Add extrapolation keyword

src/DataInterpolations.jl

@@ -36,6 +36,12 @@
     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)
+end
+
 export LinearInterpolation, QuadraticInterpolation, LagrangeInterpolation,
     AkimaInterpolation, ConstantInterpolation, QuadraticSpline, CubicSpline,
     BSplineInterpolation, BSplineApprox

src/derivatives.jl

@@ -1,4 +1,7 @@
-derivative(A, t) = derivative(A, t, firstindex(A.t) - 1)[1]
+function derivative(A, t)
+    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
+    derivative(A, t, firstindex(A.t) - 1)[1]
+end
 
 function derivative(A::LinearInterpolation{<:AbstractVector}, t::Number, iguess)
     idx = searchsortedfirstcorrelated(A.t, t, iguess)
@@ -33,6 +36,7 @@
 end
 
 function derivative(A::LagrangeInterpolation{<:AbstractVector}, t::Number)
+    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     idxs = findRequiredIdxs(A, t)
     if A.t[idxs[1]] == t
         return zero(A.u[idxs[1]])
@@ -68,6 +72,7 @@
 end
 
 function derivative(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number)
+    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     idxs = findRequiredIdxs(A, t)
     if A.t[idxs[1]] == t
         return zero(A.u[:, idxs[1]])
@@ -115,10 +120,12 @@
 end
 
 function derivative(A::ConstantInterpolation{<:AbstractVector}, t::Number)
+    ((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)
+    ((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
 

src/interpolation_caches.jl

@@ -2,34 +2,38 @@
 struct LinearInterpolation{uType, tType, FT, T} <: AbstractInterpolation{FT, T}
     u::uType
     t::tType
-    function LinearInterpolation{FT}(u, t) where {FT}
-        new{typeof(u), typeof(t), FT, eltype(u)}(u, t)
+    extrapolate::Bool
+    function LinearInterpolation{FT}(u, t, extrapolate) where {FT}
+        new{typeof(u), typeof(t), FT, eltype(u)}(u, t, extrapolate)
     end
 end
 
-function LinearInterpolation(u, t)
+function LinearInterpolation(u, t; extrapolate = true)
     u, t = munge_data(u, t)
-    LinearInterpolation{true}(u, t)
+    LinearInterpolation{true}(u, t, extrapolate)
 end
 
 ### Quadratic Interpolation
 struct QuadraticInterpolation{uType, tType, FT, T} <: AbstractInterpolation{FT, T}
     u::uType
     t::tType
     mode::Symbol
-    function QuadraticInterpolation{FT}(u, t, mode) where {FT}
+    extrapolate::Bool
+    function QuadraticInterpolation{FT}(u, t, mode, extrapolate) where {FT}
         mode ∈ (:Forward, :Backward) ||
             error("mode should be :Forward or :Backward for QuadraticInterpolation")
-        new{typeof(u), typeof(t), FT, eltype(u)}(u, t, mode)
+        new{typeof(u), typeof(t), FT, eltype(u)}(u, t, mode, extrapolate)
     end
 end
 
-function QuadraticInterpolation(u, t, mode)
+function QuadraticInterpolation(u, t, mode; extrapolate = true)
     u, t = munge_data(u, t)
-    QuadraticInterpolation{true}(u, t, mode)
+    QuadraticInterpolation{true}(u, t, mode, extrapolate)
 end
 
-QuadraticInterpolation(u, t) = QuadraticInterpolation(u, t, :Forward)
+function QuadraticInterpolation(u, t; extrapolate = true)
+    QuadraticInterpolation(u, t, :Forward; extrapolate)
+end
 
 ### Lagrange Interpolation
 struct LagrangeInterpolation{uType, tType, FT, T, bcacheType} <:
@@ -38,22 +42,27 @@ struct LagrangeInterpolation{uType, tType, FT, T, bcacheType} <:
     t::tType
     n::Int
     bcache::bcacheType
-    function LagrangeInterpolation{FT}(u, t, n) where {FT}
+    extrapolate::Bool
+    function LagrangeInterpolation{FT}(u, t, n, extrapolate) where {FT}
         bcache = zeros(eltype(u[1]), n + 1)
         fill!(bcache, NaN)
-        new{typeof(u), typeof(t), FT, eltype(u), typeof(bcache)}(u, t, n, bcache)
+        new{typeof(u), typeof(t), FT, eltype(u), typeof(bcache)}(u,
+            t,
+            n,
+            bcache,
+            extrapolate)
     end
 end
 
