dot is quite slow in multinest Arrays

[XingyuZhang2018]

The Minimal Working Example (MWE) for this bug:

using LinearAlgebra
using BenchmarkTools
using Random
using CUDA
using Test
@testset "dot $atype" for atype in [Array, CuArray]
    Random.seed!(100)
    N = 10^2
    A = atype(rand(ComplexF64, N,N))
    B = [A]
    C = [B]
    D = [C]
    @btime CUDA.@sync dot($A, $A)
    @btime CUDA.@sync dot($B, $B)
    @btime CUDA.@sync dot($C, $C)
    @btime CUDA.@sync dot($D, $D)
end

  1.400 μs (0 allocations: 0 bytes)
  2.522 μs (0 allocations: 0 bytes)
  4.743 μs (0 allocations: 0 bytes)
  9.200 μs (0 allocations: 0 bytes)
Test Summary: | Total   Time
dot Array     |     0  13.9s
  84.900 μs (14 allocations: 240 bytes)
  207.000 μs (28 allocations: 480 bytes)
  874.700 μs (56 allocations: 960 bytes)
  2.081 ms (112 allocations: 1.88 KiB)
Test Summary: | Total   Time
dot CuArray   |     0  44.5s

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    ZygoteDistancesExt = "Distances"
    ZygoteTrackerExt = "Tracker"

    [deps.Zygote.weakdeps]
    Colors = "5ae59095-9a9b-59fe-a467-6f913c188581"
    Distances = "b4f34e82-e78d-54a5-968a-f98e89d6e8f7"
    Tracker = "9f7883ad-71c0-57eb-9f7f-b5c9e6d3789c"

[[deps.ZygoteRules]]
deps = ["ChainRulesCore", "MacroTools"]
git-tree-sha1 = "27798139afc0a2afa7b1824c206d5e87ea587a00"
uuid = "700de1a5-db45-46bc-99cf-38207098b444"
version = "0.2.5"

[[deps.demumble_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "6498e3581023f8e530f34760d18f75a69e3a4ea8"
uuid = "1e29f10c-031c-5a83-9565-69cddfc27673"
version = "1.3.0+0"

[[deps.libblastrampoline_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850b90-86db-534c-a0d3-1478176c7d93"
version = "5.11.0+0"

[[deps.nghttp2_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "8e850ede-7688-5339-a07c-302acd2aaf8d"
version = "1.59.0+0"

[[deps.oneTBB_jll]]
deps = ["Artifacts", "JLLWrappers", "Libdl"]
git-tree-sha1 = "7d0ea0f4895ef2f5cb83645fa689e52cb55cf493"
uuid = "1317d2d5-d96f-522e-a858-c73665f53c3e"
version = "2021.12.0+0"

[[deps.p7zip_jll]]
deps = ["Artifacts", "Libdl"]
uuid = "3f19e933-33d8-53b3-aaab-bd5110c3b7a0"
version = "17.4.0+2"

Expected behavior

A clear and concise description of what you expected to happen.

Version info

Details on Julia:

Julia Version 1.11.1
Commit 8f5b7ca12a (2024-10-16 10:53 UTC)
Build Info:
  Official https://julialang.org/ release
Platform Info:
  OS: Windows (x86_64-w64-mingw32)
  CPU: 32 × Intel(R) Core(TM) i9-14900KF
  WORD_SIZE: 64
  LLVM: libLLVM-16.0.6 (ORCJIT, alderlake)
Threads: 1 default, 0 interactive, 1 GC (on 32 virtual cores)
Environment:
  JULIA_EDITOR = code
  JULIA_NUM_THREADS = 1

Details on CUDA:

CUDA runtime 12.6, artifact installation
CUDA driver 12.7
NVIDIA driver 565.90.0

CUDA libraries:
- CUBLAS: 12.6.3
- CURAND: 10.3.7
- CUFFT: 11.3.0
- CUSOLVER: 11.7.1
- CUSPARSE: 12.5.4
- CUPTI: 2024.3.2 (API 24.0.0)
- NVML: 12.0.0+565.90

Julia packages:
- CUDA: 5.5.2
- CUDA_Driver_jll: 0.10.3+0
- CUDA_Runtime_jll: 0.15.3+0

Toolchain:
- Julia: 1.11.1
- LLVM: 16.0.6

1 device:
  0: NVIDIA GeForce RTX 4090 (sm_89, 21.585 GiB / 23.988 GiB available)