Merge pull request #247 from sathvikbhagavan/sb/sym_second_order

refactor!: remove indexing dispatches and add dispatch for higher order derivatives with Symbolics

Author: ChrisRackauckas

ext/DataInterpolationsOptimExt.jl

@@ -31,7 +31,7 @@ function Curvefit(u,
         mfit = optimize(od, lb, ub, p0, Fminbox(alg))
     end
     pmin = Optim.minimizer(mfit)
-    CurvefitCache{true}(u, t, model, p0, ub, lb, alg, pmin, extrapolate)
+    CurvefitCache(u, t, model, p0, ub, lb, alg, pmin, extrapolate)
 end
 
 # Curvefit

ext/DataInterpolationsRegularizationToolsExt.jl

@@ -75,7 +75,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
     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{true}(u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolate)
+    RegularizationSmooth(u, û, t, t̂, wls, wr, d, λ, alg, Aitp, extrapolate)
 end
 """
 Direct smoothing, no `t̂` or weights
@@ -94,7 +94,7 @@ 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, extrapolate)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,
@@ -121,7 +121,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
     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)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,
@@ -149,7 +149,7 @@ function RegularizationSmooth(u::AbstractVector, t::AbstractVector, t̂::Abstrac
     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)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,
@@ -179,7 +179,7 @@ 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, extrapolate)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,
@@ -209,7 +209,7 @@ 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, extrapolate)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,
@@ -240,7 +240,7 @@ 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, extrapolate)
-    RegularizationSmooth{true}(u,
+    RegularizationSmooth(u,
         û,
         t,
         t̂,

ext/DataInterpolationsSymbolicsExt.jl

@@ -21,6 +21,10 @@ function derivative(interp::AbstractInterpolation, t::Num, order = 1)
 end
 SymbolicUtils.promote_symtype(::typeof(derivative), _...) = Real
 
+function Symbolics.derivative(::typeof(derivative), args::NTuple{3, Any}, ::Val{2})
+    Symbolics.unwrap(derivative(args[1], Symbolics.wrap(args[2]), args[3] + 1))
+end
+
 function Symbolics.derivative(interp::AbstractInterpolation, args::NTuple{1, Any}, ::Val{1})
     Symbolics.unwrap(derivative(interp, Symbolics.wrap(args[1])))
 end

src/DataInterpolations.jl

@@ -2,18 +2,7 @@ module DataInterpolations
 
 ### Interface Functionality
 
-abstract type AbstractInterpolation{FT, T} <: AbstractVector{T} end
-
-Base.size(A::AbstractInterpolation) = size(A.u)
-Base.size(A::AbstractInterpolation{true}) = length(A.u) .+ size(A.t)
-Base.getindex(A::AbstractInterpolation, i) = A.u[i]
-function Base.getindex(A::AbstractInterpolation{true}, i)
-    i <= length(A.u) ? A.u[i] : A.t[i - length(A.u)]
-end
-Base.setindex!(A::AbstractInterpolation, x, i) = A.u[i] = x
-function Base.setindex!(A::AbstractInterpolation{true}, x, i)
-    i <= length(A.u) ? (A.u[i] = x) : (A.t[i - length(A.u)] = x)
-end
+abstract type AbstractInterpolation{T} end
 
 using LinearAlgebra, RecipesBase
 using PrettyTables
@@ -67,7 +56,7 @@ export LinearInterpolation, QuadraticInterpolation, LagrangeInterpolation,
 
 # added for RegularizationSmooth, JJS 11/27/21
 ### Regularization data smoothing and interpolation
-struct RegularizationSmooth{uType, tType, FT, T, T2} <: AbstractInterpolation{FT, T}
+struct RegularizationSmooth{uType, tType, T, T2} <: AbstractInterpolation{T}
     u::uType
     û::uType
     t::tType
@@ -77,9 +66,9 @@ struct RegularizationSmooth{uType, tType, FT, T, T2} <: AbstractInterpolation{FT
     d::Int       # derivative degree used to calculate the roughness
     λ::T2        # regularization parameter
     alg::Symbol  # how to determine λ: `:fixed`, `:gcv_svd`, `:gcv_tr`, `L_curve`
-    Aitp::AbstractInterpolation{FT, T}
+    Aitp::AbstractInterpolation{T}
     extrapolate::Bool
-    function RegularizationSmooth{FT}(u,
+    function RegularizationSmooth(u,
             û,
             t,
             t̂,
@@ -89,8 +78,8 @@ struct RegularizationSmooth{uType, tType, FT, T, T2} <: AbstractInterpolation{FT
             λ,
             alg,
             Aitp,
-            extrapolate) where {FT}
-        new{typeof(u), typeof(t), FT, eltype(u), typeof(λ)}(u,
+            extrapolate)
+        new{typeof(u), typeof(t), eltype(u), typeof(λ)}(u,
             û,
             t,
             t̂,
@@ -116,9 +105,8 @@ struct CurvefitCache{
     lbType,
     algType,
     pminType,
-    FT,
     T
-} <: AbstractInterpolation{FT, T}
+} <: AbstractInterpolation{T}
     u::uType
     t::tType
     m::mType        # model type
@@ -128,10 +116,10 @@ struct CurvefitCache{
     alg::algType    # alg to optimize cost function
     pmin::pminType  # optimized params
     extrapolate::Bool
-    function CurvefitCache{FT}(u, t, m, p0, ub, lb, alg, pmin, extrapolate) where {FT}
+    function CurvefitCache(u, t, m, p0, ub, lb, alg, pmin, extrapolate)
         new{typeof(u), typeof(t), typeof(m),
             typeof(p0), typeof(ub), typeof(lb),
-            typeof(alg), typeof(pmin), FT, eltype(u)}(u,
+            typeof(alg), typeof(pmin), eltype(u)}(u,
             t,
             m,
             p0,
@@ -150,7 +138,4 @@ end
 
 export Curvefit
 
-# Deprecated April 2020
-export ZeroSpline
-
 end # module

src/integrals.jl

@@ -14,7 +14,7 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     if A.t[idx2] == t2
         idx2 -= 1
     end
-    total = zero(eltype(A))
+    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]