svd`, `:gcv_tr`, `L_curve`
     Aitp::ITP
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     function RegularizationSmooth(u,
             û,
             t,
@@ -132,8 +132,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
             λ,
             alg,
             Aitp,
-            extrapolation_down,
-            extrapolation_up)
+            extrapolation_left,
+            extrapolation_right)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), eltype(u), typeof(λ), N, typeof(Aitp)}(
             u,
@@ -146,8 +146,8 @@ struct RegularizationSmooth{uType, tType, T, T2, N, ITP <: AbstractInterpolation
             λ,
             alg,
             Aitp,
-            extrapolation_down,
-            extrapolation_up)
+            extrapolation_left,
+            extrapolation_right)
     end
 end
 
diff --git a/src/derivatives.jl b/src/derivatives.jl
index e43fe2c4..6b1f02e6 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -14,16 +14,16 @@ function derivative(A, t, order = 1)
 end
 
 function _extrapolate_derivative_down(A, t, order)
-    (; extrapolation_down) = A
+    (; extrapolation_left) = A
     typed_zero = zero(first(A.u) / one(A.t[1]))
-    if extrapolation_down == ExtrapolationType.none
+    if extrapolation_left == ExtrapolationType.none
         throw(DownExtrapolationError())
-    elseif extrapolation_down == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.constant
         typed_zero
-    elseif extrapolation_down == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.linear
         (order == 1) ? derivative(A, first(A.t)) : typed_zero
     else
-        # extrapolation_down == ExtrapolationType.extension
+        # extrapolation_left == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
@@ -33,16 +33,16 @@ function _extrapolate_derivative_down(A, t, order)
 end
 
 function _extrapolate_derivative_up(A, t, order)
-    (; extrapolation_up) = A
+    (; extrapolation_right) = A
     typed_zero = zero(first(A.u) / one(A.t[1]))
-    if extrapolation_up == ExtrapolationType.none
+    if extrapolation_right == ExtrapolationType.none
         throw(UpExtrapolationError())
-    elseif extrapolation_up == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.constant
         typed_zero
-    elseif extrapolation_up == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.linear
         (order == 1) ? derivative(A, last(A.t)) : typed_zero
     else
-        # extrapolation_up == ExtrapolationType.extension
+        # extrapolation_right == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
diff --git a/src/integral_inverses.jl b/src/integral_inverses.jl
index ec3bf9c3..577b98e3 100644
--- a/src/integral_inverses.jl
+++ b/src/integral_inverses.jl
@@ -37,14 +37,14 @@ struct LinearInterpolationIntInv{uType, tType, itpType, T, N} <:
        AbstractIntegralInverseInterpolation{T, N}
     u::uType
     t::tType
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     itp::itpType
     function LinearInterpolationIntInv(u, t, A)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(A), eltype(u), N}(
-            u, t, A.extrapolation_down, A.extrapolation_up, Guesser(t), A)
+            u, t, A.extrapolation_left, A.extrapolation_right, Guesser(t), A)
     end
 end
 
@@ -89,14 +89,14 @@ struct ConstantInterpolationIntInv{uType, tType, itpType, T, N} <:
        AbstractIntegralInverseInterpolation{T, N}
     u::uType
     t::tType
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     itp::itpType
     function ConstantInterpolationIntInv(u, t, A)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(A), eltype(u), N}(
-            u, t, A.extrapolation_down, A.extrapolation_up, Guesser(t), A
+            u, t, A.extrapolation_left, A.extrapolation_right, Guesser(t), A
         )
     end
 end
diff --git a/src/integrals.jl b/src/integrals.jl
index 4261ffe5..d24a79a8 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -63,31 +63,31 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
 end
 
 function _extrapolate_integral_down(A, t)
-    (; extrapolation_down) = A
-    if extrapolation_down == ExtrapolationType.none
+    (; extrapolation_left) = A
+    if extrapolation_left == ExtrapolationType.none
         throw(DownExtrapolationError())
-    elseif extrapolation_down == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.constant
         first(A.u) * (first(A.t) - t)
-    elseif extrapolation_down == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         Δt = first(A.t) - t
         (first(A.u) - slope * Δt / 2) * Δt
-    elseif extrapolation_down == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.extension
         _integral(A, 1, t, first(A.t))
     end
 end
 
 function _extrapolate_integral_up(A, t)
-    (; extrapolation_up) = A
-    if extrapolation_up == ExtrapolationType.none
+    (; extrapolation_right) = A
+    if extrapolation_right == ExtrapolationType.none
         throw(UpExtrapolationError())
-    elseif extrapolation_up == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.constant
         last(A.u) * (t - last(A.t))
-    elseif extrapolation_up == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         Δt = t - last(A.t)
         (last(A.u) + slope * Δt / 2) * Δt
-    elseif extrapolation_up == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.extension
         _integral(A, length(A.t) - 1, last(A.t), t)
     end
 end
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index 2c01aed6..4cc2670b 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -1,6 +1,6 @@
 """
-    LinearInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    LinearInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line.
 Extrapolation extends the last linear polynomial on each side.
@@ -12,13 +12,16 @@ Extrapolation extends the last linear polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation
     computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
-  - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
+  - `assume_linear_t`: boolean value to specify a faster index lookup behavior for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
     to the straight line (see [`looks_linear`](@ref)). Defaults to 1e-2.
@@ -28,37 +31,41 @@ struct LinearInterpolation{uType, tType, IType, pType, T, N} <: AbstractInterpol
     t::tType
     I::IType
     p::LinearParameterCache{pType}
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
-    function LinearInterpolation(u, t, I, p, extrapolation_down, extrapolation_up,
+    function LinearInterpolation(u, t, I, p, extrapolation_left, extrapolation_right,
             cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.slope), eltype(u), N}(
-            u, t, I, p, extrapolation_down, extrapolation_up,
+            u, t, I, p, extrapolation_left, extrapolation_right,
             Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function LinearInterpolation(
-        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     p = LinearParameterCache(u, t, cache_parameters)
     A = LinearInterpolation(
-        u, t, nothing, p, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, p, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
     LinearInterpolation(
-        u, t, I, p, extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, I, p, extrapolation_left, extrapolation_right,
+        cache_parameters, assume_linear_t)
 end
 
 """
-    QuadraticInterpolation(u, t, mode = :Forward; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    QuadraticInterpolation(u, t, mode = :Forward; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -71,10 +78,13 @@ Extrapolation extends the last quadratic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -88,36 +98,39 @@ struct QuadraticInterpolation{uType, tType, IType, pType, T, N} <:
     I::IType
     p::QuadraticParameterCache{pType}
     mode::Symbol
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuadraticInterpolation(
-            u, t, I, p, mode, extrapolation_down,
-            extrapolation_up, cache_parameters, assume_linear_t)
+            u, t, I, p, mode, extrapolation_left,
+            extrapolation_right, cache_parameters, assume_linear_t)
         mode ∈ (:Forward, :Backward) ||
             error("mode should be :Forward or :Backward for QuadraticInterpolation")
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.α), eltype(u), N}(
-            u, t, I, p, mode, extrapolation_down, extrapolation_up,
+            u, t, I, p, mode, extrapolation_left, extrapolation_right,
             Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function QuadraticInterpolation(
-        u, t, mode; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t, mode; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = QuadraticParameterCache(u, t, cache_parameters, mode)
     A = QuadraticInterpolation(
-        u, t, nothing, p, mode, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        u, t, nothing, p, mode, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticInterpolation(u, t, I, p, mode, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+    QuadraticInterpolation(u, t, I, p, mode, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
 
 function QuadraticInterpolation(u, t; kwargs...)
@@ -125,8 +138,8 @@ function QuadraticInterpolation(u, t; kwargs...)
 end
 
 """
-    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.
 
@@ -138,10 +151,13 @@ It is the method of interpolation using Lagrange polynomials of (k-1)th order pa
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
 """
 struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
        AbstractInterpolation{T, N}
@@ -150,10 +166,10 @@ struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
     n::Int
     bcache::bcacheType
     idxs::Vector{Int}
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
-    function LagrangeInterpolation(u, t, n, extrapolation_down, extrapolation_up)
+    function LagrangeInterpolation(u, t, n, extrapolation_left, extrapolation_right)
         bcache = zeros(eltype(u[1]), n + 1)
         idxs = zeros(Int, n + 1)
         fill!(bcache, NaN)
@@ -163,8 +179,8 @@ struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
             n,
             bcache,
             idxs,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t)
         )
     end
@@ -172,18 +188,21 @@ end
 
 function LagrangeInterpolation(
         u, t, n = length(t) - 1;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     if n != length(t) - 1
         error("Currently only n=length(t) - 1 is supported")
     end
-    LagrangeInterpolation(u, t, n, extrapolation_down, extrapolation_up)
+    LagrangeInterpolation(u, t, n, extrapolation_left, extrapolation_right)
 end
 
 """
-    AkimaInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    AkimaInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: [https://en.wikipedia.org/wiki/Akima_spline](https://en.wikipedia.org/wiki/Akima_spline).
 Extrapolation extends the last cubic polynomial on each side.
@@ -195,10 +214,13 @@ Extrapolation extends the last cubic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -213,14 +235,14 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
     b::bType
     c::cType
     d::dType
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function AkimaInterpolation(
-            u, t, I, b, c, d, extrapolation_down,
-            extrapolation_up, cache_parameters, assume_linear_t)
+            u, t, I, b, c, d, extrapolation_left,
+            extrapolation_right, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(b), typeof(c),
@@ -230,8 +252,8 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
             b,
             c,
             d,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -240,8 +262,11 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
 end
 
 function AkimaInterpolation(
-        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     n = length(t)
@@ -265,16 +290,16 @@ function AkimaInterpolation(
     d = (b[1:(end - 1)] .+ b[2:end] .- 2.0 .* m[3:(end - 2)]) ./ dt .^ 2
 
     A = AkimaInterpolation(
-        u, t, nothing, b, c, d, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        u, t, nothing, b, c, d, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    AkimaInterpolation(u, t, I, b, c, d, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+    AkimaInterpolation(u, t, I, b, c, d, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
 
 """
-    ConstantInterpolation(u, t; dir = :left, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    ConstantInterpolation(u, t; dir = :left, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on `dir`.
 If it is `:left`, then the value at the left point is chosen and if it is `:right`, the value at the right point is chosen.
@@ -288,10 +313,13 @@ Extrapolation extends the last constant polynomial at the end points on each sid
 ## Keyword Arguments
 
   - `dir`: indicates which value should be used for interpolation (`:left` or `:right`).
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -304,38 +332,41 @@ struct ConstantInterpolation{uType, tType, IType, T, N} <: AbstractInterpolation
     I::IType
     p::Nothing
     dir::Symbol # indicates if value to the $dir should be used for the interpolation
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function ConstantInterpolation(
-            u, t, I, dir, extrapolation_down, extrapolation_up,
+            u, t, I, dir, extrapolation_left, extrapolation_right,
             cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), eltype(u), N}(
-            u, t, I, nothing, dir, extrapolation_down, extrapolation_up,
+            u, t, I, nothing, dir, extrapolation_left, extrapolation_right,
             Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function ConstantInterpolation(
-        u, t; dir = :left, extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
+        u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     A = ConstantInterpolation(
-        u, t, nothing, dir, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, dir, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    ConstantInterpolation(u, t, I, dir, extrapolation_down, extrapolation_up,
+    ConstantInterpolation(u, t, I, dir, extrapolation_left, extrapolation_right,
         cache_parameters, assume_linear_t)
 end
 
 """
-    QuadraticSpline(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    QuadraticSpline(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -347,10 +378,13 @@ Extrapolation extends the last quadratic polynomial on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -366,14 +400,14 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
     k::kType # knot vector
     c::cType # B-spline control points
     sc::scType # Spline coefficients (preallocated memory)
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuadraticSpline(
-            u, t, I, p, k, c, sc, extrapolation_down,
-            extrapolation_up, cache_parameters, assume_linear_t)
+            u, t, I, p, k, c, sc, extrapolation_left,
+            extrapolation_right, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.α), typeof(k),
@@ -384,8 +418,8 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
             k,
             c,
             sc,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -394,10 +428,13 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2) where {uType <:
                                                                  AbstractVector{<:Number}}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
 
     n = length(t)
@@ -408,18 +445,21 @@ function QuadraticSpline(
 
     p = QuadraticSplineParameterCache(u, t, k, c, sc, cache_parameters)
     A = QuadraticSpline(
-        u, t, nothing, p, k, c, sc, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, p, k, c, sc, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
 
     n = length(t)
@@ -440,16 +480,16 @@ function QuadraticSpline(
 
     p = QuadraticSplineParameterCache(u, t, k, c, sc, cache_parameters)
     A = QuadraticSpline(
-        u, t, nothing, p, k, c, sc, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, p, k, c, sc, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+    QuadraticSpline(u, t, I, p, k, c, sc, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
 end
 
 """
-    CubicSpline(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    CubicSpline(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous.
 Second derivative on both ends are zero, which are also called "natural" boundary conditions. Extrapolation extends the last cubic polynomial on each side.
@@ -461,10 +501,13 @@ Second derivative on both ends are zero, which are also called "natural" boundar
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -479,13 +522,13 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
     p::CubicSplineParameterCache{pType}
     h::hType
     z::zType
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
-    function CubicSpline(u, t, I, p, h, z, extrapolation_down,
-            extrapolation_up, cache_parameters, assume_linear_t)
+    function CubicSpline(u, t, I, p, h, z, extrapolation_left,
+            extrapolation_right, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(p.c₁),
@@ -496,8 +539,8 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
             p,
             h,
             z,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t),
             cache_parameters,
             linear_lookup
@@ -506,11 +549,13 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
 end
 
 function CubicSpline(u::uType,
-        t;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector{<:Number}}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t) - 1
     h = vcat(0, map(k -> t[k + 1] - t[k], 1:(length(t) - 1)), 0)
@@ -531,19 +576,21 @@ function CubicSpline(u::uType,
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
 
 function CubicSpline(u::uType,
         t;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractArray{T, N}} where {T, N}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t) - 1
     h = vcat(0, map(k -> t[k + 1] - t[k], 1:(length(t) - 1)), 0)
@@ -568,18 +615,21 @@ function CubicSpline(u::uType,
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
 
 function CubicSpline(
-        u::uType, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t) - 1
     h = vcat(0, map(k -> t[k + 1] - t[k], 1:(length(t) - 1)), 0)
@@ -597,16 +647,16 @@ function CubicSpline(
 
     p = CubicSplineParameterCache(u, h, z, cache_parameters)
     A = CubicSpline(
-        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+        u, t, nothing, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
     I = cumulative_integral(A, cache_parameters)
-    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_down,
-        extrapolation_up, cache_parameters, assume_linear_t)
+    CubicSpline(u, t, I, p, h[1:(n + 1)], z, extrapolation_left,
+        extrapolation_right, cache_parameters, assume_linear_t)
 end
 
 """
-    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a curve defined by the linear combination of `n` basis functions of degree `d` where `n` is the number of data points. For more information, refer [https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html](https://pages.mtu.edu/%7Eshene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html).
 Extrapolation is a constant polynomial of the end points on each side.
@@ -621,10 +671,13 @@ Extrapolation is a constant polynomial of the end points on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
@@ -641,8 +694,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
     sc::scType  # Spline coefficients (preallocated memory)
     pVecType::Symbol
     knotVecType::Symbol
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     linear_lookup::Bool
     function BSplineInterpolation(u,
@@ -654,8 +707,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
@@ -669,8 +722,8 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t),
             linear_lookup
         )
@@ -679,8 +732,11 @@ end
 
 function BSplineInterpolation(
         u::AbstractVector, t, d, pVecType, knotVecType;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t)
     n < d + 1 && error("BSplineInterpolation needs at least d + 1, i.e. $(d+1) points.")
@@ -746,14 +802,17 @@ function BSplineInterpolation(
     sc = zeros(eltype(t), n)
     BSplineInterpolation(
         u, t, d, p, k, c, sc, pVecType, knotVecType,
-        extrapolation_down, extrapolation_up, assume_linear_t)
+        extrapolation_left, extrapolation_right, assume_linear_t)
 end
 
 function BSplineInterpolation(
         u::AbstractArray{T, N}, t, d, pVecType, knotVecType;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
         assume_linear_t = 1e-2) where {T, N}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t)
     n < d + 1 && error("BSplineInterpolation needs at least d + 1, i.e. $(d+1) points.")
@@ -822,12 +881,12 @@ function BSplineInterpolation(
     sc = zeros(eltype(t), n)
     BSplineInterpolation(
         u, t, d, p, k, c, sc, pVecType, knotVecType,
-        extrapolation_down, extrapolation_up, assume_linear_t)
+        extrapolation_left, extrapolation_right, assume_linear_t)
 end
 
 """
-    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none)
+    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a regression based B-spline. The argument choices are the same as the `BSplineInterpolation`, with the additional parameter `h < length(t)` which is the number of control points to use, with smaller `h` indicating more smoothing.
 For more information, refer [http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf](http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf).
@@ -844,10 +903,13 @@ Extrapolation is a constant polynomial of the end points on each side.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
@@ -865,8 +927,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
     sc::scType  # Spline coefficients (preallocated memory)
     pVecType::Symbol
     knotVecType::Symbol
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     linear_lookup::Bool
     function BSplineApprox(u,
@@ -879,8 +941,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             assume_linear_t
     )
         linear_lookup = seems_linear(assume_linear_t, t)
@@ -896,8 +958,8 @@ struct BSplineApprox{uType, tType, pType, kType, cType, scType, T, N} <:
             sc,
             pVecType,
             knotVecType,
-            extrapolation_down,
-            extrapolation_up,
+            extrapolation_left,
+            extrapolation_right,
             Guesser(t),
             linear_lookup
         )
@@ -906,8 +968,11 @@ end
 
 function BSplineApprox(
         u::AbstractVector, t, d, h, pVecType, knotVecType;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t)
     h < d + 1 && error("BSplineApprox needs at least d + 1, i.e. $(d+1) control points.")
@@ -994,14 +1059,17 @@ function BSplineApprox(
     sc = zeros(eltype(t), h)
     BSplineApprox(
         u, t, d, h, p, k, c, sc, pVecType, knotVecType,
-        extrapolation_down, extrapolation_up, assume_linear_t)
+        extrapolation_left, extrapolation_right, assume_linear_t)
 end
 
 function BSplineApprox(
         u::AbstractArray{T, N}, t, d, h, pVecType, knotVecType;
-        extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
         assume_linear_t = 1e-2) where {T, N}
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     n = length(t)
     h < d + 1 && error("BSplineApprox needs at least d + 1, i.e. $(d+1) control points.")
@@ -1093,11 +1161,11 @@ function BSplineApprox(
     sc = zeros(eltype(t), h)
     BSplineApprox(
         u, t, d, h, p, k, c, sc, pVecType, knotVecType,
-        extrapolation_down, extrapolation_up, assume_linear_t)
+        extrapolation_left, extrapolation_right, assume_linear_t)
 end
 """
-    CubicHermiteSpline(du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    CubicHermiteSpline(du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomial such that the value and the first derivative are equal to given values in the data points.
 