-function LagrangeInterpolation(u, t, n = nothing)
+function LagrangeInterpolation(u, t, n = nothing; extrapolate = true)
     u, t = munge_data(u, t)
     if isnothing(n)
         n = length(t) - 1 # degree
     end
     if n != length(t) - 1
         error("Currently only n=length(t) - 1 is supported")
     end
-    LagrangeInterpolation{true}(u, t, n)
+    LagrangeInterpolation{true}(u, t, n, extrapolate)
 end
 
 ### Akima Interpolation
@@ -64,17 +73,19 @@ struct AkimaInterpolation{uType, tType, bType, cType, dType, FT, T} <:
     b::bType
     c::cType
     d::dType
-    function AkimaInterpolation{FT}(u, t, b, c, d) where {FT}
+    extrapolate::Bool
+    function AkimaInterpolation{FT}(u, t, b, c, d, extrapolate) where {FT}
         new{typeof(u), typeof(t), typeof(b), typeof(c),
             typeof(d), FT, eltype(u)}(u,
             t,
             b,
             c,
-            d)
+            d,
+            extrapolate)
     end
 end
 
-function AkimaInterpolation(u, t)
+function AkimaInterpolation(u, t; extrapolate = true)
     u, t = munge_data(u, t)
     n = length(t)
     dt = diff(t)
@@ -96,22 +107,23 @@ function AkimaInterpolation(u, t)
     c = (3.0 .* m[3:(end - 2)] .- 2.0 .* b[1:(end - 1)] .- b[2:end]) ./ dt
     d = (b[1:(end - 1)] .+ b[2:end] .- 2.0 .* m[3:(end - 2)]) ./ dt .^ 2
 
-    AkimaInterpolation{true}(u, t, b, c, d)
+    AkimaInterpolation{true}(u, t, b, c, d, extrapolate)
 end
 
 ### ConstantInterpolation Interpolation
 struct ConstantInterpolation{uType, tType, dirType, FT, T} <: AbstractInterpolation{FT, T}
     u::uType
     t::tType
     dir::Symbol # indicates if value to the $dir should be used for the interpolation
-    function ConstantInterpolation{FT}(u, t, dir) where {FT}
-        new{typeof(u), typeof(t), typeof(dir), FT, eltype(u)}(u, t, dir)
+    extrapolate::Bool
+    function ConstantInterpolation{FT}(u, t, dir, extrapolate) where {FT}
+        new{typeof(u), typeof(t), typeof(dir), FT, eltype(u)}(u, t, dir, extrapolate)
     end
 end
 
-function ConstantInterpolation(u, t; dir = :left)
+function ConstantInterpolation(u, t; dir = :left, extrapolate = true)
     u, t = munge_data(u, t)
-    ConstantInterpolation{true}(u, t, dir)
+    ConstantInterpolation{true}(u, t, dir, extrapolate)
 end
 
 Base.@deprecate_binding ZeroSpline ConstantInterpolation
@@ -124,17 +136,21 @@ struct QuadraticSpline{uType, tType, tAType, dType, zType, FT, T} <:
     tA::tAType
     d::dType
     z::zType
-    function QuadraticSpline{FT}(u, t, tA, d, z) where {FT}
+    extrapolate::Bool
+    function QuadraticSpline{FT}(u, t, tA, d, z, extrapolate) where {FT}
         new{typeof(u), typeof(t), typeof(tA),
             typeof(d), typeof(z), FT, eltype(u)}(u,
             t,
             tA,
             d,
-            z)
+            z,
+            extrapolate)
     end
 end
 
