Use instances instead of types when specifying options

This opens up for actually keeping data in the options, even if that
data is not of bits types (and thus not possible to include as a type
parameter), for example a boundar condition Tangent(k) with an interpolation
object that has eltype(itp) <: Array.

Author: tomasaschan

README.md

@@ -99,25 +99,25 @@ B-splines of quadratic or higher degree require solving an equation system to ob
 Some examples:
 ```jl
 # Nearest-neighbor interpolation
-itp = interpolate(a, BSpline{Constant}, OnCell)
+itp = interpolate(a, BSpline(Constant()), OnCell())
 v = itp[5.4]   # returns a[5]
 
 # (Multi)linear interpolation
-itp = interpolate(A, BSpline{Linear}, OnGrid)
+itp = interpolate(A, BSpline(Linear()), OnGrid())
 v = itp[3.2, 4.1]  # returns 0.9*(0.8*A[3,4]+0.2*A[4,4]) + 0.1*(0.8*A[3,5]+0.2*A[4,5])
 
 # Quadratic interpolation with reflecting boundary conditions
 # Quadratic is the lowest order that has continuous gradient
-itp = interpolate(A, BSpline{Quadratic{Reflect}}, OnCell)
+itp = interpolate(A, BSpline(Quadratic(Reflect())), OnCell())
 
 # Linear interpolation in the first dimension, and no interpolation (just lookup) in the second
-itp = interpolate(A, Tuple{BSpline{Linear}, BSpline{NoInterp}}, OnGrid)
+itp = interpolate(A, (BSpline(Linear()), NoInterp()), OnGrid())
 v = itp[3.65, 5]  # returns  0.35*A[3,5] + 0.65*A[4,5]
 ```
 There are more options available, for example:
 ```jl
 # In-place interpolation
-itp = interpolate!(A, BSpline{Quadratic{InPlace}}, OnCell)
+itp = interpolate!(A, BSpline(Quadratic(InPlace())), OnCell())
 ```
 which destroys the input `A` but also does not need to allocate as much memory.
 
@@ -133,7 +133,7 @@ In 1D
 A = rand(20)
 A_x = collect(1.:40.)
 knots = (a,)
-itp = interpolate(knots,A, Gridded{Linear})
+itp = interpolate(knots,A, Gridded(Linear()))
 itp[2.0] 
 ```
 
@@ -148,22 +148,22 @@ For example:
 ```jl
 A = rand(8,20)
 knots = ([x^2 for x = 1:8], [0.2y for y = 1:20])
-itp = interpolate(knots, A, Gridded{Linear})
+itp = interpolate(knots, A, Gridded(Linear()))
 itp[4,1.2]  # approximately A[2,6]
 ```
 One may also mix modes, by specifying a mode vector in the form of an explicit tuple:
 ```jl
-itp = interpolate(knots, A, Tuple{Gridded{Linear},Gridded{Constant}})
+itp = interpolate(knots, A, (Gridded(Linear()),Gridded(Constant())))
 ```
 
 
 Presently there are only three modes for gridded:
 ```jl
-Gridded{Linear}
+Gridded(Linear())
 ```
 whereby a linear interpolation is applied between knots,
 ```jl
-Gridded{Constant}
+Gridded(Constant())
 ```
 whereby nearest neighbor interpolation is used on the applied axis,
 ```jl
@@ -174,11 +174,7 @@ coordinates results in the throwing of an error.
 
 ## Extrapolation
 
-The call to `extrapolate` defines what happens if you try to index into the interpolation object with coordinates outside of `[1, size(data,d)]` in any dimension `d`. The implemented boundary conditions are `Throw` and `Flat`, with more options planned.
-
-## More examples
-
-There's an [IJulia notebook](http://nbviewer.ipython.org/github/tlycken/Interpolations.jl/blob/master/doc/Interpolations.jl.ipynb) that shows off some of the current functionality, and outlines where we're headed. I try to keep it up to date when I make any significant improvements and/or breaking changes, but if it's not, do file a PR.
+The call to `extrapolate` defines what happens if you try to index into the interpolation object with coordinates outside of `[1, size(data,d)]` in any dimension `d`. The implemented boundary conditions are `Throw`, `Flat`, `Linear`, `Periodic` and `Reflect`, with more options planned. `Periodic` and `Reflect` require that there is a method of `Base.mod` that can handle the indices used.
 
