Add a fast path for evenly-spaced abscissae

Project.toml

@@ -25,6 +25,7 @@ DataInterpolationsSymbolicsExt = "Symbolics"
 
 [compat]
 Aqua = "0.8"
+BenchmarkTools = "1"
 ChainRulesCore = "1.24"
 FindFirstFunctions = "1.1"
 FiniteDifferences = "0.12.31"
@@ -45,6 +46,7 @@ julia = "1.10"
 
 [extras]
 Aqua = "4c88cf16-eb10-579e-8560-4a9242c79595"
+BenchmarkTools = "6e4b80f9-dd63-53aa-95a3-0cdb28fa8baf"
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
 ForwardDiff = "f6369f11-7733-5829-9624-2563aa707210"
@@ -58,4 +60,4 @@ Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 Zygote = "e88e6eb3-aa80-5325-afca-941959d7151f"
 
 [targets]
-test = ["Aqua", "SafeTestsets", "ChainRulesCore", "Optim", "RegularizationTools", "Test", "StableRNGs", "FiniteDifferences", "QuadGK", "ForwardDiff", "Symbolics", "Zygote"]
+test = ["Aqua", "BenchmarkTools", "SafeTestsets", "ChainRulesCore", "Optim", "RegularizationTools", "Test", "StableRNGs", "FiniteDifferences", "QuadGK", "ForwardDiff", "Symbolics", "Zygote"]

docs/src/manual.md

@@ -14,3 +14,9 @@ CubicHermiteSpline
 PCHIPInterpolation
 QuinticHermiteSpline
 ```
+
+# Utility Functions
+
+```@docs
+DataInterpolations.looks_linear
+```

ext/DataInterpolationsChainRulesCoreExt.jl

@@ -52,7 +52,7 @@ end
 
 function u_tangent(A::LinearInterpolation, t, Δ)
     out = zero(A.u)
-    idx = get_idx(A.t, t, A.idx_prev[])
+    idx = get_idx(A, t, A.idx_prev[])
     t_factor = (t - A.t[idx]) / (A.t[idx + 1] - A.t[idx])
     out[idx] = Δ * (one(eltype(out)) - t_factor)
     out[idx + 1] = Δ * t_factor

src/derivatives.jl

@@ -18,7 +18,7 @@ function derivative(A, t, order = 1)
 end
 
 function _derivative(A::LinearInterpolation, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess; idx_shift = -1, ub_shift = -1, side = :first)
+    idx = get_idx(A, t, iguess; idx_shift = -1, ub_shift = -1, side = :first)
     slope = get_parameters(A, idx)
     slope, idx
 end
@@ -108,7 +108,7 @@ function _derivative(A::LagrangeInterpolation{<:AbstractMatrix}, t::Number, idx)
 end
 
 function _derivative(A::AkimaInterpolation{<:AbstractVector}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess; idx_shift = -1, side = :first)
+    idx = get_idx(A, t, iguess; idx_shift = -1, side = :first)
     j = min(idx, length(A.c))  # for smooth derivative at A.t[end]
     wj = t - A.t[idx]
     (@evalpoly wj A.b[idx] 2A.c[j] 3A.d[j]), idx
@@ -130,14 +130,14 @@ end
 
 # QuadraticSpline Interpolation
 function _derivative(A::QuadraticSpline{<:AbstractVector}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess; lb = 2, ub_shift = 0, side = :first)
+    idx = get_idx(A, t, iguess; lb = 2, ub_shift = 0, side = :first)
     σ = get_parameters(A, idx - 1)
     A.z[idx - 1] + 2σ * (t - A.t[idx - 1]), idx
 end
 
 # CubicSpline Interpolation
 function _derivative(A::CubicSpline{<:AbstractVector}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     Δt₁ = t - A.t[idx]
     Δt₂ = A.t[idx + 1] - t
     dI = (-A.z[idx] * Δt₂^2 + A.z[idx + 1] * Δt₁^2) / (2A.h[idx + 1])
@@ -151,7 +151,7 @@ function _derivative(A::BSplineInterpolation{<:AbstractVector{<:Number}}, t::Num
     # change t into param [0 1]
     t < A.t[1] && return zero(A.u[1]), 1
     t > A.t[end] && return zero(A.u[end]), lastindex(t)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     n = length(A.t)
     scale = (A.p[idx + 1] - A.p[idx]) / (A.t[idx + 1] - A.t[idx])
     t_ = A.p[idx] + (t - A.t[idx]) * scale
@@ -173,7 +173,7 @@ function _derivative(A::BSplineApprox{<:AbstractVector{<:Number}}, t::Number, ig
     # change t into param [0 1]
     t < A.t[1] && return zero(A.u[1]), 1
     t > A.t[end] && return zero(A.u[end]), lastindex(t)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     scale = (A.p[idx + 1] - A.p[idx]) / (A.t[idx + 1] - A.t[idx])
     t_ = A.p[idx] + (t - A.t[idx]) * scale
     N = t isa ForwardDiff.Dual ? zeros(eltype(t), A.h) : A.N
@@ -192,7 +192,7 @@ end
 # Cubic Hermite Spline
 function _derivative(
         A::CubicHermiteSpline{<:AbstractVector{<:Number}}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     Δt₀ = t - A.t[idx]
     Δt₁ = t - A.t[idx + 1]
     out = A.du[idx]
@@ -204,7 +204,7 @@ end
 # Quintic Hermite Spline
 function _derivative(
         A::QuinticHermiteSpline{<:AbstractVector{<:Number}}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     Δt₀ = t - A.t[idx]
     Δt₁ = t - A.t[idx + 1]
     out = A.du[idx] + A.ddu[idx] * Δt₀

src/integral_inverses.jl

@@ -59,7 +59,7 @@ end
 
 function _interpolate(
         A::LinearInterpolationIntInv{<:AbstractVector{<:Number}}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess)
+    idx = get_idx(A, t, iguess)
     Δt = t - A.t[idx]
     x = A.itp.u[idx]
     slope = get_parameters(A.itp, idx)
@@ -104,13 +104,13 @@ end
 
 function _interpolate(
         A::ConstantInterpolationIntInv{<:AbstractVector{<:Number}}, t::Number, iguess)
-    idx = get_idx(A.t, t, iguess; ub_shift = 0)
+    idx = get_idx(A, t, iguess; ub_shift = 0)
     if A.itp.dir === :left
         # :left means that value to the left is used for interpolation
-        idx_ = get_idx(A.t, t, idx; lb = 1, ub_shift = 0)
+        idx_ = get_idx(A, t, idx; lb = 1, ub_shift = 0)
     else
         # :right means that value to the right is used for interpolation
-        idx_ = get_idx(A.t, t, idx; side = :first, lb = 1, ub_shift = 0)
+        idx_ = get_idx(A, t, idx; side = :first, lb = 1, ub_shift = 0)
     end
     A.u[idx] + (t - A.t[idx]) / A.itp.u[idx_], idx
 end

src/integrals.jl

@@ -8,9 +8,9 @@ function integral(A::AbstractInterpolation, t1::Number, t2::Number)
     ((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.t, t1, 0)
+    idx1 = get_idx(A, t1, 0)
     # the index less than t2
-    idx2 = get_idx(A.t, t2, 0; idx_shift = -1, side = :first)
+    idx2 = get_idx(A, t2, 0; idx_shift = -1, side = :first)
 
     if A.cache_parameters
         total = A.I[idx2] - A.I[idx1]