`LinearAlgebra.norm(x)` falls back to generic implementation for `x::Transpose` and `x::Adjoint`

[jondeuce]

Describe the bug

LinearAlgebra.norm(x) falls back to the generic implementation for x::Transpose and x::Adjoint, as the following method is only defined on DenseCuArrays:

CUDA.jl/lib/cublas/linalg.jl

Lines 106 to 112 in a4ddc54

	function LinearAlgebra.norm(x::DenseCuArray{<:Union{Float16, ComplexF16, CublasFloat}}, p::Real=2)
	if p == 2
	return nrm2(x)
	else
	return invoke(norm, Tuple{AbstractGPUArray, Real}, x, p)
	end
	end

To reproduce

The Minimal Working Example (MWE) for this bug:

julia> using CUDA, LinearAlgebra

julia> CUDA.allowscalar(false);

julia> A = CUDA.rand(2, 3);

julia> norm(A); # works

julia> norm(A') # falls back to generic and fails
ERROR: Scalar indexing is disallowed.
Invocation of getindex resulted in scalar indexing of a GPU array.
This is typically caused by calling an iterating implementation of a method.
Such implementations *do not* execute on the GPU, but very slowly on the CPU,
and therefore are only permitted from the REPL for prototyping purposes.
If you did intend to index this array, annotate the caller with @allowscalar.
Stacktrace:
  [1] error(s::String)
    @ Base ./error.jl:35
  [2] assertscalar(op::String)
    @ GPUArraysCore ~/.julia/packages/GPUArraysCore/HaQcr/src/GPUArraysCore.jl:103
  [3] getindex(::CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}, ::Int64, ::Int64)
    @ GPUArrays ~/.julia/packages/GPUArrays/6STCb/src/host/indexing.jl:9
  [4] getindex
    @ ~/.julia/juliaup/julia-1.8.5+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/adjtrans.jl:180 [inlined]
  [5] _getindex
    @ ./abstractarray.jl:1291 [inlined]
  [6] getindex
    @ ./abstractarray.jl:1241 [inlined]
  [7] iterate
    @ ./abstractarray.jl:1167 [inlined]
  [8] iterate
    @ ./abstractarray.jl:1165 [inlined]
  [9] generic_norm2(x::Adjoint{Float32, CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.8.5+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/generic.jl:465
 [10] norm2
    @ ~/.julia/juliaup/julia-1.8.5+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/generic.jl:524 [inlined]
 [11] norm(itr::Adjoint{Float32, CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}}, p::Int64)
    @ LinearAlgebra ~/.julia/juliaup/julia-1.8.5+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/generic.jl:593
 [12] norm(itr::Adjoint{Float32, CuArray{Float32, 2, CUDA.Mem.DeviceBuffer}})
    @ LinearAlgebra ~/.julia/juliaup/julia-1.8.5+0.x64.linux.gnu/share/julia/stdlib/v1.8/LinearAlgebra/src/generic.jl:591
 [13] top-level scope
    @ REPL[5]:1
 [14] top-level scope
    @ ~/.julia/packages/CUDA/ZdCxS/src/initialization.jl:155

julia> norm(transpose(A)) # same failure
ERROR: Scalar indexing is disallowed.
[...]

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Expected behavior

The norm of the parent array should be returned, as norm(x, p) == norm(parent(x), p) for x::Transpose or x::Adjoint with real or complex elements.

For example, defining the following methods fixes the issue:

using CUDA, LinearAlgebra
using CUDA.CUBLAS: CublasFloat

for trtype in (:Transpose, :Adjoint)
    @eval begin
        # The vector `p`-norm is invariant to permutation and complex conjugation of the elements of `x`, and therefore `norm(x, p) == norm(parent(x), p)` for `x::Transpose` and `x::Adjoint`
        LinearAlgebra.norm(x::$trtype{<:Any, <:DenseCuVecOrMat{<:Union{Float16, ComplexF16, CublasFloat}}}, p::Real = 2) = norm(parent(x), p)
    end
end

Version info

Details on Julia:

julia> versioninfo()
Julia Version 1.8.5
Commit 17cfb8e65ea (2023-01-08 06:45 UTC)
Platform Info:
  OS: Linux (x86_64-linux-gnu)
  CPU: 32 × AMD Ryzen 9 3950X 16-Core Processor
  WORD_SIZE: 64
  LIBM: libopenlibm
  LLVM: libLLVM-13.0.1 (ORCJIT, znver2)
  Threads: 4 on 32 virtual cores
Environment:
  JULIA_CONDAPKG_BACKEND = System
  JULIA_CONDAPKG_EXE = ~/miniconda3/bin/conda
  JULIA_PROJECT = ~/Documents/CUBLAS_norm_bug
  JULIA_NUM_THREADS = 4
  JULIA_EDITOR = code

Details on CUDA:

julia> CUDA.versioninfo()
CUDA runtime 11.8, artifact installation
CUDA driver 11.2
NVIDIA driver 460.106.0

Libraries: 
- CUBLAS: 11.11.3
- CURAND: 10.3.0
- CUFFT: 10.9.0
- CUSOLVER: 11.4.1
- CUSPARSE: 11.7.5
- CUPTI: 18.0.0
- NVML: 11.0.0+460.106.0

Toolchain:
- Julia: 1.8.5
- LLVM: 13.0.1
- PTX ISA support: 3.2, 4.0, 4.1, 4.2, 4.3, 5.0, 6.0, 6.1, 6.3, 6.4, 6.5, 7.0, 7.1, 7.2
- Device capability support: sm_35, sm_37, sm_50, sm_52, sm_53, sm_60, sm_61, sm_62, sm_70, sm_72, sm_75, sm_80, sm_86

1 device:
  0: GeForce RTX 3080 (sm_86, 9.063 GiB / 9.780 GiB available)

Additional context

I would be happy to make a quick PR with the above patch if it seems reasonable.

[maleadt]

Is there a reason Base doesn't have norm dispatch to the parent array for Adjoint/Transpose?
Other than that, such a patch looks good to me, but LinAlg isn't my domain of course.

[jondeuce]

I'll look into it, but it's possible there is trickiness due to adjoint and transpose acting recursively in general, i.e. [x, y]' == [[x'] [y']] when x and y are arrays. But for simple Float/Complex values there is no issue, since norm is invariant to permutation of elements and/or complex conjugation.

With that being said, there is already a similar definition for adjoint/transpose of vectors in Base: https://github.com/JuliaLang/julia/blob/5eab4516797d31216fb468d2ce3aaea3e426954f/stdlib/LinearAlgebra/src/generic.jl#L808

So maybe this should be a PR to Base after all... I will open an issue. It is easy enough to work around for now; I am currently just including the proposed patch in my own code, but of course that is some piracy I would like to avoid.

[jondeuce]

A more general fix has been merged into base now 👍🏻. I'm not sure what, if anything, you would like to do about this issue in the meantime. The patch proposed above could, for example, be defined only if VERSION is below an appropriate value?

[maleadt]

The patch proposed above could, for example, be defined only if VERSION is below an appropriate value?

Yeah that'd be a good workaround. Would probably belong in GPUArrays though, where we define norm?

[jondeuce]

Ahh I see, yes that makes more sense; best to be as generic as possible. I'm not sure which Julia version will be the cutoff, though, but I can ask.

[maleadt]

This seems to work now.