-function QuadraticSpline(u::uType, t) where {uType <: AbstractVector{<:Number}}
+function QuadraticSpline(u::uType,
+    t;
+    extrapolate = true) where {uType <: AbstractVector{<:Number}}
     u, t = munge_data(u, t)
     s = length(t)
     dl = ones(eltype(t), s - 1)
@@ -147,10 +163,10 @@ function QuadraticSpline(u::uType, t) where {uType <: AbstractVector{<:Number}}
 
     d = map(i -> i == 1 ? typed_zero : 2 // 1 * (u[i] - u[i - 1]) / (t[i] - t[i - 1]), 1:s)
     z = tA \ d
-    QuadraticSpline{true}(u, t, tA, d, z)
+    QuadraticSpline{true}(u, t, tA, d, z, extrapolate)
 end
 
-function QuadraticSpline(u::uType, t) where {uType <: AbstractVector}
+function QuadraticSpline(u::uType, t; extrapolate = true) where {uType <: AbstractVector}
     u, t = munge_data(u, t)
     s = length(t)
     dl = ones(eltype(t), s - 1)
@@ -163,7 +179,7 @@ function QuadraticSpline(u::uType, t) where {uType <: AbstractVector}
     d = transpose(reshape(reduce(hcat, d_), :, s))
     z_ = reshape(transpose(tA \ d), size(u[1])..., :)
     z = [z_s for z_s in eachslice(z_, dims = ndims(z_))]
-    QuadraticSpline{true}(u, t, tA, d, z)
+    QuadraticSpline{true}(u, t, tA, d, z, extrapolate)
 end
 
 # Cubic Spline Interpolation
@@ -172,12 +188,19 @@ struct CubicSpline{uType, tType, hType, zType, FT, T} <: AbstractInterpolation{F
     t::tType
     h::hType
     z::zType
-    function CubicSpline{FT}(u, t, h, z) where {FT}
-        new{typeof(u), typeof(t), typeof(h), typeof(z), FT, eltype(u)}(u, t, h, z)
+    extrapolate::Bool
+    function CubicSpline{FT}(u, t, h, z, extrapolate) where {FT}
+        new{typeof(u), typeof(t), typeof(h), typeof(z), FT, eltype(u)}(u,
+            t,
+            h,
+            z,
+            extrapolate)
     end
 end
 
-function CubicSpline(u::uType, t) where {uType <: AbstractVector{<:Number}}
+function CubicSpline(u::uType,
+    t;
+    extrapolate = true) where {uType <: AbstractVector{<:Number}}
     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)
@@ -194,10 +217,10 @@ function CubicSpline(u::uType, t) where {uType <: AbstractVector{<:Number}}
                  6(u[i + 1] - u[i]) / h[i + 1] - 6(u[i] - u[i - 1]) / h[i],
         1:(n + 1))
     z = tA \ d
-    CubicSpline{true}(u, t, h[1:(n + 1)], z)
+    CubicSpline{true}(u, t, h[1:(n + 1)], z, extrapolate)
 end
 
-function CubicSpline(u::uType, t) where {uType <: AbstractVector}
+function CubicSpline(u::uType, t; extrapolate = true) where {uType <: AbstractVector}
     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)
@@ -211,7 +234,7 @@ function CubicSpline(u::uType, t) where {uType <: AbstractVector}
     d = transpose(reshape(reduce(hcat, d_), :, n + 1))
     z_ = reshape(transpose(tA \ d), size(u[1])..., :)
     z = [z_s for z_s in eachslice(z_, dims = ndims(z_))]
-    CubicSpline{true}(u, t, h[1:(n + 1)], z)
+    CubicSpline{true}(u, t, h[1:(n + 1)], z, extrapolate)
 end
 
 ### BSpline Curve Interpolation
@@ -225,19 +248,29 @@ struct BSplineInterpolation{uType, tType, pType, kType, cType, FT, T} <:
     c::cType  # control points
     pVecType::Symbol
     knotVecType::Symbol
-    function BSplineInterpolation{FT}(u, t, d, p, k, c, pVecType, knotVecType) where {FT}
+    extrapolate::Bool
+    function BSplineInterpolation{FT}(u,
+        t,
+        d,
+        p,
+        k,
+        c,
+        pVecType,
+        knotVecType,
+        extrapolate) where {FT}
         new{typeof(u), typeof(t), typeof(p), typeof(k), typeof(c), FT, eltype(u)}(u,
             t,
             d,
             p,
             k,
             c,
             pVecType,
-            knotVecType)
+            knotVecType,
+            extrapolate)
     end
 end
 