@@ -1109,10 +1177,13 @@ It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomi
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1126,40 +1197,43 @@ struct CubicHermiteSpline{uType, tType, IType, duType, pType, T, N} <:
     t::tType
     I::IType
     p::CubicHermiteParameterCache{pType}
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function CubicHermiteSpline(
-            du, u, t, I, p, extrapolation_down, extrapolation_up,
+            du, u, t, I, p, extrapolation_left, extrapolation_right,
             cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(du), typeof(p.c₁), eltype(u), N}(
-            du, u, t, I, p, extrapolation_down, extrapolation_up,
+            du, u, t, I, p, extrapolation_left, extrapolation_right,
             Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function CubicHermiteSpline(
-        du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du) "Length of `u` is not equal to length of `du`."
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = CubicHermiteParameterCache(du, u, t, cache_parameters)
     A = CubicHermiteSpline(
-        du, u, t, nothing, p, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        du, u, t, nothing, p, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
-    CubicHermiteSpline(du, u, t, I, p, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+    CubicHermiteSpline(du, u, t, I, p, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
 
 """
-    PCHIPInterpolation(u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    PCHIPInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a PCHIP Interpolation, which is a type of [`CubicHermiteSpline`](@ref) where the derivative values `du` are derived from the input data
 in such a way that the interpolation never overshoots the data. See [here](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/interp.pdf),
@@ -1172,28 +1246,28 @@ section 3.4 for more details.
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
     to the straight line (see [`looks_linear`](@ref)). Defaults to 1e-2.
 """
-function PCHIPInterpolation(
-        u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+function PCHIPInterpolation(u, t; kwargs...)
     u, t = munge_data(u, t)
     du = du_PCHIP(u, t)
-    CubicHermiteSpline(
-        du, u, t; extrapolation_down, extrapolation_up, cache_parameters, assume_linear_t)
+    CubicHermiteSpline(du, u, t; kwargs...)
 end
 
 """
-    QuinticHermiteSpline(ddu, du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    QuinticHermiteSpline(ddu, du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
 
 It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polynomial such that the value and the first and second derivative are equal to given values in the data points.
 
@@ -1206,10 +1280,13 @@ It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polyno
 
 ## Keyword Arguments
 
-  - `extrapolate_down`: The extrapolation type beyond the data in the negative `t` direction.
-    Defaults to `ExtrapolationType.none`.
-  - `extrapolate_up`: The extrapolation type beyond the data in the positive `t` direction.
-    Defaults to `ExtrapolationType.none`.
+  - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
+    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
+    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+  - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
+    the possible options.
+  - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
+    the possible options.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1224,36 +1301,39 @@ struct QuinticHermiteSpline{uType, tType, IType, duType, dduType, pType, T, N} <
     t::tType
     I::IType
     p::QuinticHermiteParameterCache{pType}
-    extrapolation_down::ExtrapolationType.T
-    extrapolation_up::ExtrapolationType.T
+    extrapolation_left::ExtrapolationType.T
+    extrapolation_right::ExtrapolationType.T
     iguesser::Guesser{tType}
     cache_parameters::Bool
     linear_lookup::Bool
     function QuinticHermiteSpline(
-            ddu, du, u, t, I, p, extrapolation_down,
-            extrapolation_up, cache_parameters, assume_linear_t)
+            ddu, du, u, t, I, p, extrapolation_left,
+            extrapolation_right, cache_parameters, assume_linear_t)
         linear_lookup = seems_linear(assume_linear_t, t)
         N = get_output_dim(u)
         new{typeof(u), typeof(t), typeof(I), typeof(du),
             typeof(ddu), typeof(p.c₁), eltype(u), N}(
-            ddu, du, u, t, I, p, extrapolation_down, extrapolation_up,
+            ddu, du, u, t, I, p, extrapolation_left, extrapolation_right,
             Guesser(t), cache_parameters, linear_lookup)
     end
 end
 
 function QuinticHermiteSpline(
-        ddu, du, u, t; extrapolation_down::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_up::ExtrapolationType.T = ExtrapolationType.none,
+        ddu, du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
         cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du)==length(ddu) "Length of `u` is not equal to length of `du` or `ddu`."
+    extrapolation_left, extrapolation_right = munge_extrapolation(
+        extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
     linear_lookup = seems_linear(assume_linear_t, t)
     p = QuinticHermiteParameterCache(ddu, du, u, t, cache_parameters)
     A = QuinticHermiteSpline(
-        ddu, du, u, t, nothing, p, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        ddu, du, u, t, nothing, p, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
     I = cumulative_integral(A, cache_parameters)
     QuinticHermiteSpline(
-        ddu, du, u, t, I, p, extrapolation_down,
-        extrapolation_up, cache_parameters, linear_lookup)
+        ddu, du, u, t, I, p, extrapolation_left,
+        extrapolation_right, cache_parameters, linear_lookup)
 end
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index 74494ff5..a691fbb2 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -9,33 +9,33 @@ function _interpolate(A, t)
 end
 
 function _extrapolate_down(A, t)
-    (; extrapolation_down) = A
-    if extrapolation_down == ExtrapolationType.none
+    (; extrapolation_left) = A
+    if extrapolation_left == ExtrapolationType.none
         throw(DownExtrapolationError())
-    elseif extrapolation_down == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.constant
         slope = derivative(A, first(A.t))
         first(A.u) + slope * zero(t)
-    elseif extrapolation_down == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
     else
-        # extrapolation_down == ExtrapolationType.extension
+        # extrapolation_left == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
 
 function _extrapolate_up(A, t)
-    (; extrapolation_up) = A
-    if extrapolation_up == ExtrapolationType.none
+    (; extrapolation_right) = A
+    if extrapolation_right == ExtrapolationType.none
         throw(UpExtrapolationError())
-    elseif extrapolation_up == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.constant
         slope = derivative(A, last(A.t))
         last(A.u) + slope * zero(t)
-    elseif extrapolation_up == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
     else
-        # extrapolation_up == ExtrapolationType.extension
+        # extrapolation_right == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
     end
 end
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 0f922a93..f12bfa07 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -303,3 +303,11 @@ function integrate_quintic_polynomial(t1, t2, offset, a, b, c, d, e, f)
      cube_diff_factor * (c / 3 + f * t_cb_sum / 6)) +
     e * (t2_rel^5 - t1_rel^5) / 5
 end
+
+function munge_extrapolation(extrapolation, extrapolation_left, extrapolation_right)
+    if extrapolation == ExtrapolationType.none
+        extrapolation_left, extrapolation_right
+    else
+        extrapolation, extrapolation
+    end
+end
diff --git a/test/derivative_tests.jl b/test/derivative_tests.jl
index d81f346b..df96b0fb 100644
--- a/test/derivative_tests.jl
+++ b/test/derivative_tests.jl
@@ -11,8 +11,8 @@ using ForwardDiff
 function test_derivatives(method; args = [], kwargs = [], name::String)
     kwargs_extrapolation = (method == Curvefit) ?
                            [:extrapolate => true] :
-                           [:extrapolation_up => ExtrapolationType.extension,
-        :extrapolation_down => ExtrapolationType.extension]
+                           [:extrapolation_right => ExtrapolationType.extension,
+        :extrapolation_left => ExtrapolationType.extension]
     func = method(args...; kwargs..., kwargs_extrapolation...)
     (; t) = func
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
@@ -241,8 +241,7 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(CubicHermiteSpline; args = [du, u, t],
         name = "Cubic Hermite Spline")
-    A = CubicHermiteSpline(du, u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative(A, 100.0)≈0.0105409 rtol=1e-5
     @test derivative(A, 300.0)≈-0.0806717 rtol=1e-5
@@ -255,8 +254,7 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(QuinticHermiteSpline; args = [ddu, du, u, t],
         name = "Quintic Hermite Spline")
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative.(Ref(A), t, 2) ≈ ddu
     @test derivative(A, 100.0)≈0.0103916 rtol=1e-5
@@ -335,8 +333,7 @@ end
 @testset "Jacobian tests" begin
     u = rand(5)
     t = 0:4
-    interp = LinearInterpolation(u, t, extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    interp = LinearInterpolation(u, t, extrapolation = ExtrapolationType.extension)
     grad1 = ForwardDiff.derivative(interp, 2.4)
 
     myvec = rand(20) .* 4.0
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index e87fd340..9ba616f4 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -2,8 +2,8 @@ using DataInterpolations
 
 function test_extrapolation_errors(method, u, t)
     A = method(u, t)
-    @test A.extrapolation_up == ExtrapolationType.none
-    @test A.extrapolation_down == ExtrapolationType.none
+    @test A.extrapolation_right == ExtrapolationType.none
+    @test A.extrapolation_left == ExtrapolationType.none
     for (error_type, t_eval) in zip(
         (DataInterpolations.DownExtrapolationError,
             DataInterpolations.UpExtrapolationError),
@@ -19,8 +19,8 @@ function test_extrapolation_errors(method, u, t)
 end
 
 function test_constant_extrapolation(method, u, t)
-    A = method(u, t; extrapolation_down = ExtrapolationType.constant,
-        extrapolation_up = ExtrapolationType.constant)
+    A = method(u, t; extrapolation_left = ExtrapolationType.constant,
+        extrapolation_right = ExtrapolationType.constant)
     t_lower = first(t) - 1
     t_upper = last(t) + 1
     @test A(t_lower) == first(u)
@@ -41,7 +41,7 @@ end
 
     for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
         # Down extrapolation
-        A = LinearInterpolation(u, t; extrapolation_down = extrapolation_type)
+        A = LinearInterpolation(u, t; extrapolation_left = extrapolation_type)
         t_eval = 0.0
         @test A(t_eval) == 0.0
         @test DataInterpolations.derivative(A, t_eval) == 1.0
@@ -50,7 +50,7 @@ end
         t_eval = 3.0
 
         # Up extrapolation
-        A = LinearInterpolation(u, t; extrapolation_up = extrapolation_type)
+        A = LinearInterpolation(u, t; extrapolation_right = extrapolation_type)
         t_eval = 3.0
         @test A(t_eval) == 3.0
         @test DataInterpolations.derivative(A, t_eval) == 1.0
@@ -68,7 +68,7 @@ end
     test_constant_extrapolation(LinearInterpolation, u, t)
 
     # Linear down extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.linear)
+    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.linear)
     t_eval = 0.0
     @test A(t_eval) ≈ -2.5
     @test DataInterpolations.derivative(A, t_eval) == 3.5
@@ -76,7 +76,7 @@ end
     @test DataInterpolations.integral(A, t_eval) ≈ 0.75
 
     # Linear up extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.linear)
+    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.linear)
     t_eval = 4.0
     @test A(t_eval) ≈ -0.5
     @test DataInterpolations.derivative(A, t_eval) == -2.5
@@ -86,7 +86,7 @@ end
     # Extension down extrapolation
     f = t -> (-3t^2 + 13t - 8) / 2
     df = t -> (-6t + 13) / 2
-    A = QuadraticInterpolation(u, t; extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.extension)
     t_eval = 0.0
     @test A(t_eval) ≈ -4.0
     @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
@@ -94,7 +94,7 @@ end
     @test DataInterpolations.integral(A, t_eval) ≈ 1.25
 
     # Extension up extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.extension)
     t_eval = 4.0
     @test A(t_eval) ≈ -2.0
     @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
diff --git a/test/integral_inverse_tests.jl b/test/integral_inverse_tests.jl
index 0e9e4cf2..9ba0b158 100644
--- a/test/integral_inverse_tests.jl
+++ b/test/integral_inverse_tests.jl
@@ -3,8 +3,7 @@ using DataInterpolations: integral, derivative, invert_integral
 using FiniteDifferences
 
 function test_integral_inverses(method; args = [], kwargs = [])
-    A = method(args...; kwargs..., extrapolation_down = ExtrapolationType.extension,
-        extrapolation_up = ExtrapolationType.extension)
+    A = method(args...; kwargs..., extrapolation = ExtrapolationType.extension)
     @test hasfield(typeof(A), :I)
     A_intinv = invert_integral(A)
     @test A_intinv isa DataInterpolations.AbstractIntegralInverseInterpolation
diff --git a/test/integral_tests.jl b/test/integral_tests.jl
index 142e0d1f..c37d9d8d 100644
--- a/test/integral_tests.jl
+++ b/test/integral_tests.jl
@@ -6,8 +6,8 @@ using RegularizationTools
 using StableRNGs
 
 function test_integral(method; args = [], kwargs = [], name::String)
-    func = method(args...; kwargs..., extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    func = method(args...; kwargs..., extrapolation_left = ExtrapolationType.extension,
+        extrapolation_right = ExtrapolationType.extension)
     (; t) = func
     t1 = minimum(t)
     t2 = maximum(t)
diff --git a/test/interface.jl b/test/interface.jl
index 40fb25f6..29f6864d 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -18,10 +18,8 @@ end
 @testset "Symbolics" begin
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
-    B = LinearInterpolation(u .^ 2, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    B = LinearInterpolation(u .^ 2, t; extrapolation = ExtrapolationType.extension)
     @variables t x(t)
     substitute(A(t), Dict(t => x))
     t_val = 2.7
diff --git a/test/interpolation_tests.jl b/test/interpolation_tests.jl
index 14bc93b8..3b374c00 100644
--- a/test/interpolation_tests.jl
+++ b/test/interpolation_tests.jl
@@ -8,8 +8,8 @@ function test_interpolation_type(T)
     @test T <: DataInterpolations.AbstractInterpolation
     @test hasfield(T, :u)
     @test hasfield(T, :t)
-    @test hasfield(T, :extrapolation_up)
-    @test hasfield(T, :extrapolation_down)
+    @test hasfield(T, :extrapolation_right)
+    @test hasfield(T, :extrapolation_left)
     @test hasfield(T, :iguesser)
     @test !isempty(methods(DataInterpolations._interpolate, (T, Any, Number)))
     @test !isempty(methods(DataInterpolations._integral, (T, Number, Number, Number)))
@@ -31,8 +31,7 @@ end
     for t in (1.0:10.0, 1.0collect(1:10))
         u = 2.0collect(1:10)
         #t = 1.0collect(1:10)
-        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
         for (_t, _u) in zip(t, u)
             @test A(_t) == _u
@@ -42,8 +41,7 @@ end
         @test A(11) == 22
 
         u = vcat(2.0collect(1:10)', 3.0collect(1:10)')
-        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
         for (_t, _u) in zip(t, eachcol(u))
             @test A(_t) == _u
@@ -56,8 +54,7 @@ end
         y = 2:4
         u_ = x' .* y
         u = [u_[:, i] for i in 1:size(u_, 2)]
-        A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
         @test A(0) == [0.0, 0.0, 0.0]
         @test A(5.5) == [11.0, 16.5, 22.0]
         @test A(11) == [22.0, 33.0, 44.0]
@@ -68,8 +65,7 @@ end
     u_ = x' .* y
     u = [u_[:, i:(i + 1)] for i in 1:2:10]
     t = 1.0collect(2:2:10)
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
     @test A(0) == [-2.0 0.0; -3.0 0.0; -4.0 0.0]
     @test A(3) == [4.0 6.0; 6.0 9.0; 8.0 12.0]
@@ -79,8 +75,7 @@ end
     # with NaNs (#113)
     u = [NaN, 1.0, 2.0, 3.0]
     t = 1:4
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test isnan(A(1.0))
     @test A(2.0) == 1.0
     @test A(2.5) == 1.5
@@ -88,8 +83,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, NaN, 2.0, 3.0]
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test isnan(A(2.0))
     @test isnan(A(2.5))
@@ -97,8 +91,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, NaN, 3.0]
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test isnan(A(2.5))
@@ -106,8 +99,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, 2.0, NaN]
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test A(3.0) == 2.0
@@ -117,20 +109,16 @@ end
     # Test type stability
     u = Float32.(1:5)
     t = Float32.(1:5)
-    A1 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A1 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     u = 1:5
     t = 1:5
-    A2 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A2 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     u = [1 // i for i in 1:5]
     t = (1:5)
-    A3 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A3 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     u = [1 // i for i in 1:5]
     t = [1 // (6 - i) for i in 1:5]
-    A4 = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A4 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
     F32 = Float32(1)
     F64 = Float64(1)
@@ -150,15 +138,13 @@ end
     # Nan time value:
     t = 0.0:3  # Floats
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
     t = 0:3  # Integers
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
@@ -171,8 +157,7 @@ end
     # Test array-valued interpolation
     u = collect.(2.0collect(1:10))
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(0) == fill(0.0)
     @test A(5.5) == fill(11.0)
     @test A(11) == fill(22)
@@ -187,8 +172,7 @@ end
     # Test extrapolation
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-1.0) == -2.0
     @test A(11.0) == 22.0
     A = LinearInterpolation(u, t)
@@ -202,8 +186,7 @@ end
 
