Extend extrapolation methods to allow for arbitrary arrays.

Author: michakraus

src/extrapolation/aitken_neville.jl

@@ -11,18 +11,18 @@ where
 * `ti`: interpolation nodes
 * `xi`: interpolation values
 """
-function aitken_neville!(x::AbstractVector, t::TT, ti::AbstractVector{TT}, xi::AbstractMatrix) where {TT}
-    @assert length(ti) == size(xi,2)
-    @assert length(x)  == size(xi,1)
+function aitken_neville!(x::AbstractArray, t::TT, ti::AbstractVector{TT}, xi::AbstractVector) where {TT}
+    @assert length(ti) == length(xi)
+    
+    for _xi in xi
+        @assert axes(x) == axes(_xi)
+    end
 
     for j in eachindex(ti)
-        for i in 1:(length(ti)-j)
-            for k in axes(x,1)
-                xi[k,i] = xi[k,i+1] + (xi[k,i] - xi[k,i+1]) * (ti[i+j] - t) / (ti[i+j] - ti[i])
-            end
+        for i in eachindex(ti)[begin:end-j]
+            @. xi[i] = xi[i+1] + (xi[i] - xi[i+1]) * (ti[i+j] - t) / (ti[i+j] - ti[i])
         end
     end
-    for k in eachindex(x)
-        x[k] = xi[k,1]
-    end
+
+    copyto!(x, xi[1])
 end

src/extrapolation/euler.jl

@@ -34,30 +34,24 @@ struct EulerExtrapolation <: Extrapolation
 end
 
 
-function extrapolate!(t₀::TT, x₀::AbstractVector{DT},
-                      t₁::TT, x₁::AbstractVector{DT},
+function extrapolate!(t₀::TT, x₀::AbstractArray{DT},
+                      t₁::TT, x₁::AbstractArray{DT},
                       problem::AbstractProblemODE,
                       extrap::EulerExtrapolation) where {DT,TT}
 
     @assert axes(x₀) == axes(x₁)
 
     local F   = collect(1:(extrap.s+1))
     local σ   = (t₁ - t₀) ./ F
-    local pts = repeat(x₀, outer = [1, extrap.s+1])
+    local pts = [copy(x₀) for _ in F]
 
-    local xᵢ = zero(x₀)
     local vᵢ = zero(x₀)
 
     for i in F
         for _ in 1:(F[i]-1)
-            tᵢ = t₀ + σ[i]
-            for k in axes(pts,1)
-                xᵢ[k] = pts[k,i]
-            end
-            initialguess(problem).v(vᵢ, tᵢ, xᵢ, parameters(problem))
-            for k in axes(pts,1)
-                pts[k,i] += σ[i] * vᵢ[k]
-            end
+            tᵢ  = t₀ + σ[i]
+            initialguess(problem).v(vᵢ, tᵢ, pts[i], parameters(problem))
+            pts[i] .+= σ[i] * vᵢ
         end
     end
 

src/extrapolation/midpoint.jl

@@ -92,8 +92,8 @@ end
 
 
 function extrapolate!(
-        t₀::TT, x₀::AbstractVector{DT},
-        t₁::TT, x₁::AbstractVector{DT},
+        t₀::TT, x₀::AbstractArray{DT},
+        t₁::TT, x₁::AbstractArray{DT},
         problem::Union{AbstractProblemODE, SODEProblem},
         extrap::MidpointExtrapolation) where {DT,TT}
 
@@ -102,7 +102,7 @@ function extrapolate!(
     local F   = [2i*one(TT) for i in 1:extrap.s+1]
     local σ   = (t₁ - t₀) ./ F
     local σ²  = σ.^2
-    local pts = zeros(DT, axes(x₀)..., extrap.s+1)
+    local pts = [zero(x₀) for _ in 1:extrap.s+1]
 
     local xᵢ₁ = zero(x₀)
     local xᵢ₂ = zero(x₀)
@@ -112,7 +112,7 @@ function extrapolate!(
 
     initialguess(problem).v(v₀, t₀, x₀, parameters(problem))
 
-    for i in 1:extrap.s+1
+    for i in eachindex(pts)
         tᵢ   = t₀ + σ[i]
         xᵢ₁ .= x₀
         xᵢ₂ .= x₀ .+ σ[i] .* v₀
@@ -122,9 +122,7 @@ function extrapolate!(
             xᵢ₁ .= xᵢ₂
             xᵢ₂ .= xᵢₜ
         end
-        for k in axes(pts,1)
-            pts[k,i] += xᵢ₂[k]
-        end
+        pts[i] .+= xᵢ₂
     end
 
     aitken_neville!(x₁, zero(TT), σ², pts)
@@ -150,8 +148,8 @@ function extrapolate!(t₀::TT, q₀::AbstractVector{DT}, p₀::AbstractVector{D
     local σ   = (t₁ - t₀) ./ F
     local σ2  = σ.^2
 
-    local qts = zeros(DT, axes(q₀)..., extrap.s+1)
-    local pts = zeros(DT, axes(p₀)..., extrap.s+1)
+    local qts = [zero(q₀) for _ in 1:extrap.s+1]
+    local pts = [zero(p₀) for _ in 1:extrap.s+1]
 
     local qᵢ₁= zero(q₀)
     local qᵢ₂= zero(q₀)
@@ -186,12 +184,8 @@ function extrapolate!(t₀::TT, q₀::AbstractVector{DT}, p₀::AbstractVector{D
             pᵢ₁ .= pᵢ₂
             pᵢ₂ .= pᵢₜ
         end
-        for k in axes(qts,1)
-            qts[k,i] += qᵢ₂[k]
-        end
-        for k in axes(pts,1)
-            pts[k,i] += pᵢ₂[k]
-        end
+        qts[i] .+= qᵢ₂
+        pts[i] .+= pᵢ₂
     end
 
     aitken_neville!(q₁, zero(TT), σ2, qts)
@@ -219,8 +213,8 @@ function extrapolate!(
     local σ   = (t₁ - t₀) ./ F
     local σ2  = σ.^2
 
-    local qts = zeros(DT, axes(q₀)..., extrap.s+1)
-    local pts = zeros(DT, axes(p₀)..., extrap.s+1)
+    local qts = [zero(q₀) for _ in 1:extrap.s+1]
+    local pts = [zero(p₀) for _ in 1:extrap.s+1]
 
     local qᵢ₁= zero(q₀)
     local qᵢ₂= zero(q₀)
@@ -255,12 +249,8 @@ function extrapolate!(
             pᵢ₁ .= pᵢ₂
             pᵢ₂ .= pᵢₜ
         end
-        for k in axes(qts,1)
-            qts[k,i] += qᵢ₂[k]
-        end
-        for k in axes(pts,1)
-            pts[k,i] += pᵢ₂[k]
-        end
+        qts[i] .+= qᵢ₂
+        pts[i] .+= pᵢ₂
     end
 
     aitken_neville!(q₁, zero(TT), σ2, qts)