 ## Performance shootout
 

doc/devdocs.md

@@ -18,7 +18,7 @@ First let's create an interpolation object:
     0.134746
     0.430876
 
-    julia> yitp = interpolate(A, BSpline{Linear}, OnGrid)
+    julia> yitp = interpolate(A, BSpline(Linear()), OnGrid())
     5-element Interpolations.BSplineInterpolation{Float64,1,Float64,Interpolations.BSpline{Interpolations.Linear},Interpolations.OnGrid}:
     0.74838
     0.995383

src/b-splines/b-splines.jl

@@ -9,14 +9,14 @@ export
 abstract Degree{N}
 
 immutable BSpline{D<:Degree} <: InterpolationType end
-BSpline{D<:Degree}(::Type{D}) = BSpline{D}
+BSpline{D<:Degree}(::D) = BSpline{D}()
 
 bsplinetype{D<:Degree}(::Type{BSpline{D}}) = D
 
 immutable BSplineInterpolation{T,N,TCoefs,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},pad} <: AbstractInterpolation{T,N,IT,GT}
     coefs::Array{TCoefs,N}
 end
-function BSplineInterpolation{N,TCoefs,TWeights<:Real,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},pad}(::Type{TWeights}, A::AbstractArray{TCoefs,N}, ::Type{IT}, ::Type{GT}, ::Val{pad})
+function BSplineInterpolation{N,TCoefs,TWeights<:Real,IT<:DimSpec{BSpline},GT<:DimSpec{GridType},pad}(::Type{TWeights}, A::AbstractArray{TCoefs,N}, ::IT, ::GT, ::Val{pad})
     isleaftype(IT) || error("The b-spline type must be a leaf type (was $IT)")
     isleaftype(TCoefs) || warn("For performance reasons, consider using an array of a concrete type (eltype(A) == $(eltype(A)))")
 
@@ -49,12 +49,12 @@ count_interp_dims{T,N,TCoefs,IT<:DimSpec{InterpolationType},GT<:DimSpec{GridType
     end
 end
 
-function interpolate{TWeights,TCoefs,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(::Type{TWeights}, ::Type{TCoefs}, A, ::Type{IT}, ::Type{GT})
+function interpolate{TWeights,TCoefs,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(::Type{TWeights}, ::Type{TCoefs}, A, it::IT, gt::GT)
     Apad, Pad = prefilter(TWeights, TCoefs, A, IT, GT)
-    BSplineInterpolation(TWeights, Apad, IT, GT, Pad)
+    BSplineInterpolation(TWeights, Apad, it, gt, Pad)
 end
-function interpolate{IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(A::AbstractArray, ::Type{IT}, ::Type{GT})
-    interpolate(tweight(A), tcoef(A), A, IT, GT)
+function interpolate{IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(A::AbstractArray, it::IT, gt::GT)
+    interpolate(tweight(A), tcoef(A), A, it, gt)
 end
 
 # We can't just return a tuple-of-types due to julia #12500
@@ -68,9 +68,9 @@ tcoef(A::AbstractArray{Float32}) = Float32
 tcoef(A::AbstractArray{Rational{Int}}) = Rational{Int}
 tcoef{T<:Integer}(A::AbstractArray{T}) = typeof(float(zero(T)))
 
-interpolate!{TWeights,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(::Type{TWeights}, A, ::Type{IT}, ::Type{GT}) = BSplineInterpolation(TWeights, prefilter!(TWeights, A, IT, GT), IT, GT, Val{0}())
-function interpolate!{IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(A::AbstractArray, ::Type{IT}, ::Type{GT})
-    interpolate!(tweight(A), A, IT, GT)
+interpolate!{TWeights,IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(::Type{TWeights}, A, it::IT, gt::GT) = BSplineInterpolation(TWeights, prefilter!(TWeights, A, IT, GT), it, gt, Val{0}())
+function interpolate!{IT<:DimSpec{BSpline},GT<:DimSpec{GridType}}(A::AbstractArray, it::IT, gt::GT)
+    interpolate!(tweight(A), A, it, gt)
 end
 
 include("constant.jl")

src/b-splines/quadratic.jl

@@ -1,5 +1,5 @@
 immutable Quadratic{BC<:BoundaryCondition} <: Degree{2} end
-Quadratic{BC<:BoundaryCondition}(::Type{BC}) = Quadratic{BC}
+Quadratic{BC<:BoundaryCondition}(::BC) = Quadratic{BC}()
 
