Add GPU support for LBFGSData

[blegat]

• Add tests

[Copilot]

🟡 Changes recommended

GPU shifted solves and diagonal extraction still mix CPU and GPU storage, and the new paths lack tests.

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Pull request overview

Adds configurable vector storage to LBFGSData/LBFGSOperator for GPU backends and updates shifted-system dispatch.

Changes:

• Adds V storage parameter and GPU-aware constructors.
• Generalizes LBFGS operations and shifted-system methods.
• No GPU tests were added.

File summaries

File	Description
src/lbfgs.jl	Adds configurable storage backend support.
src/utilities.jl	Updates shifted-system method dispatch.

Review details

Suppressed comments (2)

src/lbfgs.jl:61

• Selecting a GPU V only moves Ax and the history vectors to the device; the shifted-system scratch buffers constructed immediately below remain Matrix{T}/Vector{T} on the CPU. Consequently solve_shifted_system!(..., B, b, σ) with CuVector inputs mixes CPU views with GPU b (and copies from GPU into shifted_u), so the new generic method fails with scalar indexing disabled instead of solving. Allocate these temporaries on the same backend, or otherwise implement a device-compatible shifted solve, before advertising GPU support.

    V(undef, n),

src/lbfgs.jl:119

• Changing storage_type to V makes GPU operators advertise GPU storage, but diag(op) still allocates Vector{T} later in this file. After any update, diag! combines that CPU destination with data.a/data.b GPU arrays, which is incompatible with CUDA.allowscalar(false) and does not provide a usable GPU diagonal. Make diag allocate from the operator's storage backend (or require a backend-provided output) and cover this path.

storage_type(op::LBFGSOperator{T, I, F, Ft, Fct, V}) where {T, I, F, Ft, Fct, V} = V

• Files reviewed: 2/2 changed files
• Comments generated: 1
• Review effort level: Lite

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[blegat]

Should be covered now