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -219,8 +202,7 @@ end
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
     A = QuadraticInterpolation(
-        u, t, :Backward; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+        u, t, :Backward; extrapolation = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -258,8 +240,7 @@ end
 
     # Matrix interpolation test
     u = [1.0 4.0 9.0 16.0; 1.0 4.0 9.0 16.0]
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
 
     for (_t, _u) in zip(t, eachcol(u))
         @test A(_t) == _u
@@ -272,8 +253,7 @@ end
 
     u_ = [1.0, 4.0, 9.0, 16.0]' .* ones(5)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(0) == zeros(5)
     @test A(1.5) == 2.25 * ones(5)
     @test A(2.5) == 6.25 * ones(5)
@@ -281,8 +261,7 @@ end
     @test A(5.0) == 25.0 * ones(5)
 
     u = [repeat(u[i], 1, 3) for i in 1:4]
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(0) == zeros(5, 3)
     @test A(1.5) == 2.25 * ones(5, 3)
     @test A(2.5) == 6.25 * ones(5, 3)
@@ -292,8 +271,7 @@ end
     # Test extrapolation
     u = [1.0, 4.5, 6.0, 2.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(0.0) == -4.5
     @test A(5.0) == -7.5
     A = QuadraticInterpolation(u, t)
@@ -353,8 +331,7 @@ end
     # Test extrapolation
     u = [1.0, 4.0, 9.0]
     t = [1.0, 2.0, 3.0]
-    A = LagrangeInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = LagrangeInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(0.0) == 0.0
     @test A(4.0) == 16.0
     A = LagrangeInterpolation(u, t)
@@ -385,8 +362,7 @@ end
     test_cached_index(A)
 
     # Test extrapolation
-    A = AkimaInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = AkimaInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-1.0) ≈ -5.0
     @test A(11.0) ≈ -3.924742268041234
     A = AkimaInterpolation(u, t)
@@ -401,8 +377,7 @@ end
 
     @testset "Vector case" for u in [[1.0, 2.0, 0.0, 1.0], ["B", "C", "A", "B"]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -414,8 +389,7 @@ end
         @test A(4.5) == u[1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -433,8 +407,7 @@ end
         ["B" "C" "A" "B"; "B" "C" "A" "B"]
     ]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 2]
@@ -446,8 +419,7 @@ end
         @test A(4.5) == u[:, 1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 1]
@@ -464,8 +436,7 @@ end
         [[1.0, 2.0], [0.0, 1.0], [1.0, 2.0], [0.0, 1.0]],
         [["B", "C"], ["A", "B"], ["B", "C"], ["A", "B"]]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -477,8 +448,7 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -495,8 +465,7 @@ end
         [[1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0], [1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0]],
         [["B" "C"; "B" "C"], ["A" "B"; "A" "B"], ["B" "C"; "B" "C"], ["A" "B"; "A" "B"]]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -508,8 +477,7 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -524,8 +492,7 @@ end
 
     # Test extrapolation
     u = [1.0, 2.0, 0.0, 1.0]
-    A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-1.0) == 1.0
     @test A(11.0) == 1.0
     A = ConstantInterpolation(u, t)
@@ -535,8 +502,7 @@ end
     # Test extrapolation with infs with regularly spaced t
     u = [1.67e7, 1.6867e7, 1.7034e7, 1.7201e7, 1.7368e7]
     t = [0.0, 0.1, 0.2, 0.3, 0.4]
-    A = ConstantInterpolation(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension)
     @test A(Inf) == last(u)
     @test A(-Inf) == first(u)
 end
@@ -547,8 +513,7 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
 
     # Solution
     P₁ = x -> 0.5 * (x + 1) * (x + 2)
@@ -564,16 +529,14 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-2.0) == P₁(-2.0) * ones(4)
     @test A(-0.5) == P₁(-0.5) * ones(4)
     @test A(0.7) == P₁(0.7) * ones(4)
     @test A(2.0) == P₁(2.0) * ones(4)
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-2.0) == P₁(-2.0) * ones(4, 3)
     @test A(-0.5) == P₁(-0.5) * ones(4, 3)
     @test A(0.7) == P₁(0.7) * ones(4, 3)
@@ -582,8 +545,7 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = QuadraticSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-2.0) == 0.0
     @test A(2.0) == 6.0
     A = QuadraticSpline(u, t)
@@ -597,8 +559,7 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
     test_cached_index(A)
 
     # Solution
@@ -617,8 +578,7 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4)
     end
@@ -627,8 +587,7 @@ end
     end
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4, 3)
     end
@@ -639,8 +598,7 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = CubicSpline(u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
     @test A(-2.0) ≈ -1.0
     @test A(2.0) ≈ 5.0
     A = CubicSpline(u, t)
@@ -685,8 +643,7 @@ end
 
         # Test extrapolation
         A = BSplineInterpolation(
-            u, t, 2, :Uniform, :Uniform; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, 2, :Uniform, :Uniform; extrapolation = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :Uniform, :Uniform)
@@ -707,8 +664,7 @@ end
 
         # Test extrapolation
         A = BSplineInterpolation(
-            u, t, 2, :ArcLen, :Average; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, 2, :ArcLen, :Average; extrapolation = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
@@ -766,8 +722,7 @@ end
 
         # Test extrapolation
         A = BSplineApprox(
-            u, t, 2, 4, :Uniform, :Uniform; extrapolation_up = ExtrapolationType.extension,
-            extrapolation_down = ExtrapolationType.extension)
+            u, t, 2, 4, :Uniform, :Uniform; extrapolation = ExtrapolationType.extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineApprox(u, t, 2, 4, :Uniform, :Uniform)
@@ -813,8 +768,7 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = CubicHermiteSpline(du, u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.106770 rtol=1e-5
     @test A(300.0)≈9.901542 rtol=1e-5
@@ -842,8 +796,7 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.107996 rtol=1e-5
     @test A(300.0)≈11.364162 rtol=1e-5
diff --git a/test/regularization.jl b/test/regularization.jl
index 3e6579cf..6d850475 100644
--- a/test/regularization.jl
+++ b/test/regularization.jl
@@ -181,7 +181,7 @@ end
 
 @testset "Extrapolation" begin
     A = RegularizationSmooth(
-        uₒ, tₒ; alg = :fixed, extrapolation_up = ExtrapolationType.extension)
+        uₒ, tₒ; alg = :fixed, extrapolation_right = ExtrapolationType.extension)
     @test A(10.0) == A.Aitp(10.0)
     A = RegularizationSmooth(uₒ, tₒ; alg = :fixed)
     @test_throws DataInterpolations.UpExtrapolationError A(10.0)
diff --git a/test/zygote_tests.jl b/test/zygote_tests.jl
index 6476ee0f..d8d178df 100644
--- a/test/zygote_tests.jl
+++ b/test/zygote_tests.jl
@@ -4,8 +4,7 @@ using Zygote
 
 function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name::String)
     func = method(args..., u, t, args_after...; kwargs...,
-        extrapolation_up = ExtrapolationType.extension,
-        extrapolation_down = ExtrapolationType.extension)
+        extrapolation = ExtrapolationType.extension)
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
     trange_exclude = filter(x -> !in(x, t), trange)
     @testset "$name, derivatives w.r.t. input" begin
@@ -22,8 +21,7 @@ function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name
         @testset "$name, derivatives w.r.t. u" begin
             function f(u)
                 A = method(args..., u, t, args_after...; kwargs...,
-                    extrapolation_up = ExtrapolationType.extension,
-                    extrapolation_down = ExtrapolationType.extension)
+                    extrapolation = ExtrapolationType.extension)
                 out = if u isa AbstractVector{<:Real}
                     zero(eltype(u))
                 elseif u isa AbstractMatrix

From c1f6f7e622f16cb82de113a82242f566a2c18a28 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Thu, 21 Nov 2024 12:00:03 +0100
Subject: [PATCH 13/20] Comments adressed

---
 docs/src/extrapolation_methods.md | 14 +++++-
 src/DataInterpolations.jl         | 16 +++---
 src/derivatives.jl                |  4 +-
 src/integrals.jl                  |  4 +-
 src/interpolation_caches.jl       | 84 ++++++++++++++++---------------
 src/interpolation_methods.jl      |  4 +-
 test/derivative_tests.jl          |  5 +-
 test/extrapolation_tests.jl       |  4 +-
 test/integral_tests.jl            |  9 ++--
 test/interpolation_tests.jl       | 42 ++++++++--------
 test/regularization.jl            |  2 +-
 11 files changed, 102 insertions(+), 86 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index 5b6286ba..09f8f0ae 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -13,7 +13,7 @@ A = QuadraticSpline(u, t)
 plot(A)
 ```
 
-Extrapolation behavior can be set left and right of the data simultaneously with the `extension` keyword, or left and right separately with the `extension_left` and `extension_right` keywords respectively.
+Extrapolation behavior can be set left and right of the data simultaneously with the `extension` keyword, or left and right separately with the `extrapolation_left` and `extrapolation_right` keywords respectively.
 
 ## `ExtrapolationType.none`
 
@@ -51,3 +51,15 @@ plot(A)
 plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
 plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
 ```
+
+## Mixed extrapolation
+
+You can also have different extrapolation types left and right of the data.
+
+```@example tutorial
+A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.constant,
+    extrapolation_right = ExtrapolationType.linear)
+plot(A)
+plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
+plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+```
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index ee15a452..962b21a9 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -64,16 +64,16 @@ function Base.showerror(io::IO, ::ExtrapolationError)
     print(io, EXTRAPOLATION_ERROR)
 end
 
-const DOWN_EXTRAPOLATION_ERROR = "Cannot extrapolate down as `extrapolation_left` keyword passed was `none`"
-struct DownExtrapolationError <: Exception end
-function Base.showerror(io::IO, ::DownExtrapolationError)
-    print(io, DOWN_EXTRAPOLATION_ERROR)
+const LEFT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t < first(A.t) as the `extrapolation_left` kwarg passed was `ExtrapolationType.none`"
+struct LeftExtrapolationError <: Exception end
+function Base.showerror(io::IO, ::LeftExtrapolationError)
+    print(io, LEFT_EXTRAPOLATION_ERROR)
 end
 
-const UP_EXTRAPOLATION_ERROR = "Cannot extrapolate up as `extrapolation_right` keyword passed was `none`"
-struct UpExtrapolationError <: Exception end
-function Base.showerror(io::IO, ::UpExtrapolationError)
-    print(io, UP_EXTRAPOLATION_ERROR)
+const RIGHT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t > last(A.t) as the `extrapolation_tight` kwarg passed was `ExtrapolationType.none`"
+struct RightExtrapolationError <: Exception end
+function Base.showerror(io::IO, ::RightExtrapolationError)
+    print(io, RIGHT_EXTRAPOLATION_ERROR)
 end
 
 const INTEGRAL_NOT_FOUND_ERROR = "Cannot integrate it analytically. Please use Numerical Integration methods."
diff --git a/src/derivatives.jl b/src/derivatives.jl
index 6b1f02e6..da007025 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -17,7 +17,7 @@ function _extrapolate_derivative_down(A, t, order)
     (; extrapolation_left) = A
     typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_left == ExtrapolationType.none
-        throw(DownExtrapolationError())
+        throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.constant
         typed_zero
     elseif extrapolation_left == ExtrapolationType.linear
@@ -36,7 +36,7 @@ function _extrapolate_derivative_up(A, t, order)
     (; extrapolation_right) = A
     typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_right == ExtrapolationType.none
-        throw(UpExtrapolationError())
+        throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.constant
         typed_zero
     elseif extrapolation_right == ExtrapolationType.linear
diff --git a/src/integrals.jl b/src/integrals.jl
index d24a79a8..af2eb3bd 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -65,7 +65,7 @@ end
 function _extrapolate_integral_down(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
-        throw(DownExtrapolationError())
+        throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.constant
         first(A.u) * (first(A.t) - t)
     elseif extrapolation_left == ExtrapolationType.linear
@@ -80,7 +80,7 @@ end
 function _extrapolate_integral_up(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
-        throw(UpExtrapolationError())
+        throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.constant
         last(A.u) * (t - last(A.t))
     elseif extrapolation_right == ExtrapolationType.linear
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index 4cc2670b..faeec06a 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -1,6 +1,7 @@
 """
-    LinearInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    LinearInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none, 
+    extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, 
+    cache_parameters = false)
 
 It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line.
 Extrapolation extends the last linear polynomial on each side.
@@ -16,9 +17,9 @@ Extrapolation extends the last linear polynomial on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation
     computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behavior for
@@ -65,7 +66,8 @@ end
 
 """
     QuadraticInterpolation(u, t, mode = :Forward; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, 
+        cache_parameters = false)
 
 It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -82,9 +84,9 @@ Extrapolation extends the last quadratic polynomial on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -138,8 +140,8 @@ function QuadraticInterpolation(u, t; kwargs...)
 end
 
 """
-    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation::ExtrapolationType.T = ExtrapolationType.none, 
+    extrapolation_left::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.
 
@@ -155,9 +157,9 @@ It is the method of interpolation using Lagrange polynomials of (k-1)th order pa
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
 """
 struct LagrangeInterpolation{uType, tType, T, bcacheType, N} <:
        AbstractInterpolation{T, N}
@@ -201,7 +203,7 @@ function LagrangeInterpolation(
 end
 
 """
-    AkimaInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    AkimaInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: [https://en.wikipedia.org/wiki/Akima_spline](https://en.wikipedia.org/wiki/Akima_spline).
@@ -218,9 +220,9 @@ Extrapolation extends the last cubic polynomial on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -298,7 +300,7 @@ function AkimaInterpolation(
 end
 
 """
-    ConstantInterpolation(u, t; dir = :left, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    ConstantInterpolation(u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on `dir`.
@@ -317,9 +319,9 @@ Extrapolation extends the last constant polynomial at the end points on each sid
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -365,7 +367,7 @@ function ConstantInterpolation(
 end
 
 """
-    QuadraticSpline(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    QuadraticSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous.
@@ -382,9 +384,9 @@ Extrapolation extends the last quadratic polynomial on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -488,7 +490,7 @@ function QuadraticSpline(
 end
 
 """
-    CubicSpline(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    CubicSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous.
@@ -505,9 +507,9 @@ Second derivative on both ends are zero, which are also called "natural" boundar
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -655,8 +657,8 @@ function CubicSpline(
 end
 
 """
-    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a curve defined by the linear combination of `n` basis functions of degree `d` where `n` is the number of data points. For more information, refer [https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html](https://pages.mtu.edu/%7Eshene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html).
 Extrapolation is a constant polynomial of the end points on each side.
@@ -675,10 +677,10 @@ Extrapolation is a constant polynomial of the end points on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
-  - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
+  - `assume_linear_t`: boolean value to specify a faster index lookup behavior for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
     to the straight line (see [`looks_linear`](@ref)). Defaults to 1e-2.
@@ -885,7 +887,7 @@ function BSplineInterpolation(
 end
 
 """
-    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a regression based B-spline. The argument choices are the same as the `BSplineInterpolation`, with the additional parameter `h < length(t)` which is the number of control points to use, with smaller `h` indicating more smoothing.
@@ -907,9 +909,9 @@ Extrapolation is a constant polynomial of the end points on each side.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
     for a test based on the normalized standard deviation of the difference with respect
@@ -1164,7 +1166,7 @@ function BSplineApprox(
         extrapolation_left, extrapolation_right, assume_linear_t)
 end
 """
-    CubicHermiteSpline(du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+    CubicHermiteSpline(du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
         extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
 
 It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomial such that the value and the first derivative are equal to given values in the data points.
@@ -1181,9 +1183,9 @@ It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomi
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1232,8 +1234,8 @@ function CubicHermiteSpline(
 end
 
 """
-    PCHIPInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+    PCHIPInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a PCHIP Interpolation, which is a type of [`CubicHermiteSpline`](@ref) where the derivative values `du` are derived from the input data
 in such a way that the interpolation never overshoots the data. See [here](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/interp.pdf),
@@ -1250,9 +1252,9 @@ section 3.4 for more details.
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
@@ -1267,7 +1269,7 @@ end
 
 """
     QuinticHermiteSpline(ddu, du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, safetycopy = true)
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
 
 It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polynomial such that the value and the first and second derivative are equal to given values in the data points.
 