 function define_indices_d{BC}(::Type{BSpline{Quadratic{BC}}}, d, pad)
     symix, symixm, symixp = symbol("ix_",d), symbol("ixm_",d), symbol("ixp_",d)

src/extrapolation/extrapolation.jl

@@ -3,7 +3,7 @@ export Throw
 type Extrapolation{T,N,ITPT,IT,GT,ET} <: AbstractInterpolationWrapper{T,N,ITPT,IT,GT}
     itp::ITPT
 end
-Extrapolation{T,ITPT,IT,GT,ET}(::Type{T}, N, itp::ITPT, ::Type{IT}, ::Type{GT}, ::Type{ET}) =
+Extrapolation{T,ITPT,IT,GT,ET}(::Type{T}, N, itp::ITPT, ::Type{IT}, ::Type{GT}, et::ET) =
     Extrapolation{T,N,ITPT,IT,GT,ET}(itp)
 
 """
@@ -14,15 +14,15 @@ The scheme can take any of these values:
 * `Throw` - throws a BoundsError for out-of-bounds indices
 * `Flat` - for constant extrapolation, taking the closest in-bounds value
 * `Linear` - linear extrapolation (the wrapped interpolation object must support gradient)
-* `Reflect` - reflecting extrapolation
-* `Periodic` - periodic extrapolation
+* `Reflect` - reflecting extrapolation (indices must support `mod`)
+* `Periodic` - periodic extrapolation (indices must support `mod`)
 
-You can also combine schemes in tuples. For example, the scheme `Tuple{Linear, Flat}` will use linear extrapolation in the first dimension, and constant in the second.
+You can also combine schemes in tuples. For example, the scheme `(Linear(), Flat())` will use linear extrapolation in the first dimension, and constant in the second.
 
-Finally, you can specify different extrapolation behavior in different direction. `Tuple{Tuple{Linear,Flat}, Flat}` will extrapolate linearly in the first dimension if the index is too small, but use constant etrapolation if it is too large, and always use constant extrapolation in the second dimension.
+Finally, you can specify different extrapolation behavior in different direction. `((Linear(),Flat()), Flat())` will extrapolate linearly in the first dimension if the index is too small, but use constant etrapolation if it is too large, and always use constant extrapolation in the second dimension.
 """
-extrapolate{T,N,IT,GT,ET}(itp::AbstractInterpolation{T,N,IT,GT}, ::Type{ET}) =
-    Extrapolation(T,N,itp,IT,GT,ET)
+extrapolate{T,N,IT,GT}(itp::AbstractInterpolation{T,N,IT,GT}, et) =
+    Extrapolation(T,N,itp,IT,GT,et)
 
 include("throw.jl")
 include("flat.jl")

src/extrapolation/filled.jl

@@ -1,6 +1,5 @@
 nindexes(N::Int) = N == 1 ? "1 index" : "$N indexes"
 
-
 type FilledExtrapolation{T,N,ITP<:AbstractInterpolation,IT,GT,FT} <: AbstractExtrapolation{T,N,ITP,IT,GT}
     itp::ITP
     fillvalue::FT

src/gridded/gridded.jl

@@ -1,7 +1,7 @@
 export Gridded
 
 immutable Gridded{D<:Degree} <: InterpolationType end
-Gridded{D<:Degree}(::Type{D}) = Gridded{D}
+Gridded{D<:Degree}(::D) = Gridded{D}()
 
 griddedtype{D<:Degree}(::Type{Gridded{D}}) = D
 
@@ -13,7 +13,7 @@ immutable GriddedInterpolation{T,N,TCoefs,IT<:DimSpec{Gridded},K<:Tuple{Vararg{V
     knots::K
     coefs::Array{TCoefs,N}
 end
-function GriddedInterpolation{N,TCoefs,TWeights<:Real,IT<:DimSpec{Gridded},pad}(::Type{TWeights}, knots::NTuple{N,GridIndex}, A::AbstractArray{TCoefs,N}, ::Type{IT}, ::Val{pad})
+function GriddedInterpolation{N,TCoefs,TWeights<:Real,IT<:DimSpec{Gridded},pad}(::Type{TWeights}, knots::NTuple{N,GridIndex}, A::AbstractArray{TCoefs,N}, ::IT, ::Val{pad})
     isleaftype(IT) || error("The b-spline type must be a leaf type (was $IT)")
     isleaftype(TCoefs) || warn("For performance reasons, consider using an array of a concrete type (eltype(A) == $(eltype(A)))")
 
