Fix interpolant evaluation error

src/interpolation.jl

@@ -4,6 +4,10 @@
     cache
 end
 
+function DiffEqBase.interp_summary(interp::MIRKInterpolation)
+    return "MIRK Order $(interp.cache.order) Interpolation"
+end
+
 function (id::MIRKInterpolation)(tvals, idxs, deriv, p, continuity::Symbol = :left)
     interpolation(tvals, id, idxs, deriv, p, continuity)
 end
@@ -12,15 +16,11 @@
     interpolation!(val, tvals, id, idxs, deriv, p, continuity)
 end
 
-@inline function interpolation(tvals,
-    id::I,
-    idxs,
-    deriv::D,
-    p,
+# FIXME: Fix the interpolation outside the tspan
+
+@inline function interpolation(tvals, id::I, idxs, deriv::D, p,
     continuity::Symbol = :left) where {I, D}
-    t = id.t
-    u = id.u
-    cache = id.cache
+    @unpack t, u, cache = id
     tdir = sign(t[end] - t[1])
     idx = sortperm(tvals, rev = tdir < 0)
 
@@ -33,56 +33,29 @@
     end
 
     for j in idx
-        tval = tvals[j]
-        i = interval(t, tval)
-        dt = t[i + 1] - t[i]
-        θ = (tval - t[i]) / dt
-        weights, _ = interp_weights(θ, cache.alg)
-        z = zeros(cache.M)
-        sum_stages!(z, cache, weights, i)
-        vals[j] = copy(z)
+        z = similar(cache.fᵢ₂_cache)
+        interp_eval!(z, id.cache, tvals[j], id.cache.mesh, id.cache.mesh_dt)
+        vals[j] = z
     end
-    DiffEqArray(vals, tvals)
+    return DiffEqArray(vals, tvals)
 end
 
-@inline function interpolation!(vals,
-    tvals,
-    id::I,
-    idxs,
-    deriv::D,
-    p,
+@inline function interpolation!(vals, tvals, id::I, idxs, deriv::D, p,
     continuity::Symbol = :left) where {I, D}
-    t = id.t
-    cache = id.cache
+    @unpack t, cache = id
     tdir = sign(t[end] - t[1])
     idx = sortperm(tvals, rev = tdir < 0)
 
     for j in idx
-        tval = tvals[j]
-        i = interval(t, tval)
-        dt = t[i] - t[i - 1]
-        θ = (tval - t[i]) / dt
-        weights, _ = interp_weights(θ, cache.alg)
-        z = zeros(cache.M)
-        sum_stages!(z, cache, weights, i)
-        vals[j] = copy(z)
+        z = similar(cache.fᵢ₂_cache)
+        interp_eval!(z, id.cache, tvals[j], id.cache.mesh, id.cache.mesh_dt)
+        vals[j] = z
     end
 end
 
-@inline function interpolation(tval::Number,
-    id::I,
-    idxs,
-    deriv::D,
-    p,
+@inline function interpolation(tval::Number, id::I, idxs, deriv::D, p,
     continuity::Symbol = :left) where {I, D}
-    t = id.t
-    cache = id.cache
-    i = interval(t, tval)
-    dt = t[i] - t[i - 1]
-    θ = (tval - t[i]) / dt
-    weights, _ = interp_weights(θ, cache.alg)
-    z = zeros(cache.M)
-    sum_stages!(z, cache, weights, i)
-    val = copy(z)
-    val
+    z = similar(id.cache.fᵢ₂_cache)
+    interp_eval!(z, id.cache, tval, id.cache.mesh, id.cache.mesh_dt)
+    return z
 end

test/interpolation_test.jl

@@ -0,0 +1,33 @@
+using BoundaryValueDiffEq, DiffEqBase, DiffEqDevTools, LinearAlgebra, Test
+
+λ = 1
+function prob_bvp_linear_analytic(u, λ, t)
+    a = 1 / sqrt(λ)
+    [(exp(-a * t) - exp((t - 2) * a)) / (1 - exp(-2 * a)),
+        (-a * exp(-t * a) - a * exp((t - 2) * a)) / (1 - exp(-2 * a))]
+end
+function prob_bvp_linear_f!(du, u, p, t)
+    du[1] = u[2]
+    du[2] = 1 / p * u[1]
+end
+function prob_bvp_linear_bc!(res, u, p, t)
+    res[1] = u[1][1] - 1
+    res[2] = u[end][1]
+end
+prob_bvp_linear_function = ODEFunction(prob_bvp_linear_f!, analytic = prob_bvp_linear_analytic)
+prob_bvp_linear_tspan = (0.0, 1.0)
+prob_bvp_linear = BVProblem(prob_bvp_linear_function, prob_bvp_linear_bc!,
+    [1.0, 0.0], prob_bvp_linear_tspan, λ)
+testTol = 1e-6
+
+for order in (2, 3, 4, 5, 6)
+    s = Symbol("MIRK$(order)")
+    @eval mirk_solver(::Val{$order}) = $(s)()
+end
+
+@testset "Interpolation" begin
+    @testset "MIRK$order" for order in (2, 3, 4, 5, 6)
+        @time sol = solve(prob_bvp_linear, mirk_solver(Val(order)); dt = 0.001)
+        @test sol(0.001) ≈ [0.998687464, -1.312035941] atol=testTol
+    end
+end

test/runtests.jl

@@ -33,4 +33,10 @@ using Test, SafeTestsets
             include("non_vector_inputs.jl")
         end
     end
+
+    @time @testset "Interpolation Tests" begin
+        @time @safetestset "MIRK Interpolation Test" begin
+            include("interpolation_test.jl")
+        end
+    end
 end