@@ -1284,9 +1286,9 @@ It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polyno
     are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
     `ExtrapolationType.linear` and `ExtrapolationType.extension`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
-    the possible options.
+    the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `cache_parameters`: precompute parameters at initialization for faster interpolation computations. Note: if activated, `u` and `t` should not be modified. Defaults to `false`.
   - `assume_linear_t`: boolean value to specify a faster index lookup behaviour for
     evenly-distributed abscissae. Alternatively, a numerical threshold may be specified
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index a691fbb2..a781acf3 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -11,7 +11,7 @@ end
 function _extrapolate_down(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
-        throw(DownExtrapolationError())
+        throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.constant
         slope = derivative(A, first(A.t))
         first(A.u) + slope * zero(t)
@@ -27,7 +27,7 @@ end
 function _extrapolate_up(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
-        throw(UpExtrapolationError())
+        throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.constant
         slope = derivative(A, last(A.t))
         last(A.u) + slope * zero(t)
diff --git a/test/derivative_tests.jl b/test/derivative_tests.jl
index df96b0fb..e9e33328 100644
--- a/test/derivative_tests.jl
+++ b/test/derivative_tests.jl
@@ -76,8 +76,9 @@ function test_derivatives(method; args = [], kwargs = [], name::String)
         @test_throws DataInterpolations.ExtrapolationError derivative(func, t[1] - 1.0)
         @test_throws DataInterpolations.ExtrapolationError derivative(func, t[end] + 1.0)
     else
-        @test_throws DataInterpolations.DownExtrapolationError derivative(func, t[1] - 1.0)
-        @test_throws DataInterpolations.UpExtrapolationError derivative(func, t[end] + 1.0)
+        @test_throws DataInterpolations.LeftExtrapolationError derivative(func, t[1] - 1.0)
+        @test_throws DataInterpolations.RightExtrapolationError derivative(
+            func, t[end] + 1.0)
     end
     @test_throws DataInterpolations.DerivativeNotFoundError derivative(
         func, t[1], 3)
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index 9ba616f4..7fa75f06 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -5,8 +5,8 @@ function test_extrapolation_errors(method, u, t)
     @test A.extrapolation_right == ExtrapolationType.none
     @test A.extrapolation_left == ExtrapolationType.none
     for (error_type, t_eval) in zip(
-        (DataInterpolations.DownExtrapolationError,
-            DataInterpolations.UpExtrapolationError),
+        (DataInterpolations.LeftExtrapolationError,
+            DataInterpolations.RightExtrapolationError),
         (first(t) - 1, last(t) + 1))
         @test_throws error_type A(t_eval)
         @test_throws error_type DataInterpolations.derivative(
diff --git a/test/integral_tests.jl b/test/integral_tests.jl
index c37d9d8d..09ba655b 100644
--- a/test/integral_tests.jl
+++ b/test/integral_tests.jl
@@ -49,10 +49,11 @@ function test_integral(method; args = [], kwargs = [], name::String)
         @test isapprox(qint, aint, atol = 1e-6, rtol = 1e-8)
     end
     func = method(args...; kwargs...)
-    @test_throws DataInterpolations.DownExtrapolationError integral(func, t[1] - 1.0)
-    @test_throws DataInterpolations.UpExtrapolationError integral(func, t[end] + 1.0)
-    @test_throws DataInterpolations.DownExtrapolationError integral(func, t[1] - 1.0, t[2])
-    @test_throws DataInterpolations.UpExtrapolationError integral(func, t[1], t[end] + 1.0)
+    @test_throws DataInterpolations.LeftExtrapolationError integral(func, t[1] - 1.0)
+    @test_throws DataInterpolations.RightExtrapolationError integral(func, t[end] + 1.0)
+    @test_throws DataInterpolations.LeftExtrapolationError integral(func, t[1] - 1.0, t[2])
+    @test_throws DataInterpolations.RightExtrapolationError integral(
+        func, t[1], t[end] + 1.0)
 end
 
 @testset "LinearInterpolation" begin
diff --git a/test/interpolation_tests.jl b/test/interpolation_tests.jl
index 3b374c00..83a0bef1 100644
--- a/test/interpolation_tests.jl
+++ b/test/interpolation_tests.jl
@@ -176,9 +176,9 @@ end
     @test A(-1.0) == -2.0
     @test A(11.0) == 22.0
     A = LinearInterpolation(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
-    @test_throws DataInterpolations.DownExtrapolationError A([-1.0, 11.0])
+    @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(11.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A([-1.0, 11.0])
 end
 
 @testset "Quadratic Interpolation" begin
@@ -275,8 +275,8 @@ end
     @test A(0.0) == -4.5
     @test A(5.0) == -7.5
     A = QuadraticInterpolation(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(0.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(5.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(0.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(5.0)
 end
 
 @testset "Lagrange Interpolation" begin
@@ -335,8 +335,8 @@ end
     @test A(0.0) == 0.0
     @test A(4.0) == 16.0
     A = LagrangeInterpolation(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(4.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(4.0)
 end
 
 @testset "Akima Interpolation" begin
@@ -366,8 +366,8 @@ end
     @test A(-1.0) ≈ -5.0
     @test A(11.0) ≈ -3.924742268041234
     A = AkimaInterpolation(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(11.0)
 end
 
 @testset "ConstantInterpolation" begin
@@ -496,8 +496,8 @@ end
     @test A(-1.0) == 1.0
     @test A(11.0) == 1.0
     A = ConstantInterpolation(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(11.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(11.0)
 
     # Test extrapolation with infs with regularly spaced t
     u = [1.67e7, 1.6867e7, 1.7034e7, 1.7201e7, 1.7368e7]
@@ -549,8 +549,8 @@ end
     @test A(-2.0) == 0.0
     @test A(2.0) == 6.0
     A = QuadraticSpline(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-2.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(2.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(-2.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(2.0)
 end
 
 @testset "CubicSpline Interpolation" begin
@@ -602,8 +602,8 @@ end
     @test A(-2.0) ≈ -1.0
     @test A(2.0) ≈ 5.0
     A = CubicSpline(u, t)
-    @test_throws DataInterpolations.DownExtrapolationError A(-2.0)
-    @test_throws DataInterpolations.UpExtrapolationError A(2.0)
+    @test_throws DataInterpolations.LeftExtrapolationError A(-2.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(2.0)
 
     @testset "AbstractMatrix" begin
         t = 0.1:0.1:1.0
@@ -647,8 +647,8 @@ end
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :Uniform, :Uniform)
-        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
+        @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.RightExtrapolationError A(300.0)
 
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
 
@@ -668,8 +668,8 @@ end
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
-        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
+        @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.RightExtrapolationError A(300.0)
 
         @testset "AbstractMatrix" begin
             t = 0.1:0.1:1.0
@@ -726,8 +726,8 @@ end
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineApprox(u, t, 2, 4, :Uniform, :Uniform)
-        @test_throws DataInterpolations.DownExtrapolationError A(-1.0)
-        @test_throws DataInterpolations.UpExtrapolationError A(300.0)
+        @test_throws DataInterpolations.LeftExtrapolationError A(-1.0)
+        @test_throws DataInterpolations.RightExtrapolationError A(300.0)
 
         @testset "AbstractMatrix" begin
             t = 0.1:0.1:1.0
diff --git a/test/regularization.jl b/test/regularization.jl
index 6d850475..a3f4ef1c 100644
--- a/test/regularization.jl
+++ b/test/regularization.jl
@@ -184,7 +184,7 @@ end
         uₒ, tₒ; alg = :fixed, extrapolation_right = ExtrapolationType.extension)
     @test A(10.0) == A.Aitp(10.0)
     A = RegularizationSmooth(uₒ, tₒ; alg = :fixed)
-    @test_throws DataInterpolations.UpExtrapolationError A(10.0)
+    @test_throws DataInterpolations.RightExtrapolationError A(10.0)
 end
 
 @testset "Type inference" begin

From 16766f62b54c5ea586caba8999e297c2dada0e59 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Fri, 22 Nov 2024 12:49:13 +0100
Subject: [PATCH 14/20] Interpolation POC

---
 docs/src/extrapolation_methods.md | 49 +++++++++++++++++++++++--------
 src/DataInterpolations.jl         |  2 +-
 src/interpolation_methods.jl      | 22 ++++++++++----
 src/interpolation_utils.jl        | 14 +++++++++
 4 files changed, 69 insertions(+), 18 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index 09f8f0ae..c9e35962 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -7,8 +7,8 @@ using DataInterpolations, Plots
 
 u = [0.86, 0.65, 0.44, 0.76, 0.73]
 t = [0.0022, 0.68, 1.41, 2.22, 2.46]
-t_eval_down = range(-1, first(t), length = 25)
-t_eval_up = range(last(t), 3.5, length = 25)
+t_eval_left = range(-1, first(t), length = 25)
+t_eval_right = range(last(t), 3.5, length = 25)
 A = QuadraticSpline(u, t)
 plot(A)
 ```
@@ -26,8 +26,8 @@ This extrapolation type extends the interpolation with the boundary values of th
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.constant)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
 
 ## `ExtrapolationType.linear`
@@ -37,8 +37,8 @@ This extrapolation type extends the interpolation with a linear continuation of
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.linear)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
 
 ## `ExtrapolationType.extension`
@@ -48,8 +48,33 @@ This extrapolation type extends the interpolation with a continuation of the exp
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+```
+
+## `ExtrapolationType.periodic`
+
+this extrapolation type extends the interpolation such that `A(t + T) == A(t)` for all `t`, where the period is given by `T = last(A.t) - first(A.t)`.
+
+```@example tutorial
+T = last(A.t) - first(A.t)
+t_eval_left = range(first(t) - 2T, first(t), length = 100)
+t_eval_right = range(last(t), last(t) + 2T, length = 100)
+A = QuadraticSpline(u,t; extrapolation = ExtrapolationType.periodic)
+plot(A)
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
+```
+
+## `ExtrapolationType.reflective`
+
+this extrapolation type extends the interpolation such that `A(t_ + t) == A(t_ - t)` for all `t_, t` such that `(t_ - first(A.t)) % T == 0` and `0 < t < T`, where `T = last(A.t) - first(A.t)`.
+
+```@example tutorial
+A = QuadraticSpline(u,t; extrapolation = ExtrapolationType.reflective)
+plot(A)
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
 
 ## Mixed extrapolation
@@ -57,9 +82,9 @@ plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
 You can also have different extrapolation types left and right of the data.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.constant,
-    extrapolation_right = ExtrapolationType.linear)
+A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.reflective,
+    extrapolation_right = ExtrapolationType.periodic)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index 962b21a9..e04ad136 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -11,7 +11,7 @@ using EnumX
 import FindFirstFunctions: searchsortedfirstcorrelated, searchsortedlastcorrelated,
                            Guesser
 
-@enumx ExtrapolationType none constant linear extension
+@enumx ExtrapolationType none constant linear extension periodic reflective
 
 include("parameter_caches.jl")
 include("interpolation_caches.jl")
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index a781acf3..c69deb49 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -18,9 +18,15 @@ function _extrapolate_down(A, t)
     elseif extrapolation_left == ExtrapolationType.linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
-    else
-        # extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
+    elseif extrapolation_left == ExtrapolationType.periodic
+        t_, _ = transformation_periodic(A, t)
+        _interpolate(A, t_, A.iguesser)
+    else
+        # extrapolation_left == ExtrapolationType.reflective
+        t_, _ = transformation_reflective(A, t)
+        _interpolate(A, t_, A.iguesser)
     end
 end
 
@@ -34,10 +40,16 @@ function _extrapolate_up(A, t)
     elseif extrapolation_right == ExtrapolationType.linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
-    else
-        # extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.extension
         _interpolate(A, t, A.iguesser)
-    end
+    elseif extrapolation_right == ExtrapolationType.periodic
+        t_, _ = transformation_periodic(A, t)
+        _interpolate(A, t_, A.iguesser)
+    else
+        # extrapolation_right == ExtrapolationType.reflective
+        t_, _ = transformation_reflective(A, t)
+        _interpolate(A, t_, A.iguesser)
+    end 
 end
 
 # Linear Interpolation
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index f12bfa07..8882a070 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -311,3 +311,17 @@ function munge_extrapolation(extrapolation, extrapolation_left, extrapolation_ri
         extrapolation, extrapolation
     end
 end
+
+function transformation_periodic(A, t)
+    Δt = last(A.t) - first(A.t)
+    n, t_ = fldmod(t - first(A.t), Δt)
+    t_ += first(A.t)
+    t_, n
+end
+
+function transformation_reflective(A, t)
+    Δt = last(A.t) - first(A.t)
+    n, t_ = fldmod(t - first(A.t), Δt)
+    t_ = isodd(n) ? last(A.t) - t_ : first(A.t) + t_
+    t_, n
+end
\ No newline at end of file

From 0c3b36055a850cfe36aab0e3d080e7ec867f41b0 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Fri, 22 Nov 2024 13:19:34 +0100
Subject: [PATCH 15/20] Derivatives POC

---
 src/derivatives.jl | 20 ++++++++++++++++----
 1 file changed, 16 insertions(+), 4 deletions(-)

diff --git a/src/derivatives.jl b/src/derivatives.jl
index da007025..1d790e66 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -22,13 +22,19 @@ function _extrapolate_derivative_down(A, t, order)
         typed_zero
     elseif extrapolation_left == ExtrapolationType.linear
         (order == 1) ? derivative(A, first(A.t)) : typed_zero
-    else
-        # extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
+    elseif extrapolation_left == ExtrapolationType.periodic
+        t_, _ = transformation_periodic(A, t)
+        derivative(A, t_, order)
+    else
+        # extrapolation_left == ExtrapolationType.reflective
+        t_, _ = transformation_reflective(A, t)
+        derivative(A, t_, order)
     end
 end
 
@@ -41,13 +47,19 @@ function _extrapolate_derivative_up(A, t, order)
         typed_zero
     elseif extrapolation_right == ExtrapolationType.linear
         (order == 1) ? derivative(A, last(A.t)) : typed_zero
-    else
-        # extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
+    elseif extrapolation_right == ExtrapolationType.periodic
+        t_, _ = transformation_periodic(A, t)
+        derivative(A, t_, order)
+    else
+        # extrapolation_right == ExtrapolationType.reflective
+        t_, _ = transformation_reflective(A, t)
+        derivative(A, t_, order)
     end
 end
 

From d547e32f76b20a27ff5d8e6bcfe85448a7f4844e Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Fri, 22 Nov 2024 13:53:57 +0100
Subject: [PATCH 16/20] Integrals POC

---
 src/integrals.jl           | 38 ++++++++++++++++++++++++++++++++++++++
 src/interpolation_utils.jl |  2 ++
 2 files changed, 40 insertions(+)

diff --git a/src/integrals.jl b/src/integrals.jl
index af2eb3bd..a8da0d3a 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -74,6 +74,25 @@ function _extrapolate_integral_down(A, t)
         (first(A.u) - slope * Δt / 2) * Δt
     elseif extrapolation_left == ExtrapolationType.extension
         _integral(A, 1, t, first(A.t))
+    elseif extrapolation_left == ExtrapolationType.periodic
+        t_, n = transformation_periodic(A, t)
+        out = -integral(A, t_)
+        if !iszero(n)
+            out -= n * integral(A, first(A.t), last(A.t))
+        end
+        out
+    else
+        # extrapolation_left == ExtrapolationType.reflective
+        t_, n = transformation_reflective(A, t)
+        out = if isodd(n)
+            -integral(A, t_, last(A.t))
+        else
+            -integral(A, t_)
+        end
+        if !iszero(n)
+            out -= n * integral(A, first(A.t), last(A.t))
+        end
+        out
     end
 end
 
@@ -89,6 +108,25 @@ function _extrapolate_integral_up(A, t)
         (last(A.u) + slope * Δt / 2) * Δt
     elseif extrapolation_right == ExtrapolationType.extension
         _integral(A, length(A.t) - 1, last(A.t), t)
+    elseif extrapolation_right == ExtrapolationType.periodic
+        t_, n = transformation_periodic(A, t)
+        out = integral(A, first(A.t), t_)
+        if !iszero(n)
+            out += n * integral(A, first(A.t), last(A.t))
+        end
+        out
+    else
+        # extrapolation_right == ExtrapolationType.reflective
+        t_, n = transformation_reflective(A, t)
+        out = if iseven(n)
+            integral(A, t_, last(A.t))
+        else
+            integral(A, t_)
+        end
+        if !iszero(n)
+            out += n * integral(A, first(A.t), last(A.t))
+        end
+        out
     end
 end
 
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 8882a070..fff61eca 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -316,6 +316,7 @@ function transformation_periodic(A, t)
     Δt = last(A.t) - first(A.t)
     n, t_ = fldmod(t - first(A.t), Δt)
     t_ += first(A.t)
+    (n > 0) && (n -= 1)
     t_, n
 end
 
@@ -323,5 +324,6 @@ function transformation_reflective(A, t)
     Δt = last(A.t) - first(A.t)
     n, t_ = fldmod(t - first(A.t), Δt)
     t_ = isodd(n) ? last(A.t) - t_ : first(A.t) + t_
+    (n > 0) && (n -= 1)
     t_, n
 end
\ No newline at end of file

From 6023946a81fa7f89cff1b9b286621e1a1e69c856 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Fri, 22 Nov 2024 15:03:43 +0100
Subject: [PATCH 17/20] Add tests + formatting

---
 docs/src/extrapolation_methods.md |  4 +-
 src/derivatives.jl                |  8 ++--
 src/integrals.jl                  |  5 ++-
 src/interpolation_methods.jl      |  2 +-
 src/interpolation_utils.jl        |  2 +-
 test/extrapolation_tests.jl       | 75 +++++++++++++++++--------------
 test/parameter_tests.jl           | 13 ++++++
 7 files changed, 67 insertions(+), 42 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index c9e35962..fbce5d0f 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -60,7 +60,7 @@ this extrapolation type extends the interpolation such that `A(t + T) == A(t)` f
 T = last(A.t) - first(A.t)
 t_eval_left = range(first(t) - 2T, first(t), length = 100)
 t_eval_right = range(last(t), last(t) + 2T, length = 100)
-A = QuadraticSpline(u,t; extrapolation = ExtrapolationType.periodic)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.periodic)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
@@ -71,7 +71,7 @@ plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 this extrapolation type extends the interpolation such that `A(t_ + t) == A(t_ - t)` for all `t_, t` such that `(t_ - first(A.t)) % T == 0` and `0 < t < T`, where `T = last(A.t) - first(A.t)`.
 
