Memory allocations when solving ODE with `ScaledOperator`

[albertomercurio]

Describe the bug 🐞

When solving a simple ODE using a ScaledOperator, I see many memory allocations. If I initialize the operator as a MatrixOperator, everything is fine. I think this issue might be related to #246. I also have the same problem using dense matrices.

Expected behavior

Just to have the minimum memory allocations required for an ODE. The memory allocations don't have to scale with the integration time.

Minimal Reproducible Example 👇

T = Float64
N = 100
A = -1 * MatrixOperator(sprand(T, N, N, 0.1))

v = rand(T, N)
A = cache_operator(A, rand(T, N))

tspan = (0.0, 2.0)

prob = ODEProblem{true}(A, v, tspan)
@benchmark solve($prob, Tsit5(), saveat=$[tspan[end]])

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  37.844 μs …  12.317 ms  ┊ GC (min … max): 0.00% … 99.32%
 Time  (median):     43.317 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   44.688 μs ± 122.845 μs  ┊ GC (mean ± σ):  2.74% ±  0.99%

    █▃        ▁▁▃▂                                              
  ▂▆███▇▆▆▆▆▆▆█████▇▆▅▄▄▄▃▃▃▃▃▃▂▂▂▂▂▂▂▂▂▂▂▂▁▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂▂ ▃
  37.8 μs         Histogram: frequency by time         64.8 μs <

 Memory estimate: 34.66 KiB, allocs estimate: 425.

And with a simple MatrixOperator everything is fine

A = MatrixOperator(-1 * sprand(T, N, N, 0.1))

v = rand(T, N)
A = cache_operator(A, rand(T, N))

tspan = (0.0, 2.0)

prob = ODEProblem{true}(A, v, tspan)
@benchmark solve($prob, Tsit5(), saveat=$[tspan[end]])

BenchmarkTools.Trial: 10000 samples with 1 evaluation.
 Range (min … max):  31.964 μs … 224.430 μs  ┊ GC (min … max): 0.00% … 0.00%
 Time  (median):     36.132 μs               ┊ GC (median):    0.00%
 Time  (mean ± σ):   36.747 μs ±   4.241 μs  ┊ GC (mean ± σ):  0.00% ± 0.00%

     ▁         ▁█▅▂▂▂    ▂                                      
  ▁▁▆█▆▃▃▂▃▃▅▅▅██████▇▇▇██▇▇▆▆▅▅▄▄▄▃▃▃▃▃▃▂▃▃▂▂▃▃▂▂▂▂▂▂▁▂▁▁▁▁▁▁ ▃
  32 μs           Histogram: frequency by time         44.8 μs <

 Memory estimate: 17.25 KiB, allocs estimate: 54.

Environment (please complete the following information):

• Output of using Pkg; Pkg.status()

Status `~/GitHub/Research/Undef/Benchmark QuantumToolbox Stable/Dev Version/Project.toml`
  [6e4b80f9] BenchmarkTools v1.5.0
  [f68482b8] Cthulhu v2.15.2
  [1dea7af3] OrdinaryDiffEq v6.89.0
  [6c2fb7c5] QuantumToolbox v0.18.0 `~/.julia/dev/QuantumToolbox`
  [295af30f] Revise v3.6.1
  [c0aeaf25] SciMLOperators v0.3.10

• Output of versioninfo()

Julia Version 1.11.0
Commit 501a4f25c2b (2024-10-07 11:40 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × 13th Gen Intel(R) Core(TM) i9-13900KF
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 16 default, 0 interactive, 8 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 16

[ChrisRackauckas]

We had some regressions here with the v1.0 release, but I'm not quite sure why. I setup an AllocCheck.jl file to make it easy to dive into.

[albertomercurio]

I made a PR #288 that fixes again this issue.