@@ -48,16 +48,16 @@ iextract{T<:GridType}(::Type{T}, d) = T
     end
 end
 
-function interpolate{TWeights,TCoefs,Tel,N,IT<:DimSpec{Gridded}}(::Type{TWeights}, ::Type{TCoefs}, knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, ::Type{IT})
-    GriddedInterpolation(TWeights, knots, A, IT, Val{0}())
+function interpolate{TWeights,TCoefs,Tel,N,IT<:DimSpec{Gridded}}(::Type{TWeights}, ::Type{TCoefs}, knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, it::IT)
+    GriddedInterpolation(TWeights, knots, A, it, Val{0}())
 end
-function interpolate{Tel,N,IT<:DimSpec{Gridded}}(knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, ::Type{IT})
-    interpolate(tweight(A), tcoef(A), knots, A, IT)
+function interpolate{Tel,N,IT<:DimSpec{Gridded}}(knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, it::IT)
+    interpolate(tweight(A), tcoef(A), knots, A, it)
 end
 
-interpolate!{TWeights,Tel,N,IT<:DimSpec{Gridded}}(::Type{TWeights}, knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, ::Type{IT}) = GriddedInterpolation(TWeights, knots, A, IT, Val{0}())
-function interpolate!{Tel,N,IT<:DimSpec{Gridded}}(knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, ::Type{IT})
-    interpolate!(tweight(A), tcoef(A), knots, A, IT)
+interpolate!{TWeights,Tel,N,IT<:DimSpec{Gridded}}(::Type{TWeights}, knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, it::IT) = GriddedInterpolation(TWeights, knots, A, it, Val{0}())
+function interpolate!{Tel,N,IT<:DimSpec{Gridded}}(knots::NTuple{N,GridIndex}, A::AbstractArray{Tel,N}, it::IT)
+    interpolate!(tweight(A), tcoef(A), knots, A, it)
 end
 
 include("constant.jl")

test/b-splines/constant.jl

@@ -10,12 +10,12 @@ A2 = rand(Float64, N1, N1) * 100
 A3 = rand(Float64, N1, N1, N1) * 100
 
 for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
-    itp1c = @inferred(constructor(copier(A1), BSpline(Constant), OnCell))
-    itp1g = @inferred(constructor(copier(A1), BSpline(Constant), OnGrid))
-    itp2c = @inferred(constructor(copier(A2), BSpline(Constant), OnCell))
-    itp2g = @inferred(constructor(copier(A2), BSpline(Constant), OnGrid))
-    itp3c = @inferred(constructor(copier(A3), BSpline(Constant), OnCell))
-    itp3g = @inferred(constructor(copier(A3), BSpline(Constant), OnGrid))
+    itp1c = @inferred(constructor(copier(A1), BSpline(Constant()), OnCell()))
+    itp1g = @inferred(constructor(copier(A1), BSpline(Constant()), OnGrid()))
+    itp2c = @inferred(constructor(copier(A2), BSpline(Constant()), OnCell()))
+    itp2g = @inferred(constructor(copier(A2), BSpline(Constant()), OnGrid()))
+    itp3c = @inferred(constructor(copier(A3), BSpline(Constant()), OnCell()))
+    itp3g = @inferred(constructor(copier(A3), BSpline(Constant()), OnGrid()))
 
     # Evaluation on provided data points
     # 1D

test/b-splines/linear.jl

@@ -10,7 +10,7 @@ f(x) = g1(x)
 A1 = Float64[f(x) for x in 1:xmax]
 
 for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
-    itp1c = @inferred(constructor(copier(A1), BSpline(Linear), OnCell))
+    itp1c = @inferred(constructor(copier(A1), BSpline(Linear()), OnCell()))
 