 ```@example tutorial
-A = QuadraticSpline(u,t; extrapolation = ExtrapolationType.reflective)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.reflective)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
diff --git a/src/derivatives.jl b/src/derivatives.jl
index 1d790e66..7ee8fe2e 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -33,8 +33,8 @@ function _extrapolate_derivative_down(A, t, order)
         derivative(A, t_, order)
     else
         # extrapolation_left == ExtrapolationType.reflective
-        t_, _ = transformation_reflective(A, t)
-        derivative(A, t_, order)
+        t_, n = transformation_reflective(A, t)
+        isodd(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
     end
 end
 
@@ -58,8 +58,8 @@ function _extrapolate_derivative_up(A, t, order)
         derivative(A, t_, order)
     else
         # extrapolation_right == ExtrapolationType.reflective
-        t_, _ = transformation_reflective(A, t)
-        derivative(A, t_, order)
+        t_, n = transformation_reflective(A, t)
+        iseven(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
     end
 end
 
diff --git a/src/integrals.jl b/src/integrals.jl
index a8da0d3a..6948f8f9 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -52,7 +52,10 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
 
     # Complete intervals
     if A.cache_parameters
-        total += A.I[idx2] - A.I[idx1 + 1]
+        total += A.I[idx2 - 1]
+        if idx1 > 0
+            total -= A.I[idx1]
+        end
     else
         for idx in (idx1 + 1):(idx2 - 1)
             total += _integral(A, idx, A.t[idx], A.t[idx + 1])
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index c69deb49..a0437b02 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -49,7 +49,7 @@ function _extrapolate_up(A, t)
         # extrapolation_right == ExtrapolationType.reflective
         t_, _ = transformation_reflective(A, t)
         _interpolate(A, t_, A.iguesser)
-    end 
+    end
 end
 
 # Linear Interpolation
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index fff61eca..3f1e9682 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -326,4 +326,4 @@ function transformation_reflective(A, t)
     t_ = isodd(n) ? last(A.t) - t_ : first(A.t) + t_
     (n > 0) && (n -= 1)
     t_, n
-end
\ No newline at end of file
+end
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index 7fa75f06..fa12be1b 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -1,43 +1,53 @@
-using DataInterpolations
+using DataInterpolations, Test
+using ForwardDiff
+using QuadGK
 
-function test_extrapolation_errors(method, u, t)
-    A = method(u, t)
-    @test A.extrapolation_right == ExtrapolationType.none
-    @test A.extrapolation_left == ExtrapolationType.none
-    for (error_type, t_eval) in zip(
-        (DataInterpolations.LeftExtrapolationError,
-            DataInterpolations.RightExtrapolationError),
-        (first(t) - 1, last(t) + 1))
-        @test_throws error_type A(t_eval)
-        @test_throws error_type DataInterpolations.derivative(
-            A, t_eval)
-        @test_throws error_type DataInterpolations.derivative(
-            A, t_eval, 2)
-        @test_throws error_type DataInterpolations.integral(
-            A, t_eval)
+function test_extrapolation(method, u, t)
+    @testset "Extrapolation errors" begin
+        A = method(u, t)
+        @test A.extrapolation_right == ExtrapolationType.none
+        @test A.extrapolation_left == ExtrapolationType.none
+        for (error_type, t_eval) in zip(
+            (DataInterpolations.LeftExtrapolationError,
+                DataInterpolations.RightExtrapolationError),
+            (first(t) - 1, last(t) + 1))
+            @test_throws error_type A(t_eval)
+            @test_throws error_type DataInterpolations.derivative(
+                A, t_eval)
+            @test_throws error_type DataInterpolations.derivative(
+                A, t_eval, 2)
+            @test_throws error_type DataInterpolations.integral(
+                A, t_eval)
+        end
     end
-end
 
-function test_constant_extrapolation(method, u, t)
-    A = method(u, t; extrapolation_left = ExtrapolationType.constant,
-        extrapolation_right = ExtrapolationType.constant)
-    t_lower = first(t) - 1
-    t_upper = last(t) + 1
-    @test A(t_lower) == first(u)
-    @test A(t_upper) == last(u)
-    @test DataInterpolations.derivative(A, t_lower) == 0
-    @test DataInterpolations.derivative(A, t_upper) == 0
-    @test DataInterpolations.integral(A, t_lower, first(t)) ≈
-          first(u) * (first(t) - t_lower)
-    @test DataInterpolations.integral(A, last(t), t_upper) ≈ last(u) * (t_upper - last(t))
+    for extrapolation_type in instances(ExtrapolationType.T)
+        (extrapolation_type == ExtrapolationType.none) && continue
+        @testset "extrapolation type $extrapolation_type" begin
+            A = method(u, t; extrapolation = extrapolation_type)
+
+            t_eval = first(t) - 1.5
+            @test DataInterpolations.derivative(A, t_eval) ≈
+                  ForwardDiff.derivative(A, t_eval)
+
+            t_eval = last(t) + 1.5
+            @test DataInterpolations.derivative(A, t_eval) ≈
+                  ForwardDiff.derivative(A, t_eval)
+
+            T = last(A.t) - first(A.t)
+            t1 = first(t) - 2.5T
+            t2 = last(t) + 3.5T
+            @test DataInterpolations.integral(A, t1, t2) ≈
+                  quadgk(A, t1, t2; atol = 1e-12, rtol = 1e-12)[1]
+        end
+    end
 end
 
 @testset "Linear Interpolation" begin
     u = [1.0, 2.0]
     t = [1.0, 2.0]
 
-    test_extrapolation_errors(LinearInterpolation, u, t)
-    test_constant_extrapolation(LinearInterpolation, u, t)
+    test_extrapolation(LinearInterpolation, u, t)
 
     for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
         # Down extrapolation
@@ -64,8 +74,7 @@ end
     u = [1.0, 3.0, 2.0]
     t = 1:3
 
-    test_extrapolation_errors(QuadraticInterpolation, u, t)
-    test_constant_extrapolation(LinearInterpolation, u, t)
+    test_extrapolation(QuadraticInterpolation, u, t)
 
     # Linear down extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.linear)
diff --git a/test/parameter_tests.jl b/test/parameter_tests.jl
index 3afe2a17..1f8ff574 100644
--- a/test/parameter_tests.jl
+++ b/test/parameter_tests.jl
@@ -1,10 +1,18 @@
 using DataInterpolations
 
+function test_cached_integration(method, args...)
+    A_c = method(args...; cache_parameters = true)
+    A_nc = method(args...; cache_parameters = false)
+    @test DataInterpolations.integral(A_c, last(A_c.t)) ≈
+          DataInterpolations.integral(A_nc, last(A_nc.t))
+end
+
 @testset "Linear Interpolation" begin
     u = [1.0, 5.0, 3.0, 4.0, 4.0]
     t = collect(1:5)
     A = LinearInterpolation(u, t; cache_parameters = true)
     @test A.p.slope ≈ [4.0, -2.0, 1.0, 0.0]
+    test_cached_integration(LinearInterpolation, u, t)
 end
 
 @testset "Quadratic Interpolation" begin
@@ -13,6 +21,7 @@ end
     A = QuadraticInterpolation(u, t; cache_parameters = true)
     @test A.p.α ≈ [-3.0, 1.5, -0.5, -0.5]
     @test A.p.β ≈ [7.0, -3.5, 1.5, 0.5]
+    test_cached_integration(QuadraticInterpolation, u, t)
 end
 
 @testset "Quadratic Spline" begin
@@ -21,6 +30,7 @@ end
     A = QuadraticSpline(u, t; cache_parameters = true)
     @test A.p.α ≈ [-9.5, 3.5, -0.5, -0.5]
     @test A.p.β ≈ [13.5, -5.5, 1.5, 0.5]
+    test_cached_integration(QuadraticSpline, u, t)
 end
 
 @testset "Cubic Spline" begin
@@ -29,6 +39,7 @@ end
     A = CubicSpline(u, t; cache_parameters = true)
     @test A.p.c₁ ≈ [6.839285714285714, 1.642857142857143, 4.589285714285714, 4.0]
     @test A.p.c₂ ≈ [1.0, 6.839285714285714, 1.642857142857143, 4.589285714285714]
+    test_cached_integration(CubicSpline, u, t)
 end
 
 @testset "Cubic Hermite Spline" begin
@@ -38,6 +49,7 @@ end
     A = CubicHermiteSpline(du, u, t; cache_parameters = true)
     @test A.p.c₁ ≈ [-1.0, -5.0, -5.0, -8.0]
     @test A.p.c₂ ≈ [0.0, 13.0, 12.0, 9.0]
+    test_cached_integration(CubicHermiteSpline, du, u, t)
 end
 
 @testset "Quintic Hermite Spline" begin
@@ -49,4 +61,5 @@ end
     @test A.p.c₁ ≈ [-1.0, -6.5, -8.0, -10.0]
     @test A.p.c₂ ≈ [1.0, 19.5, 20.0, 19.0]
     @test A.p.c₃ ≈ [1.5, -37.5, -37.0, -26.5]
+    test_cached_integration(QuinticHermiteSpline, ddu, du, u, t)
 end

From 2af470598a44daa752c57205d94a956e298ef710 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Sun, 24 Nov 2024 16:11:59 +0100
Subject: [PATCH 18/20] comments addressed

---
 docs/src/extrapolation_methods.md | 20 ++++++++++----------
 src/derivatives.jl                | 18 ++++++++----------
 src/integrals.jl                  | 12 ++++++------
 src/interpolation_methods.jl      |  8 ++++----
 test/extrapolation_tests.jl       | 12 ++++++------
 5 files changed, 34 insertions(+), 36 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index 09f8f0ae..c442a7f9 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -7,8 +7,8 @@ using DataInterpolations, Plots
 
 u = [0.86, 0.65, 0.44, 0.76, 0.73]
 t = [0.0022, 0.68, 1.41, 2.22, 2.46]
-t_eval_down = range(-1, first(t), length = 25)
-t_eval_up = range(last(t), 3.5, length = 25)
+t_eval_left = range(-1, first(t), length = 25)
+t_eval_right = range(last(t), 3.5, length = 25)
 A = QuadraticSpline(u, t)
 plot(A)
 ```
@@ -26,8 +26,8 @@ This extrapolation type extends the interpolation with the boundary values of th
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.constant)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.linear`
@@ -37,8 +37,8 @@ This extrapolation type extends the interpolation with a linear continuation of
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.linear)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## `ExtrapolationType.extension`
@@ -48,8 +48,8 @@ This extrapolation type extends the interpolation with a continuation of the exp
 ```@example tutorial
 A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
 ## Mixed extrapolation
@@ -60,6 +60,6 @@ You can also have different extrapolation types left and right of the data.
 A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.constant,
     extrapolation_right = ExtrapolationType.linear)
 plot(A)
-plot!(t_eval_down, A.(t_eval_down); label = "extrapolation down")
-plot!(t_eval_up, A.(t_eval_up); label = "extrapolation up")
+plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
+plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
diff --git a/src/derivatives.jl b/src/derivatives.jl
index da007025..30994075 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -1,9 +1,9 @@
 function derivative(A, t, order = 1)
     (order ∉ (1, 2)) && throw(DerivativeNotFoundError())
     if t < first(A.t)
-        _extrapolate_derivative_down(A, t, order)
+        _extrapolate_derivative_left(A, t, order)
     elseif t > last(A.t)
-        _extrapolate_derivative_up(A, t, order)
+        _extrapolate_derivative_right(A, t, order)
     else
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
@@ -13,15 +13,14 @@ function derivative(A, t, order = 1)
     end
 end
 
-function _extrapolate_derivative_down(A, t, order)
+function _extrapolate_derivative_left(A, t, order)
     (; extrapolation_left) = A
-    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
     elseif extrapolation_left == ExtrapolationType.constant
-        typed_zero
+        zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_left == ExtrapolationType.linear
-        (order == 1) ? derivative(A, first(A.t)) : typed_zero
+        (order == 1) ? derivative(A, first(A.t)) : zero(first(A.u) / one(A.t[1]))
     else
         # extrapolation_left == ExtrapolationType.extension
         iguess = A.iguesser
@@ -32,15 +31,14 @@ function _extrapolate_derivative_down(A, t, order)
     end
 end
 
-function _extrapolate_derivative_up(A, t, order)
+function _extrapolate_derivative_right(A, t, order)
     (; extrapolation_right) = A
-    typed_zero = zero(first(A.u) / one(A.t[1]))
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
     elseif extrapolation_right == ExtrapolationType.constant
-        typed_zero
+        zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_right == ExtrapolationType.linear
-        (order == 1) ? derivative(A, last(A.t)) : typed_zero
+        (order == 1) ? derivative(A, last(A.t)) : zero(first(A.u) / one(A.t[1]))
     else
         # extrapolation_right == ExtrapolationType.extension
         iguess = A.iguesser
diff --git a/src/integrals.jl b/src/integrals.jl
index af2eb3bd..1da09b83 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -24,11 +24,11 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     if t1 < first(A.t)
         if t2 < first(A.t)
             # If interval is entirely below data
-            return _extrapolate_integral_down(A, t2) - extrapolate_integral_down(A.t1)
+            return _extrapolate_integral_left(A, t2) - extrapolate_integral_left(A.t1)
         end
 
         idx1 -= 1 # Make sure lowest complete interval is included
-        total += _extrapolate_integral_down(A, t1)
+        total += _extrapolate_integral_left(A, t1)
     else
         total += _integral(A, idx1, t1, A.t[idx1 + 1])
     end
@@ -37,11 +37,11 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     if t2 > last(A.t)
         if t1 > last(A.t)
             # If interval is entirely above data
-            return _extrapolate_integral_up(A, t2) - extrapolate_integral_up(A.t, t1)
+            return _extrapolate_integral_right(A, t2) - extrapolate_integral_right(A.t, t1)
         end
 
         idx2 += 1 # Make sure highest complete interval is included
-        total += _extrapolate_integral_up(A, t2)
+        total += _extrapolate_integral_right(A, t2)
     else
         total += _integral(A, idx2, A.t[idx2], t2)
     end
@@ -62,7 +62,7 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     return total
 end
 
-function _extrapolate_integral_down(A, t)
+function _extrapolate_integral_left(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
@@ -77,7 +77,7 @@ function _extrapolate_integral_down(A, t)
     end
 end
 
-function _extrapolate_integral_up(A, t)
+function _extrapolate_integral_right(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index a781acf3..266c80c0 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -1,14 +1,14 @@
 function _interpolate(A, t)
     if t < first(A.t)
-        _extrapolate_down(A, t)
+        _extrapolate_left(A, t)
     elseif t > last(A.t)
-        _extrapolate_up(A, t)
+        _extrapolate_right(A, t)
     else
         _interpolate(A, t, A.iguesser)
     end
 end
 
-function _extrapolate_down(A, t)
+function _extrapolate_left(A, t)
     (; extrapolation_left) = A
     if extrapolation_left == ExtrapolationType.none
         throw(LeftExtrapolationError())
@@ -24,7 +24,7 @@ function _extrapolate_down(A, t)
     end
 end
 
