fix InvertibleOperator caching, add tests

src/matrix.jl

@@ -238,6 +238,14 @@ islinear(L::InvertibleOperator) = islinear(L.L)
 has_ldiv(L::InvertibleOperator) = has_mul(L.F)
 has_ldiv!(L::InvertibleOperator) = has_ldiv!(L.F)
 
+function cache_internals(L::InvertibleOperator, u::AbstractVecOrMat)
+
+    @set! L.L = cache_operator(L.L, u)
+    @set! L.F = cache_operator(L.F, u)
+
+    L
+end
+
 # operator application
 Base.:*(L::InvertibleOperator, x::AbstractVecOrMat) = L.L * x
 Base.:\(L::InvertibleOperator, x::AbstractVecOrMat) = L.F \ x

test/matrix.jl

@@ -1,7 +1,7 @@
 using SciMLOperators, LinearAlgebra
 using Random
 
-using SciMLOperators: InvertibleOperator, ⊗
+using SciMLOperators: InvertibleOperator, InvertedOperator, ⊗
 using FFTW
 
 Random.seed!(0)
@@ -60,6 +60,32 @@ K = 19
     v=rand(N,K); w=copy(v); @test mul!(v, AA, u, α, β) ≈ α*A*u + β*w
 end
 
+@testset "InvertibleOperator test" begin
+    u = rand(N,K)
+    p = nothing
+    t = 0
+    α = rand()
+    β = rand()
+
+    d = rand(N, K)
+    D  = DiagonalOperator(d)
+    Di = DiagonalOperator(inv.(d)) |> InvertedOperator
+
+    L = InvertibleOperator(D, Di)
+    L = cache_operator(L, u)
+
+    @test iscached(L)
+
+    @test L * u ≈ d .* u
+    @test L \ u ≈ d .\ u
+
+    v=rand(N,K); @test mul!(v, L, u) ≈ d .* u
+    v=rand(N,K); w=copy(v); @test mul!(v, L, u, α, β) ≈ α*(d .* u) + β*w
+
+    v=rand(N,K); @test ldiv!(v, L, u) ≈ d .\ u
+    v=copy(u); @test ldiv!(L, v) ≈ d .\ u
+end
+
 @testset "MatrixOperator update test" begin
     u = rand(N,K)
     p = rand(N)