     # Just interpolation
     for x in 1:.2:xmax
@@ -20,7 +20,7 @@ for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
     # Rational element types
     fr(x) = (x^2) // 40 + 2
     A1R = Rational{Int}[fr(x) for x in 1:10]
-    itp1r = @inferred(constructor(copier(A1R), BSpline(Linear), OnGrid))
+    itp1r = @inferred(constructor(copier(A1R), BSpline(Linear()), OnGrid()))
     @test @inferred(size(itp1r)) == size(A1R)
     @test_approx_eq_eps itp1r[23//10] fr(23//10) abs(.1*fr(23//10))
     @test typeof(itp1r[23//10]) == Rational{Int}
@@ -31,7 +31,7 @@ for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
     f(x,y) = g1(x)*g2(y)
     ymax = 10
     A2 = Float64[f(x,y) for x in 1:xmax, y in 1:ymax]
-    itp2 = @inferred(constructor(copier(A2), BSpline(Linear), OnGrid))
+    itp2 = @inferred(constructor(copier(A2), BSpline(Linear()), OnGrid()))
     @test @inferred(size(itp2)) == size(A2)
 
     for x in 2.1:.2:xmax-1, y in 1.9:.2:ymax-.9

test/b-splines/mixed.jl

@@ -7,8 +7,8 @@ N = 10
 for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
     A2 = rand(Float64, N, N) * 100
     for BC in (Flat,Line,Free,Periodic,Reflect,Natural), GT in (OnGrid, OnCell)
-        itp_a = @inferred(constructor(copier(A2), Tuple{BSpline(Linear), BSpline(Quadratic(BC))}, GT))
-        itp_b = @inferred(constructor(copier(A2), Tuple{BSpline(Quadratic(BC)), BSpline(Linear)}, GT))
+        itp_a = @inferred(constructor(copier(A2), (BSpline(Linear()), BSpline(Quadratic(BC()))), GT()))
+        itp_b = @inferred(constructor(copier(A2), (BSpline(Quadratic(BC())), BSpline(Linear())), GT()))
         @test @inferred(size(itp_a)) == size(A2)
         @test @inferred(size(itp_b)) == size(A2)
 

test/b-splines/multivalued.jl

@@ -23,20 +23,20 @@ Base.promote_rule{T1,T2<:Number}(::Type{MyPair{T1}}, ::Type{T2}) = MyPair{promot
 
 # 1d
 A = reinterpret(MyPair{Float64}, rand(2, 10), (10,))
-itp = interpolate(A, BSpline(Constant), OnGrid)
+itp = interpolate(A, BSpline(Constant()), OnGrid())
 itp[3.2]
-itp = interpolate(A, BSpline(Linear), OnGrid)
+itp = interpolate(A, BSpline(Linear()), OnGrid())
 itp[3.2]
-itp = interpolate(A, BSpline(Quadratic(Flat)), OnGrid)
+itp = interpolate(A, BSpline(Quadratic(Flat())), OnGrid())
 itp[3.2]
 
 # 2d
 A = reinterpret(MyPair{Float64}, rand(2, 10, 5), (10,5))
-itp = interpolate(A, BSpline(Constant), OnGrid)
+itp = interpolate(A, BSpline(Constant()), OnGrid())
 itp[3.2,1.8]
-itp = interpolate(A, BSpline(Linear), OnGrid)
+itp = interpolate(A, BSpline(Linear()), OnGrid())
 itp[3.2,1.8]
-itp = interpolate(A, BSpline(Quadratic(Flat)), OnGrid)
+itp = interpolate(A, BSpline(Quadratic(Flat())), OnGrid())
 itp[3.2,1.8]
 
 end

test/b-splines/quadratic.jl

@@ -7,7 +7,7 @@ for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
     xmax = 10
     A = Float64[f(x) for x in 1:xmax]
     for BC in (Flat,Line,Free,Periodic,Reflect,Natural), GT in (OnGrid, OnCell)
-        itp1 = @inferred(constructor(copier(A), BSpline(Quadratic(BC)), GT))
+        itp1 = @inferred(constructor(copier(A), BSpline(Quadratic(BC())), GT()))
         @test @inferred(size(itp1)) == size(A)
 
         # test that inner region is close to data
@@ -37,7 +37,7 @@ for (constructor, copier) in ((interpolate, x->x), (interpolate!, copy))
 