-function _extrapolate_up(A, t)
+function _extrapolate_right(A, t)
     (; extrapolation_right) = A
     if extrapolation_right == ExtrapolationType.none
         throw(RightExtrapolationError())
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index 7fa75f06..0429c540 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -40,7 +40,7 @@ end
     test_constant_extrapolation(LinearInterpolation, u, t)
 
     for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
-        # Down extrapolation
+        # Left extrapolation
         A = LinearInterpolation(u, t; extrapolation_left = extrapolation_type)
         t_eval = 0.0
         @test A(t_eval) == 0.0
@@ -49,7 +49,7 @@ end
         @test DataInterpolations.integral(A, t_eval) == -0.5
         t_eval = 3.0
 
-        # Up extrapolation
+        # Right extrapolation
         A = LinearInterpolation(u, t; extrapolation_right = extrapolation_type)
         t_eval = 3.0
         @test A(t_eval) == 3.0
@@ -67,7 +67,7 @@ end
     test_extrapolation_errors(QuadraticInterpolation, u, t)
     test_constant_extrapolation(LinearInterpolation, u, t)
 
-    # Linear down extrapolation
+    # Linear left extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.linear)
     t_eval = 0.0
     @test A(t_eval) ≈ -2.5
@@ -75,7 +75,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
     @test DataInterpolations.integral(A, t_eval) ≈ 0.75
 
-    # Linear up extrapolation
+    # Linear right extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.linear)
     t_eval = 4.0
     @test A(t_eval) ≈ -0.5
@@ -83,7 +83,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == 0.0
     @test DataInterpolations.integral(A, t[end], t_eval) ≈ 0.75
 
-    # Extension down extrapolation
+    # Extension left extrapolation
     f = t -> (-3t^2 + 13t - 8) / 2
     df = t -> (-6t + 13) / 2
     A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.extension)
@@ -93,7 +93,7 @@ end
     @test DataInterpolations.derivative(A, t_eval, 2) == -3
     @test DataInterpolations.integral(A, t_eval) ≈ 1.25
 
-    # Extension up extrapolation
+    # Extension right extrapolation
     A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.extension)
     t_eval = 4.0
     @test A(t_eval) ≈ -2.0

From e0011f2a0ddf17c4d69aace7d7d7cdd187719635 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Mon, 25 Nov 2024 14:28:14 +0100
Subject: [PATCH 19/20] fix merge error

---
 src/derivatives.jl | 6 ++----
 1 file changed, 2 insertions(+), 4 deletions(-)

diff --git a/src/derivatives.jl b/src/derivatives.jl
index e7ed9cb3..800077a3 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -21,8 +21,7 @@ function _extrapolate_derivative_left(A, t, order)
         zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_left == ExtrapolationType.linear
         (order == 1) ? derivative(A, first(A.t)) : zero(first(A.u) / one(A.t[1]))
-    else
-        # extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
@@ -46,8 +45,7 @@ function _extrapolate_derivative_right(A, t, order)
         zero(first(A.u) / one(A.t[1]))
     elseif extrapolation_right == ExtrapolationType.linear
         (order == 1) ? derivative(A, last(A.t)) : zero(first(A.u) / one(A.t[1]))
-    else
-        # extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin

From 120e56fbbc46fef3e8358e0f2f8c22a035320087 Mon Sep 17 00:00:00 2001
From: Bart de Koning <bart123-4@hotmail.com>
Date: Tue, 26 Nov 2024 07:57:11 +0100
Subject: [PATCH 20/20] Capitalize extrapolation types

---
 docs/src/extrapolation_methods.md             |  26 +--
 docs/src/interface.md                         |   4 +-
 ...ataInterpolationsRegularizationToolsExt.jl |  28 +--
 src/DataInterpolations.jl                     |   6 +-
 src/derivatives.jl                            |  24 +--
 src/integrals.jl                              |  24 +--
 src/interpolation_caches.jl                   | 190 +++++++++---------
 src/interpolation_methods.jl                  |  24 +--
 src/interpolation_utils.jl                    |   2 +-
 test/derivative_tests.jl                      |  10 +-
 test/extrapolation_tests.jl                   |  16 +-
 test/integral_inverse_tests.jl                |   2 +-
 test/integral_tests.jl                        |   4 +-
 test/interface.jl                             |   4 +-
 test/interpolation_tests.jl                   |  94 ++++-----
 test/regularization.jl                        |   2 +-
 test/zygote_tests.jl                          |   4 +-
 17 files changed, 232 insertions(+), 232 deletions(-)

diff --git a/docs/src/extrapolation_methods.md b/docs/src/extrapolation_methods.md
index 488746e8..7344b9fe 100644
--- a/docs/src/extrapolation_methods.md
+++ b/docs/src/extrapolation_methods.md
@@ -15,44 +15,44 @@ plot(A)
 
 Extrapolation behavior can be set left and right of the data simultaneously with the `extension` keyword, or left and right separately with the `extrapolation_left` and `extrapolation_right` keywords respectively.
 
-## `ExtrapolationType.none`
+## `ExtrapolationType.None`
 
 This extrapolation type will throw an error when the input `t` is beyond the data in the specified direction.
 
-## `ExtrapolationType.constant`
+## `ExtrapolationType.Constant`
 
 This extrapolation type extends the interpolation with the boundary values of the data `u`.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.constant)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Constant)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
-## `ExtrapolationType.linear`
+## `ExtrapolationType.Linear`
 
 This extrapolation type extends the interpolation with a linear continuation of the interpolation, making it $C^1$ smooth at the data boundaries.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.linear)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Linear)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
 ```
 
-## `ExtrapolationType.extension`
+## `ExtrapolationType.Extension`
 
 This extrapolation type extends the interpolation with a continuation of the expression for the interpolation at the boundary intervals for maximum smoothness.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
 
-## `ExtrapolationType.periodic`
+## `ExtrapolationType.Periodic`
 
 this extrapolation type extends the interpolation such that `A(t + T) == A(t)` for all `t`, where the period is given by `T = last(A.t) - first(A.t)`.
 
@@ -60,18 +60,18 @@ this extrapolation type extends the interpolation such that `A(t + T) == A(t)` f
 T = last(A.t) - first(A.t)
 t_eval_left = range(first(t) - 2T, first(t), length = 100)
 t_eval_right = range(last(t), last(t) + 2T, length = 100)
-A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.periodic)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Periodic)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 ```
 
-## `ExtrapolationType.reflective`
+## `ExtrapolationType.Reflective`
 
 this extrapolation type extends the interpolation such that `A(t_ + t) == A(t_ - t)` for all `t_, t` such that `(t_ - first(A.t)) % T == 0` and `0 < t < T`, where `T = last(A.t) - first(A.t)`.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.reflective)
+A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Reflective)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation down")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
@@ -82,8 +82,8 @@ plot!(t_eval_right, A.(t_eval_right); label = "extrapolation up")
 You can also have different extrapolation types left and right of the data.
 
 ```@example tutorial
-A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.reflective,
-    extrapolation_right = ExtrapolationType.periodic)
+A = QuadraticSpline(u, t; extrapolation_left = ExtrapolationType.Reflective,
+    extrapolation_right = ExtrapolationType.Periodic)
 plot(A)
 plot!(t_eval_left, A.(t_eval_left); label = "extrapolation left")
 plot!(t_eval_right, A.(t_eval_right); label = "extrapolation right")
diff --git a/docs/src/interface.md b/docs/src/interface.md
index 21bfd27a..738287ee 100644
--- a/docs/src/interface.md
+++ b/docs/src/interface.md
@@ -17,7 +17,7 @@ t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
 
 All interpolation methods return an object from which we can compute the value of the dependent variable at any time point.
 