-function BSplineInterpolation(u, t, d, pVecType, knotVecType)
+function BSplineInterpolation(u, t, d, pVecType, knotVecType; extrapolate = true)
     u, t = munge_data(u, t)
     n = length(t)
     s = zero(eltype(u))
@@ -298,7 +331,7 @@ function BSplineInterpolation(u, t, d, pVecType, knotVecType)
     # control points
     N = spline_coefficients(n, d, k, p)
     c = vec(N \ u[:, :])
-    BSplineInterpolation{true}(u, t, d, p, k, c, pVecType, knotVecType)
+    BSplineInterpolation{true}(u, t, d, p, k, c, pVecType, knotVecType, extrapolate)
 end
 
 ### BSpline Curve Approx
@@ -313,7 +346,17 @@ struct BSplineApprox{uType, tType, pType, kType, cType, FT, T} <:
     c::cType  # control points
     pVecType::Symbol
     knotVecType::Symbol
-    function BSplineApprox{FT}(u, t, d, h, p, k, c, pVecType, knotVecType) where {FT}
+    extrapolate::Bool
+    function BSplineApprox{FT}(u,
+        t,
+        d,
+        h,
+        p,
+        k,
+        c,
+        pVecType,
+        knotVecType,
+        extrapolate) where {FT}
         new{typeof(u), typeof(t), typeof(p), typeof(k), typeof(c), FT, eltype(u)}(u,
             t,
             d,
@@ -322,11 +365,12 @@ struct BSplineApprox{uType, tType, pType, kType, cType, FT, T} <:
             k,
             c,
             pVecType,
-            knotVecType)
+            knotVecType,
+            extrapolate)
     end
 end
 
-function BSplineApprox(u, t, d, h, pVecType, knotVecType)
+function BSplineApprox(u, t, d, h, pVecType, knotVecType; extrapolate = true)
     u, t = munge_data(u, t)
     n = length(t)
     s = zero(eltype(u))
@@ -409,5 +453,5 @@ function BSplineApprox(u, t, d, h, pVecType, knotVecType)
     M = transpose(N) * N
     P = M \ Q
     c[2:(end - 1)] .= vec(P)
-    BSplineApprox{true}(u, t, d, h, p, k, c, pVecType, knotVecType)
+    BSplineApprox{true}(u, t, d, h, p, k, c, pVecType, knotVecType, extrapolate)
 end

src/interpolation_methods.jl

@@ -1,4 +1,8 @@
-_interpolate(interp, t) = _interpolate(interp, t, firstindex(interp.t) - 1)[1]
+function _interpolate(interp, t)
+    ((t < interp.t[1] || t > interp.t[end]) && !interp.extrapolate) &&
+        throw(ExtrapolationError())
+    _interpolate(interp, t, firstindex(interp.t) - 1)[1]
+end
 
 # Linear Interpolation
 function _interpolate(A::LinearInterpolation{<:AbstractVector}, t::Number, iguess)
@@ -53,6 +57,7 @@ end
 
 # Lagrange Interpolation
 function _interpolate(A::LagrangeInterpolation{<:AbstractVector}, t::Number)
+    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     idxs = findRequiredIdxs(A, t)
     if A.t[idxs[1]] == t
         return A.u[idxs[1]]
@@ -81,6 +86,7 @@ function _interpolate(A::LagrangeInterpolation{<:AbstractVector}, t::Number)
 end
 
 function _interpolate(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number)
+    ((t < A.t[1] || t > A.t[end]) && !A.extrapolate) && throw(ExtrapolationError())
     idxs = findRequiredIdxs(A, t)
     if A.t[idxs[1]] == t
         return A.u[:, idxs[1]]

src/interpolation_utils.jl

@@ -125,4 +125,4 @@ function searchsortedlastcorrelated(v::AbstractVector, x, guess)
 end
 
 searchsortedfirstcorrelated(r::AbstractRange, x, _) = searchsortedfirst(r, x)
-searchsortedlastcorrelated(r::AbstractRange, x, _) = searchsortedlast(r, x)
+searchsortedlastcorrelated(r::AbstractRange, x, _) = searchsortedlast(r, x)