     # test that inner region is close to data
     for BC in (Flat,Line,Free,Periodic,Reflect,Natural), GT in (OnGrid, OnCell)
-        itp2 = @inferred(constructor(copier(A), BSpline(Quadratic(BC)), GT))
+        itp2 = @inferred(constructor(copier(A), BSpline(Quadratic(BC())), GT()))
         @test @inferred(size(itp2)) == size(A)
 
         for x in 3.1:.2:xmax-3, y in 3.1:2:ymax-3
@@ -50,15 +50,15 @@ let
     f(x) = sin((x-3)*2pi/9 - 1)
     xmax = 10
     A = Float64[f(x) for x in 1:xmax]
-    itp1 = interpolate!(copy(A), BSpline(Quadratic(InPlace)), OnCell)
+    itp1 = interpolate!(copy(A), BSpline(Quadratic(InPlace())), OnCell())
     for i = 1:xmax
         @test_approx_eq itp1[i] A[i]
     end
 
     f(x,y) = sin(x/10)*cos(y/6)
     xmax, ymax = 30,10
     A = Float64[f(x,y) for x in 1:xmax, y in 1:ymax]
-    itp2 = interpolate!(copy(A), BSpline(Quadratic(InPlace)), OnCell)
+    itp2 = interpolate!(copy(A), BSpline(Quadratic(InPlace())), OnCell())
     for j = 1:ymax, i = 1:xmax
         @test_approx_eq itp2[i,j] A[i,j]
     end

test/extrapolation/runtests.jl

@@ -7,14 +7,14 @@ f(x) = sin((x-3)*2pi/9 - 1)
 xmax = 10
 A = Float64[f(x) for x in 1:xmax]
 
-itpg = interpolate(A, BSpline(Linear), OnGrid)
+itpg = interpolate(A, BSpline(Linear()), OnGrid())
 
-etpg = extrapolate(itpg, Flat)
+etpg = extrapolate(itpg, Flat())
 
 @test etpg[-3] == etpg[-4.5] == etpg[0.9] == etpg[1.0] == A[1]
 @test etpg[10.1] == etpg[11] == etpg[148.298452] == A[end]
 
-etpf = @inferred(extrapolate(itpg, NaN))
+etpf = @inferred(extrapolate(itpg, FillValue(NaN)))
 
 @test @inferred(size(etpf)) == (xmax,)
 @test isnan(@inferred(getindex(etpf, -2.5)))
@@ -29,7 +29,7 @@ etpf = @inferred(extrapolate(itpg, NaN))
 
 @test isa(@inferred(getindex(etpf, dual(-2.5,1))), Dual)
 
-etpl = extrapolate(itpg, Linear)
+etpl = extrapolate(itpg, Linear())
 k_lo = A[2] - A[1]
 x_lo = -3.2
 @test_approx_eq etpl[x_lo] A[1]+k_lo*(x_lo-1)
@@ -41,19 +41,19 @@ x_hi = xmax + 5.7
 xmax, ymax = 8,8
 g(x, y) = (x^2 + 3x - 8) * (-2y^2 + y + 1)
 
-itp2g = interpolate(Float64[g(x,y) for x in 1:xmax, y in 1:ymax], Tuple{BSpline(Quadratic(Free)), BSpline(Linear)}, OnGrid)
-etp2g = extrapolate(itp2g, Tuple{Linear, Flat})
+itp2g = interpolate(Float64[g(x,y) for x in 1:xmax, y in 1:ymax], (BSpline(Quadratic(Free())), BSpline(Linear())), OnGrid())
+etp2g = extrapolate(itp2g, (Linear(), Flat()))
 
 @test_approx_eq @inferred(getindex(etp2g, -.5, 4)) itp2g[1,4]-1.5*epsilon(etp2g[dual(1,1),4])
 @test_approx_eq @inferred(getindex(etp2g, 5, 100)) itp2g[5,ymax]
 
-etp2ud = extrapolate(itp2g, Tuple{Tuple{Linear, Flat}, Flat})
+etp2ud = extrapolate(itp2g, ((Linear(), Flat()), Flat()))
 @test_approx_eq @inferred(getindex(etp2ud, -.5, 4)) itp2g[1,4] - 1.5*epsilon(etp2g[dual(1,1),4])
 @test @inferred(getindex(etp2ud, 5, -4)) == etp2ud[5,1]
 @test @inferred(getindex(etp2ud, 100, 4)) == etp2ud[8,4]
 @test @inferred(getindex(etp2ud, -.5, 100)) == itp2g[1,8] - 1.5 * epsilon(etp2g[dual(1,1),8])
 
-etp2ll = extrapolate(itp2g, Linear)
+etp2ll = extrapolate(itp2g, Linear())
 @test_approx_eq @inferred(getindex(etp2ll, -.5, 100)) itp2g[1,8]-1.5*epsilon(etp2ll[dual(1,1),8]) + (100-8) * epsilon(etp2ll[1,dual(8,1)])