-We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolation = ExtrapolationType.extension` keyword if we want to allow the interpolation to go beyond the range of the timepoints in the positive `t` direction. The default value is `extrapolation = ExtrapolationType.none`. For more information on extrapolation see [Extrapolation methods](extrapolation_methods.md).
+We will use the `CubicSpline` method for demonstration, but the API is the same for all the methods. We can also pass the `extrapolation = ExtrapolationType.Extension` keyword if we want to allow the interpolation to go beyond the range of the timepoints in the positive `t` direction. The default value is `extrapolation = ExtrapolationType.None`. For more information on extrapolation see [Extrapolation methods](extrapolation_methods.md).
 
 ```@example interface
 A1 = CubicSpline(u, t)
@@ -25,7 +25,7 @@ A1 = CubicSpline(u, t)
 # For interpolation do, A(t)
 A1(100.0)
 
-A2 = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
+A2 = CubicSpline(u, t; extrapolation = ExtrapolationType.Extension)
 
 # Extrapolation
 A2(300.0)
diff --git a/ext/DataInterpolationsRegularizationToolsExt.jl b/ext/DataInterpolationsRegularizationToolsExt.jl
index 84693c49..cf0e1de3 100644
--- a/ext/DataInterpolationsRegularizationToolsExt.jl
+++ b/ext/DataInterpolationsRegularizationToolsExt.jl
@@ -70,8 +70,8 @@ A = RegularizationSmooth(u, t, t̂, wls, wr, d; λ = 1.0, alg = :gcv_svd)
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
         λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     M = _mapping_matrix(t̂, t)
     Wls½ = LA.diagm(sqrt.(wls))
@@ -90,8 +90,8 @@ A = RegularizationSmooth(u, t, d; λ = 1.0, alg = :gcv_svd, extrapolate = false)
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, d::Int = 2;
         λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -122,8 +122,8 @@ A = RegularizationSmooth(u, t, t̂, d; λ = 1.0, alg = :gcv_svd, extrapolate = f
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
@@ -153,8 +153,8 @@ A = RegularizationSmooth(u, t, t̂, wls, d; λ = 1.0, alg = :gcv_svd, extrapolat
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::AbstractVector,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     N, N̂ = length(t), length(t̂)
     M = _mapping_matrix(t̂, t)
@@ -185,8 +185,8 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, d::Int = 2; λ::Real = 1.0,
-        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        alg::Symbol = :gcv_svd, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -219,8 +219,8 @@ A = RegularizationSmooth(
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::AbstractVector, wr::AbstractVector, d::Int = 2;
         λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
@@ -252,8 +252,8 @@ A = RegularizationSmooth(
 """
 function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Nothing,
         wls::Symbol, d::Int = 2; λ::Real = 1.0, alg::Symbol = :gcv_svd,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     u, t = munge_data(u, t)
     t̂ = t
     N = length(t)
diff --git a/src/DataInterpolations.jl b/src/DataInterpolations.jl
index e04ad136..22dc7345 100644
--- a/src/DataInterpolations.jl
+++ b/src/DataInterpolations.jl
@@ -11,7 +11,7 @@ using EnumX
 import FindFirstFunctions: searchsortedfirstcorrelated, searchsortedlastcorrelated,
                            Guesser
 
-@enumx ExtrapolationType none constant linear extension periodic reflective
+@enumx ExtrapolationType None Constant Linear Extension Periodic Reflective
 
 include("parameter_caches.jl")
 include("interpolation_caches.jl")
@@ -64,13 +64,13 @@ function Base.showerror(io::IO, ::ExtrapolationError)
     print(io, EXTRAPOLATION_ERROR)
 end
 
-const LEFT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t < first(A.t) as the `extrapolation_left` kwarg passed was `ExtrapolationType.none`"
+const LEFT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t < first(A.t) as the `extrapolation_left` kwarg passed was `ExtrapolationType.None`"
 struct LeftExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::LeftExtrapolationError)
     print(io, LEFT_EXTRAPOLATION_ERROR)
 end
 
-const RIGHT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t > last(A.t) as the `extrapolation_tight` kwarg passed was `ExtrapolationType.none`"
+const RIGHT_EXTRAPOLATION_ERROR = "Cannot extrapolate for t > last(A.t) as the `extrapolation_tight` kwarg passed was `ExtrapolationType.None`"
 struct RightExtrapolationError <: Exception end
 function Base.showerror(io::IO, ::RightExtrapolationError)
     print(io, RIGHT_EXTRAPOLATION_ERROR)
diff --git a/src/derivatives.jl b/src/derivatives.jl
index 800077a3..a81ef368 100644
--- a/src/derivatives.jl
+++ b/src/derivatives.jl
@@ -15,23 +15,23 @@ end
 
 function _extrapolate_derivative_left(A, t, order)
     (; extrapolation_left) = A
-    if extrapolation_left == ExtrapolationType.none
+    if extrapolation_left == ExtrapolationType.None
         throw(LeftExtrapolationError())
-    elseif extrapolation_left == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.Constant
         zero(first(A.u) / one(A.t[1]))
-    elseif extrapolation_left == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.Linear
         (order == 1) ? derivative(A, first(A.t)) : zero(first(A.u) / one(A.t[1]))
-    elseif extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.Extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
-    elseif extrapolation_left == ExtrapolationType.periodic
+    elseif extrapolation_left == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
         derivative(A, t_, order)
     else
-        # extrapolation_left == ExtrapolationType.reflective
+        # extrapolation_left == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
         isodd(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
     end
@@ -39,23 +39,23 @@ end
 
 function _extrapolate_derivative_right(A, t, order)
     (; extrapolation_right) = A
-    if extrapolation_right == ExtrapolationType.none
+    if extrapolation_right == ExtrapolationType.None
         throw(RightExtrapolationError())
-    elseif extrapolation_right == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.Constant
         zero(first(A.u) / one(A.t[1]))
-    elseif extrapolation_right == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.Linear
         (order == 1) ? derivative(A, last(A.t)) : zero(first(A.u) / one(A.t[1]))
-    elseif extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.Extension
         iguess = A.iguesser
         (order == 1) ? _derivative(A, t, iguess) :
         ForwardDiff.derivative(t -> begin
                 _derivative(A, t, iguess)
             end, t)
-    elseif extrapolation_right == ExtrapolationType.periodic
+    elseif extrapolation_right == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
         derivative(A, t_, order)
     else
-        # extrapolation_right == ExtrapolationType.reflective
+        # extrapolation_right == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
         iseven(n) ? -derivative(A, t_, order) : derivative(A, t_, order)
     end
diff --git a/src/integrals.jl b/src/integrals.jl
index baabc634..41e52e4a 100644
--- a/src/integrals.jl
+++ b/src/integrals.jl
@@ -67,17 +67,17 @@ end
 
 function _extrapolate_integral_left(A, t)
     (; extrapolation_left) = A
-    if extrapolation_left == ExtrapolationType.none
+    if extrapolation_left == ExtrapolationType.None
         throw(LeftExtrapolationError())
-    elseif extrapolation_left == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.Constant
         first(A.u) * (first(A.t) - t)
-    elseif extrapolation_left == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.Linear
         slope = derivative(A, first(A.t))
         Δt = first(A.t) - t
         (first(A.u) - slope * Δt / 2) * Δt
-    elseif extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.Extension
         _integral(A, 1, t, first(A.t))
-    elseif extrapolation_left == ExtrapolationType.periodic
+    elseif extrapolation_left == ExtrapolationType.Periodic
         t_, n = transformation_periodic(A, t)
         out = -integral(A, t_)
         if !iszero(n)
@@ -85,7 +85,7 @@ function _extrapolate_integral_left(A, t)
         end
         out
     else
-        # extrapolation_left == ExtrapolationType.reflective
+        # extrapolation_left == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
         out = if isodd(n)
             -integral(A, t_, last(A.t))
@@ -101,17 +101,17 @@ end
 
 function _extrapolate_integral_right(A, t)
     (; extrapolation_right) = A
-    if extrapolation_right == ExtrapolationType.none
+    if extrapolation_right == ExtrapolationType.None
         throw(RightExtrapolationError())
-    elseif extrapolation_right == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.Constant
         last(A.u) * (t - last(A.t))
-    elseif extrapolation_right == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.Linear
         slope = derivative(A, last(A.t))
         Δt = t - last(A.t)
         (last(A.u) + slope * Δt / 2) * Δt
-    elseif extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.Extension
         _integral(A, length(A.t) - 1, last(A.t), t)
-    elseif extrapolation_right == ExtrapolationType.periodic
+    elseif extrapolation_right == ExtrapolationType.Periodic
         t_, n = transformation_periodic(A, t)
         out = integral(A, first(A.t), t_)
         if !iszero(n)
@@ -119,7 +119,7 @@ function _extrapolate_integral_right(A, t)
         end
         out
     else
-        # extrapolation_right == ExtrapolationType.reflective
+        # extrapolation_right == ExtrapolationType.Reflective
         t_, n = transformation_reflective(A, t)
         out = if iseven(n)
             integral(A, t_, last(A.t))
diff --git a/src/interpolation_caches.jl b/src/interpolation_caches.jl
index faeec06a..ad2e1eb0 100644
--- a/src/interpolation_caches.jl
+++ b/src/interpolation_caches.jl
@@ -1,6 +1,6 @@
 """
-    LinearInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none, 
-    extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, 
+    LinearInterpolation(u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.None, 
+    extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, 
     cache_parameters = false)
 
 It is the method of interpolating between the data points using a linear polynomial. For any point, two data points one each side are chosen and connected with a line.
@@ -14,8 +14,8 @@ Extrapolation extends the last linear polynomial on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -48,9 +48,9 @@ struct LinearInterpolation{uType, tType, IType, pType, T, N} <: AbstractInterpol
 end
 
 function LinearInterpolation(
-        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -65,8 +65,8 @@ function LinearInterpolation(
 end
 
 """
-    QuadraticInterpolation(u, t, mode = :Forward; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, 
+    QuadraticInterpolation(u, t, mode = :Forward; extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, 
         cache_parameters = false)
 
 It is the method of interpolating between the data points using quadratic polynomials. For any point, three data points nearby are taken to fit a quadratic polynomial.
@@ -81,8 +81,8 @@ Extrapolation extends the last quadratic polynomial on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -119,9 +119,9 @@ struct QuadraticInterpolation{uType, tType, IType, pType, T, N} <:
 end
 
 function QuadraticInterpolation(
-        u, t, mode; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t, mode; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -140,8 +140,8 @@ function QuadraticInterpolation(u, t; kwargs...)
 end
 
 """
-    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation::ExtrapolationType.T = ExtrapolationType.none, 
-    extrapolation_left::ExtrapolationType.T = ExtrapolationType.none, extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    LagrangeInterpolation(u, t, n = length(t) - 1; extrapolation::ExtrapolationType.T = ExtrapolationType.None, 
+    extrapolation_left::ExtrapolationType.T = ExtrapolationType.None, extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
 
 It is the method of interpolation using Lagrange polynomials of (k-1)th order passing through all the data points where k is the number of data points.
 
@@ -154,8 +154,8 @@ It is the method of interpolation using Lagrange polynomials of (k-1)th order pa
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -190,9 +190,9 @@ end
 
 function LagrangeInterpolation(
         u, t, n = length(t) - 1;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -203,8 +203,8 @@ function LagrangeInterpolation(
 end
 
 """
-    AkimaInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    AkimaInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false)
 
 It is a spline interpolation built from cubic polynomials. It forms a continuously differentiable function. For more details, refer: [https://en.wikipedia.org/wiki/Akima_spline](https://en.wikipedia.org/wiki/Akima_spline).
 Extrapolation extends the last cubic polynomial on each side.
@@ -217,8 +217,8 @@ Extrapolation extends the last cubic polynomial on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -264,9 +264,9 @@ struct AkimaInterpolation{uType, tType, IType, bType, cType, dType, T, N} <:
 end
 
 function AkimaInterpolation(
-        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -300,8 +300,8 @@ function AkimaInterpolation(
 end
 
 """
-    ConstantInterpolation(u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    ConstantInterpolation(u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false)
 
 It is the method of interpolating using a constant polynomial. For any point, two adjacent data points are found on either side (left and right). The value at that point depends on `dir`.
 If it is `:left`, then the value at the left point is chosen and if it is `:right`, the value at the right point is chosen.
@@ -316,8 +316,8 @@ Extrapolation extends the last constant polynomial at the end points on each sid
 
   - `dir`: indicates which value should be used for interpolation (`:left` or `:right`).
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -351,9 +351,9 @@ struct ConstantInterpolation{uType, tType, IType, T, N} <: AbstractInterpolation
 end
 
 function ConstantInterpolation(
-        u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
+        u, t; dir = :left, extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         cache_parameters = false, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
@@ -367,8 +367,8 @@ function ConstantInterpolation(
 end
 
 """
-    QuadraticSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    QuadraticSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false)
 
 It is a spline interpolation using piecewise quadratic polynomials between each pair of data points. Its first derivative is also continuous.
 Extrapolation extends the last quadratic polynomial on each side.
@@ -381,8 +381,8 @@ Extrapolation extends the last quadratic polynomial on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -430,9 +430,9 @@ struct QuadraticSpline{uType, tType, IType, pType, kType, cType, scType, T, N} <
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         cache_parameters = false, assume_linear_t = 1e-2) where {uType <:
                                                                  AbstractVector{<:Number}}
     extrapolation_left, extrapolation_right = munge_extrapolation(
@@ -455,9 +455,9 @@ function QuadraticSpline(
 end
 
 function QuadraticSpline(
-        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
     extrapolation_left, extrapolation_right = munge_extrapolation(
@@ -490,8 +490,8 @@ function QuadraticSpline(
 end
 
 """
-    CubicSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    CubicSpline(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false)
 
 It is a spline interpolation using piecewise cubic polynomials between each pair of data points. Its first and second derivative is also continuous.
 Second derivative on both ends are zero, which are also called "natural" boundary conditions. Extrapolation extends the last cubic polynomial on each side.
@@ -504,8 +504,8 @@ Second derivative on both ends are zero, which are also called "natural" boundar
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -551,9 +551,9 @@ struct CubicSpline{uType, tType, IType, pType, hType, zType, T, N} <:
 end
 
 function CubicSpline(u::uType,
-        t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector{<:Number}}
     extrapolation_left, extrapolation_right = munge_extrapolation(
@@ -587,8 +587,8 @@ end
 
 function CubicSpline(u::uType,
         t;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractArray{T, N}} where {T, N}
     extrapolation_left, extrapolation_right = munge_extrapolation(
@@ -625,9 +625,9 @@ function CubicSpline(u::uType,
 end
 
 function CubicSpline(
-        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false,
+        u::uType, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false,
         assume_linear_t = 1e-2) where {uType <:
                                        AbstractVector}
     extrapolation_left, extrapolation_right = munge_extrapolation(
@@ -657,8 +657,8 @@ function CubicSpline(
 end
 
 """
-    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
 
 It is a curve defined by the linear combination of `n` basis functions of degree `d` where `n` is the number of data points. For more information, refer [https://pages.mtu.edu/~shene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html](https://pages.mtu.edu/%7Eshene/COURSES/cs3621/NOTES/spline/B-spline/bspline-curve.html).
 Extrapolation is a constant polynomial of the end points on each side.
@@ -674,8 +674,8 @@ Extrapolation is a constant polynomial of the end points on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -734,9 +734,9 @@ end
 
 function BSplineInterpolation(
         u::AbstractVector, t, d, pVecType, knotVecType;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -809,9 +809,9 @@ end
 
 function BSplineInterpolation(
         u::AbstractArray{T, N}, t, d, pVecType, knotVecType;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         assume_linear_t = 1e-2) where {T, N}
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
@@ -887,8 +887,8 @@ function BSplineInterpolation(
 end
 
 """
-    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
 
 It is a regression based B-spline. The argument choices are the same as the `BSplineInterpolation`, with the additional parameter `h < length(t)` which is the number of control points to use, with smaller `h` indicating more smoothing.
 For more information, refer [http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf](http://www.cad.zju.edu.cn/home/zhx/GM/009/00-bsia.pdf).
@@ -906,8 +906,8 @@ Extrapolation is a constant polynomial of the end points on each side.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -970,9 +970,9 @@ end
 
 function BSplineApprox(
         u::AbstractVector, t, d, h, pVecType, knotVecType;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, assume_linear_t = 1e-2)
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, assume_linear_t = 1e-2)
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
     u, t = munge_data(u, t)
@@ -1066,9 +1066,9 @@ end
 
 function BSplineApprox(
         u::AbstractArray{T, N}, t, d, h, pVecType, knotVecType;
-        extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
+        extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         assume_linear_t = 1e-2) where {T, N}
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
@@ -1166,8 +1166,8 @@ function BSplineApprox(
         extrapolation_left, extrapolation_right, assume_linear_t)
 end
 """
-    CubicHermiteSpline(du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false)
+    CubicHermiteSpline(du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false)
 
 It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomial such that the value and the first derivative are equal to given values in the data points.
 
@@ -1180,8 +1180,8 @@ It is a Cubic Hermite interpolation, which is a piece-wise third degree polynomi
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -1216,9 +1216,9 @@ struct CubicHermiteSpline{uType, tType, IType, duType, pType, T, N} <:
 end
 
 function CubicHermiteSpline(
-        du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none, cache_parameters = false, assume_linear_t = 1e-2)
+        du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None, cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du) "Length of `u` is not equal to length of `du`."
     extrapolation_left, extrapolation_right = munge_extrapolation(
         extrapolation, extrapolation_left, extrapolation_right)
@@ -1234,8 +1234,8 @@ function CubicHermiteSpline(
 end
 
 """
-    PCHIPInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none, extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    PCHIPInterpolation(u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None, extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
 
 It is a PCHIP Interpolation, which is a type of [`CubicHermiteSpline`](@ref) where the derivative values `du` are derived from the input data
 in such a way that the interpolation never overshoots the data. See [here](https://www.mathworks.com/content/dam/mathworks/mathworks-dot-com/moler/interp.pdf),
@@ -1249,8 +1249,8 @@ section 3.4 for more details.
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -1268,8 +1268,8 @@ function PCHIPInterpolation(u, t; kwargs...)
 end
 
 """
-    QuinticHermiteSpline(ddu, du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none)
+    QuinticHermiteSpline(ddu, du, u, t; extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None)
 
 It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polynomial such that the value and the first and second derivative are equal to given values in the data points.
 
@@ -1283,8 +1283,8 @@ It is a Quintic Hermite interpolation, which is a piece-wise fifth degree polyno
 ## Keyword Arguments
 
   - `extrapolation`: The extrapolation type applied left and right of the data. Possible options
-    are `ExtrapolationType.none` (default), `ExtrapolationType.constant`,
-    `ExtrapolationType.linear` and `ExtrapolationType.extension`.
+    are `ExtrapolationType.None` (default), `ExtrapolationType.Constant`, `ExtrapolationType.Linear`
+    `ExtrapolationType.Extension`, `ExtrapolationType.Periodic` and `ExtrapolationType.Reflective`.
   - `extrapolation_left`: The extrapolation type applied left of the data. See `extrapolation` for
     the possible options. This keyword is ignored if `extrapolation != Extrapolation.none`.
   - `extrapolation_right`: The extrapolation type applied right of the data. See `extrapolation` for
@@ -1321,9 +1321,9 @@ struct QuinticHermiteSpline{uType, tType, IType, duType, dduType, pType, T, N} <
 end
 
 function QuinticHermiteSpline(
-        ddu, du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_left::ExtrapolationType.T = ExtrapolationType.none,
-        extrapolation_right::ExtrapolationType.T = ExtrapolationType.none,
+        ddu, du, u, t; extrapolation::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_left::ExtrapolationType.T = ExtrapolationType.None,
