handle some composite cache caching

Author: ChrisRackauckas

src/OrdinaryDiffEq.jl

@@ -180,6 +180,7 @@ using DocStringExtensions
         du[3] = u[1]*u[2] - (8/3)*u[3]
       end
       lorenzprob = ODEProblem(lorenz,[1.0;0.0;0.0],(0.0,1.0))
+      solve(lorenzprob,BS3())
       solve(lorenzprob,Tsit5())
       solve(lorenzprob,Vern7())
       solve(lorenzprob,Vern9())
@@ -188,6 +189,16 @@ using DocStringExtensions
       solve(lorenzprob,Rodas4(autodiff=false))
       solve(lorenzprob,KenCarp4(autodiff=false))
       solve(lorenzprob,Rodas5())
+      solve(lorenzprob,QNDF())
+      solve(lorenzprob,QNDF(autodiff=false))
+      solve(lorenzprob,AutoTsit5(Rosenbrock23()))
+      solve(lorenzprob,AutoTsit5(Rosenbrock23(autodiff=false)))
+      solve(lorenzprob,AutoTsit5(TRBDF2(autodiff=false)))
+      solve(lorenzprob,AutoVern7(Rodas4(autodiff=false)))
+      solve(lorenzprob,AutoVern7(TRBDF2(autodiff=false)))
+      solve(lorenzprob,AutoVern9(Rodas5(autodiff=false)))
+      solve(lorenzprob,AutoVern9(KenCarp47(autodiff=false)))
+      solve(lorenzprob,AutoVern7(Rodas5()))
       break
     end
   end

src/alg_utils.jl

@@ -63,6 +63,14 @@ end
 issplit(alg::Union{OrdinaryDiffEqAlgorithm,DAEAlgorithm}) = false
 issplit(alg::SplitAlgorithms) = true
 
+function _composite_beta1_default(algs::Tuple{T1,T2}, current, ::Type{QT}, beta2) where {T1, T2, QT}
+  if current == 1
+    return QT(beta1_default(algs[1], beta2))
+  elseif current == 2
+    return QT(beta1_default(algs[2], beta2))
+  end
+end
+
 @generated function _composite_beta1_default(algs::T, current, ::Type{QT}, beta2) where {T <: Tuple, QT}
   expr = Expr(:block)
   for i in 1:length(T.types)
@@ -74,6 +82,15 @@ issplit(alg::SplitAlgorithms) = true
   end
   return expr
 end
+
+function _composite_beta2_default(algs::Tuple{T1,T2}, current, ::Type{QT}) where {T1, T2, QT}
+  if current == 1
+    return QT(beta2_default(algs[1]))
+  elseif current == 2
+    return QT(beta2_default(algs[2]))
+  end
+end
+
 @generated function _composite_beta2_default(algs::T, current, ::Type{QT}) where {T <: Tuple, QT}
   expr = Expr(:block)
   for i in 1:length(T.types)