+        extrapolation_right::ExtrapolationType.T = ExtrapolationType.None,
         cache_parameters = false, assume_linear_t = 1e-2)
     @assert length(u)==length(du)==length(ddu) "Length of `u` is not equal to length of `du` or `ddu`."
     extrapolation_left, extrapolation_right = munge_extrapolation(
diff --git a/src/interpolation_methods.jl b/src/interpolation_methods.jl
index d7cab62a..71a2db3c 100644
--- a/src/interpolation_methods.jl
+++ b/src/interpolation_methods.jl
@@ -10,21 +10,21 @@ end
 
 function _extrapolate_left(A, t)
     (; extrapolation_left) = A
-    if extrapolation_left == ExtrapolationType.none
+    if extrapolation_left == ExtrapolationType.None
         throw(LeftExtrapolationError())
-    elseif extrapolation_left == ExtrapolationType.constant
+    elseif extrapolation_left == ExtrapolationType.Constant
         slope = derivative(A, first(A.t))
         first(A.u) + slope * zero(t)
-    elseif extrapolation_left == ExtrapolationType.linear
+    elseif extrapolation_left == ExtrapolationType.Linear
         slope = derivative(A, first(A.t))
         first(A.u) + slope * (t - first(A.t))
-    elseif extrapolation_left == ExtrapolationType.extension
+    elseif extrapolation_left == ExtrapolationType.Extension
         _interpolate(A, t, A.iguesser)
-    elseif extrapolation_left == ExtrapolationType.periodic
+    elseif extrapolation_left == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
         _interpolate(A, t_, A.iguesser)
     else
-        # extrapolation_left == ExtrapolationType.reflective
+        # extrapolation_left == ExtrapolationType.Reflective
         t_, _ = transformation_reflective(A, t)
         _interpolate(A, t_, A.iguesser)
     end
@@ -32,21 +32,21 @@ end
 
 function _extrapolate_right(A, t)
     (; extrapolation_right) = A
-    if extrapolation_right == ExtrapolationType.none
+    if extrapolation_right == ExtrapolationType.None
         throw(RightExtrapolationError())
-    elseif extrapolation_right == ExtrapolationType.constant
+    elseif extrapolation_right == ExtrapolationType.Constant
         slope = derivative(A, last(A.t))
         last(A.u) + slope * zero(t)
-    elseif extrapolation_right == ExtrapolationType.linear
+    elseif extrapolation_right == ExtrapolationType.Linear
         slope = derivative(A, last(A.t))
         last(A.u) + slope * (t - last(A.t))
-    elseif extrapolation_right == ExtrapolationType.extension
+    elseif extrapolation_right == ExtrapolationType.Extension
         _interpolate(A, t, A.iguesser)
-    elseif extrapolation_right == ExtrapolationType.periodic
+    elseif extrapolation_right == ExtrapolationType.Periodic
         t_, _ = transformation_periodic(A, t)
         _interpolate(A, t_, A.iguesser)
     else
-        # extrapolation_right == ExtrapolationType.reflective
+        # extrapolation_right == ExtrapolationType.Reflective
         t_, _ = transformation_reflective(A, t)
         _interpolate(A, t_, A.iguesser)
     end
diff --git a/src/interpolation_utils.jl b/src/interpolation_utils.jl
index 3f1e9682..1a0aaef4 100644
--- a/src/interpolation_utils.jl
+++ b/src/interpolation_utils.jl
@@ -305,7 +305,7 @@ function integrate_quintic_polynomial(t1, t2, offset, a, b, c, d, e, f)
 end
 
 function munge_extrapolation(extrapolation, extrapolation_left, extrapolation_right)
-    if extrapolation == ExtrapolationType.none
+    if extrapolation == ExtrapolationType.None
         extrapolation_left, extrapolation_right
     else
         extrapolation, extrapolation
diff --git a/test/derivative_tests.jl b/test/derivative_tests.jl
index e9e33328..376b3310 100644
--- a/test/derivative_tests.jl
+++ b/test/derivative_tests.jl
@@ -11,8 +11,8 @@ using ForwardDiff
 function test_derivatives(method; args = [], kwargs = [], name::String)
     kwargs_extrapolation = (method == Curvefit) ?
                            [:extrapolate => true] :
-                           [:extrapolation_right => ExtrapolationType.extension,
-        :extrapolation_left => ExtrapolationType.extension]
+                           [:extrapolation_right => ExtrapolationType.Extension,
+        :extrapolation_left => ExtrapolationType.Extension]
     func = method(args...; kwargs..., kwargs_extrapolation...)
     (; t) = func
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
@@ -242,7 +242,7 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(CubicHermiteSpline; args = [du, u, t],
         name = "Cubic Hermite Spline")
-    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.Extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative(A, 100.0)≈0.0105409 rtol=1e-5
     @test derivative(A, 300.0)≈-0.0806717 rtol=1e-5
@@ -255,7 +255,7 @@ end
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
     test_derivatives(QuinticHermiteSpline; args = [ddu, du, u, t],
         name = "Quintic Hermite Spline")
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.extension)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.Extension)
     @test derivative.(Ref(A), t) ≈ du
     @test derivative.(Ref(A), t, 2) ≈ ddu
     @test derivative(A, 100.0)≈0.0103916 rtol=1e-5
@@ -334,7 +334,7 @@ end
 @testset "Jacobian tests" begin
     u = rand(5)
     t = 0:4
-    interp = LinearInterpolation(u, t, extrapolation = ExtrapolationType.extension)
+    interp = LinearInterpolation(u, t, extrapolation = ExtrapolationType.Extension)
     grad1 = ForwardDiff.derivative(interp, 2.4)
 
     myvec = rand(20) .* 4.0
diff --git a/test/extrapolation_tests.jl b/test/extrapolation_tests.jl
index 12f7b2bb..ad37fc0d 100644
--- a/test/extrapolation_tests.jl
+++ b/test/extrapolation_tests.jl
@@ -5,8 +5,8 @@ using QuadGK
 function test_extrapolation(method, u, t)
     @testset "Extrapolation errors" begin
         A = method(u, t)
-        @test A.extrapolation_right == ExtrapolationType.none
-        @test A.extrapolation_left == ExtrapolationType.none
+        @test A.extrapolation_right == ExtrapolationType.None
+        @test A.extrapolation_left == ExtrapolationType.None
         for (error_type, t_eval) in zip(
             (DataInterpolations.LeftExtrapolationError,
                 DataInterpolations.RightExtrapolationError),
@@ -22,7 +22,7 @@ function test_extrapolation(method, u, t)
     end
 
     for extrapolation_type in instances(ExtrapolationType.T)
-        (extrapolation_type == ExtrapolationType.none) && continue
+        (extrapolation_type == ExtrapolationType.None) && continue
         @testset "extrapolation type $extrapolation_type" begin
             A = method(u, t; extrapolation = extrapolation_type)
 
@@ -49,7 +49,7 @@ end
 
     test_extrapolation(LinearInterpolation, u, t)
 
-    for extrapolation_type in [ExtrapolationType.linear, ExtrapolationType.extension]
+    for extrapolation_type in [ExtrapolationType.Linear, ExtrapolationType.Extension]
         # Left extrapolation
         A = LinearInterpolation(u, t; extrapolation_left = extrapolation_type)
         t_eval = 0.0
@@ -77,7 +77,7 @@ end
     test_extrapolation(QuadraticInterpolation, u, t)
 
     # Linear left extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.linear)
+    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.Linear)
     t_eval = 0.0
     @test A(t_eval) ≈ -2.5
     @test DataInterpolations.derivative(A, t_eval) == 3.5
@@ -85,7 +85,7 @@ end
     @test DataInterpolations.integral(A, t_eval) ≈ 0.75
 
     # Linear right extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.linear)
+    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.Linear)
     t_eval = 4.0
     @test A(t_eval) ≈ -0.5
     @test DataInterpolations.derivative(A, t_eval) == -2.5
@@ -95,7 +95,7 @@ end
     # Extension left extrapolation
     f = t -> (-3t^2 + 13t - 8) / 2
     df = t -> (-6t + 13) / 2
-    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation_left = ExtrapolationType.Extension)
     t_eval = 0.0
     @test A(t_eval) ≈ -4.0
     @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
@@ -103,7 +103,7 @@ end
     @test DataInterpolations.integral(A, t_eval) ≈ 1.25
 
     # Extension right extrapolation
-    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation_right = ExtrapolationType.Extension)
     t_eval = 4.0
     @test A(t_eval) ≈ -2.0
     @test DataInterpolations.derivative(A, t_eval) == df(t_eval)
diff --git a/test/integral_inverse_tests.jl b/test/integral_inverse_tests.jl
index 9ba0b158..494e4943 100644
--- a/test/integral_inverse_tests.jl
+++ b/test/integral_inverse_tests.jl
@@ -3,7 +3,7 @@ using DataInterpolations: integral, derivative, invert_integral
 using FiniteDifferences
 
 function test_integral_inverses(method; args = [], kwargs = [])
-    A = method(args...; kwargs..., extrapolation = ExtrapolationType.extension)
+    A = method(args...; kwargs..., extrapolation = ExtrapolationType.Extension)
     @test hasfield(typeof(A), :I)
     A_intinv = invert_integral(A)
     @test A_intinv isa DataInterpolations.AbstractIntegralInverseInterpolation
diff --git a/test/integral_tests.jl b/test/integral_tests.jl
index 09ba655b..283b8dce 100644
--- a/test/integral_tests.jl
+++ b/test/integral_tests.jl
@@ -6,8 +6,8 @@ using RegularizationTools
 using StableRNGs
 
 function test_integral(method; args = [], kwargs = [], name::String)
-    func = method(args...; kwargs..., extrapolation_left = ExtrapolationType.extension,
-        extrapolation_right = ExtrapolationType.extension)
+    func = method(args...; kwargs..., extrapolation_left = ExtrapolationType.Extension,
+        extrapolation_right = ExtrapolationType.Extension)
     (; t) = func
     t1 = minimum(t)
     t2 = maximum(t)
diff --git a/test/interface.jl b/test/interface.jl
index 29f6864d..b0e48d06 100644
--- a/test/interface.jl
+++ b/test/interface.jl
@@ -18,8 +18,8 @@ end
 @testset "Symbolics" begin
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
-    B = LinearInterpolation(u .^ 2, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
+    B = LinearInterpolation(u .^ 2, t; extrapolation = ExtrapolationType.Extension)
     @variables t x(t)
     substitute(A(t), Dict(t => x))
     t_val = 2.7
diff --git a/test/interpolation_tests.jl b/test/interpolation_tests.jl
index 83a0bef1..08d8fb3f 100644
--- a/test/interpolation_tests.jl
+++ b/test/interpolation_tests.jl
@@ -31,7 +31,7 @@ end
     for t in (1.0:10.0, 1.0collect(1:10))
         u = 2.0collect(1:10)
         #t = 1.0collect(1:10)
-        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
         for (_t, _u) in zip(t, u)
             @test A(_t) == _u
@@ -41,7 +41,7 @@ end
         @test A(11) == 22
 
         u = vcat(2.0collect(1:10)', 3.0collect(1:10)')
-        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
         for (_t, _u) in zip(t, eachcol(u))
             @test A(_t) == _u
@@ -54,7 +54,7 @@ end
         y = 2:4
         u_ = x' .* y
         u = [u_[:, i] for i in 1:size(u_, 2)]
-        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+        A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
         @test A(0) == [0.0, 0.0, 0.0]
         @test A(5.5) == [11.0, 16.5, 22.0]
         @test A(11) == [22.0, 33.0, 44.0]
@@ -65,7 +65,7 @@ end
     u_ = x' .* y
     u = [u_[:, i:(i + 1)] for i in 1:2:10]
     t = 1.0collect(2:2:10)
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
     @test A(0) == [-2.0 0.0; -3.0 0.0; -4.0 0.0]
     @test A(3) == [4.0 6.0; 6.0 9.0; 8.0 12.0]
@@ -75,7 +75,7 @@ end
     # with NaNs (#113)
     u = [NaN, 1.0, 2.0, 3.0]
     t = 1:4
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test isnan(A(1.0))
     @test A(2.0) == 1.0
     @test A(2.5) == 1.5
@@ -83,7 +83,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, NaN, 2.0, 3.0]
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(1.0) == 0.0
     @test isnan(A(2.0))
     @test isnan(A(2.5))
@@ -91,7 +91,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, NaN, 3.0]
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test isnan(A(2.5))
@@ -99,7 +99,7 @@ end
     @test A(4.0) == 3.0
 
     u = [0.0, 1.0, 2.0, NaN]
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(1.0) == 0.0
     @test A(2.0) == 1.0
     @test A(3.0) == 2.0
@@ -109,16 +109,16 @@ end
     # Test type stability
     u = Float32.(1:5)
     t = Float32.(1:5)
-    A1 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A1 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     u = 1:5
     t = 1:5
-    A2 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A2 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     u = [1 // i for i in 1:5]
     t = (1:5)
-    A3 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A3 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     u = [1 // i for i in 1:5]
     t = [1 // (6 - i) for i in 1:5]
-    A4 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A4 = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
     F32 = Float32(1)
     F64 = Float64(1)
@@ -138,13 +138,13 @@ end
     # Nan time value:
     t = 0.0:3  # Floats
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
     t = 0:3  # Integers
     u = [0, -2, -1, -2]
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     dA = t -> ForwardDiff.derivative(A, t)
     @test isnan(dA(NaN))
 
@@ -157,7 +157,7 @@ end
     # Test array-valued interpolation
     u = collect.(2.0collect(1:10))
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(0) == fill(0.0)
     @test A(5.5) == fill(11.0)
     @test A(11) == fill(22)
@@ -172,7 +172,7 @@ end
     # Test extrapolation
     u = 2.0collect(1:10)
     t = 1.0collect(1:10)
-    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LinearInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-1.0) == -2.0
     @test A(11.0) == 22.0
     A = LinearInterpolation(u, t)
@@ -186,7 +186,7 @@ end
 
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -202,7 +202,7 @@ end
     u = [1.0, 4.0, 9.0, 16.0]
     t = [1.0, 2.0, 3.0, 4.0]
     A = QuadraticInterpolation(
-        u, t, :Backward; extrapolation = ExtrapolationType.extension)
+        u, t, :Backward; extrapolation = ExtrapolationType.Extension)
 
     for (_t, _u) in zip(t, u)
         @test A(_t) == _u
@@ -240,7 +240,7 @@ end
 
     # Matrix interpolation test
     u = [1.0 4.0 9.0 16.0; 1.0 4.0 9.0 16.0]
-    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
 
     for (_t, _u) in zip(t, eachcol(u))
         @test A(_t) == _u
@@ -253,7 +253,7 @@ end
 
     u_ = [1.0, 4.0, 9.0, 16.0]' .* ones(5)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(0) == zeros(5)
     @test A(1.5) == 2.25 * ones(5)
     @test A(2.5) == 6.25 * ones(5)
@@ -261,7 +261,7 @@ end
     @test A(5.0) == 25.0 * ones(5)
 
     u = [repeat(u[i], 1, 3) for i in 1:4]
-    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(0) == zeros(5, 3)
     @test A(1.5) == 2.25 * ones(5, 3)
     @test A(2.5) == 6.25 * ones(5, 3)
@@ -271,7 +271,7 @@ end
     # Test extrapolation
     u = [1.0, 4.5, 6.0, 2.0]
     t = [1.0, 2.0, 3.0, 4.0]
-    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(0.0) == -4.5
     @test A(5.0) == -7.5
     A = QuadraticInterpolation(u, t)
@@ -331,7 +331,7 @@ end
     # Test extrapolation
     u = [1.0, 4.0, 9.0]
     t = [1.0, 2.0, 3.0]
-    A = LagrangeInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = LagrangeInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(0.0) == 0.0
     @test A(4.0) == 16.0
     A = LagrangeInterpolation(u, t)
@@ -362,7 +362,7 @@ end
     test_cached_index(A)
 
     # Test extrapolation
-    A = AkimaInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = AkimaInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-1.0) ≈ -5.0
     @test A(11.0) ≈ -3.924742268041234
     A = AkimaInterpolation(u, t)
@@ -377,7 +377,7 @@ end
 
     @testset "Vector case" for u in [[1.0, 2.0, 0.0, 1.0], ["B", "C", "A", "B"]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.Extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -389,7 +389,7 @@ end
         @test A(4.5) == u[1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -407,7 +407,7 @@ end
         ["B" "C" "A" "B"; "B" "C" "A" "B"]
     ]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.Extension)
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 2]
@@ -419,7 +419,7 @@ end
         @test A(4.5) == u[:, 1]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension) # dir=:left is default
         @test A(0.5) == u[:, 1]
         @test A(1.0) == u[:, 1]
         @test A(1.5) == u[:, 1]
@@ -436,7 +436,7 @@ end
         [[1.0, 2.0], [0.0, 1.0], [1.0, 2.0], [0.0, 1.0]],
         [["B", "C"], ["A", "B"], ["B", "C"], ["A", "B"]]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.Extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -448,7 +448,7 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -465,7 +465,7 @@ end
         [[1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0], [1.0 2.0; 1.0 2.0], [0.0 1.0; 0.0 1.0]],
         [["B" "C"; "B" "C"], ["A" "B"; "A" "B"], ["B" "C"; "B" "C"], ["A" "B"; "A" "B"]]]
         A = ConstantInterpolation(
-            u, t, dir = :right; extrapolation = ExtrapolationType.extension)
+            u, t, dir = :right; extrapolation = ExtrapolationType.Extension)
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[2]
@@ -477,7 +477,7 @@ end
         @test A(4.5) == u[4]
         test_cached_index(A)
 
-        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension) # dir=:left is default
+        A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension) # dir=:left is default
         @test A(0.5) == u[1]
         @test A(1.0) == u[1]
         @test A(1.5) == u[1]
@@ -492,7 +492,7 @@ end
 
     # Test extrapolation
     u = [1.0, 2.0, 0.0, 1.0]
-    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-1.0) == 1.0
     @test A(11.0) == 1.0
     A = ConstantInterpolation(u, t)
@@ -502,7 +502,7 @@ end
     # Test extrapolation with infs with regularly spaced t
     u = [1.67e7, 1.6867e7, 1.7034e7, 1.7201e7, 1.7368e7]
     t = [0.0, 0.1, 0.2, 0.3, 0.4]
-    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.extension)
+    A = ConstantInterpolation(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(Inf) == last(u)
     @test A(-Inf) == first(u)
 end
@@ -513,7 +513,7 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
 
     # Solution
     P₁ = x -> 0.5 * (x + 1) * (x + 2)
@@ -529,14 +529,14 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-2.0) == P₁(-2.0) * ones(4)
     @test A(-0.5) == P₁(-0.5) * ones(4)
     @test A(0.7) == P₁(0.7) * ones(4)
     @test A(2.0) == P₁(2.0) * ones(4)
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-2.0) == P₁(-2.0) * ones(4, 3)
     @test A(-0.5) == P₁(-0.5) * ones(4, 3)
     @test A(0.7) == P₁(0.7) * ones(4, 3)
@@ -545,7 +545,7 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = QuadraticSpline(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-2.0) == 0.0
     @test A(2.0) == 6.0
     A = QuadraticSpline(u, t)
@@ -559,7 +559,7 @@ end
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
 
-    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.Extension)
     test_cached_index(A)
 
     # Solution
@@ -578,7 +578,7 @@ end
 
     u_ = [0.0, 1.0, 3.0]' .* ones(4)
     u = [u_[:, i] for i in 1:size(u_, 2)]
-    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.Extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4)
     end
@@ -587,7 +587,7 @@ end
     end
 
     u = [repeat(u[i], 1, 3) for i in 1:3]
-    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.Extension)
     for x in (-1.5, -0.5, -0.7)
         @test A(x) ≈ P₁(x) * ones(4, 3)
     end
@@ -598,7 +598,7 @@ end
     # Test extrapolation
     u = [0.0, 1.0, 3.0]
     t = [-1.0, 0.0, 1.0]
-    A = CubicSpline(u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicSpline(u, t; extrapolation = ExtrapolationType.Extension)
     @test A(-2.0) ≈ -1.0
     @test A(2.0) ≈ 5.0
     A = CubicSpline(u, t)
@@ -643,7 +643,7 @@ end
 
         # Test extrapolation
         A = BSplineInterpolation(
-            u, t, 2, :Uniform, :Uniform; extrapolation = ExtrapolationType.extension)
+            u, t, 2, :Uniform, :Uniform; extrapolation = ExtrapolationType.Extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :Uniform, :Uniform)
@@ -664,7 +664,7 @@ end
 
         # Test extrapolation
         A = BSplineInterpolation(
-            u, t, 2, :ArcLen, :Average; extrapolation = ExtrapolationType.extension)
+            u, t, 2, :ArcLen, :Average; extrapolation = ExtrapolationType.Extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineInterpolation(u, t, 2, :ArcLen, :Average)
@@ -722,7 +722,7 @@ end
 
         # Test extrapolation
         A = BSplineApprox(
-            u, t, 2, 4, :Uniform, :Uniform; extrapolation = ExtrapolationType.extension)
+            u, t, 2, 4, :Uniform, :Uniform; extrapolation = ExtrapolationType.Extension)
         @test A(-1.0) == u[1]
         @test A(300.0) == u[end]
         A = BSplineApprox(u, t, 2, 4, :Uniform, :Uniform)
@@ -768,7 +768,7 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.extension)
+    A = CubicHermiteSpline(du, u, t; extrapolation = ExtrapolationType.Extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.106770 rtol=1e-5
     @test A(300.0)≈9.901542 rtol=1e-5
@@ -796,7 +796,7 @@ end
     du = [-0.047, -0.058, 0.054, 0.012, -0.068, 0.0]
     u = [14.7, 11.51, 10.41, 14.95, 12.24, 11.22]
     t = [0.0, 62.25, 109.66, 162.66, 205.8, 252.3]
-    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.extension)
+    A = QuinticHermiteSpline(ddu, du, u, t; extrapolation = ExtrapolationType.Extension)
     @test A.(t) ≈ u
     @test A(100.0)≈10.107996 rtol=1e-5
     @test A(300.0)≈11.364162 rtol=1e-5
diff --git a/test/regularization.jl b/test/regularization.jl
index a3f4ef1c..eb8abca0 100644
--- a/test/regularization.jl
+++ b/test/regularization.jl
@@ -181,7 +181,7 @@ end
 
 @testset "Extrapolation" begin
     A = RegularizationSmooth(
-        uₒ, tₒ; alg = :fixed, extrapolation_right = ExtrapolationType.extension)
+        uₒ, tₒ; alg = :fixed, extrapolation_right = ExtrapolationType.Extension)
     @test A(10.0) == A.Aitp(10.0)
     A = RegularizationSmooth(uₒ, tₒ; alg = :fixed)
     @test_throws DataInterpolations.RightExtrapolationError A(10.0)
diff --git a/test/zygote_tests.jl b/test/zygote_tests.jl
index d8d178df..da4bf381 100644
--- a/test/zygote_tests.jl
+++ b/test/zygote_tests.jl
@@ -4,7 +4,7 @@ using Zygote
 
 function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name::String)
     func = method(args..., u, t, args_after...; kwargs...,
-        extrapolation = ExtrapolationType.extension)
+        extrapolation = ExtrapolationType.Extension)
     trange = collect(range(minimum(t) - 5.0, maximum(t) + 5.0, step = 0.1))
     trange_exclude = filter(x -> !in(x, t), trange)
     @testset "$name, derivatives w.r.t. input" begin
@@ -21,7 +21,7 @@ function test_zygote(method, u, t; args = [], args_after = [], kwargs = [], name
         @testset "$name, derivatives w.r.t. u" begin
             function f(u)
                 A = method(args..., u, t, args_after...; kwargs...,
-                    extrapolation = ExtrapolationType.extension)
+                    extrapolation = ExtrapolationType.Extension)
                 out = if u isa AbstractVector{<:Real}
                     zero(eltype(u))
                 elseif u isa AbstractMatrix